Related papers: Analytical solution for the long- and short-range …
We study the Euler Alignment system of collective behavior, equipped with `topological' interaction protocols, which were introduced to the mathematical literature by Shvydkoy and Tadmor. Interactions subject to these protocols may depend…
Recent advancements have demonstrated that fully Eulerian methods can effectively model frictionless contact between deformable solids. Unlike traditional Lagrangian approaches, which require contact detection and resolution algorithms, the…
The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields…
In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially…
We study theoretically layered spin systems where long-range dipolar interactions play a relevant role. By choosing a specific sample shape, we are able to reduce the complex Hamiltonian of the system to that of a much simpler coupled…
The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical…
Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with…
We investigate an opinion model consisting of a large group of interacting agents, whose opinions are represented as numbers in $[-1,1]$. At each update time, two random agents are selected, and the opinion of the first agent is updated…
Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of…
Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann-Lema\^itre-Robertson-Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered.…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their…
We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than…
This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…
The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…
We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schroedinger equation for fermionic many-particle systems in quantum mechanics. The method…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
We derive the effective potential for composite fields in a class of (quasi-) planar models with long-range interactions. This class of models can be relevant for high temperature superconductors and graphite. The fractal structure of the…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…