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Many ferroelectric solid solutions exhibit enhanced electro-mechanical properties at the morphotropic boundary separating two phases with different orientations of polarization. The mechanism of properties enhancement is associated with…
We prove global existence of a solution to an initial and boundary value problem for a highly nonlinear PDE system. The problem arises from a thermomechanical dissipative model describing hydrogen storage by use of metal hydrides. In order…
Transition metal dichalcogenides exhibit a wide range of semiconducting, metallic, correlated, and topological electronic states that arise from strong coupling between lattice structure, dimensionality, and electronic degrees of freedom.…
In fluid-fluid phase transitions problems featuring small scale heterogeneity, we see that when the scale heterogeneity is sufficiently small, the periodic potential function $W(x,p)$ can be replaced with a homogenized potential function…
Porous membranes are thin solid structures that allow the flow to pass through their tiny openings, called pores. Flow inertia may play a significant role in several filtration flows of natural and engineering interest. Here, we develop a…
We consider the facilitated exclusion process, which is a nonergodic, kinetically constrained exclusion process. We show that in the hydrodynamic limit, its macroscopic behavior is governed by a free boundary problem. The particles evolve…
In this paper, we consider the homogenization of evolutionary incompressible purely viscous non-Newtonian flows of Carreau-Yasuda type in porous media with small perforation parameter $0< \varepsilon \ll 1$, where the small holes are…
We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the…
A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The…
We analyze the effect of temperature on the yielding transition of amorphous solids using different coarse-grained model approaches. On one hand we use an elasto-plastic model, with temperature introduced in the form of an Arrhenius…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
We study the conduction of heat across a narrow solid strip trapped by an external potential and in contact with its own liquid. Structural changes, consisting of addition and deletion of crystal layers in the trapped solid, are produced by…
We study the hydrodynamic limit for the isothermal dynamics of an anharmonic chain under hyperbolic space-time scaling under varying tension. The temperature is kept constant by a contact with a heat bath, realised via a stochastic…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
We review the current issues of nonequilibrium phase transitions, in particular, in the early universe. Phase transitions cannot maintain thermal equilibrium and become nonequilibrium when the thermal relaxation time scale is greater than…
We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
We consider a thin heterogeneous layer consisted of the thin beams (of radius $r$) and we study the limit behaviour of this problem as the periodicity $\varepsilon$, the thickness $\delta$ and the radius $r$ of the beams tend to zero. The…
The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under…