This article examines the wavelet transforms and the machine learning methods in accelerating large eddy simulations of turbulent flows. An overarching challenge of large eddy simulations is to accurately represent the cascade of kinetic energy across the cut-off length scale. Taylor hypothesis suggests that the energy cascade occurs through the process of vortex stretching. However, Richardson hypothesis assumes the self-amplification of the strain field and a hierarchical break down of large eddies lead the energy cascade. The large eddy simulations typically employs the self-amplification of the strain in formulating subgrid models. However, several studies also proposed subgrid models based on vortex stretching. The wavelet-based coherent vortex simulation of turbulence directly accounts for vortex stretching in overall forward scatter of energy, while allowing local backscatter. The wavelet-based large eddy simulation adapts the grid to capture the creation of small-scale eddies, while adopting subgrid models based on the self-amplification of strain. The advancement of artificial intelligence in turbulence modelling is currently evolving around accelerating the numerical simulations of turbulent flow. However, there is a clear connection between the application of wavelet transfroms and neural networks for directly solving the Navier-Stokes equation, indicating some potential benefits of wavelet methods over the neural networks.

specific finite detail modeling of the human body gives a capability primary enhancement to the prediction of damage risk all through automobile impacts. currently, car crash protection coun-termeasure improvement is based on an aggregate of testing with installed anthropomorphic check devices (i.e., ATD or dummy) and a mixture of multibody (dummy) and finite element de-tail (vehicle) modeling. If an incredibly easy finite element detail version can be advanced to cap-ture extra statistics beyond the abilities of the multi-body structures, it might allow advanced countermeasure improvement thru more targeted prediction of overall performance. Numerous research have been done on finite element analysis of broken femurs. However, there are two missing pieces of information: 1- choosing the right material properties and 2- designing a precise model including the inner structure of the bone. In this research, most of the chosen material properties for femur bone will be discussed and evaluated.

Simulation programs contain Computational Fluid Dynamics - CFD codes and are a useful tool used for gas flow through porous materials. Conducting numerical simulations allows for detailed analysis of hydrodynamic phenomena. The results of numerical modeling should always be verifiable based on experimental data. Only their compliance with the results of experimental tests is a determinant of the correctness of the applied method. As part of the work, experimental studies of hydrodynamics of gas flow through an isotropic porous material were carried out and numerical simulation for material of the same shape was used. In the CFD modeling Kolmogorov's hypothesis for the transport of kinetic energy of turbulence k and transport of dissipation rate of kinetic energy of turbulence ε was used.

Two isotropic pitches were prepared by air blowing and nitrogen distillation method using ethylene tar (ET) as a raw material. And correspondent carbon fibers were obtained through conventional melt spinning, stabilization and carbonization. The structures and properties of resultant pitches and fibers were characterized and their differences were discussed in this work. The results showed that introduction of the oxygen by air blowing method could quickly increase the yield and softening point of pitch. Moreover, the air blown pitch (ABP) composed of linear methylene chains of aromatic molecules while the nitrogen distilled pitch (NDP) mainly contained polycondensed aromatic rings, which was due to the oxygen containing functional groups existed in ABP could impede order stack of pitch molecules and form methylene bridge structure, instead of aromatic condensed structure like NDP. Meanwhile, the spinnability of ABP was not decreased even containing 2.31 wt% oxygen. In contrast, ABP had narrower molecular weight distribution, which contributed to better stabilization properties and higher tensile strength of carbon fiber. The tensile strength of carbon fibers from ABP was reached to 860 MPa with fiber diameter of about 10 μm, which was higher than that of NDP-derived carbon fibers of 640 MPa.

Although neural network architectures are critical for their performance, how the structural characteristics of a neural network affect its performance has still not been fully explored. We here map architectures of neural network to directed acyclic graphs, and find that incoherence, a structural characteristic to measure the order of directed acyclic graphs, is a good indicator for the performance of corresponding neural networks. Therefore we propose a deep isotropic neural network architecture by folding a chain of same blocks then connecting the blocks with skip connections at different distances. Our models, named FoldNet, have two distinguishing features compared with traditional residual neural netowrks. First, the distances between block pairs connected by skip connections increase from always equal to one to specially selected different values, which lead to more incoherent graphs and let the neural network explore larger receptive fields and thus enhance its multi-scale representation ability. Second, the number of direct paths increases from one to multiple, which leads to a larger proportion of shorter paths and thus improve the direct propagation of information throughout the entire network. Image classification results on CIFAR-10 and Tiny ImageNet benchmarks suggested that our new network architecture performs better than traditional residual neural networks.

In large eddy simulation (LES) of turbulent flows, the most critical dynamical processes to be considered by dynamic subgrid models to account for an average cascade of kinetic energy from the largest to the smallest scales of the flow is not fully clear. Furthermore, evidence of vortex stretching being the primary mechanism of the cascade is not out of the question. In this article, we study some essential statistical characteristics of vortex stretching and its role in dynamic approaches of modeling subgrid-scale turbulence. We have compared the interaction of subgrid stresses with the filtered quantities among four models using invariants of the velocity gradient tensor. This technique is a single unified approach to studying a wide range of length scales in the turbulent flow. In addition, it also provides a rational basis for the statistical characteristics a subgrid model must serve in physical space to ensure an appropriate cascade of kinetic energy. Results indicate that the stretching mechanism extracts energy from the large-scale straining motion and passes it onto small-scale stretched vortices.

This paper presents an explicit method for constructing tangential and anisotropic bases in quadratic spaces. We will also provide three theorems that allow us to explicitly calculate vectors that are orthogonal or tangent to given vectors or that provide necessary and sufficient conditions for the existence of such vectors. A classical theorem on quadratic space states that every finite-dimensional quadratic space has an orthogonal basis. A result that seems to be unanswered is under what conditions a finite-dimensional quadratic space has a basis consisting of isotropic vectors. A second problem is whether or not every finite-dimensional quadratic space has a basis consisting of mutually tangent vectors, where two vectors v,w are tangent if (u·v)2=(u·u)(v·v). In this paper, we attack these two problems.

In this study, carbon blocks were fabricated using isotropic coke and coal tar pitch as raw materials, with a variation in pressure during cold isostatic pressing (CIP). The CIP pressure was set to 50, 100, 150, and 200 MPa, and the effect of the CIP pressure on the mechanical and electrical properties of the resulting carbon blocks was analyzed. Microstructural observations confirmed that after the kneading, the surface of isotropic coke was covered with the pitch components. Subsequently, after the CIP, granules, which were larger than isotropic coke and the kneaded particles, were observed. The formation of these granules was attributed to the coalescence of kneaded particles under the applied pressing pressure. This granule formation was accompanied by the development of pores, some remaining within the granules, while others were extruded, thereby existing externally. The increase in the applied pressing pressure facilitated the formation of granules, and this microstructural development contributed to enhanced mechanical and electrical properties. At a pressing pressure of 100 MPa, the maximum flexural strength was achieved at 33.3 MPa, and the minimum electrical resistivity was reached at 60.1 μΩm. The higher the pressing pressure, the larger the size of the granules. Pores around the granules tended to connect and grow larger, forming crack-like structures. This microstructural change led to degraded mechanical and electrical properties. The isotropic ratio of the carbon blocks obtained in this study was estimated based on the coefficient of thermal expansion (CTE). The results confirmed that all carbon blocks obtained proved to be isotropic. In this study, a specimen type named CIP-100 exhibited the best performance in every aspect as an isotropic carbon block.

Due to the long-term deformation settlement of foundations, issues such as damage and functional failure of buildings and structures have long been of concern in the engineering field. The creep of soil is one of the primary causes leading to long-term deformation of foundations. In this paper, the consolidation deformation, creep characteristics, and creep model of reconstituted saturated silty clay were studied by isotropic compression test and triaxial shear creep test. The results show that for the isotropic compression test, although the applied load adopts different stages of loading, as long as the final applied confining pressure is the same, the number of stages applied by the confining pressure has little effect on the final isotropic consolidation deformation of the sample and the triaxial undrained shear strength after creep. However, for the triaxial shear creep test, it is found that under the same final deviatoric stress, the final deviatoric strain of the sample is closely related to the number of loading stages of deviatoric stress. It shows that the more loading stages of the sample loaded with the same deviatoric stress, the smaller the final deviatoric strain, and the triaxial undrained shear strength of the sample after creep will increase. In addition, it is reasonable to determine the pore pressure dissipation of the sample to 95%((u0-u0)/u0=95%) as the main consolidation end time (tEOP) of the sample. The isotropic consolidation creep curves and the triaxial shear creep curves show certain nonlinearity. Then the logarithmic model and the hyperbolic model were used to fit the creep curves of the samples. It is found that the hyperbolic model has a better fitting effect than the logarithmic model, but for the triaxial shear creep test, the creep parameters of the sample change greatly. Therefore, studying the creep characteristics of soil under different pre-loading steps is of significant engineering importance for evaluating the long-term deformation of underground structures.

(1) Background: Central nervous system (CNS) development is characterized by dynamic changes in cell proliferation and differentiation. Key regulators of these transitions are the transcription factors such as SOX2 and SOX9. SOX2 is involved in the maintenance of progenitor cell state and neural stem cell multipotency, while SOX9, expressed in neurogenic niches, plays an important role in neuron/glia switch with predominant expression in astrocytes in the adult brain. (2) Methods: To validate SOX2 and SOX9 expression pattern in dissociated primary neuronal cultures derived from opossum (Monodelphis domestica), we used immunohistochemistry (IHC) and the isotropic fractionator method on fixed cortical tissue from comparable postnatal ages; (3) Results: Neurons positive for both neuronal (NeuN or TUJ1) and stem cell (SOX2) markers were identified and their presence was confirmed with all methods and postnatal age groups (P4-6, P6-18 and P30) analyzed. SOX9 showed exclusive staining in non-neuronal cells, and it was coexpressed with SOX2. (4) Conclusions: The persistence of SOX2 expression in developing cortical neurons of M. domestica during first post-natal month implies the functional role of SOX2 during neuronal differentiation and maturation, which was not previously reported in opossums.

Lung cancer (LC) stands as the foremost cause of cancer-related fatality rates worldwide. Early diagnosis significantly enhances patient survival rate. Nowadays, low dose computed tomography (LDCT) is widely employed on chest as a tool for large-scale lung cancer screening. Nonetheless, a large amount of chest radiographs causes an onerous burden on radiologists. Some computer-aided diagnostic (CAD) tools can provide insights to medical images for diagnosis and augmenting diagnostic speed. However, due to variation in parameter settings across different patients, substantial discrepancies in image voxels persist. We find different voxel-size causing a compromise between model generalization and diagnostic efficacy. This study investigates the performance disparities of diagnostic models trained on original images and LDCT images reconstructed to different voxel-sizes but isotropic. The application is to differentiate a nodule to be benign or malignant. Using 11 features, a support vector machine (SVM) is trained on LDCT images with an isotropic voxel having side-length of 1.5 mm for 225 patients in house. The result yields a favorable model performance with an accuracy of 0.9596 and an area under the receiver operating characteristic curve (ROC/AUC) of 0.9855. In addition to furnish CAD tools for clinical applications, future research is encouraged to include LDCT images from multi-centers.

A cloud of relativistic material particles is considered, for which the distortions of length and time caused by the presence of the Lorentz factor an order of magnitude greater than curvature of space-time by gravity. The gravitational mass of the cloud is found in the region where its size is insignificant. It is established that the coefficient of dependence of the cloud mass on the total rest mass of its particles includes a complete elliptic integral of the 2nd kind.

This paper presents an optimized feature-centered reflection symmetry axis detection and localization framework for object perception. The proposed framework is formed to obtain an improved reflection symmetry axis based on the salient symmetry feature. It starts with a refined Multi-scale Saliency Symmetry Model (MSSM), which is realized by applying isotropic symmetry operator on salient points in scale-space rather than all pixels. In each scale, salient points are initially extracted as local extremal from an image, and they are further refined by a multi-scale implementation for generating salient symmetry feature maps. A Symmetric Transformation Matrix is then computed using the optimal feature matching pairs, which can be explicitly used as an abstract representation of the constraint regions of symmetry objects in an image to optimize the performance of the potential symmetry axis detection. The framework has been investigated experimentally both on the classical dataset from a symmetry detection challenge and the latest dataset. It has shown that the framework can get a better or comparative result and also can be further adapted into terminated human--computer equipment for reflection symmetry object perception and tracking.

Abstract: As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation. There are numerous ways of solving the transport equation, such as the Wiener-Hopf method based on analyticity, method of singular eigenfunctions, Laplace and Fourier transforms and analytical discrete ordinates, which is arguably one of the most straightforward, to name a few. Another potential method is the PN method, where the solution is expanded in terms of full range orthogonal Legendre polynomials and with orthogonality and truncation, the moments form a set of second order ODEs. Because of the half-range boundary conditions for incoming particles however, full range Legendre expansions are inaccurate near material discontinuities. For this reason, a double PN (DPN) expansion is more appropriate, where the incoming and exit-ing flux distributions are expanded separately to preserve the discontinuity at material interfaces. Here, a new method of solution for the DPN equations is proposed and demonstrated for an iso-tropically scattering medium.

The object of this paper is the analysis of isotropic rectangular thin plates supported (simply supported or clamped) along two opposite edges whereby the other edges have arbitrary support conditions; the plates are subjected to external bending moments, concentrated or distributed, and perpendicular to the supported edges. The standard approach to this problem is to replace the bending moment with a couple of forces infinitely close and to use the known expressions of efforts and deformations for the plate subjected to concentrated forces; the results are then related to the first derivatives of those efforts and deformations with respect to the position of application of the load. In this study, the external bending moment was expanded into a Fourier series, leading to a distributed external bending moment, and the boundary conditions and continuity equations were applied. Various types of rectangular plates were analyzed, as well as plates of infinite length whose results were identical to those in the literature. In addition, results for cantilever plates of infinite length were presented.

This paper aims to analyze arbitrarily loaded isotropic rectangular thin plates with two opposite edges supported (simply supported or clamped), from which one or both are clamped, and the other edges have arbitrary support conditions. Rectangular thin plates with two opposite edges simply supported are routinely analyzed using for the deflection the simple trigonometric series of Lévy or the double trigonometric series of Navier, while the loads are expanded in Fourier series. In this paper the flexibility method (or force method) of the linear beam theory was applied whereby the unknowns were the bending moments along the opposite edges; in this regard, the primary system was the plate simply supported along the above-mentioned opposite edges and subjected to the external loads, system solved using the Lévy solution, and the redundant system was the plate simply supported along the opposite edges and subjected to bending moments along those edges. In the redundant system, a modified Lévy solution was introduced to account for the edge moments. The compatibility equations (vanishing of the slopes at selected positions of the opposite edges) were set to determine the unknowns and so the efforts in the plate. The results obtained were in good agreement with the exact results.

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to non-uniform heating (NUH) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the NUH; these derivatives are zero by constant value of the NUH, which leads to its absence in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the NUH, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection curve. Thus, the NUH appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed; the other edges having various support conditions (free, simply supported, and fixed).

The theory of special relativity has reexamined and reconstructed the concepts of space and time, which are indispensable for describing physical laws, consequently instigating a major revolution in physics in general. Although the correctness of the special theory of relativity has been con-firmed by many observations and experiments, it is unclear why the "principle of relativity" and the "principle of the constant speed of light," which form the basis of the idea, are valid. Moreo-ver, although special relativity has advanced our understanding of time, our understanding of the fundamental question, "What is time?" is still limited. The theory of special relativity regards space as a four-dimensional construct consisting of one-dimensional time and three-dimensional space. This paper proposes an alternative framework, wherein real space is uniform and isotropic four-dimensional space, and elementary particles are waves that propagate through this four-dimensional space at a constant speed. This new perspective provides evidence to support two of Einstein’s key principles—the "principle of relativity" and the "principle of the constant speed of light." Furthermore, this model clarifies what time is and why time flows at a constant rate from the past to the future.

In this paper we will consider the cosmic fluid to be dissipating i.e it has both bulk and shearing viscosity. We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for cosmic fluid which is dissipating i.e it has both shearing and bulk viscosity. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion of Bianchi type 1 in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. By this transformation we can express the mass to be moving in a scalar potential field. This definition helps us to explain the nature of expansion of universe during cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved. In the case of bulk and shearing viscous fluid we get the solution of damped harmonic oscillator after the cosmological inflation.Part I contains the calculations of bulk viscous fluids and Part II contains the calculations of bulk and shearing viscous fluid.At the end we have also provided the relation of shearing and expansion.Part III will give the approximation of low viscosity to solve the viscous fluid problem.

The lightweight and displacement-stable design of the mechanical support structure within the APTS (Acquisition, Pointing, and Tracking System) is crucial for enhancing the payload capacity of remote sensing, satellite communication, and laser systems, while still meeting specified functional requirements. This paper adopts the Solid Isotropic Material with Penalization (SIMP) method to investigate the structural topology optimization of the L-shaped bracket in the APTS, aiming to minimize structural compliance while using volume, key point displacement, and maximum stress as constraints. In the optimization model, differences in the topology of the L-shaped bracket structure are explored to minimize structural compliance, which is done under volume, key point displacement, and stress constraints, the results are compared with the initial reinforced structure. The innovative L-shaped bracket structure obtained through topology optimization uses significantly less material than the initial reinforced design, while still meeting the displacement and stress constraints. After smoothing, rounding, and finite element analysis, the displacement and stress performance of the optimized L-shaped bracket structure satisfies the set constraints. The method proposed in this paper offers an innovative solution for the lightweight design of mechanical support structures in APTS, with significant engineering application potential.

The aim of this paper is the analysis of arbitrarily loaded isotropic rectangular Kirchhoff plates supported at all corner points, whereby the edges are arbitrarily supported (simply supported, clamped, or free). Analytical methods commonly used include the single trigonometric series of Lévy, the double trigonometric series of Navier, the power series expansions, etc. In this paper the deflection surface was approximated with the sum of a particular solution to the governing differential equation (GDE) and two single series. The terms of the single series were the product of an unknown function of an independent variable and a trigonometric function of the other independent variable, whereby the trigonometric functions were chosen to vanish at the corner points. On the one hand the terms of the series were required to satisfy the homogeneous GDE, leading to two uncoupled differential equations, one for each unknown function, and so the approximate solution satisfied exactly the GDE. On the other hand the boundary conditions were satisfied only at selected collocation points along the boundary, the number of collocation points in each direction corresponding to the number of terms of the associated series. Results for several plates supported at all corner points with arbitrary edge support conditions were presented and showed good agreement with the exact results, the accuracy increasing the more terms of series were considered. Cantilevered plates and plates having two adjacent edges free will be analyzed using this approach in future research.

We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for perfect fluid. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. This definition helps us to explain the cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved.Part II is contained with some analysis of the lagrangian ; derived in Part I ; on the quintessence model.

Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number i, then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector i of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector i match the rules of multiplication and division of imaginary number i. Therefore, basis vector i is nothing but imaginary number i. Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms i, j and k. In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.