Related papers: Moments, Equilibrium Equations and Mutual Distance…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…
Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed…
Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…
The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken about the electrostatic centroid and depending only on the…
A previous work introduced pair space, which is spanned by the center of mass of a system and the relative positions (pair positions) of its constituent bodies. Here, I show that in the $N$-body Newtonian problem, a configuration that does…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
In this paper, we introduce new generalized barycentric coordinates (coined as {\em moment coordinates}) on nonconvex quadrilaterals and convex hexahedra with planar faces. This work draws on recent advances in constructing interpolants to…
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
We demonstrate an approach to solving the coagulation equation that involves using a finite number of moments of the particle size distribution. This approach is particularly useful when only general properties of the distribution, and…
We study central configurations in the four body problem, i.e., configurations in which the forces on all the bodies point to a fixed, single point in space. The newly formulated pair-space formalism yields a set of vectorial equations that…
Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…
We investigate the impact of momentum-dependent relaxation time approximation in the Boltzmann equation within the Bjorken flow framework by analyzing the moments of the single-particle distribution function. The moment equations, which…
Irrotational dust solutions of Einstein's equations are suitable models to describe the general-relativistic aspects of the gravitational instability mechanism for the formation of cosmic structures. In this paper we study their state space…
We consider $n$-body problems given by potentials of the form ${\alpha\over r^a}+{\beta\over r^b}$ with $a,b,\alpha,\beta$ constants, $0\le a<b$. To analyze the dynamics of the problem, we first prove some properties related to central…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
This paper is concerned with the inelastic Boltzmann equation without angular cutoff. We work in the spatially homogeneous case. We establish the global-in-time existence of measure-valued solutions under the generic hard potential…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…