Related papers: Variational approximation method for the long-rang…
We develop multipoint stress mixed finite element methods for linear elasticity with weak stress symmetry on cuboid grids, which can be reduced to a symmetric and positive definite cell-centered system. The methods employ the lowest-order…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
We show that viscoelastic effects play a crucial role in the damping of vibrational modes in harmonic amorphous solids. The relaxation of a given plane wave is described by a memory function of a semi-infinite one-dimensions mass-spring…
In the recently introduced Variable-Shape heaving wave energy converters, the buoy changes its shape actively in response to changing incident waves. In this study, a Lagrangian approach for the dynamic modeling of a spherical…
We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…
This paper considers weak Galerkin finite element approximations for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree $k \ (k\geq 1)$ for the stress approximation, degree $k+1$ for…
In this paper I present a simple and self-consistent framework based on microrheology that allows one to obtain the mechanical response of viscoelastic fluids and gels from the motion of probe particles immersed on it. By considering a…
In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
We describe a simple meanfield variational approach to study a number of properties of intrinsically stiff chains which are appropriate models for a large class of biopolymers. We present the calculation of the distribution of end-to-end…
We describe a two-step approach for combining interactive molecular dynamics in virtual reality (iMD-VR) with free energy (FE) calculation to explore the dynamics of biological processes at the molecular level. We refer to this combined…
The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It may describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in…
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…
A variational discrete element method is applied to simulate quasi-static crack propagation. Cracks are considered to propagate between the mesh cells through the mesh facets. The elastic behaviour is parametrized by the continuous…
A variational approach is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing monomer-monomer force constants…
We present a new, stable, mixed finite element (FE) method for linear elastostatics of nearly incompressible solids. The method is the automatic variationally stable FE (AVS-FE) method of Calo, Romkes and Valseth, in which we consider a…
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…
In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy…
A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization…