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We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we…

We study the dynamics of a polymer when it is quenched from a $\theta$ solvent into a good or bad solvent by means of a Langevin equation. The variation of the radius of gyration is studied as a function of time. For the first stage of…

We propose and analyze a mathematical model of the mechanics of gels, consisting of the laws of balance of mass and linear momentum. We consider a gel to be an immiscible and incompressible mixture of a nonlinearly elastic polymer and a…

The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…

The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…

We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…

Several advances in the theory of space-resolved viscoelasticity of liquids and other amorphous systems are discussed in the present paper. In particular, considering long-time regimes of stress relaxation in liquids we obtain the…

Dimerization and subsequent aggregation of polymers and biopolymers often occur under nonequilibrium conditions. When the initial state of the polymer is not collapsed or the final folded native state, the dynamics of dimerization can…

A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of…

We introduce a framework for model reduction of chain models for dissipative particle dynamics (DPD) simulations, where the characteristic size of the chain, pressure, density, and temperature are preserved. The proposed methodology reduces…

The irreversible adsorption of polymers to a two-dimensional solid surface is studied. An operator formalism is introduced for chemisorption from a polydisperse solution of polymers which transforms the analysis of the adsorption process to…

Self-diffusion of a polymer chain in a melt is studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Polymer chains, each of which consists of $N$ segments, are…

We aim to analyze and calculate time-dependent acoustic wave scattering by a bounded obstacle and a locally perturbed non-selfintersecting curve. The scattering problem is equivalently reformulated as an initial-boundary value problem of…

Drawing an analogy to the paradigm of quasi-elastic neutron scattering, we present a general approach for quantitatively investigating the spatiotemporal dependence of structural anisotropy relaxation in deformed polymers by using…

Mass spectrometry is used in a wide range of scientific disciplines including proteomics, pharmaceutics, forensics, and fundamental physics and chemistry. Given this ubiquity, there is a worldwide effort to improve the efficiency and…

Line-by-line calculations are becoming the standard procedure for carrying spectral simulations. However, it is important to insure the accuracy of such spectral simulations through the choice of adapted models for the simulation of key…

We present new linear energy-stable numerical schemes for numerical simulation of complex polymer-solvent mixtures. The mathematical model proposed by Zhou, Zhang and E (Physical Review E 73, 2006) consists of the Cahn-Hilliard equation…

We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will…

We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and…

The problem of estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymeric melts from the analysis of the $\alpha$-process in ordinary relaxation experiments is addressed. The system is treated with the…