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The internal dynamics of strongly interacting systems and that of biomolecules such as proteins display several important analogies, despite the huge difference in their characteristic energy and length scales. For example, in all such…
Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can…
Reinforcement learning algorithms commonly seek to optimize policies for solving one particular task. How should we explore an unknown dynamical system such that the estimated model globally approximates the dynamics and allows us to solve…
In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific…
Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…
The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their…
In this short note we sketch the statistical physics framework of the replica exchange technique when applied to molecular dynamics simulations. In particular, we draw attention to generalized move sets that allow a variety of optimizations…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
Modeling how human moves in the space is useful for policy-making in transportation, public safety, and public health. Human movements can be viewed as a dynamic process that human transits between states (\eg, locations) over time. In the…
The goal of this paper is to provide a survey and application-focused atlas of collective behavior coordination algorithms for multi-agent systems. We survey the general family of collective behavior algorithms for multi-agent systems and…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
We derive an expression for the local transverse polarization of a boost-invariant expanding system of massive particles, which involves a set of dynamical spin moments. Starting from spin kinetic theory, we obtain a closed set of equations…
LAMMPS is a widely popular classical Molecular Dynamics package. It was designed for materials modeling but it is well prepared for simulations in Soft Matter. The use packages like LAMMPS has advantages and disadvantages. The main…
We review existing approaches to mathematical modeling and analysis of multi-agent systems in which complex collective behavior arises out of local interactions between many simple agents. Though the behavior of an individual agent can be…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
We survey recent results on controlled particle systems. The control aspect introduces new challenges in the discussion of properties and suitable mean field limits. Some of the aspects are highlighted in a detailed discussion of a…
Molecular dynamics (MD) has become a powerful tool for studying biophysical systems, due to increasing computational power and availability of software. Although MD has made many contributions to better understanding these complex…
A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule,…
In this paper we propose an approach to build a decision support system that can help emergency planners and responders to detect and manage emergency situations. The internal mechanism of the system is independent from the treated…