Related papers: Mass Segregation Phenomena using the Hamiltonian M…
We consider the long-term evolution of an inhomogeneous long-range interacting $N$-body system. Placing ourselves in the dynamically hot limit, i.e. neglecting collective effects, we derive a large deviation principle for the system's…
(Abridged) The dynamical ejection of stars from star clusters affects the shape of the stellar mass function (MF) in these clusters, because the escape probability of a star depends on its mass. The objective of this paper is to provide and…
Despite significant efforts in the recent years, the physical processes responsible for the formation of passive galaxies through cosmic time remain unclear. The shape and evolution of the Stellar Mass Function (SMF) give an insight into…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
Non-equilibrium Markov State Modeling (MSM) has recently been proposed [Phys. Rev. E 94, 053001 (2016)] as a possible route to construct a physical theory of sliding friction from a long steady state atomistic simulation: the approach…
We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable…
We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider…
For noncooperative games the mean field (MF) methodology provides decentralized strategies which yield Nash equilibria for large population systems in the asymptotic limit of an infinite (mass) population. The MF control laws use only the…
We consider the out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model, by focusing in particular on the properties of single-particle diffusion. As we shall here demonstrate analytically, if the autocorrelation of momenta in…
Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory,…
We consider the covariant Lyapunov vectors (CLV) of a high-dimensional Hamiltonian flow in the case of long range potential, namely the Hamiltonian Mean Field (HMF) problem, by studying the behavior of the Lyapunov spectra and the…
Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behaviour, however, typically assume that groups…
We study the d-HMF model proposed by Atenas and Curilef, a mean field model with long-range interactions inspired by the dipole-dipole interaction. Among the challenges of this thesis is: the resolution of the d-HMF model in the canonical…
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…
Recent analyses of mass segregation diagnostics in star forming regions invite a comparison with the output of hydrodynamic simulations of star formation. In this work we investigate the state of mass segregation of 'stars' (i.e. sink…
We investigate the evolution of young star clusters using N-body simulations. We confirm that subvirial and fractal-structured clusters will dynamically mass segregate on a short timescale (within 0.5 Myr). We adopt a modified…
Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the…
After reviewing some basic relevant properties of stationary stochastic processes (SSP), we discuss the properties of the so-called Harrison-Zeldovich like spectra of mass density perturbations. These correlations are a fundamental feature…
We propose a novel method for numerical modeling of spatially inhomogeneous moment dynamics of populations with nonlocal dispersal and competition in continuous space. It is based on analytically solvable decompositions of the time…
Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…