Diffusion Boundary Conditions Research Articles

Impact of Soret and Dufour on MHD Casson fluid flow past a stretching surface with convective–diffusive conditions

The intension of current inquiry is to highlight the impact of magnetohydrodynamic Casson fluid flow across a convective surface with cross diffusion, chemical reaction, non-linear radiative heat are accounted. Convection and diffusive boundary conditions are deemed. The governing flow equations for the flow fields are converted into non-dimensional form by using appropriate similarity variables. These ODEs are solved by fourth order Runge–Kutta and Shooting method. The outcomes are bestowed with plots and table for the influence of diverse flow variables on the flow fields. We observed that depreciate temperature and appreciate concentration with the upsurge in Sorret number, whereas a negative impact is perceived with Dufour number. A decrement in Nusselt number and an enhancement in Sherwood number are observed for the intensification of non-linear radiative parameter.

Electrical conductivity of a thin film in the case of an arbitrarily oriented ellipsoidal isoenergetic surface of a conductor

The static electrical conductivity of a thin conducting film is calculated using the kinetic approach. The model of diffuse boundary conditions is used as boundary conditions for the charge carrier distribution function. The isoenergetic surface of the conducting film material is an ellipsoid of rotation that is arbitrarily oriented in the pulse space. The volume of the conductor is dominated by scattering on impurity atoms and on dislocations of electrons (holes). The electrical conductivity of the film is analyzed depending on the angles that determine the direction of the ellipsoid axis of rotation, and a comparison with the results for the case of a macroscopic sample is presented. A comparison is made with experimental data for the electrical conductivity of Bi and Si thin films.

Nonlinear age-structured population models with nonlocal diffusion and nonlocal boundary conditions

In this paper, we develop some basic theory for age-structured population models with nonlocal diffusion and nonlocal boundary conditions. We first apply the theory of integrated semigroups and non-densely defined operators to a linear equation, study the spectrum, and analyze the asymptotic behavior via asynchronous exponential growth. Then we consider a semilinear equation with nonlocal diffusion and nonlocal boundary condition, use the method of characteristic lines to find the resolvent of the infinitesimal generator and the variation of constant formula, apply Krasnoselskii's fixed point theorem to obtain the existence of nontrivial steady states, and establish the stability of steady states. Finally we generalize these results to a nonlinear equation with nonlocal diffusion and nonlocal boundary condition.

ASSESSMENT OF GEOECOLOGICAL CONSEQUENCES OF SUBDUCTION PROCESSES

t. The aim of the work is to develop a numerical-analytical method for assessing the geoecological consequences of volcanic activity accompanying the subduction process. The boundary problem was formulated, including the three-dimensional transport and diffusion equation and boundary conditions at the bottom and surface of the water. For research, a block structure with quasi-homogeneous layers is introduced. In each block, a differential factorization method is implemented and integral representations of solutions are obtained. Calculations for a model problem are carried out, conclusions are formulated about the features of the behavior of the heavy and light fractions of volcanic ejections depending on the speed of currents, intensity and duration of the eruption.

The influence of double diffusive gradient boundary condition on micropolar nano fluid flow through stretching surface with a higher order chemical reaction

The influence of double diffusive gradient boundary condition on micropolar nano fluid flow through stretching surface with a higher order chemical reaction

The influence of double diffusive gradient boundary condition on micropolar nano fluid flow through stretching surface with a higher order chemical reaction

The influence of double diffusive gradient boundary condition on micropolar nano fluid flow through stretching surface with a higher order chemical reaction

Transient behaviour of a rarefied gas around a sphere caused by impulsive rotation

Abstract

Anomalous diffusion in umbrella comb

Anomalous transport in a circular comb is considered. The circular motion takes place for a fixed radius, while radii are continuously distributed along the circle. Two scenarios of the anomalous transport, related to the reflecting and periodic angular boundary conditions, are studied. The first scenario with the reflection boundary conditions for the circular diffusion corresponds to the conformal mapping of a 2D comb Fokker-Planck equation on the circular comb. This topologically constraint motion is named umbrella comb model. In this case, the reflecting boundary conditions are imposed on the circular (rotator) motion, while the radial motion corresponds to geometric Brownian motion with vanishing to zero boundary conditions on infinity. The radial diffusion is described by the log-normal distribution, which corresponds to exponentially fast motion with the mean squared displacement (MSD) of the order of $e^t$. The second scenario corresponds to the circular diffusion with periodic boundary conditions and the outward radial diffusion with vanishing to zero boundary conditions at infinity. In this case the radial motion corresponds to normal diffusion. The circular motion in both scenarios is a superposition of cosine functions that results in the stationary Bernoulli polynomials for the probability distributions.

FTn Finite Volume Analysis of Ultrafast Laser Radiation Transport through Human Skin Cancer

In this work, we develop a numerical tool for the early detection of skin cancer using a 3D numerical transient radiative heat transfer study of ultrafast-laser transport through normal and malignant human skins. The curved-line advection method (CLAM) spatial scheme and the FTn angular scheme of the finite volume method (FVM) are investigated to analyze the above-cited physical phenomena. Both Fresnel specular and diffuse boundary conditions are analyzed. Human skin is considered based on optical properties available from other sources. The temporal radiative signals of skin with malignancies were compared to those of normal skin. Malignancies in the basal layer and epidermis were simulated. Further, the effects of laser light wavelength and the volume of the cancerous region and its scattering coefficient on these signals were studied. The results show that (1) the effect of the Fresnel boundary in the modeling was pronounced; (2) the peak magnitude for human skin with the cutaneous melanoma (CM) had the maximum value in comparison with those obtained for the two other malignancies; and (3) when cancer fully affected the living epidermis with any of these malignancies, the reflectance was more than its predicted value when affected by the basal only.

BENDING AND FREE OSCILLATIONS OF THE VISCOELASTIC TOROIDAL SHELL, T AL SHELL, TAKING IN AKING INTO ACCOUNT THE RHEOL T THE RHEOLOGICAL PROPERTIES OF THE MATERIAL

The bending of a viscoelastic toroidal shell with diffuse boundary conditions is considered in this work. The relationship between stress and strain is described by the Aviary equations. Based on the principle of calculus of variations, equations of the dynamics of the toroidal shell are obtained. It is assumed that the movement along the normal to the median surface, along the tangents to circular sections and along the shell is not previously imposed any restrictions. As result of the calculation, It was found that shell vibrations occur at higher frequencies than rod vibrations (m)

Study of gas slippage factor in anisotropic porous media using the lattice Boltzmann method

In unconventional reservoir rocks, pore anisotropy and gas high Knudsen number (Kn) effect are prominent, while gas slippage factor is a crucial parameter to evaluate their apparent permeability. To analyze the correlation of gas slippage factor with pore anisotropy of porous media and Kn, two-dimensional bundle models and anisotropic porous media with same characteristic length were skillfully constructed in this work. A multi-relaxation-time Lattice Boltzmann model combining diffusive reflection boundary condition and Bosanquet-type viscosity model was applied to simulate gas high-Kn flow (Kn = 0.05–0.53) in them. The results showed that Kn and pore-scale anisotropy jointly determine gas slippage factor of anisotropic porous media, which has nothing to do with porosity, specific surface area, and intrinsic permeability in nature. Pore-scale anisotropy leads to the distinct nonlinear changes of gas slippage factor with Kn. When pore-scale anisotropy factor is between 5.37 and 14.58, gas slippage factor of porous media is positively correlated with Kn. But as pore-scale anisotropy factor is in a range from 1.0 to 5.37, gas slippage factor decreases with an increase of Kn. In addition, gas slippage factor of porous media increases with an increase of pore-scale anisotropy as Kn is in a range of 0.18 to 0.53. This work further improves the understanding of gas slippage factor and gas high-Kn effect in anisotropic porous media.

Numerical study and stability of the Lengyel\u2013Epstein chemical model with diffusion

In this paper, a nonlinear mathematical model with diffusion is taken into account to review the dynamics of Lengyel–Epstein chemical reaction model to describe the oscillating chemical reactions. For this purpose, the dimensionless Lengyel–Epstein model with diffusion and homogeneous boundary condition is considered. The steady states with and without diffusion of the Lengyel–Epstein model are studied. The basic reproductive number is computed and the global steady states for the system are calculated. Numerical results are offered for two systems using three well known techniques to validate the main outcomes. The consequences established from this qualitative study are supported by numerical simulations characterized by distinct programs, adopting forward Euler method, Crank–Nicolson method, and nonstandard finite difference method.

Numerical considerations for advection-diffusion problems in cardiovascular hemodynamics.

Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of Péclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these challenges in the context of a stabilized finite element computational framework. To overcome numerical instabilities when backflow occurs at Neumann boundaries, we propose an approach based on the prescription of the total flux. In addition, we introduce a "consistent flux" outflow boundary condition and demonstrate its superior performance over the traditional zero diffusive flux boundary condition. Lastly, we discuss discontinuity capturing (DC) stabilization techniques to address the well-known oscillatory behavior of the solution near the concentration front in advection-dominated flows. We present numerical examples in both idealized and patient-specific geometries to demonstrate the efficacy of the proposed procedures. The three contributions discussed in this paper successfully address commonly found challenges when simulating mass transport processes in cardiovascular flows.

Organizations in reaction-diffusion systems: Effects of diffusion and boundary conditions

Chemical Organization Theory (COT) has been successfully applied to analyze complex reaction networks where species interact and new species can emerge. The COT has been well studied, but is yet to analyze high dimensional systems dynamics over time equivalent to ordinary differential equations. Moreover, spatial effects, such as diffusion and boundary conditions have also not been considered yet. Here, we extend the COT to cope with reaction-diffusion systems. Thereby we focus on the effects of diffusion and various boundary conditions. In order to demonstrate the effectiveness of our approach, we analyze two models based on partial differential equations, one of which is on HIV virus dynamics.The analysis shows interesting organizational structures when using different ranges of diffusion rates, as well as for Dirichlet and positive Neumann boundary conditions. The advantage of this novel approach is that it is based solely on the model structure (reaction rules) but is independent of kinetic details, such as rate constants. Hence, it copes with high-dimensional systems without the need of numerical simulations, and it can be applied without detailed mathematical knowledge. Our tool is available, without restriction at https://github.com/stephanpeter/orgs-rds.

Calculation of the Electrical Conductivity of a Thin Cylindrical Conducting Tube Taking into Account the Anisotropy of the Isoenergetic Surface

In the kinetic approach, the electrical conductivity of a thin conducting tube is calculated using diffuse boundary conditions for the distribution function. The case of an anisotropic isoenergetic surface of a conductor having the form of a triaxial ellipsoid, one of the axes of which is parallel to the axis of the tube, is considered. The dependences of the modulus and the conductivity argument on the effective mass of charge carriers are analyzed.

On the motion of slightly rarefied gas induced by a discontinuous surface temperature

The motion of a slightly rarefied gas in a long straight two-dimensional channel caused by a discontinuous surface temperature is investigated on the basis of kinetic theory with a special interest in the fluid-dynamic description. More precisely, the channel is longitudinally divided into two parts and each part is kept at a uniform temperature different from each other, so that the surface temperature of the whole channel has a jump discontinuity at the junction. Under the assumption that the amount of jump in the surface temperature is small, the steady behaviour of the gas induced in the channel is studied on the basis of the linearized Boltzmann equation and the diffuse reflection boundary condition in the case where the Knudsen number, defined by the ratio of the molecular mean free path and the width of the channel, is small. Using a matched asymptotic expansion method combined with Sone’s asymptotics, a Stokes system describing the overall macroscopic behaviour of the gas inside the channel is derived, with a new feature of the ‘slip boundary condition’ for the flow velocity due to the jump discontinuity in the surface temperature of the channel. This condition takes the form of a diverging singularity with source and sink located at the point of discontinuity, with a multiplicative factor determined through the analysis of a spatially two-dimensional Knudsen-layer (or a Knudsen-zone) problem. Some numerical demonstrations based on the Bhatnagar–Gross–Krook equation are also presented.

Asymptotic dynamics on a chemotaxis-Navier–Stokes system with nonlinear diffusion and inhomogeneous boundary conditions

The diffusion of cells in a viscous incompressible fluid (e.g. water) may be viewed like movement in a porous medium and there is a bidirectorial oxygen exchange between water and their surrounding air in thin fluid layers near the air–water contact surface. This leads to the following chemotaxis-Navier–Stokes system with nonlinear diffusion: [Formula: see text] endowed with the inhomogeneous boundary conditions [Formula: see text] and the initial data [Formula: see text] in [Formula: see text], where the incoming oxygen [Formula: see text] is non-negative, and the outgoing oxygen molecule is modeled by [Formula: see text] with positive coefficient [Formula: see text]. In this paper, we investigate the asymptotic dynamics of the above system in a bounded domain [Formula: see text] with the smooth boundary [Formula: see text]. We will show that arbitrary porous medium diffusion mechanism [Formula: see text] can inhibit the singularity formation. In the incoming oxygen-free case, we further prove that the solution will stabilize to the unique mass-preserving spatial equilibrium [Formula: see text] in the sense that as [Formula: see text], [Formula: see text] hold uniformly with respect to [Formula: see text], where [Formula: see text].

Boundary conditions at a thin membrane for normal diffusion, classical subdiffusion, and slow subdiffusion processes

We consider three different diffusion processes in a system with a thin membrane: normal diffusion, classical subdiffusion, and slow subdiffusion. We conduct the considerations following the rule: If a diffusion equation is derived from a certain theoretical model, boundary conditions at a thin membrane should also be derived from this model with additional assumptions taking into account selective properties of the membrane. To derive diffusion equations and boundary conditions at a thin membrane, we use a particle random walk model in one‐dimensional membrane system in which space and time variables are discrete. Then we move from discrete to continuous variables. We show that the boundary conditions depend on both selective properties of the membrane and a type of diffusion in the system.

Local Well-Posedness of Vlasov–Poisson–Boltzmann Equation with Generalized Diffuse Boundary Condition

The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani-Lampis boundary condition. We construct a uniqueness local-in-time solution based on an $L^\infty$-estimate and $W^{1,p}$-estimate. In particular, we develop a new iteration scheme along the characteristic with the Cercignani-Lampis boundary for the $L^\infty$-estimate, and an intrinsic decomposition of boundary integral for $W^{1,p}$-estimate.

Stationary Non equilibrium States in Kinetic Theory

Stationary non equilibrium solutions to the Boltzmann equation, despite their relevance in applications, are much less studied than time dependent solutions, and no general existence theory is yet available, due to serious technical difficulties. Here we review some results on the construction of stationary non equilibrium solutions, in a general domain in contact with a slightly non-homogeneous thermal reservoir, both for finite and small Knudsen number. We will describe different approaches and different techniques developed. The main focus will be on stationary solutions close to hydrodynamics. In particular, we will give an answer to the longstanding open problem of the rigorous derivation of the steady incompressible Navier–Stokes–Fourier system from the Boltzmann theory, in the presence of a small external force and diffuse boundary condition with small boundary temperature variations.