相关论文: Numerical convergence of nonlinear nonlocal contin…

A mesoscopic model for shear plasticity of amorphous materials in two dimensions is introduced, and studied through numerical simulations in order to elucidate the macroscopic (large scale) mechanical behavior. Plastic deformation is…

This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…

This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…

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…

In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic…

The growing interest in creating a parametric representation of liquid sloshing inside a container stems from its practical applications in modern engineering systems. The resonant excitation, on the other hand, can cause unstable and…

This paper is concerned with the time-dependent acoustic-elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well-posedness and stability of the…

We study the boundary regularity of local weak solutions to nonlinear parabolic systems of the form \begin{equation*} \partial_t u^i - \mathrm{div} \big( a(|Du|) Du^i \big)= f^i, \qquad i=1,\dots,N, \end{equation*} in a space-time cylinder…

An exact nonlinear scaling transformation is presented for the local three-dimensional dynamical equations of motion for differentially rotating disks. The result is relevant to arguments that have been put forth claiming that numerical…

In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM…

This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…

In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We…

We analyze nonclassical correlations between outcomes of measurements conducted on two spatial radiation modes. These correlations cannot be simulated with statistical mixtures of coherent states or, more generally, with non-negative…

Nonlocal diffusion model provides an appropriate description of the diffusion process of solute in the complex medium, which cannot be described properly by classical theory of PDE. However, the operators in the nonlocal diffusion models…

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…

This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal…

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…

We establish Schauder-type estimates for linear parabolic systems driven by variable-coefficient nonlocal pseudo-differential operators of order $s>0$. These estimates are formulated in critical time-weighted H\"older/Besov-type spaces and…

A field theory is presented for predicting damage and fracture in quasi brittle materials incorporating effects of irreversible (plastic) deformation as well as elastic moduli that soften with damage. The new observation made here is that…

We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…