Related papers: Numerical Methods for a System of Coupled Cahn-Hil…
In the present work, we address a class of Cahn-Hilliard equations characterized by a singular diffusion term. The problem is a simplified version with constant mobility of the Cahn-Hilliard-de Gennes model of phase separation in binary,…
The Flory-Huggins theory describes the phase separation of solutions containing polymers. Although it finds widespread application from polymer physics to materials science to biology, the concentrations that coexist in separate phases at…
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…
This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
Polymer mixtures fractionate between phases depending on their molecular weight. Consequently, by varying solvent conditions, a polydisperse polymer sample can be separated between phases so as to achieve a particular molecular weight…
The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of the material with the solid wall, various dynamic boundary…
We study analytically a continuum model for phase-separation in binary polymer blends based on the Flory-Huggins-De Gennes free energy, by means of the self-consistent large-$n$ limit approach. The model is solved for values of the…
A two-component system of penetrable particles interacting via a gaussian core potential is considered, which may serve as a crude model for binary polymer solutions. The pair structure and thermodynamic properties are calculated within the…
We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly…
Computational gas dynamics has become a prominent research field both in astrophysics and cosmology. In the first part of this review we intend to briefly describe several of the numerical methods used in this field, discuss their range of…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic…
The advective Cahn-Hilliard equation describes the competing processes of stirring and separation in a two-phase fluid. Intuition suggests that bubbles will form on a certain scale, and previous studies of Cahn-Hilliard dynamics seem to…
We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure…
The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection…
We present a method for the calculation of electronic structure of systems that contain tens of thousands of atoms. The method is based on the division of the system into mutually overlapping fragments and the representation of the…
Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems…
We model the flow behaviour of dense melts of flexible and semiflexible ring polymers in the presence of walls using a hybrid multiscale approach. Specifically, we perform molecular dynamics simulations and apply the Irving-Kirkwood formula…
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…