Related papers: Reconstructing double-well potentials from transit…
This survey offers an overview of recent advances in nonlocal phase transition problems, modeled by Ginzburg--Landau type energies of the form \[ \frac{1}{4}\iint_{\R^{2n}\setminus (\R^n \setminus \Omega)^2}…
We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid-solid…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…
Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of…
The Poincare's period of particle oscillations between wells is obtained in double-well potential. The dependencies of oscillation period on transmission coefficient on distance between levels are obtained. The cases of squared potentials…
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the…
We derive new duality relations that link the energy of configurations associated with a class of soft pair potentials to the corresponding energy of the dual (Fourier-transformed) potential. We apply them by showing how information about…
Motivated by solid-solid phase transitions in elastic thin films, we perform a Gamma-convergence analysis for a singularly perturbed energy describing second order phase transitions in a domain of vanishing thickness. Under a two-wells…
The double-layer potential plays an important r$\hat{\rm o}$le in solving boundary value problems of elliptic equations. Here, in this paper, we aim at introducing and investigating double layer potentials for a generalized bi-axially…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
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…
We propose a two-scale model to resolve essential features of developmental tissue deformations. The model couples individual cellular behavior to the mechanics at tissue scale. This is realized by a multiphase-field model addressing the…
We theoretically investigate the merging behaviour of two identical supersolids through dipolar Bose-Einstein condensates confined within a double-well potential. By adiabatically tuning the barrier height and the spacing between the two…
In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimensions, and we perform a simultaneous passage to…
We consider the interplay of linear double-well-potential (DWP) structures and nonlinear longrange interactions of different types, motivated by applications to nonlinear optics and matter waves. We find that, while the basic…
It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well, that highly complex behavior of the time evolution of a wave function is associated with the almost degeneracy of levels in the…
Bounded interactions are particularly important in soft-matter systems, such as colloids, microemulsions, and polymers. We derive new duality relations for a class of soft potentials, including three-body and higher-order functions, that…
We analyze the dynamics of the molecular field incoherently pumped by the photoassociation of fermionic atoms and coupled by quantum tunnelling in a double-well potential. The relative phase distribution of the molecular modes in each well…
In the quantum Hall regime, electronic correlations in double-layer two-dimensional electron systems are strong because the kinetic energy is quenched by Landau quantization. In this article we point out that these correlations are…
In quantum mechanics, asymptotic degeneracy is often considered in the context of a particle in a symmetric double-well potential, and is the phenomenon whereby pairs of energy levels come together to form doubly degenerate levels in…