Related papers: Two-dimensional collisions and conservation of mom…
We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios…
The constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at…
The phase space of hadron collider events spans hundreds of dimensions, generating an intricate geometry that we are just starting to explore. The number of possible new physics signals is exponential in the number of dimensions and…
The self-force problem---which asks how self-interaction affects a body's motion---has been poorly studied for spacetime dimensions $d \neq 4$. We remedy this for all $d \geq 3$ by nonperturbatively constructing momenta such that forces and…
The purpose of the present study is to extend the simple concept of apparent coefficient of restitution, widely approached in the literature for the case of a single-contact-point between a sphere and a wall, to the case of bouncing whose…
In this paper, we investigate collision orbits of two identical bodies placed on the surface of a two-dimensional sphere and interacting via an attracting potential of the form $V(q)=-\cot(q)$, where $q$ is the angle formed by the position…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
A survey of linearized cosmological fluid equations with a number of different matter components is made. To begin with, the one-component case is reconsidered to illustrate some important mathematical and physical points rarely discussed…
In a general setting of a Hamiltonian system with two degrees of freedom and assuming some properties for the undergoing potential, we study the dynamics close and tending to a singularity of the system which in models of $N$-body problems…
We investigate elastic, inelastic, and coalescent collisions between two-dimensional flat-top solitons supported by the cubic-quintic nonlinear Schr\"odinger equation. Numerical simulations reveal distinct collision regimes ranging from…
We consider the motion of a finite though large number $N$ of hard spheres in the whole space $\mathbb{R}^n$. Particles move freely until they experience elastic collisions. We use our recent theory of Compensated Integrability in order to…
For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and…
Motivated by evidence for the existence of dark matter, many new physics models predict the pair production of new particles, followed by the decays into two invisible particles, leading to a momentum imbalance in the visible system. For…
We aim to create deterministic collisions between orbiting bodies by applying a time-dependent external force to one or both bodies, whether the bodies are mutually repulsive, as in the two- or multi-electron atomic case or mutually…
We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a…
At time zero, there are $N$ identical point particles in the line (1D) which are characterized by their positions and velocities. Both values are given randomly and independently from each other, with arbitrary probability densities. Each…
A kinetic model with flexible velocities is presented for solving the multi-component Euler equations. The model employs a two-velocity formulation in 1D and a three-velocity formulation in 2D. In 2D, the velocities are aligned with the…
Onset of double-component convection due to different boundary conditions is studied in a diversely oriented infinite slot with broken reflection symmetry between the slot conditions for a component. Among other outcomes, the broken…
This paper deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent…
This letter investigates the motion control problem of two mobile robots under allowable collisions. Here, the allowable collisions mean that the collisions do not damage the mobile robots. The occurrence of the collisions is discussed and…