Related papers: Gaussian theory for spatially distributed self-pro…
The effective action formalism of quantum field theory is used to study the properties of the non-relativistic interacting Bose gas. The Gaussian approximation is formulated by calculating the effective action to the first order of the…
The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\mathbb{R}^n$ so that data points projected onto $E$ follow a non-gaussian distribution. Although this is an appropriate model…
We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a…
We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the…
We show that in driven systems the Gaussian nature of the fluctuating force and time-reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the…
Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…
Optimization methods are essential in solving complex problems across various domains. In this research paper, we introduce a novel optimization method called Gaussian Crunching Search (GCS). Inspired by the behaviour of particles in a…
We consider a stochastic $N$-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [2], we show that the propagation of chaos does…
The transport of coupled self-propelled particles with colored noise and potential is investigated. Large translational motion noise intensity is good for the transport in $-x$ direction, but large self-correlation time of translational…
We propose a method to obtain the equilibrium distribution for positions and velocities of a one-dimensional particle via time-averaging and Laplace transformations. We apply it to the case of a damped harmonic oscillator in contact with a…
An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
A fundamental problem in plasma physics, space science, and astrophysics is the transport of energetic particles interacting with stochastic magnetic fields. In particular the motion of particles across a large scale magnetic field is…
We perform large-scale molecular dynamics simulations to study heated granular fluids in three dimensions. Granular particles dissipate their kinetic energy due to solid frictional interaction with other particles. The velocity of each…
Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's…
In this work we investigate the collective behavior of self-propelled particles that deform due to local pairwise interactions. We demonstrate that this deformation alone can induce alignment of the velocity vectors. The onset of collective…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
For homogeneous initial conditions, Hartree (gaussian) dynamical approximations are known to have problems with thermalization, because of insufficient scattering. We attempt to improve on this by writing an arbitrary density matrix as a…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…