arXiv subjects

Wen-An Yong

Publications and source records attributed to Wen-An Yong.

34 records · Page 2Linked to original sources

arXiv2020

Boundary Conditions for Hyperbolic Relaxation Systems with Characteristic Boundaries of Type I

This work is concerned with boundary conditions for one-dimensional hyperbolic relaxation systems with characteristic boundaries. We assume that the relaxation system satisfies the structural stability condition proposed by the second author previously and the boundary is characteristic of type I (characteristic for the relaxation system but non-characteristic for the corresponding equilibrium system). For this kind of characteristic initial-boundary-value problems, we propose a modified Generalized Kreiss condition (GKC). This extends the GKC proposed by the second author for the non-characteristic boundaries to the present characteristic case. Under this modified GKC, we derive the reduced boundary condition and verify its validity by combining an energy estimate with the Laplace transform. Moreover, we show the existence of boundary-layers for nonlinear problems.

math.AP↗

arXiv2019

Properties of Conservation-dissipation Formalism of Irreversible Thermodynamics

This paper proposes four fundamental requirements for establishing PDEs (partial differential equations) modeling irreversible processes. We show that the PDEs derived via the CDF (conservation-dissipation formalism) meet all the requirements. In doing so, we find useful constraints on the freedoms of CDF and point out that a shortcoming of the formalism can be remedied with the help of the Maxwell iteration. It is proved that the iteration preserves the gradient structure and strong dissipativeness of the CDF-based PDEs. A refined formulation of the second law of thermodynamics is given to characterize the strong dissipativeness, while the gradient structure corresponds to nonlinear Onsager relations. Further advantages and limitations of CDF will also be presented.

math-ph↗

arXiv2019

Relaxation-rate formula for the entropic lattice Boltzmann method

An elegant and uniform relaxation-rate formula is presented for the entropic lattice Boltzmann method (ELBM). The formula not only guarantees the discrete time H-theorem at numerical level but also gives full consideration to the consistency with hydrodynamics. With this novel formula, the computational cost of the ELBM is significantly reduced and the method now can be efficiently used for a broad range of hydrodynamics applications including high Renolds number flows. Moreover, we demonstrate that the grid points where flow fields change drastically are effectively marked by the formula.

physics.comp-ph↗

arXiv2018

Stability Analysis of Quadrature-based Moment Methods for Kinetic Equations

In this paper, we present a systematic stability analysis of the quadrature-based moment method (QBMM) for the one-dimensional Boltzmann equation with BGK or Shakhov models. As reported in recent literature, the method has revealed its potential for modeling non-equilibrium flows, while a thorough theoretical analysis is largely missing but desirable. We show that the method can yield non-hyperbolic moment systems if the distribution function is approximated by a linear combination of $δ$-functions. On the other hand, if the $δ$-functions are replaced by their Gaussian approximations with a common variance, we prove that the moment systems are strictly hyperbolic and preserve the dissipation property (or $H$-theorem) of the kinetic equation. In the proof we also determine the equilibrium manifold that lies on the boundary of the state space. The proofs are quite technical and involve detailed analyses of the characteristic polynomials of the coefficient matrices.

math.NA↗

arXiv2018

Generalized hydrodynamics and the classical hydrodynamic limit

This work is concerned with our recently developed formalism of non-equilibrium thermodynamics. This formalism extends the classical irreversible thermodynamics which leads to classical thermodynamics and can not describe physical phenomena with long relaxations. With the extended theory, we obtain a generalized hydrodynamic system which can be used to describe the non-Newtonian fluids, heat transfer beyond Fourier's law and fluid flow in very short temporal and spatial scales. We study the mathematical structure of the generalized hydrodynamic system and show that it possesses a nice conservation-dissipation structure and therefore is symmetrizable hyperbolic. Moreover, we rigorously justify that this generalized hydrodynamic system tends to the classical hydrodynamics when the relaxation times approach to zero. This shows that the classical hydrodynamics can be derived as an approximation of our generalized one.

math.AP↗

arXiv2017

A family of single-node second-order boundary schemes for the lattice Boltzmann method

In this work, we propose a family of single-node second-order boundary schemes for the lattice Boltzmann method with general collision terms. The construction of the schemes is quite universal and simple, it does not involve concrete lattice Boltzmann models and uses the half-way bounce-back rule as a central step. The constructed schemes are all second-order accurate if so is the bounce-back rule. In addition, the proposed schemes have good stability thanks to convex combinations. The accuracy and stability of several specific schemes are numerically validated for multiple-relaxation-time models in both 2D and 3D.

physics.comp-ph↗

arXiv2015

A Novel Dissipation Property of the Master Equation

Recent studies have shown that the entropy production rate for the master equation consists of two nonnegative terms: the adiabatic and non-adiabatic parts, where the non-adiabatic part is also known as the dissipation rate of a Boltzmann-Shannon relative entropy. In this paper, we provide some nonzero lower bounds for the relative entropy, the entropy production rate, and its adiabatic and non-adiabatic parts. These nonzero lower bounds not only reveal some novel dissipative properties for general nonequilibrium processes which are much stronger than the second law of thermodynamics, but also impose some new constraints on thermodynamic constitutive relations. Moreover, we also provide a mathematical application of these nonzero lower bounds by studying the long-time behavior of the master equation. Extensions to the Tsallis statistics are also discussed, including the nonzero lower bounds for the Tsallis-type relative entropy and its dissipation rate.

physics.chem-ph↗

arXiv2015

A rigorous derivation of multicomponent diffusion laws

This article is concerned with the dynamics of a mixture of gases. Under the assumption that all the gases are isothermal and inviscid, we show that the governing equations have an elegant conservation-dissipation structure. With the help of this structure, a multicomponent diffusion law is derived mathematically rigorously. This clarifies a long-standing non-uniqueness issue in the field for the first time. The multicomponent diffusion law derived here takes the spatial gradient of an entropic variable as the thermodynamic forces and satisfies a nonlinear version of the Onsager reciprocal relations.

math-ph↗

arXiv2014

A Kinetic Model for Cell Damage Caused by Oligomer Formation

It is well-known that the formation of amyloid fiber may cause invertible damage to cells, while the underlying mechanism has not been fully uncovered. In this paper, we construct a mathematical model, consisting of infinite ODEs in the form of mass-action equations together with two reaction-convection PDEs, and then simplify it to a system of 5 ODEs by using the maximum entropy principle. This model is based on four simple assumptions, one of which is that cell damage is raised by oligomers rather than mature fibrils. With the simplified model, the effects of nucleation and elongation, fragmentation, protein and seeds concentrations on amyloid formation and cell damage are extensively explored and compared with experiments. We hope that our results can provide a valuable insight into the processes of amyloid formation and cell damage thus raised.

q-bio.BM↗

arXiv2014

Boltzmann-Equation Based Derivation of Balance Laws in Irreversible Thermodynamics

In this paper we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists of four basic steps: picking suitable state variables, choosing a strictly concave entropy function, separating entropy fluxes and production rates properly, and determining a dissipation matrix. Our approach takes the advantage of both EIT and GENERIC formalisms, and shows a direct correspondence with Levermore's moment closure hierarchies for the Boltzmann equation. This result may put various macroscopic modeling approaches starting from the general principles of non-equilibrium thermodynamics on a solid microscopic foundation based on the Boltzmann equation.

cond-mat.stat-mech↗

arXiv2014

Conservation-dissipation formalism of irreversible thermodynamics

We propose a conservation-dissipation formalism (CDF) for coarse-grained descriptions of irreversible processes. This formalism is based on a stability criterion for non-equilibrium thermodynamics. The criterion ensures that non-equilibrium states tend to equilibrium in long time. As a systematic methodology, CDF provides a feasible procedure in choosing non-equilibrium state variables and determining their evolution equations. The equations derived in CDF have a unified elegant form. They are globally hyperbolic, allow a convenient definition of weak solutions, and are amenable to existing numerics. More importantly, CDF is a genuinely nonlinear formalism and works for systems far away from equilibrium. With this formalism, we formulate novel thermodynamics theories for heat conduction in rigid bodies and non-isothermal compressible Maxwell fluid flows as two typical examples. In these examples, the non-equilibrium variables are exactly the conjugate variables of the heat fluxes or stress tensors. The new theory generalizes Cattaneo's law or Maxwell's law in a regularized and nonlinear fashion.

math-ph↗

arXiv2013

Asymptotic analysis of the lattice Boltzmann method for generalized Newtonian fluid flows

In this article, we present a detailed asymptotic analysis of the lattice Boltzmann method with two different collision mechanisms of BGK-type on the D2Q9-lattice for generalized Newtonian fluids. Unlike that based on the Chapman-Enskog expansion leading to the compressible Navier-Stokes equations, our analysis gives the incompressible ones directly and exposes certain important features of the lattice Boltzmann solutions. Moreover, our analysis provides a theoretical basis for using the iteration to compute the rate-of-strain tensor, which makes sense specially for generalized Newtonian fluids. As a by-product, a seemingly new structural condition on the generalized Newtonian fluids is singled out. This condition reads as "the magnitude of the stress tensor increases with increasing the shear rate". We verify this condition for all the existing constitutive relations which are known to us. In addition, it it straightforward to extend our analysis to MRT models or to three-dimensional lattices.

physics.flu-dyn↗

arXiv2013

Newtonian limit of Maxwell fluid flows

In this paper, we revise Maxwell's constitutive relation and formulate a system of first-order partial differential equations with two parameters for compressible viscoelastic fluid flows. The system is shown to possess a nice conservation-dissipation (relaxation) structure and therefore is symmetrizable hyperbolic. Moreover, for smooth flows we rigorously verify that the revised Maxwell's constitutive relations are compatible with Newton's law of viscosity.

math-ph↗

arXiv2012

Partial equilibrium approximations in Apoptosis

Apoptosis is one of the most basic biological processes. In apoptosis, tens of species are involved in many biochemical reactions with times scales of widely differing orders of magnitude. By the law of mass action, the process is mathematically described with a large and stiff system of ODEs (ordinary differential equations). The goal of this work is to simplify such systems of ODEs with the PEA (partial equilibrium approximation) method. In doing so, we propose a general framework of the PEA method together with some conditions, under which the PEA method can be justified rigorously. The main condition is the principle of detailed balance for fast reactions as a whole. With the justified method as a tool, we made many attempts via numerical tests to simplify the Fas-signaling pathway model due to Hua et al. (2005) and found that nine of reactions therein can be well regarded as relatively fast. This paper reports our simplification of Hua at el.'s model with the PEA method based on the fastness of the nine reactions, together with numerical results which confirm the reliability of our simplified model.

q-bio.QM↗

arXiv2011

Stability of Steady Solutions to Reaction-Hyperbolic Systems for Axonal Transport

This paper is concerned with the stability of steady solutions to initial-boundary-value problems of reaction-hyperbolic systems for axonal transport. Under proper structural assumptions, we clarify the relaxation structure of the reaction-hyperbolic systems and show the time-asymptotic stability of steady solutions or relaxation boundary-layers.

math.AP↗

arXiv2010

Weak entropy solutions of nonlinear reaction-hyperbolic systems for axonal transport

This paper is concerned with a class of nonlinear reaction-hyperbolic systems as models for axonal transport in neuroscience. We show the global existence of entropy-satisfying BV-solutions to the initial-value problems by using hyperbolic-type methods. Moreover, we rigorously justify the limit as the biochemical processes are much faster than the transport ones.

math.AP↗