Related papers: Two-well rigidity and multidimensional sharp-inter…
We address the fundamental difference between solid-solid and liquid-liquid phase transitions within the Ericksen's nonlinear elasticity paradigm. To highlight ideas, we consider the simplest nontrivial 2D problem and work with a…
We discuss some results related to a phase transition model in which the potential energy induced by a double-well function is balanced by a fractional elastic energy. In particular, we present asymptotic results (such as…
It is difficult to derive the solid--fluid transition from microscopic models. We introduce particle systems whose potentials do not decay with distance and calculate their partition function exactly using a method similar to that for…
The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models,…
We have derived and analyzed the wavefunctions and energy states for an asymmetric double quantum wells, broadened due to static interface disorder effects, within well known discreet variable representation approach for solving the…
The properties of the interface between solid and melt are key to solidification and melting, as the interfacial free energy introduces a kinetic barrier to phase transitions. This makes solidification happen below the melting temperature,…
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can…
A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to…
By developing a canonical approach that is exact, physically transparent and subtly different from standard methods, we present a systematic study with exact analytical calculations based on a Landau Level (LL) picture of the energetics of…
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…
We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…
We present a sharp-interface model of two-dimensional ramified growth during quasi-steady electrodeposition. Our model differs from previous modeling methods in that it includes the important effects of extended space-charge regions and…
A significant amount of attention was dedicated in recent years to the phenomenon of jamming of athermal amorphous solids by increasing the volume fraction of the microscopic constituents. At a critical value of the volume fraction,…
A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the…
We identify the $\Gamma$-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the phase transition thickness of the polymer phases approach zero. The limiting energy consists…
The solid-liquid interface free energy \gamma sl is a key parameter controlling nucleation and growth during solidification and other phenomena. There are intrinsic difficulties in obtaining accurate experimental values, and the previous…
By analyzing hot-wire velocity data taken in an open channel flow, an unambiguous definition of surface-layer thickness is here provided in terms of the cross-over scale between backward and forward energy fluxes. It is shown that the…
In this article we calculate the surface phase diagram of a two-dimensional hard-rod fluid confined between two hard lines. In a first stage we study the semi-infinite system consisting of an isotropic fluid in contact with a single hard…
We present a new phase-field model of solidification which allows efficient computations in the regime when interface kinetic effects dominate over capillary effects. The asymptotic analysis required to relate the parameters in the…