Related papers: Two-dimensional collisions and conservation of mom…

This paper analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODEs with constant coeffcients. The novel part of this research is that the…

This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…

Using simple models in D=0+0 and D=0+1 dimensions we construct partition functions and compute two-point correlations. The exact result is compared with saddle-point approximation and solutions of Schwinger-Dyson equations. When integrals…

This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…

We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These…

Particle correlations are very actively studied in heavy-ion collisions at ultra-relativistic energies. Here, an attempt is made at determining a proper reference for such studies, by taking properly into account the multiparticle…

Many systems in biology, physics, and engineering are modeled by nonlinear dynamical systems where the states are usually unknown and only a subset of the state variables can be physically measured. Can we understand the full system from…

We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension…

We consider two particles of spin-1/2 interacting with a one-dimensional N-spin array, which is an exactly solvable model. The dynamics of entanglement and quantum discord (QD) of the spins of the two particles is investigated by regarding…

Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…

Almost nothing is known about the layer structure of solutions to strongly coupled systems of convection-diffusion equations in two dimensions. In some special cases we present first results.

An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows…

The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…

This paper explores how competing interactions in the intermolecular potential of fluids affect their structural transitions. This study employs a versatile potential model with a hard core followed by two constant steps, representing wells…

Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…

Reinforcement learning can enable complex, adaptive behavior to be learned automatically for autonomous robotic platforms. However, practical deployment of reinforcement learning methods must contend with the fact that the training process…

Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the $2D$ conformal algebra. In the case…

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite…

The static friction between crystalline surfaces separated by a molecularly thin layer of adsorbed molecules is calculated using molecular dynamics simulations. These molecules naturally lead to a finite static friction that is consistent…

Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasi-geostrophic…