相关论文: Two-dimensional collisions and conservation of mom…
We study how different types of blow-ups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blow-ups can…
We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss…
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…
Global transverse-momentum conservation induces correlations between any number of particles, which contribute in particular to the two- and three-particle correlations measured in heavy-ion collisions. These correlations are examined in…
QCD is the accepted (that is, the effective) theory of the strong interaction; studies at colliders are no longer designed to establish this. Such studies can now be divided into two categories. The first involves the identification of…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
We examined the asymmetric deformation in collisions and the transition conditions from oblique to normal collisions and non-collisions to address the problem of oblique collisions of rigid bodies in classical mechanics. A closed solution…
Granular systems present surprisingly complicated dynamics. In particular, nonlinear interactions and energy dissipation play important roles in these dynamics. Usually, constant coefficients of restitution are introduced phenomenologically…
We study polar molecule scattering in quasi-one-dimensional geometries. Elastic and reactive collision rates are computed as a function of collision energy and electric dipole moment for different confinement strengths. The numerical…
A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects.
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…
To operate reactively in uncertain environments, robots need to be able to quickly estimate the risk that they will collide with their environment. This ability is important for both planning (to ensure that plans maintain acceptable levels…
The border-collision normal form is a piecewise-linear family of continuous maps that describe the dynamics near border-collision bifurcations. Most prior studies assume each piece of the normal form is invertible, as is generic from an…
It has recently become possible to form molecules in ultracold gases of trapped alkali metal atoms. Once formed, the molecules may undergo elastic, inelastic and reactive collisions. Inelastic and reactive collisions are particularly…
The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a…
In some cases, it is possible to show the conservation of energy by using equations of motion in mechanics. By considering these results, some people can think that the conservation of energy is the result of equations of motion or Newton's…
We introduce the concept of kinetic equations representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries,…
The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…
The collision of two D-dimensional, ultra-relativistic particles, described in General Relativity as Aichelberg-Sexl shock waves, is inelastic. In first order perturbation theory, the fraction of the initial centre of mass energy radiated…