Related papers: Solution landscape of the Onsager model identifies…
The application of numerical techniques to the study of energy landscapes of large systems relies on sufficient sampling of the stationary points. Since the number of stationary points is believed to grow exponentially with system size, we…
The kinetic Ising model on a n-isotopic chain is considered in the framework of Glauber dynamics. The chain is composed of N segments with n sites, each one occupied by a different isotope. Due to the isotopic mass difference, the n spins…
Free energy landscapes encode the kinetics, intermediates, and transition states that govern molecular processes and are thus a key target of single biomolecule research. Typical approaches to deriving optimal, error-minimizing,…
There are many ways to generate a set of nodes on the sphere for use in a variety of problems in numerical analysis. We present a survey of quickly generated point sets on $\mathbb{S}^2$, examine their equidistribution properties,…
We describe a numerical study of the potential energy landscape for the two-dimensional XY model (with no disorder), considering up to 100 spins and CPU and GPU implementations of local optimization, focusing on minima and saddles of index…
We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value…
We investigate the emergence of finite-amplitude non-zonal flows on the sphere $\mathbb{S}^2$ arising from stationary solutions to the 2D Euler equations. By restricting the Laplace-Beltrami eigenspace to the invariant subspace of the…
This paper proposes a ridgeless kernel method for solving infinite-horizon, deterministic, continuous-time models in economic dynamics, formulated as systems of differential-algebraic equations with asymptotic boundary conditions (e.g.,…
We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any…
We develop an extended Onsager real-cavity framework to describe the Casimir-Polder interaction of small molecules dissolved in dielectric liquids near planar interfaces. By analytically resolving the geometry of the cavity opening, we…
We prove the existence of a ground state positive solution of Schr\"odinger-Poisson systems in the plane of the form $$ -\Delta u + V(x)u + \frac{\gamma}{2\pi} \left(\log|\cdot| \ast u^2 \right)u = b |u|^{p-2}u \qquad\text{in}\…
We study the 1D pressureless Euler-Poisson equations with variable background states and nonlocal velocity alignment. Our main focus is the phenomenon of critical thresholds, where subcritical initial data lead to global regularity, while…
Binary classification tasks with imbalanced classes pose significant challenges in machine learning. Traditional classifiers often struggle to accurately capture the characteristics of the minority class, resulting in biased models with…
We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…
We consider Backus's problem in geophysics. This consists in reconstructing a harmonic potential outside the Earth when the intensity of the related field is measured on the Earth's surface. Thus, the boundary condition is (severely)…
The structural dynamics of a biopolymer is governed by a process of diffusion through its conformational energy landscape. In pulling experiments using optical tweezers, features of the energy landscape can be extracted from the probability…
We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional…
A nonperturbative analytical description of the SU(2)_1 quantum critical point in an explicitly dimerized two-leg spin-1/2 Heisenberg ladder is presented. It is shown that this criticality essentially coincides with that emerging in a…
The Material Point Method (MPM) is a hybrid Eulerian-Lagrangian approach capable of simulating large deformation problems of history-dependent materials. While the MPM can represent complex and evolving material domains by using Lagrangian…
In this paper we explore the phase space structures governing isomerization dynamics on a potential energy surface with four wells and an index-2 saddle. For this model, we analyze the influence that coupling both degrees of freedom of the…