The rationalization and modeling of an electric discharge in a fluid require the knowledge of electron swarm parameters. In this work, transport coefficients of alcohols, including methanol, ethanol, propanol, and butanol are reported. The electron energy distribution function, mean energy, reduced mobility, and diffusion coefficient, are calculated using the two-term expansion of the electron Boltzmann equation in the frame of BOLSIG+ and the Monte Carlo collision code METHES. For such, experimental and theoretical values of the electron-alcohol collision cross-section, covering a range of electron impact energy from 1 eV to 1000 eV, are employed. A temperature of 300K, reduced fields E/N between $1-10^4$ Td (1Td = $10^{-21}~\rm Vm^2$), and Plasma density of $10^{19}~\rm m^{-3}$ were used in simulations. The calculated coefficients are compared with data available from previous studies.

Liquid crystal torons, localized topological structures, are known for their stability and dynamic behaviour in response to external stimuli, making them attractive for advanced material applications. In this study, we investigate the flow of torons in chiral nematic liquid crystals around obstacles. We simulate the fluid flow and director field interactions using a hybrid numerical method combining lattice Boltzmann and finite difference techniques. Our results reveal that the toron dynamical behaviour depends strongly on the impact parameter from the obstacle. At impact parameters smaller than half cholesteric pitch, the flowing toron is destabilized by the interaction with the obstacle; otherwise, the flowing toron follows a trajectory with a deflection which decays exponentially with the impact parameter. Additionally, we explore the scattering of torons by multiple obstacles, providing insights into how the dynamics of these structures respond to complex environments.

Restricted Boltzmann machines (RBMs) are the building blocks of some deep learning networks. However, despite their importance, it is our perception that some very important derivations about the RBM are missing in the literature, and a beginner may feel RBM very hard to understand. We provide here these missing derivations. We cover the classic Bernoulli-Bernoulli RBM and the Gaussian-Bernoulli RBM, but leave out the ``continuous'' RBM as it is believed not as mature as the former two. This tutorial can be used as a companion or complement to the famous RBM paper ``Training restricted Boltzmann machines: An introduction'' by Fisher and Igel.

We consider that the relationship between entropy in statistical mechanics, which is the Boltzmann principle, and the complex velocity potential in complex fluid dynamics. We define the generalized complex entropy which expanded entropy from real space to complex space. We show that the complex entropy can be expressed by the composition of sources, sinks and laminar flows of the complex velocity potential. Therefore, the complex entropy is considered a special case of the complex fluid dynamics,that is, the complex velocity potential. In other words, we show that the complex entropy is expressed by the complex velocity potential. Moreover, we show that a complex number is expressed by the complex entropy. Thus, we show that the complex velocity potential is expressed by the complex entropy. Namely, we will expand entropy to complex space and see that the complex entropy is expressed by the complex velocity potential. Furthermore, we examine the possibility that it is an expansion of Boltzmann's principle and Planck distribution.

Porous materials can be characterized by well-trained neural networks. In this study, fibrous paper-type gas diffusion layers were trained with artificial data created by a stochastic geometry model. The features of the data were calculated by means of transport simulations using the Lattice–Boltzmann method based on stochastic micro-structures. A convolutional neural network was developed that can predict the permeability and tortuosity of the material, through-plane and in-plane. The characteristics of real data, both uncompressed and compressed, were predicted. The data was represented by reconstructed images of different sizes and image resolutions. Image artifacts are also a source of potential errors in the prediction. The Kozeny–Carman trend was used to evaluate the prediction of permeability and tortuosity of compressed real data. Using this method, it was possible to decide if the predictions on compressed data were appropriate.

Two-dimensional (2D) of transition metal dichalcogenides (TMDCs) are potential candidates for thermoelectric (TE) applications due to their unique structural properties. In this paper, we constructed an 2D monolayer TMDCs semiconductor γ-PbSn2(X=S, Se, Te) and first-principles calculations and Boltzmann transport theory are used to study the thermoelectric performance. We found that γ-PbSnX2 had an ultra-high carrier mobility up to 4.04×103 cm2V−1s−1 leading to a metal-like electrical conductivity. Meanwhile, γ-PbSnX2 both have high Seebeck coefficients, resulting in high power-factors, and also shows intrinsic low lattice thermal conductivity of 6-8 W/mK at room temperature. The lower lattice thermal conductivity and high power-factors resulted in excellent thermoelectric performance. The high ZT values of γ-PbSnS2 and γ-PbSnSe2 were as high as 2.65 and 2.96 at 900 K, respectively. The result suggests that the monolayer γ-PbSnX2 are better candidates for excellent thermoelectric performance.

Energy consumption of processors and memories is quickly becoming a limiting factor in the deployment of large computing systems. For this reason it is important to understand the energy performance of these processors and to study strategies allowing to use them in the most efficient way. In this work we focus on computing and energy performance of the Knights Landing Xeon Phi, the latest Intel many-core architecture processor for HPC applications. We consider the 64-core Xeon Phi 7230, and profile its performance and energy efficiency using both its on-chip MCDRAM and the off-chip DDR4 memory as the main storage for application data. As a benchmark application we use a Lattice Boltzmann code heavily optimized for this architecture, and implemented using several different arrangements of the application data in memory (data-layouts, in short). We also assess the dependence of energy consumption on data-layouts, memory configurations (DDR4 or MCDRAM), and number of threads per core. We finally consider possible trade-offs between computing performance and energy efficiency, tuning the clock frequency of the processor using the Dynamic Voltage and Frequency Scaling (DVFS) technique.

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

The liquid-vapor phase change lattice Boltzmann method is used to investigate the pinning-depinning mechanism of the contact line during droplet evaporation on the stripe-patterned surfaces in 3D space. Considering the curvature of the contact line and the direction of the unbalanced Young’s force, the local force balance theory near the stripe boundary is proposed to explain the steady state of the droplets on the stripe-patterned surfaces. An equation is proposed to evaluate the characteristic contact angle of the stabilized droplets. During the evaporation of the droplet, the stick-slip-jump behavior and the CCR-Mixed-CCA mode can be well captured by the lattice Boltzmann simulation. When the contact line is pinned to the stripe boundary, the contact line in the direction perpendicular to the stripes is slowly moving while the curvature of the contact line is gradually increasing. The gradually increasing curvature of the contact line accelerates the movement of the contact line, and the final contact line is detached from the stripe boundary. The research results provide theoretical support and guidance for the design, improvement and application of patterned surfaces in the field of micro-fluidic and evaporation heat transfer.

Grid refinement is used to save computing costs while preserving high precision of fluid simulation. In the Lattice Boltzmann Method, grid refinement often uses interpolated values. We found a method, where interpolation in space and time is not required. For this purpose, we used the moment matching condition and rescaling the non-equilibrium part of populations, and developed the recalibration procedure that allows to transfer information between different LBM stencils in the simulation domain. Then, we build non-uniform lattice which uses stencils with different shapes on the transition. The resulting procedure is verified on the 2D Poisselle flow and the advected vortex benchmark. In prospect, grids with adaptive geometry can be built with the use of the proposed method.

In this study, we mainly focus on the behavior of an electron gas produced by argon plasma that is bounded by a moving rigid flat plate. The effects of an external magnetic field on the electrons collected with each other, with positive ions, and with neutral atoms in the plasma fluid are investigated. We used the BGK model of the Boltzmann kinetic equation, which is fundamental in the study of the gas dynamics from the continuum flow to the free-molecular regimes with Maxwellian velocity distribution functions of the various species. An exact analytical solution of the model equations for the unsteady flow is given using the moment and the traveling wave methods. The behavior of the mean velocity of electrons is illustrated, which compatible with the variation of the shear stress, viscosity coefficient, and the initial and boundary conditions. Besides, the thermodynamic prediction is investigated by applying the principles of irreversible thermodynamics and Gibbs formula. It is found that the thermodynamic variables verify the Boltzmann’s H–theorem, the principle of Le Chatelier, and the Thermodynamics Second Law for the non-equilibrium processes of the system. Qualitative agreements with previous related papers are introducing. 3-Dimensional graphics for the calculating variables are offering, and their behavior is deeply discussed.

The historical idea of entropy as a property of a body has been reviewed and shown to arise from Clausius’s view of heat as motion. This view of heat, being intermediate between the now defunct idea of heat as substance and the modern view that heat represents an exchange of energy, implied that a body contains a definite quantity of heat. Heat, and therefore entropy, was thus considered a property of a body. These ideas led Clausius to develop his famous inequality and the idea that entropy always increases in irreversible, non-cyclic processes. In this paper, the notion of the entropy as a property of a body is examined in detail. A physical meaning is attached to the thermodynamic entropy by showing that a change in the function Q/T can be understood as representing a change in the number of ways that energy can be distributed among the degrees of freedom active in the system at any given temperature. The idea is illustrated with reference to solids and simple liquids. It is shown that the total thermodynamic entropy is, in general, less than the Boltzmann entropy, except for the case of a monatomic classical ideal gas in which the number of degrees of freedom is independent of temperature. Finally, entropy as a state function is discussed. It is argued that this is entirely mathematical in nature and that the entropy of a state represented in p-V space is not equivalent to a physical property of a physical system in the same thermodynamic state.

During deep-sea mining, the heavy metals pollutants can cause contamination in the marine environment. In this paper, the multiphasic coupling model is established to describe the heavy metal migration process during deep-sea mining, which takes the effects of convection-diffusion, adsorption-desorption and sedimentation-resuspension of heavy metals in the aquatic environment into full consideration. Due to the advantages of Lattice Boltzmann method, it is adopted to numerically solve the multiphasic coupling model and achieve the simulation for heavy metal migration process during deep-sea mining. In addition, taking Cadmium as an example, the concentration variations are discussed and analyzed in detail. Based on the established model and Lattice Boltzmann method, the concentration distribution of heavy metals can be accurately described to provide the reasonable bases for the evaluation of marine environmental protection.

Over the past decade, plasma waste treatment has become a more prominent technology due to increasing problems with waste disposal and realizing opportunities to generate valuable co-products. Plasma waste treatment extensively uses atmospheric pressure (RF) inductive coupled plasma (ICP) torches. In situ Optical Emission Spectroscopy (OES) is used to evaluate the developed RF ICP torch for Municipal Solid Waste (MSW) treatment and ascertain the plasma parameters to understand the physical mechanism involved. The argon plasma jet's electron temperature and plasma density outside the torch chamber are calculated using the Boltzmann plot and Stark broadening at different gas flow rates, and RF power. The expected electron temperature and plasma density behaviour were observed at a low gas flow rate. The electron temperature decreases with the RF power from 8089 K to 6097 K as demand for increasing the plasma density. An energy loss mechanism was revealed while raising the gas flow rate, as the electron temperature increases with RF power from 5750 K to 6221 K, and the plasma density decreases. This behaviour is due to the anomalous skin effect. Detecting and avoiding this phenomenon is essential as it negatively affects torch energy efficiency and waste treatment.

Thin films (100-400 nm) of Ba_xSr_1-xTiO₃ (0≤x≤1) deposited in RF-magnetron co-sputtering equipment are presented in this research work. The change of deposition rate, gap energy, and resistivity as a function of temperature- applied power change in the growth parameters was studied through the ISO colour-code lines constructed with MATLAB: By analysing the trend information and take into account the influence of the calculated "x" parameter with the Boltzmann profile fitting is proposed a method to allow a controlled set up of the RF-magnetron co-sputtering system and predict the E_g and resistivity values in the Ba_xSr_1-xTiO₃ solid solution with 0≤x≤1 for amorphous and crystalline phases. Also, a versatile tool to optimise the deposition process and material properties.

In the last ten years, plasma waste treatment has gained increasing prominence as a technology in response to growing challenges in waste disposal and the recognition of opportunities for generating valuable by-products. The efficiency and outcomes of this process are intricately linked to the characteristics of the plasma involved, such as plasma enthalpy and heat flux. We employed an experimental radio frequency inductively coupled plasma (RF-ICP) torch operating at atmospheric pressure to generate plasma. Utilizing optical emission spectroscopy (OES), we measured plasma parameters, specifically the effective electron temperature (Teff) and plasma density (ne), while varying argon gas flow rates and RF powers. Our investigations revealed that both flow rate and RF power exert significant control over plasma parameters, and we observed an unusual phenomenon within this range of discharge pressures. Consequently, both the plasma's enthalpy and the heat flux it generates are influenced by variations in both flow rate and RF power.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

The physical roots, interpretation, controversies and precise meaning of the Landauer Principle are surveyed. Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surrounding. The Landauer Principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin limit and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decrease in a temperature of a thermal bath will decrease the energy consumption of a single computation, but, in parallel, it will slow the computation. The Landauer principle bridges between John Archibald Wheeler “it from bit” paradigm and thermodynamics. Experimental verifications of the Landauer Principle are surveyed. Interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to the quantum and non-equilibrium systems is addressed. Landauer Principle represents the powerful heuristic principle bridging the physics, information theory and computer engineering.

The Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and ensure that the predictions are consistent and stable with the physical laws. PINNs opens up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar-Gross-Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts the equilibrium control equations in different discrete velocity directions within SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling inference of the fluid's non-equilibrium characteristics. The third component, a physics informed function translates the outputs of the first two networks into physical infor-mation. By minimizing the residuals of the physical partial differential equations (PDEs), the physics informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models applicable to different dimensions, named PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physical informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into the neural network through the interpretation function. Therefore, PINN-SRT-LBM allows the neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Experimental results confirm the accurate prediction of flow infor-mation at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.

Laser irradiation of metals is widely used in research and applications. In this work, we study how the material geometry affects electron-phonon coupling in nano-sized gold samples: an ultrathin layer, nano-rod, and two types of gold nanoparticles: cubic and octahedral. We use the combined tight-binding molecular dynamics Boltzmann collision integral method implemented within XTANT-3 code to evaluate the coupling parameter in irradiation targets at high electronic temperatures (up to Te~20,000 K). Our results show that the electron-phonon coupling in all objects with the same fcc atomic structure (bulk, layer, rod, cubic and octahedral nanoparticles) is nearly identical at electronic temperatures above Te~7000 K, independently of geometry and dimensionality. At low electronic temperatures, reducing dimensionality reduces the coupling parameter. Additionally, nano-objects under ultrafast energy deposition experience nonthermal damage due to expansion caused by electronic pressure, in contrast to bulk metal. Nano-object ultrafast expansion leads to ablation/emission of atoms, and disorder inside of the remaining parts. These nonthermal atomic expansion and melting are significantly faster than electron-phonon coupling, forming a dominant effect in nano-sized gold.

This paper introduces a new adaptation of the enthalpic lattice Boltzmann method (LBM) tailored to simulate the intricate dynamics of conjugate heat transfer in non-homogeneous media, showcasing considerable potential for enhancing heat exchanger designs. This approach expands upon the conventional enthalpic LBM framework by seamlessly incorporating tailored source terms, enabling precise representation of local and transient variations in the medium’s thermophysical properties. The resulting LBM model comprehensively captures the energy conservation equation, with exceptions made only for flow compressibility and viscous dissipation, thereby significantly augmenting its versatility in analyzing heat exchanger configurations. Verification tests, comprising assessments of both transient and steady-state solutions, unequivocally validate the accuracy of the proposed model, further bolstering its reliability for analyzing heat exchange processes within intricate heat exchanger geometries. To demonstrate its efficacy, simulations of conjugate heat transfer processes involving fluid natural convection within structured cavities were performed, imposing both Dirichlet and Neumann boundary conditions to emulate scenarios encountered in practical heat exchanger operations. The findings yield compelling insights, particularly in the transient regime, revealing the beneficial impact of structured cavities on enhancing heat transfer processes. These insights inform potential design optimizations for heat exchangers. The results emphasize the potential of the modified enthalpic LBM approach to elucidate complex heat transfer phenomena in non-homogeneous media and structured geometries, offering valuable implications for heat exchanger engineering and optimization.

In this study, the multi-relaxation-time lattice Boltzmann method is applied to investigate the oscillatory instability of lid-driven flows in two-dimensional semi-elliptical cavities with different vertical to horizontal aspect ratios K in the range of 1.0--3.0. The program implemented in this study is parallelized using CUDA (compute unified device architecture), a parallel computing platform, and computations are carried out on NVIDIA Tesla K40c GPU. To carry out precise calculations, the CUDA algorithm is extensively investigated, and its parallel efficiency indicates that the maximum speedup is 47.6 times faster. Furthermore, the steady--oscillatory Reynolds numbers are predicted by implementing the CUDA-based programs. The amplitude coefficient is defined to quantify the time-dependent oscillation of the velocity magnitude at the monitoring point. The simulation results indicate that the transition Reynolds numbers correlate negatively with the aspect ratio of the semi-elliptical cavity, and are smaller than those of the rectangular cavity at the same aspect ratio. In addition, the detailed vortex structures of the semi-elliptical cavity within a single period are also investigated when the Reynolds number is larger than the steady--oscillatory value to determine the effects of periodic oscillation of the velocity magnitude.

– Every physical theory involving quantum fields does require a model of the quantum vacuum. The vacuum associated to quantum gravity must incorporate the prescriptions from both the theory of relativity and quantum physics. In this work, starting from the hypothesis of nucleation of sub-Planckian bubbles from a de Sitter vacuum, we study the necessary conditions to obtain baby universes, black holes and particles. The de Sitter-Planck background is described by an “infinite” Quantum Boltzmann statistics that generates fermions and bosons, and manifests itself as a deformation of the geometry that leads to a generalized uncertainty principle and a unified expression for the generalized Compton wavelength and event horizon size, drawing a connection between quantum black holes and elementary particles, the latter seen as a collective organization of the bubbles of the vacuum described by the generalized Compton wavelength. The quantum thermodynamics of black holes is then outlined and the physical history of each bubble is found to depend on the cosmological constant described in terms of thermodynamic pressure. Finally, a suggestive treatment of the Casimir effect is provided in the de Sitter-Planck background with Quantum-Boltzmann statistics and wormholes are explored as bubble coalescence processes.

Currently, there are two approaches to the foundations of thermodynamics. One, associated with the mechanistical Clausius-Boltzmann tradition, is favored by the physics community. The other, associated with the post-mechanical Carnot tradition, is favored by the engineering community. The bold hypothesis is that the conceptual foundation of engineering thermodynamics is the more comprehensive. Therefore, contrary to the dominant consensus, engineering thermodynamics (ET) represents the true foundation of thermodynamics. The foundational issue is crucial to a number of unresolved current and historical issues in thermodynamic theory and practice. ET formally explains the limited successes of the ‘rational mechanical’ approaches as idealizing special cases. Thermodynamic phenomena are uniquely dissymmetric and can never be completely understood in terms of symmetry-based mechanical concepts. Consequently, ET understands thermodynamic phenomena in new way, in terms of the post-mechanical formulation of action. The ET concept of action and the action framework trace back to Maupertuis’s Principle of Least Action, both clarified in the engineering worldview research program of Lazare and Sadi Carnot. Despite the intervening Lagrangian ‘mechanical idealization of action’, the original dualistic, indeterminate engineering understanding of action, somewhat unexpectedly, re-emerged in Planck’s quantum of action. The link between engineering thermodynamics and quantum theory is not spurious and each of our current formulations helps us develop our understanding of the other. Both the ET and quantum theory understandings of thermodynamic phenomena, as essentially dissymmetric (viz. embracing complementary), entail that there must be an irreducible, cumulative historical, qualitatively emergent, aspect of reality.

Abstract: The main contribution of this paper is to introduce a new iterative training algorithm for restricted Boltzmann machines. The proposed learning path is inspired from online sequential extreme learning machine one of extreme learning machine variants which deals with time accumulated sequences of data with fixed or varied sizes. Recursive least squares rules are integrated for weights adaptation to avoid learning rate tuning and local minimum issues. The proposed approach is compared to one of the well known training algorithms for Boltzmann machines named “contrastive divergence”, in term of time, accuracy and algorithmic complexity under the same conditions. Results strongly encourage the new given rules during data reconstruction.

This paper reviews numerical methods used to simulate desiccation cracks in clayey soils. It examines five numerical approaches: Finite Element (FEM), Lattice Boltzmann (LBM), Discrete Element (DEM), Cellular Automaton (CAM), and Phase Field (PFM) Methods. The FEM is widely used to capture moisture diffusion, shrinkage, and cracking during drying. LBM is used to simulate fluid flow in clayey soils, while the DEM focuses on capturing the behavior of individual particles and their interactions. CAM simplifies crack evolution with computational efficiency, while PFM provides a continuous representation of crack formation and propagation. The author discusses the complexity of the problem, the continuum mechanics governing and constitutive equations that describe it, and the influence of various factors such as the multiphase nature of soils, heterogeneity, nonlinearities, coupling, scales of analysis, and computational aspects. The review highlights the characteristics, strengths, and limitations of each method. It emphasizes the importance of appropriate method selection for every problem depending on the aim of the analysis. The article concludes by reviewing the integration of multiple numerical methods to enhance the simulation of desiccation cracks in clayey soils.

Here we mathematically model black holes and the early universe following dynamics similar to RLC electrical models, focusing on their similarities at the singularity. We use this mathematically modelling to hypothesize the evolution of an expanding universe as the result of a black hole collapse followed by its evaporation. Or model consists of several steps defined by: (1) the formation of a black hole following general relativity equations; (2) growth of the black hole modelled as a resistance-capacitance-like electrical circuit; (3) expansion of space-time following the disintegration of the black hole, modelled by RLC-like dynamics. In updating this article, version 2, we will expand by presenting three additional examples related to the theory of the generalization Boltzmann's constant in curved space-time and the theory of general and especial relativity. We will calculate the critical mass to produce a black hole in the LHC, the existence of a high temperature Bose-Einstein condensate and finally we will demonstrate the existence of a tangential force to the repulsion force in the disintegration of subatomic particles. In the update of this article, version 3, we will expand to develop two examples. First, we will present the relationship between M-theory, extra dimensions with the theory of the generalization of Boltzmann's constant in curved space-time. Secondly, we will propose the idea of ​​updating the Lambda-CDM model, considering the primordial gravitational waves to correctly describe the evolution of the universe.

Different forces play a key-role in the stability of food colloid dispersions. Focus is here on those controlling attraction and/or repulsion, which concur to stabilization, phase separation, coagulation, and are quite evident in water-based systems. Combination of attractive and repulsive forces favors, or hinders, the association of colloid entities; such processes are often met in food technology. The above processes depend on the forces at work, and on colloid concentration in the medium (i.e. on inter-particle distance). Worked examples deals with milk manipulation procedures, ending in cheese formation. The whole milk-working sequence is controlled by the combination of forces leading to aggregation and phase separation of casein and other milk components. Thereafter, one gets either fresh, for prompt consumption, or aged cheeses. The combination of attractive (van der Waals, vdW, and depletion) with repulsive (double layer, DL, but also with steric) forces results in the dominance of aggregation versus dispersion modes in all steps of milk transformation, which depend on the distance among colloid particles, on the amplitude of the mentioned forces, and on their decay length. The combined role of double layer and van der Waals (vdW) forces is at the basis of the DLVO theory on colloid stability, which is properly modified when these forces overlap with steric stabilization and, eventually, with depletion. Steric effects are dispersive, depletion ones favor colloid nucleation in a single phase. The milk manipulation chain is a worked example of the intriguing association features controlled by the mentioned forces (and of ancillary ones, as well), and indicates which forces favor the formation of products such as Parmesan or Mozzarella cheese, but are not alien to the preparation of many other dairy products.

Tissue engineering has the potential for repairing large bone defects, which impose a heavy financial burden on the public health. However, difficulties with O₂ delivery to the cells residing in the interior of tissue engineering scaffolds make it challenging to grow artificial tissues of clinically-relevant sizes. This study uses image-based simulation in order to provide insight into how to better optimize the scaffold manufacturing parameters, and the culturing conditions, in order to resolve the O₂ bottleneck. To do this, high resolution 3D X-ray images of two common scaffold types (salt leached foam and non-woven fiber mesh) are fed into a Lattice Boltzmann Method fluid dynamics and reactive Lagrangian Scalar Tracking mass transfer solvers. The obtained findings indicate that the scaffolds should have maximal surface area-to-solid volume ratios, for higher chances of the molecular collisions with the cells. Furthermore, the cell culture media should be flown through the scaffold pores as fast as practically possible (without detaching or killing the cells). Finally, we have provided a parametric sweep that maps how the molecular transport within the scaffolds is affected by variations in rates of O₂ consumption by the cells. Ultimately, the results of this study are expected to benefit the computer-assisted design of tissue engineering scaffolds and culturing experiments.

Here we mathematically model black holes following dynamics similar to RC electrical model, focusing on their similarities at the singularity. We use this mathematically modelling to hypothesize the origin and growth of a black Hole. Or model consists of several steps defined by: (1) the formation of a black hole following general relativity equations; (2) growth of the black hole modelled as a resistance-capacitance-like electrical circuit. Based on the mathematical modeling of a black hole following dynamics similar to an RC circuit, for a circular motion with constant acceleration, in which the condition is fulfilled, Vt = ω r, we are going to calculate the amount of dark matter in the Milky Way galaxies and the Andromeda galaxy and subsequently the rotation curve of both galaxies to compare them with observed or measured values.

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.

In the present paper, the effect of the non-linear thermal radiation on the neutral gas mixture in the unsteady state is investigated for the first time. The unsteady BGK technique of the Boltzmann kinetic equations for a neutral non-homogenous gas is solved. The solution of the unsteady case makes the problem more general significance than the stationary one. For this purpose, the moments' method, together with the traveling wave method, is applied. The temperature and concentration are calculated for each gas component and mixture for the first time.Furthermore, the study is held for aboard range of temperatures ratio parameter and a wide range of the molar fraction. The distribution functions are calculated for each gas component and the gas mixture. The significant non-equilibrium irreversible thermodynamic characteristics the entire system is acquired analytically. That technic allows us to investigate the consistency of Boltzmann's H-theorem, Le Chatelier principle, and thermodynamics laws. Moreover, the ratios among the different participation of the internal energy alteration are evaluated via the Gibbs formula of total energy. The final results are utilized to the argon-helium non-homogenous gas at different magnitudes of radiation force strength and molar fraction parameters. 3D-graphics are presented to predict the behavior of the calculated variables, and the obtained results are theoretically discussed.

Here we will model the curvature and contraction of space-time using as a basis the equation of state of an ideal gas and the Hawking´s equation for the temperature of a black hole. We will use this mathematical model to hypothesize that the Boltzmann´s constant depends on the state of matter, that is, there is a known Boltzmann´s constant for flat space-time and an effective Boltzmann´s constant for curved space-time. This model will allow us to quantify the structure of space-time and will serve as a basis to determine the origin of gravity and the origin of elementary particles. Using the Shannon-Boltzmann-Gibbs entropy relation, we will demonstrate that information is not lost and depends on the state of matter, the information is encoded and depends on the effective Boltzmann´s constant.

Here, using the theory of electrical modelling of the neutron and proton as a three-phase alternating current electrical generator, we will begin the path to demonstrate that the interactions of electromagnetic forces, weak force and strong force that are part of the standard model, can be described by a single electromagnetic force interaction, in other words: SU(3) x SU(2) --> U(1). We will also hypothesize two particles that would give rise to gravitons. It is the interactions of the quarks (U, Û, D, ^D) that dominate the dynamics; They are responsible for the origin of bosons (photons, gluons, W⁺, W⁻, Z⁰, gravitons and Higgs boson).

We are going to demonstrate the origin of dark energy, using a Hardwire similarity, a test that is carried out in terrestrial seismic with vibroseis in the search for gas and oil. In the first instance, we are going to analyse the mathematical function of Dirac's delta and compare it with the detonation of an explosive that is carried out in the search for gas and oil. Let's understand that in both cases a frequency spectrum is produced. We will also explain the meaning of a non-causal, zero-phase system; a causal system, of minimum phase, in order to determine the mathematical behaviour that corresponds to the Big Bang. Next, following the line of seismic, we will analyse a Hardwire Similarity to demonstrate that a vibroseis source, which generates a sweep, produces, in addition to the ideal sweep of fundamental frequencies, spurious harmonic frequencies and additional noise. We will show that this additional energy generated by the spurious harmonic frequencies and additional noise adds to the energy of the fundamental frequency sweep in analogy as dark energy does.

Here, using the theory of electrical-quantum modelling of the neutron and proton as a three-phase alternating current electrical generator, we will analyse the proton decay and the inverse neutron decay and determine the following subatomic particles, Dproton, Protoniu, Dneutron and Neutroniumd.

Here we will electrically-quantum model the neutron and proton as a three-phase alternating current electric generator, for this, we will use the theory of three-phase electric generators and vector or phasor diagrams. We will use this model to hypothesize how the quarks that form neutrons and protons with a combined mass of 10 MeV/c², can generate, through quarks-antiquarks-gluon interactions, a mass of 939.56 MeV/c² for the neutron and a mass of 938.27 MeV/c² for the proton. Using quantum mechanics and the theory of the generalization of the Boltzmann constant in curved space-time we will calculate the number of quarks-antiquarks-gluons and gravitons inside a neutron. We will also analyse βˉ decay using vector diagrams, we will calculate the tension of the string T₀ and the length of the string ℓs between quarks-antiquark and finally, we will model a black hole using a neutron equivalent model. In version 2 of this article, we will update the vector diagrams of the βˉ decay and theoretically calculate the energy of the W⁻ boson, the Z⁰ boson, and the Θ angle, Θ = arc cos (W⁻/Z⁰). We will demonstrate, through vector diagrams, that quarks-antiquarks-gluon interactions are the cause of the origin of the W⁻ boson and the Z⁰ boson. We will also demonstrate how the fine structure constant α originates. It is important to make clear, in future updates, we will describe the relationship that exists between the theory described in this paper and the Isospin theory, flavour and colour theory

Here, applying the theory of the generalization of the Boltzmann constant in curved space-time, we will model the mechanism by which elementary particles are formed. We will determine the relationship between gravity and each of the elementary particles that form the standard model following analogies to that of stellar bodies. In order to achieve our goal, we will propose new models for photons, quarks and gluons; with this, we will demonstrate why there are stable and unstable elementary particles; why the first family of elementary particles forms hadrons and why the second and third families cannot form hadrons; why the fermions comply with the Pauli exclusion principle and why the bosons do not comply with the Pauli exclusion principle, etc. Finally, we will analyse the generalization of the ADS/CFT correspondence and propose a theory of everything (T.O.E.).

Here we will explain the correlation between the Kerr-Newman diagram and the theory: RLC electrical modelling of a black hole and the early universe. We will develop a black hole model that describes and explains both theories. In the development of our analysis, we will emphasize the following conditions: M² > Q² + a², M² = Q² + a² and M² < Q² + a² and we will also analyse the condition in which the mass of a black hole reaches its critical mass M = Mc. We will demonstrate that the interpretation of the Kerr-Newman diagram is equivalent to the interpretation of the theory: RLC electrical modelling of a black hole and the early universe. Finally, we will generalize the proposed model for a black hole and propose a black hole model formed by negative particles, neutroniumd, which after reaching critical conditions of mass, pressure, volume, temperature, density, etc.; decays into a positively charged black hole, protoniu. Let us remember that both models are formed by charged particles of matter (they do not contain antimatter), but their vector configuration means that the net charges of both proposed black holes are zero.