We define the notions of strong and strict recurrency for actions of countable ordered groups on $\sigma$-finite non atomic measure spaces with quasi-invariant measures. We show that strong recurrency is equivalent to non existence of weakly wandering sets of positive measure. We also show that for certain p.m.p ergodic actions the system is not strictly recurrent, which shows that strong and strict recurrency are not equivalent.

While there are well-known synthetic methods in the literature to find the image of a point under circular inversion in l2−normed geometry (Euclidean geometry), there is no similar synthetic method in Minkowski geometry, also known as the geometry of finite-dimensional Banach spaces. In this study, we have succeeded in giving a synthetic construction for the circular inversion in l1−normed spaces, which is one of the most fundamental examples of Minkowski geometry. Moreover, this synthetic construction has been given using the Euclidean circle, independently of the l1−norm.

The main purpose of this research is to use “DMAIC” and “DMADV” framework of six sigma to reduce cost of projects, increase yields, improve performance and reduce defects. This study conclude that the sigma level of cement bag production in four production lines is “4.7 DPMO” values of 710 and the possibility of defects per unit of 11 possibilities this situation was handled by using six sigma. Any business or industry run only to satisfy customer and increase their profits, this can be attained as development of quality product..For the ranking of newly established universities the certification of those institutes is very important and also a critical process. For this process we used Lean six sigma approach that can identify the wastes that affect this process.Six sigma can be applied to any work field such as education, power optimization and other types of industries Six sigma “DMAIC” approach is also used for the testing of EDA tools that occurs due to the complex coding or configurations, flows and platforms they support. To improve the process quality of SDLC it’s necessary to remove the defects of system in advance along with thorough valuation of size and it also makes project accordant with real time environment

Salmonella enterica serovar Newport bacteriophage 7-11 shares 41 homologous ORFs with Escherichia coli phage phiEco32 and both phages encode a protein similar to bacterial RNA polymerase promoter specificity  subunit. Here, we investigated the temporal pattern of 7-11 gene expression during the infection and compared it to the previously determined transcription strategy of phiEco32. Using primer extension and in vitro transcription assays we identified eight promoters recognized by host RNA polymerase holoenzyme containing 7-11  subunit SaPh711_gp47. These promoters are characterized by a bipartite consensus GTAAtg-(16)-aCTA and are located upstream of late phage genes. While dissimilar from single-element middle and late promoters of phiEco32 recognized by holoenzyme formed by the phi32_gp36  factor, the 7-11 late promoters are located at genome positions similar to those of phiEco32 middle and late promoters. Two early 7-11 promoters are recognized by RNA polymerase holoenzyme containing host primary σ70 factor. Unlike the case of phiEco32, no shut off of σ70-dependent transcription is observed during 7-11 infection and there are no middle promoters. These differences can be explained by the fact that phage 7-11 does not encode a homologue of phi32_gp79, an inhibitor of host and early phage transcription and an activator of transcription by the phi32_gp36-holoenzyme.

High dimensional statistical analysis for the yield of large-scale circuits is quite difficult due to expensive simulations, especially for the memory circuits with high sigma requirement (e.g., SRAM). In this paper, we developed an efficient sparse additive model to substitute simulations. To fit high sigma region accurately, the modeling center is moved to near failure boundary searched by scaling the shape of sampling function. To solve the model efficiently, the process variables are grouped by standard cells so that the model can be solved by our developed blockwise greedy algorithm. The experiments on the 28nm memory circuits validate that our method achieves high accuracy and efficiency compared with other state-of-art works.

In the field of delta-sigma modulators, reducing system power consumption without sacrificing accuracy has become a challenge. The summing circuit, as the main part of the cascade-of-integrator-in-feedforward delta-sigma modulator, consumes a significant amount of power in active summing. On the other hand, passive summing circuits have low power consumption but can cause attenuation in the summing results. This article proposes a low-power multi-bit delta-sigma modulator based on passive and attenuationless summation scheme. The summation circuit achieves multiplication of the voltage signal carried on the summation capacitor through bidirectional sampling technique, compensating for the inherent attenuation caused by passive summation, thus eliminating the need for active OTA to achieve perfect summation. A 2-order delta-sigma modulator based on 4-bit 1-order passive noise-shaping (NS) SAR quantizer is designed to verify the scheme. By combining a passive NS SAR as the 4-bit quantizer and the third-stage integrator of the system, and incorporating an energy-efficient cascode floating inverter amplifier (FIA) structure as the core active OTA, these elements have significantly enhanced the energy-efficiency of the modulator. Simulation results show that at a supply voltage of 1.2 V and a bandwidth of 20 kHz, the SNDR reaches 102.62 dB, power consumption is only 148.32 μW, and Schreier figure-of-merit (FoM) of SNDR is 183.92 dB.

The precipitate phases often play an important influence on the corrosion resistance of 2205 Duplex stainless steel (DSS). In the presented paper, the microstructure and corrosion resistance in the hot-rolled and cold-rolled 2205 DSS aging for different time at 850 °C was investigated by XRD, SEM and potentiodynamic polarization. It has been found that the Chi(χ) phase and Sigm(σ) phase were precipitated in turn after aging treatment of hot-rolled and cold-rolled materials, but the precipitate amount in cold-rolled material is much more than that of hot-rolled samples. The corrosion resistance of the solution-annealed cold-rolled material is similar to the hot-rolled material, but the corrosion resistance of cold-rolled material with precipitate is weaker than that of hot-rolled material after aging treatment. Pitting initiates preferentially in the Cr-depleted region from σ phase in aged hot-rolled 2205, and severe selective corrosion occurs on sigma/ferrite interfaces aged for a long aged lime. However, the initiation of pitting corrosion may take place at the phase boundary, defect and martensite in the aged cold-rolled 2205. The σ phase is further selectively dissolved by electrochemical method to investigate the difference of microstructure and corrosion behavior in hot-rolled and cold-rolled 2205 duplex stainless steel.

This paper explores the implementation of a VCO-based ADC, achieving an ENOB of 12 bits with 1MHz of sampling rate in the audio bandwidth. The solution exploits the scalability and PVT invariance of a novel digital-to-frequency converter, to reduce the size and consumed power. The architecture has been validated in a 130-nm CMOS technology node, displaying a power consumption of 105.57 μW, and a silicon footprint of 0.034 mm2, in a pseudo differential configuration. Performance can be dynamically adjusted to trade off power consumption by resolution without changing the sampling rate. In addition, the proposed architecture benefits from multiple instantiations in the same SoC, making it particularly suitable for sensor array applications, such as biomedical sensors and spatial audio arrays.

In their natural environment, bacteria are exposed to various stresses. The stress-response sigma factor SigB of gram-positive Bacillus subtilis is the best-characterized example. Unlike Bacillus subtilis, the gram-positive bacterium Streptomyces coelicolor A3(2) contains nine SigB homologues (SigBFGHIKLMN) with a major role in differentiation and response to osmotic stress. We previously constructed a two-plasmid system to identify promoters recognized by these sigma factors. Interestingly, almost all identified promoters were recognized by two or more SigB homologues. However, no specific sequences characteristic for these recognition groups were found. To examine this cross-recognition in vivo in S. coelicolor A3 (2), one of these promoters was cho-sen, which drives the expression of the sporulation-specific gene ssgB. The ssgBp promoter was inserted into a luciferase reporter plasmid and conjugated to S. coelicolor M145 and nine mutant strains containing deleted individual sigB homologous genes. Luciferase reporter activity indi-cated differential activity of this promoter in these mutant strains, suggesting overlapping pro-moter recognition by these SigB homologues. To determine which nucleotides in the ̶ 10 re-gion are responsible for the selection of a specific SigB homologue, several mutant promoters with altered last three nucleotides in this region were prepared and tested in the two-plasmid system. Some mutant promoters were specifically recognized by some SigB homologues. Mutant promoters were inserted into a luciferase reporter plasmid and conjugated to S. coelicolor A3(2) and these nine mutant strains. Luciferase reporter activity indicated differential activity of these ssgBp mutant promoters, indicating overlapping promoter recognition by these SigB homologues in S. coelicolor A3(2).

The Six Sigma (6σ) method is used to improve and optimize an organization’s products, services, and processes by constantly decreasing defects. In this paper we try implementing the 6σ methodology in Academia. The challenges and actuality of implementation of 6σ methodologies successfully in Academia are immense. However, the benefits of applying 6σ are equally great. The objective of this paper is to understand the evolution, benefits, and challenges of 6σ practices in academia through a case study of Presidency University situated in Bangalore, Karnataka, India. The problem statement in the paper is the poor performance of students in academics and by using the DMAIC approach of 6σ we try to identify and understand the causes and set out to improve them so the students can have better placement and academic opportunities. This paper is also an attempt to show the readers about the wide application of 6σ in fields other than manufacturing and how it can be beneficial.

Duplex Stainless Steels (DSS) and Superduplex Stainless Steels (SDSS) are an important class of stainless steels because they combine the benefits of austenite and ferrite phases, resulting in steels with better mechanical properties and higher corrosion resistance. Due to these characteristics are widely employed in various industries. However, the appearance of deleterious phases in their microstructure impairs the properties of DSS and SDSS. Among the deleterious phases, the main one is the sigma phase (σ), which can be nucleated when the steel is exposed to the temperature range between 650 °C and 900 °C, reducing its toughness and resistance to corrosion. In a previous work, Fonseca and collaborators used two descriptors of the microstructural path to analyze the formation of sigma phase (σ), SV, interfacial area per unit volume between sigma phase and austenite, and <λ>, mean chord length of sigma, both in function of the VV, volume fraction of sigma, known in the literature as microstructural partial path (MP). In this work, the contiguity ratio is applied for the first time to describe the microstructural path in the study of sigma phase precipitation in SDSS. The contiguity ratio showed that the distribution of the ferrite/sigma boundaries is homogeneous. Thus, it is reasonable to infer that one has a uniform distribution of sigma phase nuclei within the ferrite. About the kinetics of sigma phase formation, the DSS can be described by the classical JMAK equation, whereas for the SDSS, the kinetics tends to follow the Cahn model for grain edge nucleation. Finally, we present the 3D reconstruction of the sigma phase in SDSS. The results demonstrate that the sigma phase nucleates at the edges of the ferrite/austenite interfaces. Moreover, the sigma phase grows consuming the ferrite, but it is not fully interconnected.

Aberrant estrogen receptor (ER) signaling is a major driver of breast tumor growth and progression. Sigma 2 receptor has long been implicated in breast carcinogenesis based on pharmacological studies, but its molecular identity had been elusive until TMEM97 was identified as the receptor. Herein we report that TMEM97/sigma 2 receptor is highly expressed in ER positive breast tumors and its expression is strongly correlated with ER and progesterone receptor (PR) but not with HER2 status. High expression levels of TMEM97 are associated with reduced overall survival of patients. Breast cancer cells with increased expression of TMEM97 had growth advantage over the control cells under both nutrition limiting and sufficient conditions, while knockdown of TMEM97 expression reduced tumor cell proliferations. When compared to their vector control cells, MCF7 and T47D cells with increased TMEM97 expression presented increased resistance to tamoxifen treatment and also grew better under estrogen depleted conditions. TMEM97/sigma 2 receptor enhanced ERα transcriptional activities and increased the level of transactivated ERα, especially the nuclear soluble and chromatin bounded ERα. Increased TMEM97 also stimulated mTOR/S6K1 signaling pathways in MCF7 and T47D cells. The increased level of active, phosphorylated ERα, and the enhanced resistance to tamoxifen treatment with increased TMEM97 could be blocked by an mTOR inhibitor. Knockdown of TMEM97 expression reduced ERα and mTOR/S6K1 signaling activities, rendering the cells with increased sensitivity to tamoxifen. The observations suggest that TMEM97/sigma 2 receptor is a novel regulator of ERα activities in breast tumor cell growth.

The minimum requirement for uncertainty estimation is to use only intermediate precision (R_w), especially for measurands lacking a reference measurement system such as thyroid functions tests (TFT). In this study, measurement uncertainty (MU) for TSH and FT4 from long-term internal quality control (IQC) data was estimated while reference change values (RCV) were calculated from estimated MU. Furthermore, intermediate precision (R_w) was used to establish appropriate risk-based QC frequency. Twenty fore months of third party IQC data were collected retrospectively, on the Abbott ARCHITECT i1000sr analyzer from INSTITUT PASTEUR OF MSILA laboratory, ALGERIA. The MU, RCV and sigma-metric were estimated simply from the intermediate precision (R_w), while a nomogram relating sigma performance to run size was used to establish QC frequency. The MU for the TSH and FT4 was 12% and 8% respectively. The U _one-sided for the TSH and FT4 was 10%, 6.6% respectively. MU and U _one-sided of TSH and FT4 met quality requirements for permissible uncertainty (pU %) and allowable total error (ATE %). When monitoring thyroid replacement therapy, an upward minimum change (RCV) of 54% and 22% or a downward of 35% and 18% in serum TSH and FT4 respectively, would be considered significant. Optimal QC strategy for serum TSH was selected to run 4 QC materials every 190 patients sample and to use a multi-rule (1_3s/2_2s/R_4s/4_1s). Our results suggest that MU estimation from long-term IQC alone may be acceptable for TFT to assist physician in results interpretation and to establish appropriate QC frequency.

We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model (NLSM). We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued (2/π)ρ_c0 (ρ_c0 the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant 2/π in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. The equivalence principle is also generalized to the quantum level.

A new method, based on quantum chemical calculations, is proposed for the thermodynamically consistent reformulation of QSPR-type Linear Free-Energy Relationship (LFER) models. This reformulation permits the extraction of valuable information on intermolecular interactions and its transfer in other LFER-type models, in acidity / basicity scales or even in equation-of-state models. New molecular descriptors of electrostatic interactions are derived from the distribution of molecular surface charges obtained from COSMO-type quantum chemical calculations. The widely used and very successful Abraham’s Linear Solvation Energy Relationship (LSER) model is selected as the reference LSER model for the calculations in solute – solvent systems as well as in solute self-solvation. Hydrogen-bonding free energies, enthalpies and entropies are now derived for a variety of common solutes. The capacity of the method to address the role of conformational changes in solvation quantities is discussed. The perspectives of the LSER model with the implementation of the new descriptors are also discussed.

Bacillus subtilis is a model organism used to study molecular processes in Gram-positive bacteria. Sigma factor B, which associates with RNA polymerase, is one of the transcriptional regulators involved in the cell’s response to environmental stress. Experiments have proven that the amounts of free σB (SigB) are controlled by a system of anti- (RsbW) and anti-anti-sigma (RsbV) factors expressed from the same operon as SigB. Moreover, the phosphorylation state of RsbV is controlled by phosphatases RsbP and RsbU, which directly dephosphorylates RsbV. A set of chemical equations describing the network controlling the levels of free SigB was converted to a set of differential equations quantifying the dynamics of the network. The solution of these equations allowed the simulation of the kinetic behavior of the network and its components under real conditions. In this study, the time series of protein expression measured by mass spectrometry were utilized to investigate the role of the phosphatases RsbU/RsbP in transmitting the environmental signal. Additionally, the influence of kinetic constants and the amounts of other network components on the functioning of the network was investigated. A comparison with the same simulation performed using transcriptomic dataset showed that while the time series between the proteomic and transcriptomic datasets) are not correlated, the results are the same. This indicates that when modeling is done within one dataset, it does not matter whether the data come from the mRNA or protein level. In summary, the computational results based on experimental data provide quantitative insight into the functioning of the SigB-dependent circuit and offer a template for the quantitative study of similar systems.

This study investigates the critical success factors (CSFs) of Lean Six Sigma (LSS) implementation and their impact on organizational growth in Nigerian enterprises. The objectives were to identify crucial CSFs for successful LSS deployment and assess their significance in achieving organizational growth. A mixed-method approach was used, including literature analysis, expert judgments, and a survey of 130 participants from various industries. The survey questionnaire employed a 5-point Likert scale to collect data on LSS CSFs and implementation success metrics. Structural equation modeling (SEM) with SmartPLS 4.0 analyzed the data, revealing that LSS CSFs significantly contribute (up to 39.2 percent) to the success of LSS implementations. The study identified 12 critical LSS CSFs, categorized into workers, business, and management, each influencing LSS implementation. Recommendations include creating a supportive environment, providing comprehensive training, and prioritizing continuous improvement efforts for successful LSS deployment. Future research possibilities include longitudinal studies, sector-specific analyses, and qualitative investigations to deepen understanding and enhance LSS implementation outcomes. In conclusion, successful LSS implementation empowers Nigerian organizations with improved productivity, waste reduction, and sustainable production systems, leading to overall growth and success.

Interactions between mobile robots and human operators in common areas require a high safety especially in terms of trajectory planning, obstacle avoidance and mutual cooperation. In this connection the crossings of planned trajectories, their uncertainty based on model fluctuations, system noise and sensor noise,play an outstanding role. This paper discusses the calculation of expected areas of interactions du ring human-robot navigation with respect to fuzzy and noisy information. Expected crossing points of possible trajectories are nonlinearily associated with positions and orientations of robot and human. The nonlinear transformation of a noisy system input, such as directions of motion of human and robot, to a system output, the expected area of intersection of their trajectories, is done by two methods: statistical linearization and the sigma-point-transformation. For both approaches fuzzy approximations are presented and the inverse problem is discussed where the input distribution parameters are computed from given output distribution parameters.

In the cone of positive quadratic forms C^{8 x 8}, it is shown that there exists in the neighbourhood of the quadratic form Q_{F_{22}} a large cluster of non-equivalent \Sigma_0-subcones of positive volume which are as well minimal as maximal.

The article deals with the current state of energy consumption and CO2 emissions in the urban area of building clusters. There are many requirements, such as those set by the EU (FIT 55, decarbonisation in 2050, full electromobility in 2035, or mandatory annual reductions in energy consumption and CO2 production) or societal requirements, such as stable energy supply and its optimisation while significantly reducing CO2 emissions. This inspired us to design an energy model of a building (EMB) with smart grid implementation in a decentralized sustainable energy system. Simulation model studies were carried out to show the possibility of their application in the process of fully satisfying energy needs in terms of reducing their environmental impact. A decentralized photovoltaic system (microgrid) connected to a distribution grid. The main objective is to propose an original methodology for the design of smart "Nearly Zero Energy Buildings" (NZEB) and a subsequent solution for energy sustainability. This has led us to use HOMER, PV*SOL, Monte Carlo and DesignBuilder software which were chosen from the range of options that were and are available. Subsequently, a synthesis of the selected software solutions was carried out and a new model - the "Energy Model of a Building" (EMB) - was proposed in the process of integration with the energy performance of buildings, as an original optimization basis for designing smart buildings and smart areas, and even cities. The proposed EMB has been verified and evaluated within the experiment.

New families of direct serendipity and direct mixed finite elements on general planar, strictly convex polygons were recently defined by the authors. The finite elements of index r are H1 and H(div) conforming, respectively, and approximate optimally to order r+1 while using the minimal number of degrees of freedom. The shape function space consists of the full set of polynomials defined directly on the element and augmented with a space of supplemental functions. The supplemental functions were constructed as rational functions, which can be difficult to integrate accurately using numerical quadrature rules when the index is high. This can result in a loss of accuracy in certain cases. In this work, we propose alternative ways to construct the supplemental functions on the element as continuous piecewise polynomials. One approach results in supplemental functions that are in Hp for any p≥1. We prove the optimal approximation property for these new finite elements. We also perform numerical tests on them, comparing results for the original supplemental functions and the various alternatives. The new piecewise polynomial supplements can be integrated accurately, and therefore show better robustness with respect to the underlying meshes used.

Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.

Every finite simple group P can be generated by two of its elements. Pairs of generators forP are available in the Atlas of finite group representations as (not necessarily minimal) permutation representations P . It is unusual but significant to recognize that a P is a Grothendieck’s dessin d’enfant D and that a wealth of standard graphs and finite geometries G - such as near polygons and their generalizations - are stabilized by a D. In our paper, tripods P − D − G of rank larger than two,corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurationsdefined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G's have a contextuality parameterclose to its maximal value 1.

Molecular descriptors are essential in mathematical chemistry for studying quantitative structure-property relationships (QSPR), and topological indices are a valuable source of information about molecular properties such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. The molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs, windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results showed that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

We developed and applied a method for characterizing bacterial promoters genome-wide by in vitro transcription coupled to transcriptome sequencing specific for native 5’-ends of transcripts. This method called ROSE (Run-Off transcription/RNA-SEquencing), only requires chromosomal DNA, ribonucleotides, RNA polymerase (RNAP) core enzyme, and a specific sigma factor, recognizing the corresponding promoters, which have to be analyzed. ROSE was performed on E. coli K-12 MG1655 genomic DNA using E. coli RNAP holoenzyme (including σ70) and yielded 3,226 transcription start sites, 2,167 of which were also identified in in vivo studies, and 598 were new. Many new promoters not yet identified by in vivo experiments might be repressed under the tested conditions. Complementary in vivo experiments with E. coli K-12 strain BW25113 and isogenic transcription factor gene knockout mutants of fis, fur, and hns were used to test this hypothesis. Comparative transcriptome analysis demonstrated that ROSE could identify bona fide promoters that were apparently repressed in vivo. In this sense, ROSE is well-suited as a bottom-up approach for characterizing transcriptional networks in bacteria and ideally complementary to top-down in vivo transcriptome studies.

This paper presents a two-stage ADC based on pseudo-differential operational transconductance amplifier (OTA), which is designed for the readout circuit of X-ray linear array sensor. This hybrid ADC employs an incremental sigma-delta ADC and a cyclic ADC, achieving a good trade-off between accuracy and conversion speed. The two stages share the same hardware to reduce power consumption and die area. A common-mood feedback module is used to suppress the influence of charge injection, and the effectiveness is demonstrated by detailed theoretical analysis. A test chip of 14-bit ADC is fabricated in 0.35μm CMOS technology. The measured root mean square (RMS) value of DNL is 0.254 LSB, and the maximum value of INL is -0.776/+1.56 LSB. The measured effective number of bits (ENOB) is 13.43 bits.

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order, on the quotient space of isomorphism classes of finite groups, that is well behaved with respect to cardinality. If $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G\leq\mathbb Z_{p_1}^{n_1}\oplus\mathbb Z_{p_2}^{n_2}\oplus\cdots\oplus\mathbb Z_{p_k}^{n_k}$ where $n=p_1^{n_1}p_2^{n_2}\cdots p_{k}^{n_k}$ is the prime factorization of $n$. We find a canonical order for the objects of $G$ and define equivalent objects of $G$, thus finding the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and we are provided with a minimal set of independent equations that define the group. We show how to find all groups of order $n$, and order them. We give examples using all groups with order smaller than $10$, and we find the canonical block form of the symmetry group $\Delta_4$. In the next section, we extend our results to the infinite case, which defines a real number as an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, as well. In general, we represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects are well assigned to tree structures. We conclude with brief comments on type theory and future work on computational aspects of these representations.

High-entropy alloys (HEAs) are of great interest in the field of materials science and engineering. Unlike conventional alloys, which contain a maximum of two base metals, this new category of materials consists of multi-principle elements and the possible number of alloy compositions, in case of HEAs, is outstandingly higher than that for conventional alloys. Here, a review on the high-entropy alloys, has been provided, on the issue whether the earliest definition of High- Entropy alloys, proposed in 2004^{[2, 4]}, is consistent with one of the four-component equiatomic Compositionally complex alloys exhibiting a “High-entropy” effect.

Call set up success rate (CSSR) in a mobile network is an important quality parameter, which directly influences overall key performance indicators (KPIs) of the network service providers. Network KPIs especially the CSSR is the fraction of the attempts to make a call that result in a successful connection to the dialled number. Nevertheless, all call attempts do not end with a connection to the dialled number. In this research, six sigma methodology is applied to improve the call quality of a legacy mobile network and subsequently to boost comprehensive CSSR of a telecom service provider. This research elucidates an empirical study of improving overall CSSR by employing DMAIC methodology consisting of five stages, e.g. Define, Measure, Analysis, Improve and Control. In addition, analytic hierarchy process (AHP) technique is used for determining the vital causes out of all the identified network parameters affecting overall CSSR. Furthermore, the identified vital parameters are being upgraded in order to improve the overall CSSR and finally the system achieved a higher CSSR.

In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

There exists a great potential for application in soil mechanics with the use of mechanistic models such as the finite element model, and other non-local models, such as the peridynamic model, since the soil mass can be modelled as a group of particles that interact with each other. In this work, we determine the bearing capacity of deep foundations where stresses are transmitted to deep deposits, which generally present better characteristics in terms of compressibility and shear strength. One of the main elements are driven piles, which must be previously designed, made and tested before their final use. In this work, a comparison with different methods is presented. The finite element method and the peridynamic model are used. Because the effect of consolidation was not taken into account, in these examples, the assumption is made that the structures are cemented in inert soil. Likewise, it is assumed that the water table has no influence on the simulations. Failure envelopes were observed where bonds between particles present high gradients of deformation and fracture. Bearing capacities were estimated and compared with those obtained from the Terzaghi and Meyerhof methods.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

The Finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990’s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational method rather than via a mathematical formulation, and the behavior of the FSLE in the turbulent inertial ranges is based primarily on scaling arguments. Here we propose an exact definition of the FSLE based on conditional averaging of the finite amplitude growth rate (FAGR) of the particle pair separation. With this new definition, we show that the FSLE is a close proxy for the inverse structural time, a concept introduced a decade before the FSLE. The (in)dependence of the FSLE on initial conditions is also discussed, as well as the links between the FAGR and other relevant Lagrangian metrics, such as the finite time Lyapunov exponent and the second order velocity structure function.

In this paper, firstly, some questionable formulas and conceptual oversights of previous reduced sigma set unscented transformation (UT) methods are revised through theoretical analysis. Then the revised UT methods based Kalman filters are used in a GPS/INS tightly-coupled system. The Kalman filter flows are the kind of square-root, since the square-root unscented Kalman filters (SRUKFs) can guarantee the stability of the system. By using the reduced sigma set SRUKFs (which contain simplex sigma set square-root unscented Kalman filter (S-SRUKF), spherical simplex sigma set square-root unscented Kalman filter (SS-SRUKF) and minimum sigma set square-root unscented Kalman filter (M-SRUKF)), the computation cost is greatly saved compared with the standard SRUKF, while the accuracy of the GPS/INS tightly-coupled system still maintained. The structure of the GPS/INS tightly-coupled system is in the form of error state, and the time updates of the state and the state covariance of SRUKFs are directly estimated without using UT, thus the computational time is also greatly saved. The pseudo-satellite is introduced to aid the system when the observation information is deficient, for example, when the GPS signal is deficient in the maneuver environment. By using the pseudo-satellite, the optimal performance of the system is guaranteed. Experiment of unmanned aerial vehicle (UAV) showed that the pseudo-satellite aided mechanism worked well.

Eddy current based approaches have been investigated for a wide range of inspection applications. Dodd-Deeds model and the truncated region eigenfunction expansion (TREE) method are widely applied in various occasions, mostly for the cases that the sample is relatively larger than the radius of the sensor coil. The TREE method converts the integral expressions to the summation of many terms in the truncated region. In a recent work, the impedance of the co-axial air-cored sensor due to a plate of finite radius was calculated by the modified Dodd-Deeds analytical approach proposed by authors. In this paper, combining the modified analytical solution and the TREE method, a new finite region eigenfunction expansion (FREE) method is proposed. This method involves modifying its initial summation point from the first zero of the Bessel function to a value related to the radius of the plate, therefore makes it suitable for plate with finite dimensions. Experiments and simulations have been carried out and compared for the verification of the proposed method. Further, the planar size measurements of the metallic circular plate can be achieved by utilising the measured peak frequency feature.

Traumatic brain injury (TBI) is an important global clinical issue, requiring not only prevention but also effective treatment. Following TBI, diverse parallel and intertwined pathological mechanisms affecting biochemical, neurochemical, and inflammatory pathways can have severe impact on the patient’s quality of life. The current review summarizes evidence for utility of amantadine in TBI in connection to its mechanism of action. Amantadine combining multiple mechanisms of action may offer both neuroprotective and neuroactivating effects in TBI patients. Indeed, use of amantadine in TBI has been encouraged by several clinical practice guidelines/recommendations. Amantadine is also available as infusion which may be of particular benefit in unconscious patients with TBI, due to immediate delivery to the central nervous system and the possibility of precise dosing. In other situations, orally administered amantadine may be used. There are several questions that remain to be addressed: Can amantadine be effective in disorders of consciousness requiring long-term treatment and in combination with drugs approved for treatment of TBI? Do the observed beneficial effects of amantadine extend to disorders of consciousness due to factors other than TBI? Well controlled clinical studies are warranted to ultimately confirm its utility in the TBI and provide answers these questions.

Solventogenic Clostridium species are important for establishing sustainable industrial bioproduction of fuels and important chemicals. The inherent versatility of these species in substrate utilization and the range of solvents produced during acetone butanol-ethanol (ABE) fermentation make solventogenic Clostridium an attractive choice for biotechnological applications such as production of fuels and chemicals. The functional qualities of these microbes have thus been identified to be due to complex regulatory networks that play essential roles in modulating the metabolism of this group of bacteria. Genomes of solventogenic Clostridium species have relatively greater prevalence of genes that are intricately controlled by various regulatory molecules than most other species. Consequently, the use of genetic or metabolic engineering strategies that do not consider the underlying regulatory mechanisms will not be effective. Several regulatory factors involved in substrate uptake/utilization, sporulation, solvent production, and stress responses (Carbon Catabolite Protein A, Spo0A, AbrB, Rex, CsrA) have been identified and characterized. In this review, the focus is on newly identified regulatory factors in solventogenic Clostridium species, the interaction of these factors with previously identified molecules, and potential implications on substrate utilization, solvent production, and resistance/tolerance to lignocellulose-derived microbial inhibitory compounds.

We compare Chiral Perturbation Theory (ChPT) and the Linear Sigma Model (LSM) as realizations of low energy QCD for light mesons in a chirally imbalanced medium. The relations between the low-energy constants of the Chiral Lagrangian and the corresponding constants of the Linear Sigma Model are established as well as the expressions for the decay constant of $\pi $-meson in the medium and for the mass of the $a_0$. In the large $N_c$ count taken from QCD the correspondence of ChPT and LSM is remarkably good and give a solid ground for search of chiral imbalance manifestation in pion physics. A possible experimental detection of chiral imbalance (and therefore a phase with Local Parity Breaking) is outlined in the charged pion decays inside the fireball.

The cosmological constant problem is examined by taking an Einstein--scalar with a Higgs-type potential and scrutinizing the infrared structure induced by finite temperature effects. A variant optimal perturbation theory is implemented in the recently proposed quantum-gravitational framework. The optimized renormalized mass, i.e., the renormalized mass determined by the variant optimal perturbation theory, of the scalar field turns out to be on the order of the temperature. This shifts the cosmological constant problem to compatibility of the consequent perturbative analysis. The compatibility is guaranteed essentially by renormalization group invariance of physical quantities. We point out the resummation behind the invariance.

Computing the rotation tensor is vital in the analysis of deformable bodies. This paper describes an explicit expression for the SO(3) rotation tensor R of the deformation gradient F, and successfully establishes an intrinsic relation between the exponential mapping Q = exp A and the deformation F. As an application, Truesdell's simple shear deformation is revisited.

The variable-length arbitrary Lagrange-Euler (ALE)-ANCF finite element, which employ nonrational interpolating polynomials, cannot exactly describe the rational cubic Bezier curves such as conic and circular curves. The rational absolute nodal coordinate formulation (RANCF) finite element, whose reference length (undeformed length) is constant, can exactly represent the rational cubic Bezier curves. A new variable-length finite element called the ALE-RANCF finite element, which is capable of accurately describe the rational cubic Bezier curves, is proposed by combining the desirable features of the ALE-ANCF and RANCF finite element. In order to control the reference length of ALE-RANCF element within a suitable range, element segmentation and merging schemes are proposed. It is demonstrated that exact geometry and mechanic is maintained after the ALE-RANCF element is divided into two shorter ones, and compared with the ALE-ANCF elements, there are smaller deviations and oscillations after two ALE-RANCF elements are merged into a longer one. Numerical examples are presented and the feasibility and advantages of the ALE-RANCF finite element are demonstrated.

In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension for the sake of simplicity. The underlying finite volume scheme is conservative and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with high solution gradients or any other special features. No interpolation procedure is employed, thus an unnecessary solution smearing is avoided. Thus, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

This work combines compressive sensing and short word-length techniques to achieve localization and target tracking in wireless sensor networks with energy-efficient communication between the network anchors and the fusion center. Gradient descent localization is performed using time-of-arrival (TOA) data which are indicative of the distance between anchors and the target thereby achieving range-based localization. The short word-length techniques considered are delta modulation and sigma-delta modulation. The energy efficiency is due to the reduction of the data volume transmitted from anchors to the fusion center by employing any of the two delta modulation variants with compressive sensing techniques. Delta modulation allows the transmission of one bit per TOA sample. The communication energy efficiency is increased by RⱮ, R≥1, where R is the sample reduction ratio of compressive sensing and Ɱ is the number of bits originally present in a TOA-sample word. It is found that the localization system involving sigma-delta modulation has a superior performance to that using delta-modulation or pure compressive sampling alone, in terms of both energy efficiency and localization error in the presence of TOA measurement noise, owing to the noise shaping property of sigma-delta modulation.

There are different ways to analyse energy absorbance (EA) in the human auditory system. In previous research, we developed a complete finite element model (FEM) of the human auditory system. In this mentioned work, the external auditory canal (EAC), middle ear, and inner ear (spiral cochlea, vestibule, and semi-circular canals) were modelled based on human temporal bone histological sections. Multiple acoustic, structure and fluid-coupled analyses were conducted using the FEM to perform harmonic analyses in the 0.1–10 kHz range. Once the FEM had been validated with published experimental data, the FEM numerical results were used to calculate the EA or energy reflected (ER) by the tympanic membrane. This EA was also measured in clinical audiology tests which were used as a diagnostic parameter. A mathematical approach was developed to calculate the EA and ER, with numerical and experimental results showing adequate correlation up to 1 kHz. Another published FEM had adapted its boundary conditions to replicate experimental results. Here, we recalculated those numerical results by applying the natural boundary conditions of human hearing and found that the results almost totally agreed with our FEM. This boundary problem is frequent and problematic in experimental hearing test protocols: the more invasive they are, the more the results are affected. One of the main objectives of using FEMs is to explore how the experimental test conditions influence the results. Further work will still be required to uncover the relationship between the middle ear structure and EA to clarify how to best use FEMs. Moreover, the FEM boundary conditions must be more representative in future work to ensure their adequate interpretation.

This study investigates the magnetization of Cobalt (Co) nanoparticles with two different crystal structures: a centered cubic (fcc) and an hexagonal close packed (hcp), under the magnetic field of the Earth. For that reason, the hysteresis loops of the two material samples are exported and compared with the corresponding value by experimental procedure in the laboratory under the Earth’s magnetization. For both samples, the nanoparticle number variation and the nearest neighbor distance effect, in the Co hysteresis loop are investigated, structural information that is useful for the sample preparation. For the simulations the Finite Element Method (FEM) was used, while experiments are conducted using a measurement set-up based on fluxgate magnetometers. From the simulation, it is proven that, for both samples, the nanoparticle number effect does not change the hysteresis loop. In contrast, when the distance between the nanoparticles increases, the magnetization obtains smaller value. This study aims to build a novel, simple and economical measurement arrangement enabling in situ magnetic measurements for ferromagnetic nano-material characterization. As the need for continuous knowledge of the condition and the phase of ferromagnetic nanoparticles that is crucial in many applications, like catalytic processes, this work aims to introduce an alternative approach that will add another dimension to conventional chemical reaction engineering this of the magnetic state of the material resolved in time and space and to contribute in the field of the monitoring and the early fault diagnosis of nanoparticle materials.

Introducing the Moving Least-Squares Aided Finite Element Method (MLS-FEM), we present a robust computational technique that effectively evaluates the development of mixing in polymeric mixing devices. Our approach uses the Moving Least-Squares (MLS) interpolant to enhance the classic finite element shape functions. As a result, it becomes possible to treat fixed or moving components, such as rotors of a mixer, as discontinuities within the flow domain. This allows analysis of the flow field with a background mesh independent of the rotors' shape, orientation, and position. We compared the MLS-FEM results with the classical boundary-fitted mesh FEM, which comprises the mesh regeneration steps by the movement of the rotors. We then showed that the new method provides accurate results for the flow field parameters (i.e., the velocity components and the pressure values) and the mixing evolution without requiring mesh regeneration and without compromising accuracy.

Optimization of Magnetohydrodynamics parameters on the velocity profile and temperature distribution of incompressible fluid flow on a porous channel was evaluated. The fluid flow was considered to be unsteady, incompressible and flowing in 2-D in porous channel. The effects of magnetic parameter, Darcy’s number and fluid pressure on velocity profiles, and the effect of variable viscosity and Eckert number on temperature distribution in incompressible fluid flow were determined. The flow was considered to be in a channel running along the x-axis on which the magnetic field exist and finally along the y-axis on the porous part of the channel. The resulting model equations were solved by Finite Difference Method (FDM) in MATLAB software. Analysis of results indicated that increasing Darcy’s number and fluid pressure leads to increase in fluid velocity profile, while increasing magnetic parameter decreases fluid velocity profile. Also, it was observed that increase in both Eckert number and fluid viscosity lead to increase in temperature distribution. Optimization in temperature was achieved by increasing the magnetic field while viscosity was optimized by increasing the length of the porous part of the channel. This study will helpful to contribute alternative equations and methodology to engineering and in factories where getting the MHD parameters optimally is the main objective, particularly on temperature, velocity and pressure.

Cancer diseases lead to the second-highest death rate all over the world. The dynamics of invasion of cancer cells into the human body tissues and metastasis are the main causes of death in patients with cancer. This study deals with theoretical investigation of the dynamics of invasion of cancer cells for tumour growths in human body tissues using discretized Cahn-Hilliard, concentration and reaction-diffusion equations which were solved by Finite Difference Method with the aid of MATLAB computer software. A Crank-Nicolson numerical scheme was developed for the discretized model equations. The numerical result obtained was used to describe the dynamics of cancer invasion of tissues with respect to cancer cells density on tumour growth, turbulence and mobility and equilibrium between charge and discharge of cancer cells. The results of the study provide new insights into combating cancer disease by providing mitigating and intervention measures to this major health problem.

Evidence regarding the effect of the onlay preparation design for different CAD/CAM restorative materials considering the preservation of cusps is lacking. Molars were 3D modeled in four preparation designs for onlay restoration: traditional design with functional cusp coverage (TFC), non-retentive design with functional cusp coverage (NFC), traditional design with non-functional cusp coverage (TNFC), non-retentive design with non-functional cusp coverage (NNFC). Restorations were simulated with two CAD/CAM restorative materials: LD – lithium disilicate (IPS e.max CAD) and RC - resin composite (GrandioBloc). A 100 N axial load was applied to the occlusal surface simulating the centric contact point. Von Mises (VM) and maximum principal (Pmax) stresses were evaluated for restorations, cement layer and dental substrate. The non-retentive preparation design reduced the stress concentration in the tooth structure in comparison to the conventional retentive design. For LD onlays, the stress distribution on the restoration intaglio surface showed that the preparation design as well as the prepared cusp, influenced the stress magnitude. The non-retentive preparation design provided better load distribution in both restorative materials and more advantageous for tooth structure. The resin composite restoration on non-functional cusp is recommended when functional cusp is preserved, in order to associate conservative dentistry and low stress magnitude.

Abstract-Digital Phase Plane is presented in this paper. For constant input second order digital systems with arbitrary initial conditions for arbitrary quantizaters, this digital phase plane shows, in plot form, the state trajectory and the asymptotic stability, including the existence and the position of arbitrary period limit cycles.

We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-ladder operators are defined from mode-ladder operators via the unitary transformation of systems involved in arbitrary inhomogeneous dielectric media. Then, one can expand electromagnetic field operators through the coordinate-ladder operators weighted by non-orthogonal and spatially-localized bases, which are propagators of initial quantum electromagnetic (complex-valued) field operators. Here, we call them QEM-CV-propagators. However, there are no general closed form solutions available for them. This inspires us to develop a quantum finite-difference time-domain (Q-FDTD) scheme to numerically time evolve QEM-CV-propagators. In order to check the validity of the proposed Q-FDTD scheme, we perform computer simulations to observe the Hong-Ou-Mandel effect resulting from the destructive interference of two photons in a 50/50 quantum beam splitter.

A finite-difference approach with non-uniform meshes was presented for simulating magnetotelluric responses in 2D structures. We presented the formulation of this scheme and gave some sights into its successful implementation, and compared finite-difference solution with known numerical results and simple analytical solutions. First, a homogeneous half-space model was tested and the finite-difference approach can provide very good accuracy for 2D magnetotelluric modeling. Then we compared to the analytical solutions for the two-layered model, the relative errors of the apparent resistivity and the impedance phase were both increased when the frequency was increased. In the end, we compare our finite-difference simulation results with COMMEMI 2D-0 model with the finite-element solutions. Both results are in close agreement to each other. These comparisons confirm the validity and reliability of our finite-difference algorithm.

The present work deals with the development of finite element methodology for obtaining the stress distributions in thick cylindrical HK40 stainless steel pipe that carry high temperature fluids. The material properties and loading are assumed to be random variables. Thermal stresses that are generated along radial, axial and tangential directions are computed generally using analytical expressions which are very complex. To circumvent such an issue, the probability theory and mathematical statistics have been applied to many engineering problems which allows to determine the safety both quantitatively and objectively based on the concepts of reliability. Monte Carlo simulation methodology is used to study the probabilistic characteristics of thermal stresses which is used for estimating the probabilistic distributions of stresses against the variations arising due to material properties and load. A 2-D Probabilistic finite element code is developed in MATLAB and the deterministic solution is compared with ABAQUS solutions. The values of stresses that are obtained from the variation of elastic modulus are found to be low as compared to the case where the load alone is varying. The probability of failure of the pipe structure is predicted against the variations in internal pressure and thermal gradient. These finite element framework developments are useful for the life estimation of piping structures in high temperature applications and subsequently quantifying the uncertainties in loading and material properties.

To reduce weight and simplify maintenance, ship structures frequently include openings and cut-outs. While these features offer practical advantages, they can weaken the structural integrity of key components. This study explores the effects of these geometric discontinuities on the double-bottom floor plates of a Panamax-class container ship under axial and transverse loads. Through numerical simulations and experimental testing, we analyzed different cut-out configurations and stiffening strategies to assess their impact on stress distribution, plate thickness and fatigue behavior. The results reveal that side cut-outs significantly increase stress, particularly under transverse loads, while central openings have less impact. Additionally, increasing plate thickness consistently reduces stress levels across all models, improving structural durability. Fatigue analysis shows that certain stiffening configurations, particularly those with longitudinal stiffeners in the bottom plates, enhance fatigue life. These findings offer critical design insights for optimizing hull structures, balancing weight reduction with strength improvement. The study provides valuable recommendations for reducing stress concentrations and extending the fatigue life of ship components, contributing to more efficient and safer ship designs.

The finite volume method (FVM) is a kind of numerical analysis method that is simple and can take into account the topography as the finite element method (FEM). The adjoint state method (ASM) can easily and efficiently calculate the gradient vector of the objective function for the inversion. We developed a program to apply these methods to 3-D Magnetotelluric (MT) inversion and verified it using test models. In the forward modelling, it was confirmed that the program could perform analysis properly and efficiently considering topography and subsurface resistivity heterogeneity. Furthermore, we conducted the inversion using a synthetic open dataset and could reconstruct the true model of the dataset. The comparison with the previous work revealed that the computation time was comparable in spite of the fact that we calculated without MPI implementation, which the previous work used.

This paper is devoted to the finite time internal and the external synchronization (hybrid synchronization) for complex networks by means of intermittent control. Different from most previous research achievements, the finite time synchronization include internal and the external synchronization, this article employs the intermittent control to drive the complex networks to achieve synchronization in finite time. To be specific, the internal and the external synchronization all achieve consistent synchronization in finite time by devise Lyapunov function. Finally, numerical examples are presented to illustrate the validness of theoretical results.

Objective: Despite long simulation times, recently developed finite element analysis (FEA) models of knee joints have demonstrated their suitability for predicting individual risk of onset and progression of knee osteoarthritis. Therefore, the objective of this study was to assess the feasibility of machine learning (ML) to replicate outcomes obtained from FEA when simulating mechanical responses and predicting cartilage degeneration within knee joint. Design: Two ML models based on the Gaussian Process Regression (GPR) algorithms were developed. The first model (GPR1) utilized age, weight, and anatomical joint dimensions as predictor variables to predict tissue mechanical responses and cartilage degeneration based on FEA data. The second model (GPR2) utilized age, weight, height, and gender to predict anatomical joint dimensions, which were then used as inputs in the GPR1 model. Finally, the GPR1 and combined GPR1+GPR2 models were used to investigate the importance of clinical imaging when making personalized predictions for knees from healthy subjects with no history of knee injuries. Results: In the GPR1 model, R2 of 0.9 was exceeded for most of the predicted mechanical parameters. The GPR2 model was able to predict knee shape with R2 of 0.67 - 0.9. Both GPR1 and combined GPR1+GPR2 models offered equally good performance (AUC = 0.73 - 0.74) at classifying patients at high risk for the onset and development of knee osteoarthritis. Conclusions: In the future, real-time and easy-to-use GPR models may provide a rapid technology to evaluate mechanical responses within knee for researchers or clinicians who have no former knowledge from FEA.

(1) Background: This study aimed to compare the effect of polyetheretherketone (PEEK) and titanium abutments on implant prosthetic systems and supporting bone using three-dimensional finite element analysis (FEA); (2) Methods: A three-dimensional finite element analysis was conducted using CATIA and Abaqus software to model mandibular first molar implant systems with titanium and PEEK abutments. Under external loading conditions, finite element analysis was conducted for the stresses in implant components and surrounding bones of each group; (3) Results: The implant fixture of the PEEK model exhibited the highest von Mises stress (VMS). The lowest VMS was observed in the abutment screw of the titanium model. Both implant systems demonstrated similar stress distribution and magnitudes in cortical and cancellous bones; (4) Conclusion: PEEK abutments show similar stress distribution in surrounding bone compared to titanium. However, PEEK absorbs the stresses within the implant system and exhibits the highest VMS values due to its low mechanical and physical properties. Therefore, PEEK abutments need improved mechanical properties for better clinical application.

This paper introduces a low-tech capacitive micromachined ultrasonic transducer (CMUT) designed with low environmental footprint materials. The fabrication process involves a copper plate as the fixed bottom electrode, a polymer-based adhesive as a dielectric material, and an aluminum foil as the top electrode.Finite element simulations include studies of displacement, mechanical stresses, and eigenfrequency. Experimental measurements validate the device's electromechanical behavior, showing an eigenfrequency of 88.6 kHz and a displacement of 22 pm. The low-tech CMUT demonstrates potential for applications such as ultrasonic actuation and energy harvesting, offering simplicity, biocompatibility, and low environmental impact. While not directly ready for applications, these transducers provide hands-on experience with technology similar to high-performance silicon-based implementations. These low-tech MUTs are perfect practical case studies for teaching purposes, combining simulation and experimental validation.

The ANSYS 2024R1 student edition was used to create a finite element model of a basketball rim and backboard. This finite element model included the use of steel for the rim and its mount, a tempered glass backboard, and an aluminum frame behind the backboard. After a mesh was created, fixed support boundary conditions were applied to the four corners of the aluminum frame. The subsequently calculated mode shapes and frequencies were compared to empirical modal analysis previously done at the United States Military Academy at West Point, New York. Four mode shapes and frequencies agreed rather well between the theoretical finite element analysis and previously published empirical modal analysis, specifically where the rim was vibrating in the vertical direction, which was the direction that the accelerometer was aligned for modal analysis. However, three mode shapes missed by the empirical modal analysis were found where the vibration of the rim was confined to the horizontal plane, which was orthogonal to the orientation of our accelerometer.

The design of water Vessel fender system can minimize impact energy, which could result in severe vessel or offshore structure damage during collision. In order to protect Offshore structures and vessels from damage after impact, a Fender design approach is proposed which uses Soft materials like rubber, sand, inflated rubber tube, etc. to reduce damage on impacted vessels as well as offshore structures like wind turbines, bridges, oil drilling platforms in water etc. The fender is designed in such a way that it can handle vessels made of different material, sizes, and weights.The proposed solution is a fender consisting of a number of layers of soft sandwich materials, each layer getting softer as it moves away from the structure i.e. Hard-Soft fender design which can absorb impact energy upon collision. To handle lighter vessels made of soft or brittle materials, the outer layer is made of inflatable or Very soft foam rubber; however, the inner layer covering the offshore structure is made of hard material to handle heavy vessels made of hard material such as steel. Furthermore, the use of sand as a natural fender along waterways such as narrow channels is also proposed to reduce the cost of fender installation and catastrophic vessel impact damage on rocky ground since it produces less deformation just like rubber fender as demonstrated in the simulation. Finite Element Analysis using ANSYS software, Explicit Dynamic Autodyn, was performed. The results showed a considerable decrease in the total deformation and internal energy of the vessel and fended structure when collision occurs. Furthermore, the result showed that Hard-Soft fender layer performs much better than Soft-Hard-Soft followed by Soft-Hard Fender layer design.

In this paper, we aim to address the challenge of airflow interference during fault detection in high-speed train bogies by introducing a flow field and investigating the characteristics of the sound field distribution of critical components under its influence. This approach overcomes the limitation observed in previous studies that ignored the impact of the flow field. Furthermore, we evaluate and compare various layouts for inter-track acoustic sensor arrays. The proposed sensing methods hold significant practical engineering value, and the collected data serves as a valuable reference for acquiring acoustic signals from key bogie components in future research.

An estimation of the electric sources in the heart were conducted using a novel method, based on Huygens’ Principle, aiming at a direct estimation of equivalent bioelectric sources over the heart surface in real time. The main scope of this work was to establish a new, fast approach for the solution of the inverse electrocardiography problem. The study was based on recorded electrocardiograms (ECGs). Based on the Huygens’ principle, measurements obtained from a patient’s thorax surface were interpolated over the surface of the employed volume conductor model and considered as a secondary Huygens’ sources. These sources, being non-zero only over the surface under study, were employed to determine the weighting factors of the eigen-functions expansion describing the generated voltage distribution over the whole volume conductor volume. With the availability of the potential distribution stemming from measurements, the electromagnetics reciprocity theorem is applied once again to yield the equivalent sources over the pericardium. The methodology is self validated, since the surface potentials calculated from these equivalent sources are in very good agreement with ECG measurements. The ultimate aim of this effort is to create a tool providing the equivalent epicardial voltage or current sources in real time, i.e. during the ECG measurements with multiple electrodes.

Model-based approaches form the basis of the majority of damage detection and localization studies; however, built-in online detection technique can offer an alternative for future structural health monitoring technologies. Thus, in this paper, we present a dynamic localization algorithm for damage localization in functionally graded plates. The method depends on the creation of a grid matrix that contains the dynamic response of the structure over time. Subsequently, an optimization process is carried out via a linear equation representing the information contained within the grid to achieve accurate localization of damage. Due to the inherent sparsity of the localization nature, the FISTA algorithm has been employed as a problem solver. The approach is tested in the case of the functionally graded plate under clamped free boundary conditions. Several, damage scenarios were investigated for the case of damage signals on and off the grid. The results show that the proposed approach is capable of accurately predicting damage position and can be suitable for use in low size data systems.

A novel phase-field method based numerical approach to modeling the compaction process of sedi- ments is presented. Water-logged rock or soil sediments are deposited on the water basins over time and the increasing volume of the sediment compacts under its own weight and external pressure. Coupled evolution of mass conservation, Darcy flow, and the viscoelastic constitutive response, in conjunction with the evolution of porosity and permeability, make this problem highly non-linear and involve moving boundaries. We adopt a phase-field approach to represent the moving sediment interface, and the underlying multiphasic model permits for studying compaction in dynamically evolving sediments. This approach does not necessitate a change of domain sizes as is the case of existing traditional models of sedimentation but rather treats sedimentation growth as a problem of interface motion. We first model a classical compaction problem in 1D to compare with existing results in the literature, and then extend the framework to 2D to model the compaction process taking place under the influence of gravity. The model is then extensively applied to understand the effect of the sediment initial state and the sediment material properties on the compaction process and its spatiotemporal evolution. Lastly, a strong validation of our phase-field treatment results against predictions from traditional methods of solving open boundary sediment compaction problems, and a good agreement between the conventional understanding and the numerical predictions of porosity dependence on the fluid pore pressure for various cases of geological interest, are used to demonstrate the applicability and scalability of this novel numerical framework to model more advanced sediment compaction problems and geometries.

Brain tumors are abnormal cells growth in the brain tissues that can be cancerous, or not. In any case, they could be a very aggressive disease that should be detected as early as possible. Usually, magnetic resonance imaging (MRI) is the main tool commonly adopted by neurologists and radiologists to identify and classify any possible anomalies present in the brain anatomy. In the present work, an automatic unsupervised method called Z2-$\gamma$, based on the use of adaptive finite-elements and suitable pre-processing and post-processing techniques, is introduced. In particular, the proposed methodology is able to automatically classify whether a given MR image represents a healthy or a diseased brain and in this latter case, is able to locate the tumor area.

Here we consider sums of finite products of Chebyshev polynomials of the third and fourth kinds. Then we represent each of those sums of finite products as linear combinations of the four kinds of Chebyshev polynomials which involve the hypergeometric function ₃F₂.

Polymer nanocomposites are composed of polymer materials reinforced with nano fillers. In the present study the effective thermal conductivity of the composites filled with nanofillers has been investigated using commercially available finite element software ABAQUS 6.11. The nanofillers used were alumina particles and multi-walled carbon nanotubes (MWNTs) and the matrix was considered to be made of epoxy. For the analysis 2D and 3D Representative Volume Elements (RVEs) were generated using Random Sequential Adsorption (RSA) algorithm using MATLAB and Python scripts. Thermal conductivity was found out for 2D and 3D RVEs for different area and weight fractions respectively. Two different shapes of the alumina nanoparticles were considered: spherical (circular) and ellipsoidal (elliptical) for 3D (2D) analysis. It was found that the thermal conductivity was increased with the addition of nanofillers. The increase in thermal conductivity was approximately same for both types of inclusions at corresponding area or weight fractions in 2D or 3D analysis. The results showed that addition of MWNTs to the composites lead to a significant increase in thermal conductivity than spherical or ellipsoidal inclusions.

The article presents the results of experimental studies on wound models made in ballistic gel casts and dressed with a vacuum dressing. Compared to previously published articles, the thesis presents quantitative parameters describing the behavior of wounds under the influence of vacuum. A significant reduction in wound volume was noted. This effect is independent of the size of the wound. The experimental studies results were supported by numerical calculations using the finite element method.

In this paper, we integrate the Finite Element Method (FEM) with orthogonal polynomial approximation in high-dimensional spaces to innovatively model the Moon’s surface gravity anomaly. Our aim is to approximate solutions to Laplace’s classical differential equations of gravity, employing classical Chebyshev polynomials as basis functions. Using classical Chebyshev polynomials as basis functions, the least-squares approximation was used to approximate discrete samples of the approximation function. These test functions provide an understanding of errors in approximation and corresponding errors due to differentiation and integration. These test functions provide an understanding of errors in approximation and corresponding errors due to differentiation and integration. The first application of this project is to substitute the globally-valid classical spherical harmonic series of approximations with locally-valid series of orthogonal polynomial approximations (i.e. using the FEM approach). With an error tolerance set at 10−9ms−2, we use this method to adapt the gravity model radially upwards from the lunar surface. The results showcase a need for a higher degree of approximation on and near the lunar surface, with the necessity decreasing as the radius increases. Notably, this method achieves a computational speedup of five orders of magnitude when applying the method to radial adaptation. More intrinsically, our second application involves using the methodology as an effective tool in solving boundary value problems. Specifically, we implement this approach to solve classical differential equations involved with high precision, long-term orbit propagation. This application provides a four-order of magnitude speedup in computational time while maintaining an error within the 10−10ms−2 error range for various orbit propagation tests. Alongside the advancements in orthogonal approximation theory, the FEM enables revolutionary speedups in orbit propagation without compromising accuracy.

This work focuses on the well-known issue of mass conservation in the context of the finite element technique for computational fluid dynamic simulations. Specifically, non-conventional finite element families for solving Navier-Stokes equations are investigated to address the mathematical constraint of incompressible flows. Raviart-Thomas finite elements are employed for the achievement of a discrete free-divergence velocity. In particular, the proposed algorithm projects the velocity field into the discrete free-divergence space by using the lowest-order Raviart-Thomas element. This decomposition is applied in the context of the projection method, a numerical algorithm employed for solving Navier-Stokes equations. Numerical examples validate the approach’s effectiveness, considering different types of computational grids. Additionally, the presented paper considers an interface advection problem using marker approximation, in the context of multiphase flow simulations. Numerical tests, equipped with an analytical velocity field for the surface advection, are presented to compare exact and non-exact divergence-free velocity interpolation.

Boeing and Airbus developed a special testing procedure to investigate the compressive response of laminates that have been impacted (following standards ASTM D 7137 and DIN 65561). This study focuses on both experimental and numerical analysis of Kevlar plates subjected to compression after impact. To ensure high quality and appropriate mechanical properties, the composite plates were manufactured using autoclaving. The DIN 65561 protocol was followed for all three test systems. Initially, ultrasonic C-scanning was performed on all plates before testing to confirm they were free of any significant defects arising from the manufacturing process. Subsequently, low-energy impact testing was conducted at levels ranging from 0 to 8 Joules. Three specimens were tested at each energy level. After the impact, all specimens underwent ultrasonic C-scanning again to assess the internal delamination damage caused by the impactor. Finally, both pristine and impacted specimens were subjected to compressive testing using the special jig specified in DIN 65561. The compressive impact strength results obtained from these tests were plotted against the delamination area measured by C-scanning. This data was then compared to results obtained from specimens with artificial damage. Semi-empirical equations were used to fit both sets of curves. The same procedure (impact testing, C-scanning, and data analysis) was repeated to investigate the relationship between impact energy and total delamination area. Lastly, finite element modeling was employed to predict the buckling stresses that develop under compression in the impacted systems studied. These modelling approaches have demonstrated good accuracy in reproducing experimental results for CAI tests.

Graphene foam prepared by chemical vapor deposition method is a promising thermal interfacial material. However, the thermal properties of graphene foam highly depend on the experimental fabrication conditions during the chemical vapor deposition process. Aiming to reveal how to prepare the appropriate graphene foam for the various thermal management scenarios, the influence of experimental conditions on thermal properties of graphene foam is investigated. Furthermore, the contribution of thermal conductivity and thermal radiation to the effective thermal coefficient of graphene foam is carried out for comparison. Research results show that, the porosity and the cross-section shape of struts of growth template are two critical factors to affect the thermal transport of graphene foam, especially with the increase of temperature. In addition, the deposition time of graphene determines the wall thickness and affects the thermal conductivity directly. The thermal radiation contributes more than thermal conductivity when the temperature climbs continuously. Comparatively, the effective thermal coefficient of graphene foam composite with high porosity and circular shape struts is much superior to others at high temperature. The research findings can provide important guidance for the graphene foam fabrication and its applications in the field of thermal management.

The use of tuning forks to measure fluid density and viscosity is widely employed in fields such as food, medicine, textiles, automobiles, petrochemicals, and deep drilling. The explicit analytical model based on Euler-Bernoulli cantilever beam theory for the relationship between tuning fork resonance characteristics and the density and viscosity of fluid is only applicable to the situation where the fluid viscous effect is very small. In this paper, the finite element method is used to simulate the influence of large variations in fluid density and viscosity on the resonance characteristic parameters (resonant frequency and quality factor) of the tuning fork. The numerical simulation results are compared with the analytical analysis results and experimental measurement results. Then, the sensitivity of tuning fork resonance characteristic parameters to fluid density and viscosity is studied. The results show that compared with the analytical results, the numerical simulation results have a higher degree of agreement with the experimental measurement results. The relative difference in resonant frequency is less than 2%, and the relative difference in quality factor is less than 4%. This indicates that the finite element method includes the influence of fluid viscosity on tuning fork resonance parameters, which is more in line with the actual conditions than the analytical model. Simulating and analyzing the sensitivity of the tuning fork to fluid density and viscosity by the finite element method, it is possible to consider the situation where fluid density and viscosity vary over a large range. Compared with experimental measurements, this method has higher efficiency and can significantly save time and economic costs. This study can overcome the limitation of existing explicit analytical models, which are only applicable when the viscous effects of the fluid are very small. It enables a more accurate simulation of the coupling vibration between tuning forks and fluids, thereby providing theoretical references for further optimizing tuning fork structural parameters to enhance the accuracy of measuring fluid characteristic parameters.

This study investigates the impact of specimen size on the mechanical properties of wood, specifically focusing on compression strength, elastic modulus, and Poisson's ratio. Compression tests were conducted using three different specimen sizes (20mm×20mm×30mm, 40mm×40mm×60mm, 60mm×90mm×90mm) in the longitudinal, radial, and tangential directions. Mechanical parameters, failure mechanisms, load-displacement curves, and stress-strain relationships were systematically analyzed for each size. The study also evaluated the influence of specimen size on the accuracy of finite element numerical simulations by utilizing the obtained mechanical parameters. The results reveal a significant correlation between compressive strength and specimen size, indicating a decrease in compressive strength with increasing specimen size. Conversely, elastic modulus and Poisson's ratio exhibit less sensitivity to variations in specimen size. Notably, parameters derived from small-sized specimens (20mm×20mm×30mm) exhibited substantial errors, while those obtained from medium-sized (40mm×40mm×60mm) and large-sized specimens (60mm×90mm×90mm) demonstrated greater reliability, providing precise results in finite element numerical simulations.

Lightweight component design is effectively achievable through the sandwich structures, many past research studies in the aerospace and racing sectors (since 1920s) has proven it. To extend their application into automotive and other transport industries, the manufacturing cycle times must be reduced. This can be achieved by thermoplastic sandwich materials of continuous fibre-reinforced thermoplastic (CFRTP) cover layers and thermoplastic honeycomb cores. To widespread the application of flat thermoplastic-based sandwich panels into complex parts, a novel forming technology was developed by the Fraunhofer Institute of Microstructure of Materials and Systems (IMWS). For an increase in reproducibility of the sandwich component production and a decrease in manufacturing defects, numerical modelling methods and experimental validation are needed. The finite element (FE) modelling of this thermoforming process is a thermo-mechanical assignment with all three: material, geometry, and boundary non-linearities. In the scope of this work, the material behavior of different sandwich components (cover layers, honeycomb core, interface) under thermo-mechanical loads is characterized in detail, and a complex numerical model is developed to describe the thermoforming process of thermoplastic-based sandwich laminate. The critical forming condition like wrinkling that occurs due to friction in a sandwich or poor intra-ply shear in cross-ply studied, validated, and optimized. A thermoplastic sandwich made of polypropylene (PP) honeycomb core and polypropylene glass fibre (PP/GF) cross-ply as cover layers was used for this study, and numerical modelling was executed in LS-DYNA software.

The insufficient toughness of concrete can lead to the occurrence of crack expansion, ultimately resulting in a decline in the physical and mechanical properties such as bearing capacity and deformation characteristics of structural components. In severe cases, this may lead to brittle failure, where the entire structure and system fail suddenly without significant deformation after being stressed. Additionally, during the process of shear and bending failure of reinforced concrete beams, the cracks generated on the side of the beam are mostly I-II composite cracks. Considering the material nonlinearity and geometric irregularity of reinforced concrete, it is of great significance to study the dynamic evolution law of crack expansion in reinforced concrete members. Based on experimental data, this paper aims to utilize the nonlinear finite element simulation software Abaqus to conduct finite element simulations of crack expansion in simple supported reinforced concrete beams. By accurately controlling the constitutive curves of concrete and reinforcement materials, the design of seismic performance of structural members can be enhanced, thereby making essential contributions to the preliminary analysis of actual crack control engineering. The nonlinear finite element results indicate that the joint cracks of the frame with the floor slab primarily manifest as flexural cracks, with the concrete damage degree of the floor slab being higher than that of the beam. This finding underscores the importance of considering the behavior of concrete and reinforcement materials in designing for seismic performance and crack control in actual engineering applications.

In this study, the autofrettage method, which is used to increase the durability of cylindrical parts, was applied to a barrel made of steel material according to the AISI 4340 standard. Assuming that the barrel works continuously under the pressure of 400 MPa, optimum autofrettage was performed. The stresses occurring on the barrel before and after autofretage were calculated. Additionally, analytical equivalent stress values (Von-Mises) formed on the part's wall were compared with numerical analysis results obtained with a commercial finite element program ANSYS®, and their compatibility was examined. As a result of the calculations and analysis performed, it was observed that autofretage has positive effect on increasing the pressure carrying capacity of the barrel. After autofrettage the cylindrical part, it was determined that the Von-Mises stress values formed in the part wall changed and these stresses took the lowest value at a point (elastic-plastic interface). It has been evaluated that this point gives the optimal autofretage pressure value for a certain operating pressure. After the autofrettage application, it was determined that the Von-Mises Stress value in the barrel wall decreased by 25.27 % and the pressure carrying capacity of the barrel increased without any design or dimensional change. It has been seen that the analytical and numerical analysis results are consistent with each other, and it is expected that this study will guide and contribute to the studies to be conducted on increasing the strength or lightening the weight of the parts.

In order to examine the impact of geometric configuration of the human vocal tract on the redistribution of acoustic energy in the frequency spectrum, it is necessary to assemble computation models, which facilitate simple modification of the model’s geometric characteristics. This article describes how the human vocal tract model was constructed using so-called super-elements using the improved reduced system method. The mentioned procedure allows using such a model for demanding optimization calculations, for which the model is modified on the super-element level. Furthermore, the article presents an alternative approach, in which an isoparametric element of a higher degree polynomial was derived. Both approaches were compared and used to find the geometric configuration of the human vocal tract amplifying acoustic energy values on the frequency spectrum to around 3kHz.

In recent years, with the increase in maritime trade, the necessity of increasing the capacities of the ports has emerged. However, while it is planned to increase the capacities of the ports, it is important that the port continues to operate at the same time. In this respect, the old port structures should not be damaged during the capacity increase. In this study, the strengthening of a port in Guinea is discussed as a case study. In the study, the existing quay wall was evaluated, and geotechnical and structural alternatives of the new structure to be built for capacity increase were evaluated. A combined system was designed as a pile foundation and a reinforced foundation with plastic piles so as not to damage the existing quay wall. The pile capacities obtained as a result of the analyses were verified by loading tests.

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically, the K-BKZ-PSM (Kaye–Bernstein, Kearsley, Zapas - Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation, and the marker-particle method (known as \emph{Marker-and-Cell}) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K-BKZ-PSM fluid in a pipe.

This paper presents a finite element analysis of the bi-directional orthogonal model, which incorporates individual crack strain separation and tracking. The objective of the research is to expand the current shear friction model to manage bi-directional cracking at any angle, allowing for a more universal model that can be applied to intricate structures and non-proportional loading cases. The proposed model was initially developed as a total strain-based model, with the assumption that crack strains are equivalent to total strains, but was subsequently recalculated to improve accuracy by separating crack strains from total strains. Furthermore, a separate crack strain formulation was created to account for strains in the concrete's uncracked portions and locked-in crack strains. The article then discusses the testing of various convergence methods and loading programs to achieve high convergence. Comparative analyses of the generalized shear friction model with other models for crack orientation and loading cases similar to those of a reinforced concrete membrane are also presented. The MATLAB program successfully applied the bi-directional cracking model for one finite element under a uniform cyclical strain state, using a secant stiffness formulation.

Crystallization often occurs in the laser welding of amorphous alloys, reducing the amorphous alloys’ properties. So, it is necessary to simulate the temperature field curve of the welding area by computer and then determine the power and laser moving speed of laser welding. In this paper, the temperature field curve of Zr41.2Ti13.8Cu12.5Ni10Be22.5(Vit1) amorphous alloy in laser welding is obtained by finite element analysis. The continuous heating curve (CHT) of Vit1 is fitted by the Vogel-Fulcher-Tammann (VFT) equation and the Kissinger equation. If the temperature field curve intersects with the CHT curve, crystallization occurs. The experiment results show that the VFT equation can be used to predict the crystallization of Vit1 better in laser welding. The tem-perature and welding time are increased by using low welding speed. Therefore, the temperature of the weld zone cannot fall in time, resulting intersection of the temperature field curve and the CHT curve. So, crystallization can be avoided if the welding speed is controlled within a rea-sonable range, and the highest temperature is kept under the CHT curve.

The successful handling of large semiconductor wafers is crucial for scaling up their production. Early-stage warpage control allows to prevent undesirable asymmetric warpage, known as wafer bifurcation or buckling. Indeed, even in a gravity-free environment, thinning an 8" or 12" semiconductor wafer can result in warpage and bifurcation. To mitigate this issue, the taiko method, which involves creating a thicker ring region around the rim of the wafer, has been widely used. Previous research has focused on the theoretical factors affecting the warpage of a backside metalized taiko wafer. This work extends the case to a front-side metalized taiko wafer and introduces the concept of the equivalent thickness of a taiko wafer. The equivalent thickness of a taiko wafer, influenced by the ring region, lies in between the thickness of the central region and that of the annular region. Because of the limited number of taiko wafers that can be produced on a production line, modelling can be beneficial. In this work we compared the results of a developed analytical model with those obtained from a finite element analysis (FEA) approach with ANSYSY® software to model the equivalent thickness of a taiko wafer. We investigated the curvature as a function of the stress of the metal layer, considering key design factors such as the substrate region thickness, the thickness of the thin metal film, the step height, and the width of the ring region. By systematically varying the thickness of the central region of the taiko wafer, we explored the curvature as a function of stress induced by thermal load in the linear regime and determined the slopes in the linear region of the curvature vs. stress curves. The aim of this study is to identify regularities and similarities with the Stoney equation and investigate the validity of the analytical approach for the case of a taiko substrate. It results that there is a good agreement between the analytical model of a taiko wafer and the numerical analysis gained by the FEA methods.

Wearable thermoelectric generators (w-TEGs) convert thermal energy into electrical energy to realize self-powering of intelligent electronic devices, thus reducing the burden of battery replacement and charging, and improving the usage time and efficiency of electronic devices. Through finite element simulation, this study successfully designed high-performance thermoelectric generator and made it into wearable thermoelectric module by adopting “rigid device - flexible connection” method. It was found that higher convective heat transfer coefficient on cold-end leads to larger effective temperature difference and better power generation performance of device in typical wearable scenario. Meanwhile, at same convective heat transfer coefficient on the cold-end, longer TE leg length leads to larger temperature difference established at both ends of device, larger device output power and open-circuit voltage. However, when the convective heat transfer coefficient increases to a certain level, optimization effect of increasing TE leg length on device power generation performance will gradually diminish. For devices with fixed temperature difference between two ends, longer TE leg length leads to higher resistance of TEG, resulting in lower device output power but slight increase in open-circuit voltage. Finally, sixteen 16×4×2 mm2 TEGs (L=1.38 mm, W=0.6 mm) and two modules were fabricated and tested. At hot end temperature Th=33 ℃ and cold end temperature Tc=30 ℃, the actual maximum output power Pout of TEG is about 0.2 mW, and the actual maximum output power Pout of TEG module is about 1.602 mW, which is highly consistent with the simulated value. This work brings great convenience to research and development of wearable thermoelectric modules and provides new, environmentally friendly and efficient power solution for wearable devices.

The link of fracture analysis of large ships is an essential part of the structural safety of ships. However, the finite element analysis of large structure according to the traditional method not only has high requirements on the computer, but also the influence of the mesh encryption at special locations makes further requirements on the accuracy of the ship. In this paper, based on the extended finite element method (XFEM) and the multi-point constraint method (MPC), the dynamic crack expansion process of the rectangular plate containing cracks under the multi-scale model is comparatively studied by using ABAQUS simulation software Finally, the applicability of the method is verified by applying the multi-scale model of ship nodes. The results show that the computational effort of the multi-scale model is significantly reduced with the same accuracy and allowable error, which proves the accuracy and efficiency of the method.

This paper presents the experimental and numerical studies of the vertical stress distribution beneath the centerline of circular footings resting on the sand. Vertical stress values due to circular load in medium-dense sand were measured using soil stress transducers. Reduced-scale laboratory model tests were carried out in a square-shaped test box and vertical stresses were measured at the centerline of the circular footing at different depths of the sand. In order to determine the effect of footing width on vertical stress distribution, laboratory experiments were performed on circular footings of different diameters. In addition, a series of finite element analyses was carried out on the test model to validate the findings of the experimental study. In the numerical analysis, the sand was modeled as a non-linear elastoplastic material. The analyses were performed using the finite element method with two-dimensional axisymmetric and three-dimensional conditions. The results obtained from laboratory model tests and numerical analysis were compared with the vertical stress values obtained from the theoretical solution in the literature. Vertical stress distribution in horizontal planes at any depth from the footing base shows the same characteristic form in all methods. However, some differences were observed between experimental, numerical, and theoretical results and discussed.

This article presents a case study on the structural assessment of a reinforced concrete (RC) foundation exposed to low temperatures. The foundation supports a 19,500 m³-capacity tank with low-temperature (-89°C) ethane. Icing and bubbling were observed on the tank’s surface soon after it started operations. Condensation was also observed at the bottom of the 0.8 m-depth RC slab, which raised concerns about the structural condition of the concrete. This study provides details of the field and analytical investigations conducted to assess the structural condition of the foundation. Heat transfer finite element (FE) analyses were performed to examine the concrete sections subjected to low temperatures. It was found that the ethane leakage produced a low temperature on the top side of the concrete foundation of +9.7°C. Overall, the temperatures calculated by the FE analyses were in good agreement with actual field measurements, within a ±5% accuracy. The simplified heat transfer equation for porous media used in this study was sufficiently accurate to model the effects of the ethane leakage in the concrete foundation, provided the ambient temperature at the site is taken into account in the analysis. The results also confirm that reinforcing bars can be neglected in the thermal analysis of massive concrete slabs. The results from the field measurements and FE analyses confirmed that the structural integrity of the RC foundation was never compromised. The approaches, methods and techniques discussed in this article are deemed suitable to solve the practical and scientific challenges involved in the structural assessment and repairs of large special structures. Accordingly, they can serve as useful reference and guidance for engineers and practitioners working in the field of forensic engineering.

The Gol'denveizer problem of a torus was studied analytically by Audoly and Pomeau (2002), and the accuracy of the Audoly and Pomeau linear law was confirmed numerically by Sun (2021). However, the law does not include the major radius R of the torus. To find the influence of the major radius, we used finite element numerical simulation to simulate different cases, and we propose a modified Audoly and Pomeau linear law for vertical deformation, which includes R. A linear law of horizontal deformation is presented as well. Our studies show that the Audoly and Pomeau linear law has high accuracy. With modified vertical and horizontal deformation, a displacement-compatible relation between them is formulated.

Orofacial injuries are common occurrences during contact sports activities; however, there is an absence of data regarding the performance of hybrid occlusal splint mouthguards, especially during compressive loading. To evaluate the total deformation and stress concentration, a skull model was selected and duplicated to receive two different designs of mouthguard devices: one model received a conventional custom-made mouthguard (MG) with 4-mm thickness and the other received a novel hybrid occlusal splint-mouthguard (HMG) with the same thickness. Both models were subdivided into finite elements. The frictionless contacts were used, and a nonlinear analysis was performed simulating the compressive loading in occlusion. The results were presented in von-Mises stress maps (MPa) and Total Deformation (mm). A higher stress concentration in teeth was observed for the model with the conventional MG, while the HMG design displayed a promising mechanical response with lower stress magnitude. The HMG de-sign displayed a higher magnitude of stress on its occlusal portion than the MG design. The hybrid mouthguard (HMG) reduced (1) jaw displacement during chewing and (2) the generated stresses in maxil-lary and mandibular teeth.

Energy efficiency and leakage magnetic field (LMF) are two important issues in electric vehicle inductive chargers. In this work, the maximum achievable coil efficiency and the corresponding LMF strength are formulated as functions of hardware parameters, and figure of merits (FOM) are proposed for assessing the efficiency and LMF performance of the coil assembly pair. The impacts of the coil assemblies’ geometric parameters on both FOMs are examined with the aid of finite element analysis (FEA), and measures to improve the FOMs are extracted from FEA results. A coil assembly pair is manually optimized within given dimensional limits. Compared with the initial design, the optimized one achieves higher efficiency and lower LMF strength while consuming less copper. The performance improvement is verified by FEA results and experimental data measured on an 85 kHz electric vehicle inductive charger prototype. The key measures for coil assembly optimization are summarized.

Steel is one of the essential materials in the world's civilization. It is essential to produce many products such as pipelines, mechanical elements in machines, vehicles, profiles, and beam sections for buildings in many industries. Until the '50s of the 20th century, steel products required a complex process known as ingot casting; for years, steelmakers focused on developing and simplifying this process. The result was the con-tinuous casting process (CCP); it is the most productive method to produce steel. The CCP allows producing significant volumes of steel sections without interruption and is more productive than the formal ingot casting process. The CCP begins by transferring the liquid steel from the steel-ladle to a tundish. This tundish or vessel distributes the liquid steel, by flowing through its volume, to one or more strands having wa-ter-cooled copper molds. The mold is the primary cooling system, PCS, solidifying a steel shell to withstand a liquid core and its friction forces with the mold wall. Further down the mold, the rolls drive the steel section in the SCS. Here the steel section is cooled, solidifying the remaining liquid core, by sprays placed in every cooling segment all around the billet and along the curved section of the machine. Finally, the steel strand goes towards a horizontal-straight free-spray zone, losing heat by radiation mechanism, where the billet cools down further to total solidification. A moving torch cutting-scissor splits the billet to the desired length at the end of this heat-radiant zone.

Our aim is to implement and test some less known numerical methods that might be used to solve an advection equation. The description is restricted to information necessary to implement and test the presented methods and it is given only for one-dimensional case.

The effect of the different dental implants positioning region on the stress performance of the implant-supported prosthesis is not yet clear. This study evaluated the dental treatment with six dental implants in three different models and three different occlusal loading conditions, in terms of the biomechanical response of implants, prosthetic screw and maxilla, using three-dimensional finite element analysis. The finite element models were modelled containing external hexagon implants, as well as a Cobalt-Chromium superstructure. Three types of loads were applied: in the area of ​​the central incisors, first premolar and in the second molars. For the finite element simulations, the von-Mises stress peaks in the implant and in the surrounding cortical bone were analyzed. All recorded results reported higher values ​​for the implant-supported prosthesis in group C compared to the groups A and B. The highest stress values, ​​regardless the evaluated model, was in the prosthesis in group C and in screws, the smallest were in group A.

In the process of metal cutting, the anti-wear performance of the tool determines the life of the tool and affects the surface quality of the workpiece. The finite element simulation method can directly show the tool wear state and morphology, but due to the limitations of the simulation time and complex boundary conditions, it has not been commonly used in tool life prediction. Based on this, a tool wear model was established on the platform of a finite element simulation software for the cutting process of titanium alloy TC4 by end milling. The key technique is to embed different types of tool wear models into the finite element model in combination with the consequent development technology. The effectiveness of the tool wear model is validated by comparing the experimental results with the simulation results. At the same time, in order to quickly predict the tool life, an empirical prediction formula of tool wear was established, and the change course of tool wear under time change was obtained.

Since large power transformers are custom-made, and their design process is a labor-intensive task, their design process is split into different parts. In tendering, the price calculation is based on the preliminary design of the transformer. Due to the complexity of this task, it belongs to the most general branch of discrete, non-linear mathematical optimization problems. Most of the published algorithms are using a copper filling factor based winding model to calculate the main dimensions of the transformer during this first, preliminary design step. Therefore, these cost optimization methods are not considering the detailed winding layout and the conductor dimensions. However, the knowledge of the exact conductor dimensions is essential to calculate the thermal behaviour of the windings and make a more accurate stray loss calculation. The paper presents a novel, evolutionary algorithm-based transformer optimization method which can determine the optimal conductor shape for the windings during this examined preliminary design stage. The accuracy of the presented FEM method was tested on an existing transformer design. Then the results of the proposed optimization method have been compared with a validated transformer design optimization algorithm.

In order to reveal the mechanism and influencing factors of high pressure jet cavitation of nozzle in submerged environment, this study focused on the evolutionary process of cavitation bubbles and combined finite volume method and mixed multi-phase flow model to analyze the cavitation, velocity distribution and experimental cavitation intensity of fishing net cleaning equipment. Results show that the cavitation inception, growth and collapse mainly occurred in the peripheral region of the flow field. Ring-shaped cavitation erosion zone appeared on the test sample target. A lot of small dense erosion pits were densely distributed in the ring-shaped erosion zone, erosion marks were observed in the center. The cavitation erosion intensity was greatly affected by the nozzle structure. As the diameter of nozzle increased from 0.6 mm to 1 mm, the maximum gas volume fraction increased by 8.53%. The nozzle outlet enlargement angle greatly increased the cavitation intensity. The nozzle with an outlet angle of 30° exhibited the optimal cavitation erosion performance . The cavitation volume fraction of the nozzle with short necking structure was slightly larger than that of the nozzle with long necking structure at the same level in the necking length rang of 3mm to 7mm. In terms of the influence of nozzle structure on the cavitation erosion effect, the nozzle diameter D ranked the first, followed by the outlet angle α, and the necking length L was at the last.

Adaptable or adapted? Whether it is a question of physical, biological or even economic systems, this problem arises when all these systems are the location of matter and energy conversion. To this interdisciplinary question we propose a theoretical framework based on the two principles of thermodynamics. Considering a finite time linear thermodynamic approach, we show that non-equilibrium systems operating in quasi-static regime are quite deterministic as long as boundary conditions are correctly defined. The Novikov-Curzon-Ahlborn approach [1,2] applied to non-endoreversible systems then makes it possible to precisely determine the conditions for obtaining characteristic operating points. As a result, power maximization principle (MPP), entropy minimization principle(mEP), efficiency maximization, or waste minimization states are only specific modalities of system operation. We show that boundary conditions play a major role in defining operating points because they define the intensity of the feedback that ultimately characterizes the operation. Armed with these thermodynamic foundations, we show that the intrinsically most efficient systems are also the most constrained in terms of controlling the entropy and dissipation production. In particular, we show that the best figure of merit necessarily leads to a vanishing production of power. On the other hand, a class of systems emerges which, although they do not offer extreme efficiency or power, have a wide range of use and therefore marked robustness. It therefore appears that the number of degrees of freedom of the system leads to an optimization of the allocation of entropy production.

This study presents the development of a number of finite element (FE) models of the pelvis using different continuum and structural modelling approaches. Four FE models were developed using different modelling approaches: continuum isotropic, continuum orthotropic, hybrid isotropic and hybrid orthotropic. The models were subjected to an iterative adaptation process based on the Mechanostat principle. Each model was adapted to a number of common daily living activities (walking, stair ascent, stair descent, sit-to-stand and stand-to-sit) by applying onto it joint and muscle loads derived using a musculoskeletal modelling framework. The resulting models, along with a structural model previously developed by the authors, were compared visually in terms of bone architecture, and their response to a single load case was compared to a continuum FE model derived from CT imaging data. The main findings of this study were that the continuum orthotropic model was the closest to the CT derived model in terms of load response albeit having less total bone volume, suggesting that the role of material directionality in influencing the maximum orthotropic Young's modulus should be included in continuum bone adaptation models. In addition, the hybrid models, where trabecular and cortical bone were distinguished, had similar outcomes, suggesting that the approach to modelling trabecular bone is less influential when the cortex is modelled separately.

In this paper we study the normal bases for Galois ring extension ${{R}} / {Z}_{p^r}$ where ${R}$ = ${GR}$(p^r, n). We present a criterion on normal basis for ${{R}} / {Z}_{p^r}$ and reduce this problem to one of finite field extension $\overline{R} / \overline{Z}_{p^r}=F_{q} / F_{p} (q=p^n)$ by Theorem 1. We determine all optimal normal bases for Galois ring extension.