Related papers: Homogenization and phase separation with space dep…
We investigate the coupled dynamics of symmetry breaking and phase separation during quenches across the critical point in a first-order phase transition. Based on the Einstein-Maxwell-scalar theory, we construct a holographic superfluid…
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…
We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting liquid and crystal phases.…
We study first- and second-order phase transitions of ferromagnetic lattice models on scale-free networks, with a degree exponent $\gamma$. Using the example of the $q$-state Potts model we derive a general self-consistency relation within…
In order to study the possible phase conjugation of optical near-fields, it is necessary to go beyond the slowly varying envelope- and electric dipole approximations that are normally applied in phase conjugation studies where spatially…
Singularities in macroscopic systems at discontinuous phase transitions are replaced in finite systems by sharp but continuous changes. Both the energy differences between metastable and stable phases and the energy barriers separating…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
We use holography to study the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order thermal phase transition. We place the theory on a cylinder in a set of homogeneous, unstable initial states. The…
We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…
A multi-scale method for the hyperbolic systems governing sediment transport in subcritical case is developed. The scale separation of this problem is due to the fact that the sediment transport is much slower than flow velocity. We first…
Two parallel helical edge channels hosting interacting electrons, when proximitized by local and nonlocal pairings, can host time-reversal-invariant pairs of topological zero modes at the system corners. Here we show that realistic…
We describe the asymptotic behaviour of the minimal inhomogeneous two-capacity of small sets in the plane with respect to a fixed open set $\Omega$. This problem is governed by two small parameters: $\varepsilon$, the size of the inclusion…
Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated…
We study the wetting model, which considers a random walk constrained to remain above a hard wall, but with additional pinning potential for each contact with the wall. This model is known to exhibit a wetting phase transition, from a…
We consider an effective Hamiltonian description of critical wetting transitions in systems with short-range forces at a corrugated (periodic) wall. We are able to recover the results obtained previously from a `microscopic'…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…
We study the D3/probe D5 system with two domain wall hypermultiplets. The conformal symmetry can be broken by a magnetic field, B, (or running coupling) which promotes condensation of the fermions on each individual domain wall. Separation…
The aim of this paper is to investigate the asymptotic behavior of a biphase tumor fluid flow derived by 2-scale homogenisation techniques in recent works. This biphase fluid flow model accounts for the capillary wall permeability, and the…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a…