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In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the…
Numerical methods are developed to solve the problem of abnormal changes of current (conductivity) in polymer composite films which may be used as current, pressure or temperature sensors. General nonlinear model includes the heat equation,…
The convective Brinkman-Forchheimer equations describe the motion of incompressible fluid flows in a saturated porous medium. This work examines the multiscale stochastic convective Brinkman-Forchheimer (SCBF) equations perturbed by…
The possible functional forms of the effective conductivity sigma_{eff} of the randomly inhomogeneous two-phase system at arbitrary values of concentrations are discussed. A new functional equation, generalizing the duality relation, is…
We investigate the features arising from hydrodynamic effects in graphene and phosphorene devices with finite heat sources, using ab initio calculations to go beyond Callaway's model and inform a full linearized scattering operator, and…
The specific heat is a central property of condensed matter systems including polymers and oligomers in their condensed phases. Yet, predictions of this quantity from molecular simulations and successful comparisons to experimental data are…
In order to characterize the higher order moments of the particle multiplicity, we implement the linear-sigma model with Polyakov-loop correction. We first studied the critical phenomena and estimated some thermodynamic quantities. Then, we…
In this work, we discuss the large time behavior of the solutions of the two dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations in bounded domains. Under the functional setting $\V\hookrightarrow\H\hookrightarrow\V'$,…
Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant…
Two-dimensional (2D) pressure field estimation in molecular dynamics (MD) simulations has been done using three-dimensional (3D) pressure field calculations followed by averaging, which is computationally expensive due to 3D convolutions.…
In this work, Flory-Huggins phase diagrams for correlated random copolymers with realistic chain lengths are calculated. This is achieved in two steps. At first we derive a distribution function of copolymer chains with respect to…
This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain H\"older-type classes in which a random field is…
We investigate the behavior of heat conduction in two-dimensional (2D) electron gases without and with a magnetic field. We perform simulations with the Multi-Particle-Collision approach, suitably adapted to account for the Lorenz force…
We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that at vanishingly small concentrations, such that the polymers are…
The thermal stability of C60 dimers and 2D pressure-polymerized C60 is studied using high-resolution capacitance dilatometry. The transformation of both the dimer and the polymer phases back to 'normal' C60 is excellently described by a…
The seek for a new universal formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general…
We present results based on an implementation of the Godunov Smoothed Particle Hydrodynamics (GSPH), originally developed by Inutsuka (2002), in the GADGET-3 hydrodynamic code. We first review the derivation of the GSPH discretization of…
The basic system of differential equations for a multiphase flow with the introduction of the probability of each phase in the flow is considered. The main analysis is focused on the case of a heterogeneous two-phase flow. The conservation…
Godunov Smoothed Particle Hydrodynamics (Godunov SPH) method is a computational fluid dynamics method that utilizes a Riemann solver and achieves the second-order accuracy in space. In this paper, we extend the Godunov SPH method to elastic…
In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the Modified Phase Field Crystal equation, a generalized damped wave equation for which the…