相关论文: Chip-firing and energy minimization on M-matrices
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
A random polymer model is a one-dimensional Jacobi matrix randomly composed of two finite building blocks. If the two associated transfer matrices commute, the corresponding energy is called critical. Such critical energies appear in…
We introduce a uniform method of proof for the following results. For {\em each} of the following conditions, there are $2^{\aleph_0}$ families of Steiner systems, satisfying that condition: i) Theorem~2.2.4: (extending \cite{Chicoetal})…
The paper suggests a new stochastic model for energy producing, dispatching, and storing in the multi-battery setting that takes into account the topology of the system of the links between the batteries, the transmission and storage…
One-dimensional systems with topological order are intimately related to the appearance of zero-energy modes localized on their boundaries. The most common example is the Kitaev chain, which displays Majorana zero-energy modes and it is…
We consider Maxwell-Chern-Simons models involving different non-minimal coupling terms to a non relativistic massive scalar and further coupled to an external uniform background charge. We study how these models can be constrained to…
Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split…
We explore the minimum energy configurations of repelling particles distributed over n possible locations forming a toric grid. We conjecture that the most energy-efficient way to distribute n/2 particles over this space is to place them in…
We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that…
In this paper, results of investigations of the simplest mechanisms of a structure formation are presented. In frameworks of the suggested model the main attention was focused on such characteristics as wiring of the system, clusters…
We consider the spherical limit of multi-matrix models on regular target graphs, for instance single or multiple Potts models, or lattices of arbitrary dimension. We show, to all orders in the low temperature expansion, that when the degree…
We prove lower bounds for energy functionals of mappings from real, complex and quaternionic projective spaces to Riemannian manifolds. For real and complex projective spaces, these lower bounds are sharp, and we characterize the family of…
Relaxation phenomena in glasses can be related to jump processes between different minima of the potential energy in the configuration space. These transitions play a key role in the low temperature regime, giving rise to tunneling systems…
We explore the conjectured duality between a class of large $N$ matrix integrals, known as multicritical matrix integrals (MMI), and the series $(2m-1,2)$ of non-unitary minimal models on a fluctuating background. We match the critical…
We analyze the properties of a Lennard-Jones system at the level of the potential energy landscape. After an exhaustive investigation of the topological features of the landscape of the systems, obtained studying small size sample, we…
Non-perturbative limitations on low-energy effective field theories (EFTs) based on the characteristics of high-energy theory are provided by the analyticity of the flat-space version of the S-matrix. Although the analyticity of the…
This monograph is about discrete energy minimization for discrete graphical models. It considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem.…
This article deals with the problem of maximizing the production of a species for a chemical network by controlling the temperature. Under the so-called mass kinetics assumption the system can be modeled as a single-input control system…
Dynamical characterization of topological phases under quantum quench dynamics has been demonstrated as a powerful and efficient tool. Previous studies have been focused on systems of which the Hamiltonian consists of matrices that commute…
In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some preliminary background, namely, defining Port-Hamiltonian…