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In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolutions than that of the momentum. The latter usually…
A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb method for the pure hard-core interacting case is used to…
Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…
A method of simulating the drying process of a soft matter solution with an implicit solvent model by moving the liquid-vapor interface is applied to various solution films and droplets. For a solution of a polymer and nanoparticles, we…
The theory of the dynamics of polymers in solution is developed coming from the hydrodynamic theory of the Brownian motion (BM) and the Rouse-Zimm (RZ) model. It is shown that the time correlation functions describing the polymer motion…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
We have conducted a triple-scale simulation of liquid water by concurrently coupling atomistic, mesoscopic, and continuum models of the liquid. The presented triple-scale hydrodynamic solver for molecular liquids enables the insertion of…
The influence of poor solvent quality on fluid demixing of a model mixture of colloids and nonadsorbing polymers is investigated using density functional theory. The colloidal particles are modelled as hard spheres and the polymer coils as…
We employ a multiscale approach to model the translocation of biopolymers through nanometer size pores. Our computational scheme combines microscopic Molecular Dynamics (MD) with a mesoscopic Lattice Boltzmann (LB) method for the solvent…
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that…
We study equilibrium properties of polymer films and droplets on a solid substrate employing particle-based simulation techniques (Molecular Dynamics) and a continuum description. Parameter-passing techniques are explored that facilitate a…
A system of diffusion-reaction equations coupled with a dissolution-precipitation model is discussed. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector…
We propose a numerical methodology for the simultaneous numerical simulation of four states of matter; gas, liquid, elastoplastic solids and plasma. The distinct, interacting physical processes are described by a combination of…
This paper enhances the Diffuse Interface Method (DIM) for simulating compressible multiphase flows across all Mach numbers by addressing the accuracy challenges posed at low Mach regimes. A correction to the Riemann solver is introduced,…
Multiparticle collision dynamics (MPCD) enables to simulate fluid dynamics including both hydrodynamics and thermal fluctuations. Its main use concerns complex fluids, where the solvent interacts with concentrated solutes, may they be…
We analyzed extensively the dynamics of polymer chains in solutions simulated with dissipative particle dynamics (DPD), with a special focus on the potential influence of a low Schmidt number of a typical DPD fluid on the simulated polymer…
The behavior of mesoscopic particles dissolved in a dilute solution of long, flexible, and nonadsorbing polymer chains is studied by field-theoretic methods. For spherical and cylindrical particles the solvation free energy for immersing a…
The quantum dynamics of a low-dimensional system in contact with a large but finite harmonic bath is theoretically investigated by coarse-graining the bath into a reduced set of effective energy states. In this model, the couplings between…
Polymer behavior in mixed solvents often exhibits intriguing phenomena, such as cosolvency, where a polymer that collapses in two individually poor solvents becomes soluble in their mixture. In this study, we employ a combination of…
A new class of multiscale scheme is presented for micro-hydrodynamic problems based on a dual representation of the fluid observables. The hybrid model is first tested against the classical flow between two parallel plates and then applied…