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We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we…
In this study, we introduce a novel stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm…
We consider driven dimer models on the square and honeycomb graphs, starting from a stationary Gibbs measure. Each model can be thought of as a two dimensional stochastic growth model of an interface, belonging to the anisotropic KPZ…
We study a classical model of thermally fluctuating polymers confined to two dimensions, experiencing a grooved periodic potential, and subject to pulling forces both along and transverse to the grooves. The equilibrium polymer…
A generalized formulation is derived for the analysis of the field manipulation properties of electromagnetic skins (EMSs) in the working regimes of interest for wireless communications. Based on such a theoretical framework, a unified…
Scaling relationships have been proposed to describe shear-driven size segregation based on intruder experiments and simulations. While these models have shown agreement with experimental and numerical results under uniform shear rate,…
The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of transport processes in semiconductor junctions. A complete phenomenological model for drift-diffusion processes in a junction has…
We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with…
This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize…
It is proposed that the rate of relaxation in a liquid is better described by the geometric mean of the van Hove distribution function, rather than the standard arithmetic mean used to obtain the mean squared displacement. The difference…
For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixed. We show…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…
Elastic turbulence (ET), observed in flows of sufficiently elastic polymer solution at small inertia, is characterized by chaotic motions and power-law scaling of energy spectrum ($E$) in both wavenumber ($k$) and frequency ($\omega$):…
We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…
The steady state properties of an interface in a stationary Couette flow are addressed within the framework of fluctuating hydrodynamics. Our study reveals that thermal fluctuations are driven out of equilibrium by an effective shear rate…
We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on average over the initial conditions, on…
We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height…
We study the transport properties and the spectral statistics of a one-dimensional closed quantum system of interacting spinless fermions in a quasiperiodic potential which produces a single particle mobility edge in the absence of…
This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…