Related papers: A variational approach to a stationary free bounda…
This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid,…
Shear transformations (i.e., localised rearrangements of particles resulting in the shear deformation of a small region of the sample) are the building blocks of mesoscale models for the flow of disordered solids. In order to compute the…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
The effects of electromagnetic vacuum fluctuations with the boundary on charged particles is investigated. They may be observed via an electron interference experiment near the conducting plate, where boundary effects of vacuum fluctuations…
We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they…
We attempt to describe surface defects in smectic A thin films by formulating a free discontinuity problem - that is, a variational problem in which the order parameter is allowed to have jump discontinuities on some (unknown) set. The free…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid…
We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character - considering either one of…
Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging.…
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the…
In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…
We consider a non-linear, one-dimensional wave equation system with finite-dimensional stochastic driving terms and with weak dissipation. A stationary process that solves the system is used to model steady-state non-equilibrium heat flow…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied…
We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \tau is employed as a…
We show how dynamical equations for liquid films and drops on uneven surfaces, including contact line dynamics and evaporation/condensation effects, may be formulated as a variational dynamics, generated via Onsager's variational principle.…
We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental…