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Numerical simulation of a binary alloy of 2D Cahn–Hilliard model for phase separation
The interfacial dynamics of a system are significant in understanding the system’s behavior. One of the special models of these systems which...
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Collective Motions of Atoms in Crystals
AbstractThe collective motions of atoms in the molecular dynamics model of a classical Lennard-Jones monocrystal are studied in the process of...
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A second-order backward differentiation formula for the numerical solution of Cahn–Hilliard–Hele–Shaw system
In this paper, a second-order, unconditionally stable numerical scheme for the Cahn–Hilliard–Hele–Shaw system is constructed, which combines the...
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Numerical method for simulating rarefaction shocks in the approximation of phase-flip hydrodynamics
A finite-difference algorithm is proposed for numerical modeling of hydrodynamic flows with rarefaction shocks, in which the fluid undergoes a...
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Fracture Propagation Using a Phase Field Approach
Phase field models have received a lot of attention during the last 20 years and they have reached maturity, being in the last years ubiquitous,...
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Numerical investigation into the dependence of the Allen–Cahn equation on the free energy
Phase-field modeling is strongly influenced by the shape of a free energy functional. In the theory of thermodynamics, it is a logarithmic type...
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\(H^1\) solutions for a Kuramoto–Sinelshchikov–Cahn–Hilliard type equation
The Kuramoto–Sinelshchikov–Cahn–Hilliard equation models the spinodal decomposition of phase separating systems in an external field, the...
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Characteristic velocity and dispersion relation of linear waves in extended thermodynamics of a van der Waals gas
We study the characteristic velocities of the extended thermodynamics of molecular rotational- and vibrational- relaxation processes for a van der...
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Critical Phenomena of Massieu–Plank Potential for Gas Mixtures Described by the Beattie–Bridgeman Equations of State
AbstractThe paper considers thermodynamics as a measurement of extensive variables, such as energy, volume and mass. In this sense, thermodynamic...
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Regularized Isothermal Phase-Field Type Model of a Two-Phase Compressible Fluid and Its One-Dimensional Spatial Discretization
AbstractWe consider a quasi-hydrodynamic regularized model of the phase field type that describes the dynamics of an isothermal compressible...
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A High-Order Discontinuous Galerkin Solver for Multiphase Flows
We present a multiphase model for incompressible flows of two immiscible fluids. Our model solves one shared set of incompressible Navier–Stokes...
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Parareal Algorithms for the Cahn-Hilliard Equation
In this work we are interested in designing time parallel algorithm for the Cahn-Hilliard (CH) equation.
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Relations to Soliton Systems
The cluster flow solution describing a particle flow with travelling clusters as formation of a jam, is related to soliton systems. In this chapter...
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Efficient fully-decoupled and fully-discrete explicit-IEQ numerical algorithm for the two-phase incompressible flow-coupled Cahn-Hilliard phase-field model
In this paper, an efficient fully-decoupled and fully-discrete numerical scheme with second-order temporal accuracy is developed to solve the...
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Rayleigh–Benard Instability: a Study by the Methods of Cahn–Hillard Theory of Nonequilibrium Phase Transitions
This article is an attempt to study the process of Rayleigh–Benard convective instability by the methods used for mathematical modeling of critical...
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Load Balanced Particle Simulation with Automated Algorithm Selection
ls1 mardyn is a molecular dynamics (MD) simulation framework for multiphase and multicomponent investigations at small scales with application in...
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Fast algorithm for viscous Cahn-Hilliard equation
The main purpose of this paper is to solve the viscous Cahn-Hilliard equation via a fast algorithm based on the two time-mesh (TT-M) finite element...
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Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise
We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white...
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Self-organization and assembly of cellular structures
There are number of highly dynamical structures within the cell nucleus, plasma membrane and the Golgi complex that can be characterized in terms of...
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RET of Dense Polyatomic Gas with Six Fields
A RET theory of dissipative dense gases is presented. In this chapter, we study, in particular, the RET theory with six fields, where we ignore the...