相关论文: Minimality via second variation for microphase sep…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional…
We study the two-dimensional two-component Coulomb gas in the canonical ensemble and at inverse temperature $\beta>2$. In this regime, the partition function diverges and the interaction needs to be cut off at a length scale $\lambda\in…
Microphase separation in polymeric systems provides a bottom-up strategy to fabricate nanostructures. Polymers that are reported to undergo microphase separation usually include block copolymers or polyelectrolytes. Neutral homopolymers,…
We study phase diagrams of a class of doped quantum dimer models on the square lattice with ground-state wave functions whose amplitudes have the form of the Gibbs weights of a classical doped dimer model. In this dimer model, parallel…
The mobility of two interacting particles in a random potential is studied, using the sensitivity of their levels to a change of boundary conditions. The delocalization in Hilbert space induced by the interaction of the two particle Fock…
We establish lower semicontinuity results for perimeter functionals with measure data on $\mathbb{R}^n$ and deduce the existence of minimizers to these functionals with Dirichlet boundary conditions, obstacles, or volume-constraints. In…
We derive the dual variational principle (principle of minimal complementary energy) for the nonlocal nonlinear scalar diffusion problem, which may be viewed as the nonlocal version of the $p$-Laplacian operator. We establish existence and…
We present a theoretical framework based on second quantization in Liouville space to treat open quantum systems. We consider an ensemble of identical quantum emitters characterized by a discrete set of quantum states. The second…
In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…
We investigate the influence of confinement on phase separation in colloid-polymer mixtures. To describe the particle interactions, the colloid-polymer model of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] is used. Grand canonical…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed number of point vortices appear in the small energy regime;…
In a real system the heating is nonuniform and a second-order phase transition into a broken symmetry phase occurs by propagation of the temperature front. Two parameters, the cooling rate $\tau_Q$ and the velocity $v_T$ of the transition…
Numerically minimizing a continuous free-energy functional which yields several modulated phases, we obtain the order-parameter profiles and interfacial free energies of symmetric and non-symmetric tilt boundaries within the lamellar phase,…
The spectral problem for an infinite periodic medium perturbed by a compact defect is considered. For a high contrast small $\ve$-size periodicity and a finite size defect we consider the critical $\ve^2$-scaling for the contrast. We employ…
We study the finite temperature properties of quantum magnets close to a continuous quantum phase transition between two distinct valence bond solid phases in two spatial dimension. Previous work has shown that such a second order quantum…
We study random copolymers consisted of two kinds of monomers with attraction between similar kinds. The mean field analysis of this system indicates a continuous phase transition into a phase with periodic microdomain structure. It is…
The microscopic eikonal phase shifts with its first and second corrections for pi nucleus collision are calculated by using the expression previously derived for the local Kisslinger potential. A physical description to different forms of…
Dielectric relaxation in disordered dielectric mixtures are presented by emphasizing the interfacial polarization. The obtained results coincide with and cause confusion with those of the low frequency dispersion behavior. The considered…