Related papers: Computing Naturally in the Billiard Ball Model
Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries…
We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and…
Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for…
A class of Hamiltonian impact systems exhibiting smooth near integrable behavior is presented. The underlying unperturbed model investigated is an integrable, separable, 2 degrees of freedom mechanical impact system with effectively bounded…
The MM principle is a device for creating optimization algorithms satisfying the ascent or descent property. The current survey emphasizes the role of the MM principle in nonlinear programming. For smooth functions, one can construct an…
Decades of hardware, methodological, and algorithmic development have propelled molecular dynamics (MD) simulations to the forefront of materials-modeling techniques, bridging the gap between electronic-structure theory and continuum…
Non-smooth and non-convex global optimization poses significant challenges across various applications, where standard gradient-based methods often struggle. We propose the Ball-Proximal Point Method, Broximal Point Method, or Ball Point…
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…
The binary Monte Carlo (MC) collision algorithm is a standard and robust method to include binary Coulomb collision effects in particle-in-cell (PIC) simulations of plasmas. Here, we show that the coupling between PIC and MC algorithms can…
In this work, the Immersed Boundary Method (IBM) with feedback forcing introduced by Goldstein et al. (1993) and often referred in the literature as the Virtual Boundary Method (VBM), is addressed. The VBM has been extensively applied both…
Matchgates are a group of two-qubit gates associated with free fermions. They are classically simulatable if restricted to act between nearest neighbors on a one-dimensional chain, but become universal for quantum computation with…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes…
We study finite two dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape. We show that such systems can be quantum simulated by…
Seemingly identical Bulk Metallic Glasses (BMG) often exhibit strikingly different mechanical properties despite having the same composition and fictive temperature. A postulated mechanism underlying these differences is the presence of…
Molecular dynamics (MD) is a powerful and popular tool for understanding the dynamical evolution of materials at the nano and mesoscopic scales. There are various flavors of MD ranging from the high fidelity albeit computationally expensive…
A collision model (CM) is a framework to describe open quantum dynamics. In its {\it memoryless} version, it models the reservoir $\mathcal R$ as consisting of a large collection of elementary ancillas: the dynamics of the open system…
We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
In many applications involving spatial point patterns, we find evidence of inhibition or repulsion. The most commonly used class of models for such settings are the Gibbs point processes. A recent alternative, at least to the statistical…