Related papers: Towards analytical solutions of the alloy solidifi…
A brief review of the Stefan problem of solidification from a mixture, and its main numerical solution methods is given. Simulation of this problem in 2D or 3D is most practically done on a regular grid, where a sharp solid-liquid interface…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
We obtain two-dimensional exact analytic solutions for the structure of the hot accretion flows without wind. We assume that the only non-zero component of the stress tensor is $T_{r\varphi}$. Furthermore we assume that the value of…
Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…
This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…
Ice templating, a route where ice crystals are used to template macroporosity, has been used to process a variety of materials with one level of macropores. We demonstrate here a variant of ice templating based on the solidification of…
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…
In this paper, we conduct a numerical analysis of the strong stabilization and polynomial decay of solutions for the initial boundary value problem associated with a system that models the dynamics of a mixture of two rigid solids with…
Global existence for weak solutions to systems of nematic liquid crystals, with non-constant fluid density has been established by several authors. In this paper, we establish the regularity and uniqueness results for solutions to the…
We give a general phenomenological description of the steady state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two component dilute alloys. The solidification of a…
The decomposition kinetics of a solid-solution into separate phases are analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. This equation and the steepest-entropy-ascent quantum…
While the ongoing search to discover new high-entropy systems is slowly expanding beyond metals, a rational and effective method for predicting "in silico" the solid solution forming ability of multi-component systems remains yet to be…
Predicting the ground state of alloy systems is challenging due to the large number of possible configurations. We identify an easily computed descriptor for the stability of binary surface alloys, the effective coordination number…
A general purely crystalline mean curvature flow equation with a nonuniform driving force term is considered. The unique existence of a level set flow is established when the driving force term is continuous and spatially Lipschitz…
This article is the continued version of the analytical solutions for the pressureless Navier-Stokes equations with density-dependent viscosity in "M.W. Yuen, Analyitcal Solutions to the Navier-Stokes Equations, J. Math. Phys., 49 (2008)…
In this paper, we establish a necessary and sufficient condition for the existence and regularity of the density of the solution to a semilinear stochastic (fractional) heat equation with measure-valued initial conditions. Under a mild cone…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
Conventional derivations of phase boundaries from the Clausius-Clapeyron (CC) relation often employ the constant latent heat approximation to maintain analytical functions of the sublimation and boiling curves. To address the complex…
We prove the existence of a unique unstable strong solution in the sense of $L^1$-norm for an abstract Rayleigh--Taylor (RT) problem arising from stratified viscous fluids in Lagrangian coordinates based on a bootstrap instability method.…
The paper is concerned with the mathematical analysis of a class of thermodynamically consistent kinetic models for nonisothermal flows of dilute polymeric fluids, based on the identification of energy storage mechanisms and entropy…