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In this paper, we establish a general convergence theorem for solutions of multivariate stochastic differential equations with countably many singular terms expressed as integrals with respect to local times. The processes under…
Nonequilibrium dynamics at interfaces is generally driven by a chemical potential. Here we demonstrate a generic technique to derive the basic equations of motion, boundary conditions and the chemical potential in a consistent way from…
The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in…
The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
Phenomenological theories of interfacial interactions have targeted terrestrial applications since long time and their exploitation has inspired our research programme to build up a macroscopic theory of gas-surface interactions targeting…
Topographical and diffuse interface reconfigurations occur with a change in the solidification rate. In this article we pursue the hypothesis that the interface configuration during solidification is determined by the rate of entropy…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
We study a system of non-identical bistable particles that is driven by a dynamical constraint and coupled through a non-local mean-field. Assuming piecewise affine constitutive laws we prove the existence of traveling wave solutions and…
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…
We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a…
In this paper, instability at an interface between two miscible liquids with identical mechanical properties but different electrical conductivities is analyzed in the presence of an electric field that is perpendicular to the interface. A…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
We analyse a 3-wave kinetic equation, derived from the elastic beam wave equation on the lattice. The ergodicity condition states that two distinct wavevectors are supposed to be connected by a finite number of collisions. In this work, we…
Interfaces in tissues are ubiquitous, both between tissue and environment as well as between populations of different cell types. The propagation of an interface can be driven mechanically. % e.g. by a difference in the respective…
We formulate a theory of dissipative hydrodynamics with spontaneously broken translations, describing charge density waves in a clean isotropic electronic crystal. We identify a novel linear transport coefficient, lattice pressure,…
Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at…
In this study we try to answer the qustion : What happens when explicit constraints are introduced such that the low energy, long wavelength modes of a system are unavailable ? This question has assumed some importance in recent years due…
Phonons in solid materials can be understood as the Goldstone bosons of the spontaneously broken spacetime symmetries. As such their low energy dynamics are greatly constrained and can be captured by standard effective field theory (EFT)…
We formulate a new theory for how caging constraints in glass-forming liquids at a surface or interface are modified and then spatially transferred, in a layer-by-layer bootstrapped manner, into the film interior in the context of the…