Related papers: Divide and Conquer: A Distributed Approach to Five…
This paper deals with the variational analysis, for every $s \in (0,1)$ and $p \in [1,+\infty)$, of $(s,p)$-Gagliardo seminorms in a periodic setting. First, we consider the space of $L^p$, $T$-periodic functions and define the energy…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
We suggest an iterative quantum protocol, allowing to solve optimization problems with a glassy energy landscape. It is based on a periodic cycling around the tricritical point of the many-body localization transition. This ensures that…
We study an optimal M-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between solutions to this problem and least-energy sign-changing…
We describe a global optimization technique using `basin-hopping' in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features which recent work…
First we argue in an informal, qualitative way that it is natural to enlarge space-time to five dimensions to be able to solve the problem of elementary particle masses. Several criteria are developed for the success of this program.…
A new approach is proposed for finding the "best cut" in a hierarchy of partitions by energy minimization. Said energy must be "climbing" i.e. it must be hierarchically and scale increasing. It encompasses separable energies and those…
The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set $\Omega \subset \mathbb R^3$ with given volume A that minimizes the sum of its surface area…
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $\mathbb{S}^2$-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of…
An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at…
We consider the problem of rigorously computing periodic minimizers to the Ohta-Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds on the distance between our numerical approximations and the…
SSP reductions are a type of polynomial reductions that also preserve the solutions of the instances. This means there is a mapping from each solution in the original instance to one in the reduced instance, allowing direct deduction of an…
The difficulty in exploring potential energy surfaces, which are nonconvex, stems from the presence of many local minima, typically separated by high barriers and often disconnected in configurational space. We obtain the global minimum on…
The multiple point principle, according to which several vacuum states with the same energy density exist, is put forward as a fine-tuning mechanism predicting the ratio between the fundamental and electroweak scales in the Standard Model…
X(5) is a paradigm for the structure at the critical point of a particular first-order phase transition for which the intrinsic energy surface has two degenerate minima separated by a low barrier. For a finite system, we show that the…
We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely…
The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this…
For the 2D Euler equations and related models of geophysical flows, minima of energy--Casimir variational problems are stable steady states of the equations (Arnol'd theorems). The same variational problems also describe sets of statistical…
We establish sufficient conditions for a function on the torus to be equal to its Steiner symmetrization and apply the result to volume-constrained minimizers of the Cahn-Hilliard energy. We also show how two-point rearrangements can be…
We consider the two-dimensional nonlinear Schr\"{o}dinger equation with a white noise potential, described by the Anderson hamiltonian. After define the corresponding energy space via the paracontrolled distribution framework from singular…