Fluctuations at a constrained liquid-solid interface

Abstract

We study the interface between a solid trapped within a bath of liquid by a suitably shaped non-uniform external potential. Such a potential may be constructed using lasers, external electric or magnetic fields or a surface template. We study a two dimensional case where a thin strip of solid, created in this way, is surrounded on either side by a bath of liquid with which it can easily exchange particles. Since height fluctuations of the interface cost energy, this interface is constrained to remain flat at all length scales. However, when such a solid is stressed by altering the depth of the potential; beyond a certain limit, it responds by relieving stress by novel interfacial fluctuations which involve addition or deletion of entire lattice layers of the crystal. This "layering" transition is a generic feature of the system regardless of the details of the interaction potential. We show how such interfacial fluctuations influence mass, momentum and energy transport across the interface. Tiny momentum impulses produce weak shock waves which travel through the interface and cause the spallation of crystal layers into the liquid. Kinetic and energetic constraints prevent spallation of partial layers from the crystal, a fact which may be of some practical use. We also study heat transport through the liquid-solid interface and obtain the resistances in liquid, solid and interfacial regions (Kapitza resistance) as the solid undergoes such layering transitions. Heat conduction, which shows strong signatures of the structural transformations, can be understood using a free volume calculation.

Multiplicative cross-correlated noise induced escape rate from a metastable state

“…In the above equation the quantity g 2 (x b )/γ in the exponential factor together with the thermal energy k B T constitutes the effective temperature, a typical signature of the open system. 17,21,32,33,34,38 Another effect of space dependent diffusion in the dynamics is the presence of reaction coordinate (x 0 and x b ) in the steady state rate expression (13) which is typically absent in the standard Kramers' expression 1 (see Eq. (14) below).…”

“…17 External perturbation on the other hand can directly excite the system mode itself (leaving the bath mode alone) or the local bath modes (leaving the system mode alone). In both the situations the additional energy input by an independent source leads to a shift in the temperature, thus creating an effective temperature like quantity, 19,20,21,32,33,34,38 keeping the underlying dynamical process stationary. Another immediate effect of the breakdown of FDR in this case is the creation of a steady state instead of an equilibrium state in the long time limit.…”

“…As the presence of the cross-correlated noise changes the Langevin dynamics of the system, 38,51 it is expected that there may exist some additional effect of crosscorrelation on the escape rate of a metastable state. Study of this additional effect can perfectly serve as a motivation of our work presented in this paper.…”

“…Study of this additional effect can perfectly serve as a motivation of our work presented in this paper. To achieve this we extend our recently developed theoretical approach 38 to study the effect of multiplicative crosscorrelated noise on the escape rate from a metastable state. In this present study, the external fluctuation applied to the system under consideration is assumed to be independent of the system's characteristic dissipation.…”

Microscopic realization of cross-correlated noise processes

“…The study of nonlinear dynamical systems perturbed cross-correlated noises has become an attractive subject in recent years 14 . Correlated noise processes have made their presence felt in a wide range of studies, such as the statistical properties of a single mode laser 15 , bistable kinetics 16 , barrier crossing dynamics 17,18 , steady state entropy production 19 and noise induced transport 20 . Recent time, it is now well accepted that the effect of correlation between additive and multiplicative noise is indispensable in explaining phenomena such as phase transition, transport of motor protein and the presence of cross-correlated noises changes the dynamics of the system 21 .…”