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Band-tail states, i.e., charge-carrier energy states located in the bandgap at the valence and conduction band edges of amorphous materials, even though not delocalized, exhibit nonzero mobility; thus, they are expected to contribute to the charge-conduction process. A microscopic model based on hydrodynamic transport equations for unipolar conduction, including trap, band-tail, and band states, and coupled to the Poisson equation is presented here. The equations are self-consistently solved by means of a numerical procedure, and the results provide qualitative and quantitative estimates of the influence of band-tail states (namely, of their energy distribution, density, and mobility) on the carrier heating, precursor of the Ovonic threshold switch. [ABSTRACT FROM AUTHOR]

The non-equilibrium Green's function (NEGF) and quantum master equation (QME) are two main classes of approaches for electronic transport. We discuss various Floquet variances of these formalisms for transport properties of a quantum dot driven via interaction with an external periodic field. We first derived two versions of the Floquet NEGF. We also explore an ansatz of the Floquet NEGF formalism for the interacting systems. In addition, we derived two versions of Floquet QME in the weak interaction regime. With each method, we elaborate on the evaluation of the expectation values of the number and current operators. We examined these methods for transport through a two-level system that is subject to periodic driving. The numerical results of all four methods show good agreement for non-interacting systems in the weak regime. Furthermore, we have observed that circular light can introduce spin current. We expect these Floquet quantum transport methods to be useful in studying molecular junctions exposed to light. [ABSTRACT FROM AUTHOR]

The Cattaneo–Vernotte model has been widely studied to take momentum relaxation into account in transport equations. Yet, the effect of reactions on the Cattaneo–Vernotte model has not been fully elucidated. At present, it is unclear how the current density associated with reactions can be expressed in the Cattaneo–Vernotte model. Herein, we derive a modified Cattaneo–Vernotte model by applying the projection operator method to the Fokker–Planck–Kramers equation with a reaction sink. The same modified Cattaneo–Vernotte model can be derived by a Grad procedure. We show that the inertial effect influences the reaction rate coefficient differently depending on whether the intrinsic reaction rate constant in the reaction sink term depends on the solute relative velocity or not. The momentum relaxation effect can be expressed by a modified Smoluchowski equation including a memory kernel using the Cattaneo–Vernotte model. When the intrinsic reaction rate constant is independent of the reactant velocity and is localized, the modified Smoluchowski equation should be generalized to include a reaction term without a memory kernel. When the intrinsic reaction rate constant depends on the relative velocity of reactants, an additional reaction term with a memory kernel is required because of competition between the current density associated with the reaction and the diffusive flux during momentum relaxation. The competition effect influences even the long-time reaction rate coefficient. [ABSTRACT FROM AUTHOR]

PINN, or physics-informed neural network, is a partial differential equation (PDE) solver realized as a neural network by incorporating the target PDE into the network as physical constraints. In this study, our focus lies in optimizing collocation point selection. We propose an active learning method to enhance the efficiency of PINN learning. The proposed method leverages variational inference based on dropout learning to assess the uncertainty inherent in the solution estimates provided by the PINN. Subsequently, it formulates an acquisition function for active learning grounded in this uncertainty assessment. By employing this acquisition function to probabilistically select collocation points, we can achieve a more expedited convergence to a reasonable solution, as opposed to relying on random sampling. The efficacy of our approach is empirically demonstrated using both Burgers' equation and the convection equation. We also show experimentally that the choice of the collocation points can affect the loss function, the fitting of initial and boundary conditions, and the sensible balance of PDE constraints. [ABSTRACT FROM AUTHOR]

Film boiling has practical applications in the current technology including steam power plants, cooling of electronic devices and emergency cooling systems. A finite difference/front tracking method is used to simulate film boiling at high density ratios on a horizontal plate subject to a constant wall heat flux. The grid resolution is relatively high (768 grids per width of the domain). The flow is dominated by Rayleigh–Taylor instability as well as Kelvin–Helmholtz instability. The flow structure includes the roll up of the interface between the gas and liquid. This happens at high density ratio (1000) where the difference between the gas and the liquid velocities across the interface is large. The jump in tangential velocity is an order of magnitude smaller at a lower density ratio (100). Hence, there is no roll up at a lower density ratio. The flow is also influenced by vortex development as a result of the baroclinic term in the vorticity transport equation. The density gradient is large at the interface at high density ratio which tends to amplify the baroclinic term. The plot of pressure gradient and density gradient shows that they are not parallel in the roll up regions. As a result, vortices in small scales develop that shed in the gas phase. The plot of the enstrophy with time shows that it is smooth and match for two grid resolutions, however at a specific time enstrophies become spiky, and they depart from each other at two grid resolutions. The spiky behavior of enstrophy is due to vortex shedding in the roll up region. [ABSTRACT FROM AUTHOR]

This study investigates the long-time vorticity dynamics of the multi-cellular configurations of the two-dimensional (2D) Taylor–Green vortex (TGV). The pseudo-spectral method is used to solve the incompressible Navier–Stokes equation to analyze the evolution of TGV arrays. The focus is on understanding vortex interactions leading to vortex filamentation and stripping (forward cascade) during primary instability; merger and reconnection (inverse cascade) among the TGV vortical cells subsequently. Here, consideration of multiple cells avoids imposing symmetries at the smallest periodic length scale, and thereby affecting disturbance growth. The initial condition is taken from the analytic solution of the TGV, and Fourier spectral method is employed to track the interactions of the initial doubly-periodic vortices. The full sequence of evolution from one equilibrium state to another for the TGV is not addressed before, as reported here to fill this gap for multiple TGV cells in both directions. By studying various vortical interactions in the ensemble, here we report the enstrophy and energy spectra for different number of TGV cells. This is crucial in understanding the very long-time evolution process, at post-critical Reynolds numbers for the 2D TGV problem in the same physical domain, (0 ≤ (x , y) ≤ 4 π) having (4 × 4) and (6 × 6) cells. Reported results show the evolution of these vortical cells from original configurations to finally a (1 × 1) vortical cells — the universal state not demonstrated before. • The present work carries out the long-time direct simulation of the 2D TGV problem in its multi-cellular configurations which has previously never been reported (as long as up to t=6000). Presented results are for cases starting with (4 × 4)- and (6 × 6)-vortical cells at t =0. • The Fourier pseudo-spectral method along with the four stage, fourth order Runge–Kutta (RK4) time integration method has previously not been used to perform direct simulation of the 2D TGV problem studied here over a very long time. • Such high accuracy method helps not only capture the primary instability followed by the inverse cascading of energy, but also this leads finally to the unique configuration with (1 × 1)-cells. • The final state is seen to be the universal configuration, irrespective of the initial number of cells. This is noted to be the case for (2 × 2)-cells, (4 × 4)-cells, (6 × 6)-cells and (8 × 8)-cells. The last case has not been shown here to keep the size of the manuscript within limit. [ABSTRACT FROM AUTHOR]

Harnessing data to discover the underlying constitutive relation of phase‐separated polymers can significantly advance the fabrication of high‐performance materials. This work introduces a novel data‐driven method to learn the constitutive equation of diffusional transport of polymers from spatiotemporal density field. In particular, the data‐driven method seamlessly integrated physics‐informed neural networks for inference of approximate solution of diffusivity, and symbolic regression that form explicit expressions of diffusivity. The efficacy and robustness of this method are demonstrated by learning the distinct forms of diffusivity for the phase separation of homopolymer blends with various compositions. In addition, the data‐driven method is generalized to extract the constitutive relation of homogenous chemical potential in the phase separation of homopolymer blends. The data‐driven framework shows the potential for model discovery of nonlinear dynamic system from the spatiotemporal state variables. [ABSTRACT FROM AUTHOR]

Interband cascade lasers (ICLs) stand out due to their low threshold current and minimal power consumption, rendering them viable sources for compact and mobile devices in the mid‐infrared. Since their first demonstration, they experienced major performance improvements. Mostly they originate from either improved material quality or the outcomes of numerical analysis of secluded parts. Encouraged by the impact of secluded models, an ICL‐specific simulation tool can lead to performance breakthroughs and a better comprehension of governing mechanisms. Drawing from an evaluation of existing tools designed for quantum cascade structures, a self‐consistent density matrix rate equation model is implemented to simulate the transport in both conduction and valence band heterostructures. Albeit the extensive inclusion of the quantum effects, special care was taken to maintain a high numerical efficiency. The charge transport model additionally considers optical field calculations, allowing for predictive calculations of light–current–voltage curves. The model is benchmarked against well‐established ICL designs and demonstrate reliable performance predictability. Additionally, detailed insights into device characteristics extracted from the model are provided. This ultimately allows to deepen the understanding of ICL and not only refine existing ones but also generate novel optimized designs. [ABSTRACT FROM AUTHOR]

In a review paper in this same volume, we present the state of the art on modeling of compressible viscous flows ranging from single‐phase to two‐phase systems. It focuses on mathematical properties related to weak stability because they are important for numerical resolution and on the homogenization process that leads from a microscopic description of two separate phases to an averaged two‐phase model. This review serves as the foundation for Parts I and II, which present averaged two‐phase models with phase exchange applicable to magma flow during volcanic eruptions. Here, in Part I, after introducing the physical processes occurring in a volcanic conduit, we detail the steps needed at both microscopic and macroscopic scales to obtain a two‐phase transient conduit flow model ensuring: (1) mass and volatile species conservation, (2) disequilibrium degassing considering both viscous relaxation and volatile diffusion, and (3) dissipation of total energy. The resulting compressible/incompressible system has eight transport equations on eight unknowns (gas volume fraction and density, dissolved water content, liquid pressure, and the velocity and temperature of both phases) as well as algebraic closures for gas pressure and bubble radius. We establish valid sets of boundary conditions such as imposing pressures and stress‐free conditions at the conduit outlet and either velocity or pressure at the inlet. This model is then used to obtain a drift‐flux system that isolates the effects of relative velocities, pressures, and temperatures. The dimensional analysis of this drift‐flux system suggests that relative velocities can be captured with a Darcy equation and that gas–liquid pressure differences partly control magma acceleration. Unlike the vanishing small gas–liquid temperature differences, bulk magma temperature is expected to vary because of gas expansion. Mass exchange being a major control of flow dynamics, we propose a limit case of mass exchange by establishing a relaxed system at chemical equilibrium. This single‐velocity, single‐temperature system is a generalization of an existing volcanic conduit flow model. Finally, we compare our full compressible/incompressible system to another existing volcanic conduit flow model where both phases are compressible. This comparison illustrates that different two‐phase systems may be obtained depending on the governing unknowns chosen. Part II presents a 1.5D version of the model established herein that is solved numerically. The numerical outputs are compared to those of another steady‐state, equilibrium degassing, isothermal model under conditions typical of an effusive eruption at an andesitic volcano. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence and uniqueness of isolated periodic traveling wave solutions of a family of nonlinear reaction–convection–diffusion equations using the monotonicity of the ratio of Abelian integrals. A numerical study is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider the partial regularity of suitable weak solution to the 3D simplify Ericksen–Leslie system modeling the hydrodynamical motion of nematic liquid crystal flow, which is a coupled system with the Navier–Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. We present a new regularity criteria for suitable weak solutions to the 3D simplified Ericksen–Leslie system. Moreover, under the condition ∥u∥Ltp,∞Lxq([−1,0]×R3)+∥∇d∥Ltp,∞Lxq([−1,0]×R3):=K<∞,with2p+3q=1and3

Structural optimization problems are often associated with the so-called shape functionals depending on a shape through its geometry and the state being a solution of given partial differential equation. In such a framework it is convenient to work with the gradient-like method based on a concept of a shape derivative and level set method. The key idea of level set method is to represent the structural boundary with zero level set of given function (level set function—LSF). Now, changing the shape of a structure under optimization is equivalent to transport the LSF in such a direction that ensures decreasing the value of the objective functional. To this end, we make use of coercive bilinear form taken from the weak formulation of elasticity problem to obtain descent direction at each iteration. This descent direction is a solution of an additional variational problem, involving the bilinear form mentioned above and the volumetric expression of the shape derivative plays the role of a linear form. In this paper, we combine level set method with radial basis functions (RBFs) used to approximate LSF. We focus on the so-called multiquadric RBFs, but other classes of RBFs are also briefly considered. This eventually leads to transformation of partial differential equation (linear transport equation governing the evolution of shapes) to a system of linear ordinary differential equations which admits analytical formula for the solution. We apply our method to compliance minimization of a cantilever problem as well as to total potential energy minimization of a structure with kinematic loading. To run all the numerical experiments, we wrote our own code in Wolfram Mathematica environment. [ABSTRACT FROM AUTHOR]

The columnar-flow approximation allows the development of computationally efficient numerical models tailored to the study of the rapidly rotating dynamics of Earth's fluid outer core. In this paper, we extend a novel columnar-flow formulation, called Plesio-Geostrophy (PG) by including thermal effects and viscous boundary conditions. The effect of both no-slip and stress-free boundaries, the latter being a novelty for columnar-flow models, are included. We obtain a set of fully 2-D evolution equations for fluid flows and temperature where no assumption is made regarding the geometry of the latter, except in the derivation of an approximate thermal diffusion operator. To test the new PG implementation, we calculated the critical parameters for onset of thermal convection in a spherical domain. We found that the PG model prediction is in better agreement with unapproximated, 3-D calculations in rapidly rotating regimes, compared to another state-of-the-art columnar-flow model. [ABSTRACT FROM AUTHOR]

A computationally inexpensive and data parsimonious direct model for identification of groundwater pollution sources that captures their location, spatial extent and flux intensities at a chosen reference time is presented in this study. The model is based upon instantaneous micro-level mass balance that is depicted by a pseudo steady state solute transport equation. Clusters of polluting locations were identified by finite differencing the solute transport equation and applying K-means clustering algorithm. The model is validated by the problem taken from Singh, Datta, and Jain (2004) and is also illustrated by applying it to an area lying between river Krishni and Hindon. Validation results showed that the model captured closely the pollution source locations; their corresponding spatial extents and flux intensities. Model captured the sources even when the concentration plumes are far away from the source locations due to advection dominated contaminant transport. Illustration results showed that the model identified the leachate flux intensity from irrigation in the form of a regional source. Further, it established a few local sources arising possibly out of localized industrial and/or municipal waste water disposal. [ABSTRACT FROM AUTHOR]

In this article, we study the weak Galerkin finite element method to solve a class of a third order singularly perturbed convection-diffusion differential equations. Using some knowledge on the exact solution, we prove a robust uniform convergence of order O (N − (k − 1 / 2)) on the layer-adapted meshes including Bakhvalov-Shishkin type, and Bakhvalov-type and almost optimal uniform error estimates of order O ((N − 1 ln ⁡ N) (k − 1 / 2)) on Shishkin-type mesh with respect to the perturbation parameter in the energy norm using high-order piecewise discontinuous polynomials of degree k. Here N is the number mesh intervals. We conduct numerical examples to support our theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates an induction heating problem in a multi-component system containing a moving non-magnetic conductor. The electromagnetic process is described by the eddy current model, and the heat transfer process is governed by the convection-diffusion equation. The two processes are coupled by a restrained Joule heat source. A temporal discretization scheme is introduced to numerically solve the corresponding variational system. With the aid of the Reynolds transport theorem and a density argument, we prove the convergence of the proposed scheme as well as the well-posedness of the variational problem. Some numerical experiments are also performed to assess the performance of the numerical scheme. [ABSTRACT FROM AUTHOR]

We propose a multiple-relaxation-time lattice Boltzmann method for anisotropic convection-diffusion equation with a divergence-free velocity field. In this approach, the convection term is handled as a source term in the lattice Boltzmann evolution equation; thus, the derivation term that may be induced by the convection term disappears. By using the Chapman-Enskog analysis, the anisotropic convection-diffusion equation is recovered up to second-order accurate in space. In particular, we also present a local scheme for computing the convection term, indicating that the present method retains the main advantages of the lattice Boltzmann method. We then test the proposed model by considering the Gaussian hill problem and an anisotropic convection diffusion equation with constant velocity and diffusion tensor. The results illustrate that our model has acceptable numerical accuracy and can be a good candidate for simulating anisotropic convection-diffusion equation. • A MRT LB model is constructed for anisotropic CDE with divergence-free velocity field. • The convection term is treated as a source term in the LB equation. • No deviation term exists in the corresponding recovered equation. [ABSTRACT FROM AUTHOR]

A three-dimensional model of polydisperse reactive sedimentation is developed by means of a multilayer shallow water approach. The model consists of a variety of solid particles of different sizes and densities, and substrates diluted in water, which produce biochemical reactions while the sedimentation process occurs. Based on the Masliyah–Lockett–Bassoon settling velocity, compressibility of the sediment and viscosity of the mixture, the system of governing equations is composed by non-homogeneous transport equations, coupled to a momentum equation describing the mass-average velocity. Besides, the free-surface depicted by the total height of the fluid column is incorporated and fully determined through the multilayer approach. A finite volume numerical scheme on Cartesian grids is proposed to approximate the model equations. Numerical simulations of the denitrification process exemplify the performance of the numerical scheme and model under different scenarios and bottom topographies. • Polydisperse reactive sedimentation. • Multilayer shallow water approach. • Denitrification and eutrophication processes. [ABSTRACT FROM AUTHOR]

In this work, two numerical techniques are compared for solving one and two-dimensional convection-diffusion equations. First technique is referred as "MCUAT tension B-spline," and the second technique is labeled as "MCUAH tension B-spline." Various aspects are examined to validate the compatibility of results, including comparisons between numerical and exact solutions and evaluation of different error norms. Present errors are compared with existing literature, presenting a remarkable improvisation. Statistical validation of work is tested via a correlation matrix heatmap generated in Python. The order of convergence of the proposed work is also included. Via an observation of comparison of results, it is claimed that UAT results are slightly better than UAH results. Different aspects of correlation, such as strongly negative correlation and perfect positive correlation, are notified. The present work will introduce new dimensions to the field of numerical techniques. [ABSTRACT FROM AUTHOR]

This paper provides mathematical analysis of an elementary fully discrete finite difference method applied to inhomogeneous (i.e., non-constant density and viscosity) incompressible Navier–Stokes system on a bounded domain. The proposed method is classical in the sense that it consists of a version of the Lax–Friedrichs explicit scheme for the transport equation and a version of Ladyzhenskaya's implicit scheme for the Navier–Stokes equations. Under the condition that the initial density profile is strictly away from zero, the scheme is proven to be strongly convergent to a weak solution (up to a subsequence) within an arbitrary time interval, which can be seen as a proof of existence of a weak solution to the system. The results contain a new Aubin–Lions–Simon type compactness method with an interpolation inequality between strong norms of the velocity and a weak norm of the product of the density and velocity. [ABSTRACT FROM AUTHOR]

Due to their prevalence in the lithosphere and their high capability of sorbing pollutants, smectite clays play a foreground role in environmental pollution studies, waste management, and soil science. In complementarity with existing approaches at the molecular or macroscopic scales, real microstructures have been employed to investigate ionic transport by diffusion through montmorillonite and water-saturated Wyoming bentonite at intermediate scales ranging between the nanometer and the micrometer. The coupled solute transport and electrostatic phenomena investigated at the nanopore scale are upscaled using the homogenization of porous media approach. Homogenization computations rely on a hierarchical description of bentonite that acknowledges the existence of pores networks at different scales. At the scale of montmorillonite layers, digitized TEM images have been employed to simulate the diffusion of ionic solutes by considering electrostatic interactions in the vicinity of the negatively charged clay platelets' surface. Finite element microstructures are created after extraction of the contours of the layers using dedicated image processing algorithms. Local electric potential distribution, anion exclusion, and cation inclusion are displayed by ion distribution maps. The effective diffusion tensor and the transport equation obtained through volume averaging are then used to simulate diffusion at the scale of a Wyoming bentonite sample composed of clay gels of variable density, solid grains, and micropores. Qualitative comparisons were made with existing diffusion data, and a particular attention is given to the anisotropy of the diffusion tensors at both the mesoscopic and macroscopic scales. [ABSTRACT FROM AUTHOR]

Using zeotropic mixtures with unique temperature glide characteristics as the working medium in heat-driven ejector refrigeration system will potentially reduce the irreversible losses in heat exchange process. However, the intrinsic link between the pure/mixture refrigerants' thermophysical properties and the entrainment performance of supersonic ejector has not yet been elucidated. In this study, a novel ejector CFD model is established by coupling the real-gas thermodynamic equation and species transport equation, then the relationships between thermophysical properties of pure/mixture refrigerants and ejector's dimensionless operational parameters were thoroughly investigated. The results indicated that the ejector expansion ratio rises as primary flow inlet temperature or refrigerant's normal boiling point increases, while the dimensionless parameters of primary nozzle are relatively insensitive to the variation of primary flow inlet temperature and refrigerant's boiling point, resulted in changes of supersonic jet expansion behaviour. Moreover, the specific volume and adiabatic index change characteristics resulted in minor fluctuations of primary nozzle's dimensionless parameters. When the bubble point temperature is fixed at 30℃ in the condenser, the saturated vapor/liquid phase pressure glide characteristics of R600a/R1234ze mixture may lead to an increasement of ejector's compression ratio. [ABSTRACT FROM AUTHOR]

This paper discusses how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order derivative for the first time. Specifically, we describe how to systematically find different invariant product linear spaces with various dimensions for the considered system. Also, we observe that the obtained invariant product linear spaces help to reduce the multi-component (N+1)-dimensional coupled NTFPDEs into a system of fractional-order ODEs, which can then be solved using the well-known analytical methods. More precisely, we illustrate the effectiveness and importance of this developed method for obtaining a long list of invariant product linear spaces for the multi-component (2+1)-dimensional coupled nonlinear time-fractional diffusion-convection-wave equations. In addition, we have shown how to find different kinds of generalized separable analytical solutions for a multi-component (2+1)-dimensional coupled nonlinear time-fractional diffusion-convection-wave equations along with the initial and boundary conditions using invariant product linear spaces obtained. Finally, we provide appropriate graphical representations of some of the derived generalized separable analytical solutions with various fractional-order values. [ABSTRACT FROM AUTHOR]

Naumure Multipurpose Project (NMP) featuring a 169 m high Concrete Face Rock Filled Dam (CFRD) is the proposed reservoir project in the West Rapti River with an installed capacity of 218.34 MW. Most of the rivers in Nepal carry significant sediment loads that will consequently catalyze reservoir sedimentation. This phenomenon prevails as the primary factor in reducing reservoirs useful life, making ineffective for both flood control and hydroelectricity generation. Ultimately, such process of sedimentation has adverse impacts on projects economic feasibility and long-term sustainability. Therefore, the objective of this research was to examine the expected sediment deposition pattern in the NMP reservoir throughout its operational period by employing 1D HEC-RAS model to simulate the sedimentation process. The model was simulated for 10, 20, 30, 40 and 50 years. Yang's equation as a sediment transport function, Active layer as a bed sorting method and Toffaleti as a fall velocity method were best suited for the river reach. The delta deposition was formed between 11 km and 22 km upstream of the dam region in the Jhimruk river, with the sediment deposition depth reaching peaks of about 23 m, 38 m, 39 m, 41 m and 49 m in 10, 20, 30, 40 and 50 years, respectively. Similarly, the delta deposition was formed between 13 km and 33 km upstream of dam region in the Madi river, with the sediment deposition depth reaching peaks of about 47 m, 62 m, 60 m, 68 m and 75 m in 10, 20, 30, 40 and 50 years respectively. Headcutting of delta deposition occurred between 20 and 30 year due to high flood during low stage of reservoir. Furthermore, the study revealed that about 6.22%, 11.61%, 15.94%, 22.96% and 25.65% of the storage capacity of NMP reservoir will be depleted in 10, 20, 30, 40 and 50 years respectively. [ABSTRACT FROM AUTHOR]

In this work, we study the formation of consensus in a hierarchical population. We derive the corresponding kinetic equations, and analyze the long time behavior of their solutions for the case of finite number of hierarchical levels, obtaining explicit formula for the consensus opinion. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive numerical investigation into the degradation mechanisms of High-Temperature Proton Exchange Membrane Fuel Cells (HT-PEMFCs) with a particular focus on catalyst layer degradation. The study integrates advanced models to accurately describe the electrochemistry of platinum and carbon oxidations, crucial processes influencing the cell's performance over time. Additionally, a heuristic model is employed to account for the loss of proton conductivity in the membrane attributed to the depletion of phosphoric acid. The degradation processes are seamlessly integrated into a 3D computational code. By utilizing optimized values for the electrochemical parameters, the numerical simulations demonstrate excellent agreement with experimental degradation observed in an HT-PEMFC operating under steady-state conditions. In addition, the numerical approach offers insights that are not easy to achieve by experimental means, such as the equilibrium of the different oxidation states of platinum and carbon. • HT-PEMFCs catalyst layer degradation is modeled through electrochemical equations. • The phosphoric acid depletion in the membrane is modeled through a heuristic model. • The unknown electrochemical parameters are obtained by solving an inverse problem. • Electrochemical and transport equations are solved in an in-house 3D OpenFOAM module. • Comparisons with experiments prove the validity of the model. [ABSTRACT FROM AUTHOR]

A shallow water wave equation including the famous Degasperis-Procesi model is considered. Firstly, the L2 conservation law for the equation is derived. Secondly, using the methods of transport equation, we establish the boundedness of solutions for the shallow water wave equation. Finally, utilizing the approaches to construct Lyapunov functions, we find local-in-space wave breaking criteria of its solutions on the line $ \mathbb {R} $ R and circle $ \mathbb {S} $ S under certain restrictions on the coefficients of the equation. [ABSTRACT FROM AUTHOR]

In this paper, the existence and the uniqueness of an evolutionary anisotropic $ p_i(x) $ p i (x) -Laplacian equation with a damping term are studied. If the damping term is with a subcritical index, by the Di Giorgi iteration technique, the $ L^{\infty } $ L ∞ -estimate of the weak solutions can be obtained. The existence of weak solution is proved by the renormalized solution method, and how the anisotropic characteristic of the considered equation affect the $ L^{\infty } $ L ∞ -estimate of the weak solutions is revealed. The uniqueness is true strongly depending on subcritical index of the damping term, and this result goes beyond previous efforts in the literature (Bertsch M, Dal Passo R, Ughi M: Discontinuous viscosity solutions of a degenerate parabolic equation. Trans Amer Math Soc. 1990;320:779–798; Li Z, Yan B, Gao W. Existence of solutions to a parabolic $ p(x)- $ p (x) − Laplace equation with convection term via $ L^{\infty }- $ L ∞ − Estimates. Electron J Differ Equ. 2015;46:1–21; Zhang Q, Shi P. Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms. Nonlinear Anal. 2010;72:2744–2752; Zhou W, Cai S. The continuity of the viscosity of the Cauchy problem of a degenerate parabolic equation not in divergence form. J Jilin University (Natural Sci.). 2004;42:341–345), etc. [ABSTRACT FROM AUTHOR]

We propose a tailored finite point method (TFPM) for solving time fractional convection dominated diffusion equations in this paper. The main idea of TFPM is to firstly approximate the diffusion, convection coefficient near each grid by a constant, and then determine the weights of the finite difference scheme by using the exact solution of the convection diffusion equation with constant coefficients. This adaptation perfectly captures the rapid transition of the solutions which contain sharp boundary layers even with coarse meshes. The accuracy and stability of the scheme are rigorously analyzed. Numerical examples are shown to verify the accuracy and reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]

We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally belong to a multiplicative group of linear transformations, to stresses, that are additive elements of a linear space of tensors. As regards the viscous stresses, we simply assume a Newtonian constitutive law, but the presence of elasticity and plastic relaxation makes the materials non‐Newtonian. Our aim is to discuss the existence of weak solutions for the corresponding systems of partial differential equations in the nonlinear large‐deformation regime. The main difficulties arise in the analysis of the transport equations necessary to describe the evolution of tensorial measures of strain. For the solid model, we only need to consider the equation for the left Cauchy–Green tensor, while for the fluid model, we add an evolution equation for the elastically‐relaxed strain. Due to the tensorial nature of the fields, available techniques cannot be applied to the analysis of such transport equations. To cope with this, we introduce the notion of charted weak solution, based on non‐standard a priori estimates, that lead to a global‐in‐time existence of solutions for the viscoelastic models in the natural functional setting associated with the energy inequality. [ABSTRACT FROM AUTHOR]

The mean flow in a turbulent boundary layer (TBL) deviates from the canonical law of the wall (LoW) when influenced by a pressure gradient. Consequently, LoW-based near-wall treatments are inadequate for such flows. Chen et al. (J. Fluid Mech. , vol. 970, 2023, A3) derived a Navier–Stokes-based velocity transformation that accurately describes the mean flow in TBLs with arbitrary pressure gradients. However, this transformation requires information on total shear stress, which is not always readily available, limiting its predictive power. In this work, we invert the transformation and develop a predictive near-wall model. Our model includes an additional transport equation that tracks the Lagrangian integration of the total shear stress. Particularly noteworthy is that the model introduces no new parameters and requires no calibration. We validate the developed model against experimental and computational data in the literature, and the results are favourable. Furthermore, we compare our model with equilibrium models. These equilibrium models inevitably fail when there are strong pressure gradients, but they prove to be sufficient for boundary layers subjected to weak, moderate and even moderately high pressure gradients. These results compel us to conclude that history effects in mean flow, which negatively impact the validity of equilibrium models, can largely be accounted for by the material time derivative term and the pressure gradient term, both of which require no additional modelling. [ABSTRACT FROM AUTHOR]

Reduction of the heat load to plasma-facing components is a crucial problem for future fusion reactors like Divertor Test Tokamak (DTT). Mitigation of the power load via increased plasma radiation with the use of puffed ions of impurities would be one way to mitigate power in the scrape-off layer. This paper presents a numerical investigation of the impact of seeded impurities on the radiation pattern and the power load to the divertor plates of the high-field DTT reactor in the single null (SN) configuration. The simulations have been done with the use of the TECXY code, which solves multi-species plasma transport equations for multiple impurity species simultaneously and all associated ionization stages in a two-dimensional poloidal geometry. TECXY represents the model of plasma transport in the scrape-off layer region by a classical set of transport equations of multi-species plasma derived by Braginskii. The paper aims to compare the mitigation capabilities of neon and argon impurities seeded in the plasma of the DTT device and to obtain a significant energy flux reduction to the target plate at the smallest possible impurity concentration. Performed investigations showed the effects of neon and argon impurities seeding separately for constant electron density at the separatrix. It has been found that the decrease in electron temperature on the divertor plates up to 3 eV at the outer and the inner divertor plates and the peak power load below 15 MW m−2 at the outer divertor plate can be achieved with argon seeding and much lower impurity concentration than that in the case of neon impurity seeding. Studies have shown the complexity of the effect of neon and argon impurities on the boundary plasma. It was found that the reduction of temperature and the power on both divertor plates was the most effective for the high upstream plasma densities. The results show also that diffusive perpendicular transport strongly affects impurity radiation and thus plasma condition at divertor plates. [ABSTRACT FROM AUTHOR]

Environmental concerns have necessitated the development of computational models predicting pollutant dispersion in natural water systems. Due to the ill-posed nature of the inverse contaminant transport equation, solving this equation using all stable and convergent inverse methods is impossible. Factors such as river geometry, unsteady and non-uniform flow, and tidal influences add to the complexity of the inverse problem. These factors have prompted the evaluation of Group Preserving Scheme for environmental applications. The inverse solution method derives a general equation for solving ordinary differential equations by addressing a dynamical system at negative time steps, ensuring convergence. Three test cases have been presented to evaluate Backward Group Preserving Scheme (BGPS). These have included validation using observational data from Missouri River, inverse simulation in a tidal river, and sensitivity analysis of parameters such as pollutant patterns, advection, dispersion, and decay coefficients. The dataset includes calibrated data from Missouri River, which demonstrated high accuracy, with Mean Relative Error (MRE) ranging from 2.8% to 5.0% for the inverse model. Under tidal conditions, accuracy decreases over time but remains robust, with a Nash–Sutcliffe efficiency of 0.77–0.96 and an MRE of 0.9%–5.9%. Sensitivity analysis revealed optimal model performance for Péclet numbers greater than 500. The model performed best with gradual, wide-peaked pollutant patterns and moderate decay rates (Damköhler number between 5 and 10). BGPS proves effective for transport simulation and concentration history reconstruction in complex rivers, including those with tidal influences, offering a robust tool for water contamination analysis in various flow conditions. [ABSTRACT FROM AUTHOR]

The physical properties of working fluids—in terms of the Prandtl number—play a crucial role in determining their thermal performance in the internal flow, especially their viscosity. This study first considers the thermo-hydraulic and entropy generation of a sinusoidal corrugated channel in two configurations: symmetrical (raccoon) and asymmetrical (serpentine). Results are presented for different ranges of operating parameters, such as 100 ≤ R e ≤ 700 and 0.72 ≤ P r ≤ 90 , and for geometrical parameters such as the wave amplitude-to-wavelength ratio 0.2 ≤ α ≤ 0.6. In addition, the results of the two channels were compared with each other's and with the straight channel. Control transport equations are solved using finite element methods. It was found that the flow inside the wavy channels generated re-circulatory reigns, and their size was affected by the wave parameters as well as the Reynolds number. Also, employing high values of P r extremely enhanced the heat transfer rate (HTR) of the wavy channels over the straight for all values of α and for both raccoon and serpentine channels. In addition, the results indicated that raccoon channels have higher HTR and performance factor compared to the serpentine channel. Finally, the thermal entropy generation dominated over the viscous entropy generation and its decrease with both Reynolds number and Prandtl number for raccoon and serpentine channels. This study focused on the heat transfer enhancement of the corrugated channels due to their importance in many industrial applications where the heat dissipation is critical to their work, including heat exchangers and heat sinks. Thus, the current numerical simulation primarily suggests utilizing the raccoon channel over the serpentine one, due to its higher thermal performance and nearly the same total entropy generation. [ABSTRACT FROM AUTHOR]

Solute transport in pulsatile viscoelastic fluid flow is relevant in nutrient transport and drug delivery in blood flow. Previous studies have extensively analyzed the effect of the shear-thinning nature of the blood but neglected the elastic property. The present study aims to fill this lacuna by analyzing the role of blood viscoelasticity on solute transport. To accomplish this, we study solute transport for a non-uniformly distributed solute slug in the pulsatile flow of an Oldroyd-B fluid through a tube in the presence of wall absorption. We employ Gill's procedure and Aris' method of moments to compute the transport coefficients K m (t) (m ≤ 4). We also numerically solve the species transport equation using a finite difference scheme to directly determine local solute concentration C (t , z , r). Consistent results for a non-viscoelastic fluid predict a negative convection coefficient K1 and a positive effective diffusivity K2 for realistic values of the parameters. However, the present analysis predicts positive K1 and negative K2 for small tubes due to flow reversal caused by the fluid elasticity. For high Λ 1 , the amplitude of oscillation for K1 and K2 exhibits scaling K 1 ∼ Λ 1 1.5 and K 2 ∼ Λ 1 2 indicating an enhancement in the dispersion due to fluid elasticity, where Λ 1 is the dimensionless relaxation time. The analysis of the skewness and (excess) kurtosis coefficients reveals inconsistency in previous studies on Newtonian fluids. Thus, we present consistent results not only for a viscoelastic fluid but also for a Newtonian fluid subjected to a pulsatile pressure gradient. In addition, the solute dispersion is significantly influenced by the non-uniformity of a solute slug. As the radius of a slug increases, solute dispersion reduces in short and moderate times; however, at large times, it is independent of the radius of a slug. [ABSTRACT FROM AUTHOR]

The space fractional advection–diffusion equation is a crucial type of fractional partial differential equation, widely used for its ability to more accurately describe natural phenomena. Due to the complexity of analytical approaches, this paper focuses on its numerical investigation. A lattice Boltzmann model for the spatial fractional convection–diffusion equation is developed, and an error analysis is carried out. The spatial fractional convection–diffusion equation is solved for several examples. The validity of the model is confirmed by comparing its numerical solutions with those obtained from other methods The results demonstrate that the lattice Boltzmann method is an effective tool for solving the space fractional convection–diffusion equation. [ABSTRACT FROM AUTHOR]

Under consideration is a nonlinear transport equation containing two nonlinearities and a coefficient of a lower-order nonlinear term depending on two or three space variables. We study the direct problem with the data on a part of the lateral surface of a cylindrical domain, explicitly construct a solution, and prove the uniqueness of the solution. Also, we state the problem of recovering the coefficient on some information about a solution to the direct problem and demonstrate that the inverse problem reduces to an X-ray tomography problem. This opens a way to its efficient numerical solution. [ABSTRACT FROM AUTHOR]

This research delves into the primary issue of polyimide (PI) insulation failures in high-frequency power transformers (HFPTs) by scrutinizing partial discharge development under high-frequency electrical stress. This study employs an experimental approach coupled with a plasma simulation model for a ball–sphere electrode structure. The simulation model integrates the particle transport equation, Poisson equation, and complex chemical reactions to ascertain microscopic parameters, including plasma distribution, electric field, electron density, electron temperature, surface, and space charge distribution. The effect of the voltage polarity and electrical energy on the PD process is also discussed. The contact point plays a pivotal role in triggering partial discharges and culminating in the breakdown of PI insulation. Asymmetry phenomena were found between positive and negative half-cycles by analyzing the PD data stage by stage. A significant number of PDs increased at every stage and the PD amplitude was higher during the negative cycle at the initial stage, but in later stages, the PD amplitude was found to be higher in the positive half-cycle, and scanning electron microscopy (SEM) revealed that the maximum damage occurred near the contact point junction. The simulation results show that the plasma initially accumulates the electron density near the contact point junction. Under the action of the electric field, plasma starts traveling at the PI surface outward from the contact point. Before the PD activity, all parameters have higher values in the plasma head. The microscopic parameters reveal maximum values near the contact point junction, during PD activities where significant damage takes place. These parameter distributions exhibit a decreasing trend over time as when the PD activity ends. The model's predictions are consistent with the experimental data. The paper lays the foundation for future research in polymer insulation design under high-frequency electrical stress. [ABSTRACT FROM AUTHOR]

The purpose of this research is to develop a combustion model that can be applied uniformly to laminar and turbulent premixed flames while considering the effect of the Lewis number (Le). The model considers the effect of Le on the transport equations of the reaction progress, which varies with the chemical species and temperature. The distribution of the reaction progress variable is approximated by a hyperbolic tangent function, while the other distribution of the reaction progress variable is estimated using the approximated distribution and transport equation of the reaction progress variable considering the Le. The validity of the model was evaluated under the conditions of propane and iso-octane with Le ≠ 1 and methane with Le = 1 (equivalence ratios of 0.5 and 1). The estimated results were found to be in good agreement with those of previous studies under all conditions. A method of introducing a turbulence model into this model is also described. the validity of the model is confirmed by a comparison with the experimental results of a turbulent methane flame. It was confirmed that the model is in good agreement with experimental results and other turbulence models, and represents approximately a conventional turbulence model. [ABSTRACT FROM AUTHOR]

In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and L 1 data. To deal with the non-coercive character of the equation and the low regularity of the right hand-side we mix the finite volume tools and the renormalized techniques. To handle the Neumann boundary conditions we choose solutions having a null median and we prove a convergence result. We present also some numerical experiments in dimension 2 to illustrate the rate of convergence. [ABSTRACT FROM AUTHOR]

The article is devoted to the existence of solutions of a system of integro-differential equations involving the drift terms in the case of the normal diffusion and the influx/efflux terms proportional to the Dirac delta function. The proof of the existence of solutions is based on a fixed point technique. We use the solvability conditions for the non- Fredholm elliptic operators in unbounded domains. We emphasize that the study of the systems is more difficult than of the scalar case and requires to overcome more cumbersome technicalities. [ABSTRACT FROM AUTHOR]

The deterministic methods are efficient for solving the neutron transport equation (NTE), but suffer from discretization errors. The increasingly complex geometric models make spatial discretization errors the primary source of discretization errors. Considering that spatial discretization errors come from inaccurate geometric shape descriptions and low-accuracy numerical schemes, this paper develops a Discontinuous Galerkin Finite Element Method for the NTE on unstructured polygonal meshes to reduce spatial discretization errors. In this method, the physical modal basis is adopted to handle the polygonal mesh and to achieve high-order accuracy in a uniform and efficient way. The numerical results of various fixed-source and k-eigenvalue benchmarks demonstrate that the method developed in this paper can give accurate solutions on polygonal meshes with high convergence rates. [ABSTRACT FROM AUTHOR]

In this paper, we study ultra-weak discontinuous Galerkin methods with generalized numerical fluxes for multi-dimensional high order partial differential equations on both unstructured simplex and Cartesian meshes. The equations we consider as examples are the nonlinear convection-diffusion equation and the biharmonic equation. Optimal error estimates are obtained for both equations under certain conditions, and the key step is to carefully design global projections to eliminate numerical errors on the cell interface terms of ultra-weak schemes on general dimensions. The well-posedness and approximation capability of these global projections are obtained for arbitrary order polynomial space based on a wide class of generalized numerical fluxes on regular meshes. These projections can serve as general analytical tools to be naturally applied to a wide class of high order equations. Numerical experiments are conducted to demonstrate these theoretical results. [ABSTRACT FROM AUTHOR]

The work deals with the existence of solutions of an integro-differential equation in the case of the normal diffusion and the influx/efflux term proportional to the Dirac delta function in the presence of the drift term. The proof of the existence of solutions relies on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains and discuss how the introduction of the transport term influences the regularity of the solutions. [ABSTRACT FROM AUTHOR]

In this paper, an analytical approach combined with a two-dimensional computational fluid dynamics (CFD) model is pursued to simulate the fluid flow in a monopropellant thruster for satellite propulsion systems. The thruster utilizes hydrogen peroxide (H2O2) as a green propellant at a concentration of 87.5%, with a catalytic bed based on spherical silver particles. Through a parametric analysis of particle diameter, we aim to optimize the design of a monopropellant thruster capable of generating a thrust of 20N. For this purpose, a program in CFD code in the commercially available ANSYS Fluent software is used to solve the energy, momentum, mass transfer, and species transport equations governing the thruster system. The local thermal non-equilibrium (LTNE) approach is used to describe the heat transfer occurring through both the solid and fluid phases within the catalyst bed. The results demonstrate that particle size significantly affects the thermal behaviour, species mass fraction, and exit velocity. An optimum diameter of 0.65mm exhibits the optimal performance of the monopropellant thruster, ensuring efficient decomposition of H2O2 at 968K and providing the required level of thrust force with a specific impulse of about 120s. [ABSTRACT FROM AUTHOR]

As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of the numerical results becomes increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation in a benchmark series, each employing a different method of solution. In 1D, there are numerous ways of analytically solving the monoenergetic transport equation, such as the Wiener–Hopf method, based on the analyticity of the solution, the method of singular eigenfunctions, inversion of the Laplace and Fourier transform solutions, and analytical discrete ordinates in the limit, which is arguably one of the most straightforward, to name a few. Another potential method is the PN (Legendre polynomial order N) method, where one expands the solution in terms of full-range orthogonal Legendre polynomials, and with orthogonality and series truncation, the moments form an open set of first-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 in half-range Legendre polynomials is more appropriate, where one separately expands incoming and exiting flux distributions to preserve the discontinuity at material interfaces. Here, we propose and demonstrate a new method of solution for the DPN equations for an isotropically scattering medium. In comparison to a well-established fully analytical response matrix/discrete ordinate solution (RM/DOM) benchmark using an entirely different method of solution for a non-absorbing 1 mfp thick slab with both isotropic and beam sources, the DPN algorithm achieves nearly 8- and 7-place precision, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a higher-order convergent numerical method for a two-parameter singularly perturbed differential equation with a discontinuous convection coefficient and a discontinuous source term. The presence of perturbation parameters generates boundary layers, and the discontinuous terms produce interior layers on both sides of the discontinuity. In order to obtain a higher-order convergent solution, a hybrid monotone finite difference scheme is constructed on a piecewise uniform Shishkin mesh, which is adapted inside the boundary and interior layers. On this mesh (including the point of discontinuity), the present method is almost second-order parameter-uniform convergent. The current scheme is compared with the standard upwind scheme, which is used at the point of discontinuity. The numerical experiments based on the proposed scheme show higher-order (almost second-order) accuracy compared to the standard upwind scheme, which provides almost first-order parameter-uniform convergence. [ABSTRACT FROM AUTHOR]

In a reinforced Galton–Watson process with reproduction law ν$$ \boldsymbol{\nu} $$ and memory parameter q∈(0,1)$$ q\in \left(0,1\right) $$, the number of children of a typical individual either, with probability q$$ q $$, repeats that of one of its forebears picked uniformly at random, or, with complementary probability 1−q$$ 1-q $$, is given by an independent sample from ν$$ \boldsymbol{\nu} $$. We estimate the average size of the population at a large generation, and in particular, we determine explicitly the Malthusian growth rate in terms of ν$$ \boldsymbol{\nu} $$ and q$$ q $$. Our approach via the analysis of transport equations owes much to works by Flajolet and co‐authors. [ABSTRACT FROM AUTHOR]

Purpose: Through the "Going Digital Initiative," the Ghanaian government has introduced policies that aim at improving the information and communication technology (ICT) infrastructure of the country. These ICT policies have benefited numerous sectors of the Ghanaian economy. In logistics management, ICT has impacted drone medical delivery in the healthcare and maritime sectors. However, the importance of ICT is not realized in the motorcycle goods transport (MGT) industry, regardless of its popularity and high economic dependency. Second, all research on motorcycles is focused on diverse social concerns, and no study has attempted to analyze ICT implementation for MGT operations. This is a significant gap in logistics management. Hence, the study aimed to investigate the impact of ICT on Ghana's MGT industry empirically. Design/methodology/approach: The study adopts a two-phase data collection approach to collect the data. The authors use partial least square structural equation modeling to analyze the study's measurement and structural assessment model. Findings: ICT positively impacts MGT and the drivers considered. The drivers positively influence MGT. The study further analyzes novel results on the relationships between the drivers and their mediating roles in enhancing MGT performance. Originality/value: The study's originality is the extension of ICT adoption and usage in MGT. The lack of literature on the importance of ICT for MGT services makes this study the primary source of literature, and the relationships investigated are unique as the research area is unexplored. [ABSTRACT FROM AUTHOR]