Related papers: Skier and loop-the-loop with friction
The paper is devoted to the study of a singularly perturbed fractional Schr\"{o}dinger equations involving critical frequency and critical growth in the presence of a magnetic field. By using variational methods, we obtain the existence of…
We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking…
We derive the kinetic equations for both the covariant and equal-time Wigner functions of Dirac particles with electromagnetic, scalar and pseudoscalar interactions. We emphasize the constraint equations for the spinor components in the…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
We introduce an algorithm for the solution of a system of radial Schr\"odinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations…
We obtain the geometric phase for states of a particle in a spherical infinite potential well with a moving wall in two different cases; First, when the radius of the well increases (or decreases) monotonically. Second, when the radius…
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…
A relativistic particle in an attractive Coulomb field as well as a static and spherically symmetric gravitational field is studied. The gravitational field is treated perturbatively and the energy levels are obtained for both spin 0…
Ideal carving occurs when a snowboarder or skier, equipped with a snowboard or carving skis, describes a perfect carved turn in which the edges of the ski alone, not the ski surface, describe the trajectory followed by the skier, without…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the…
A new quantum mechanical wave equation describing a particle with frictional forces is derived. It depends on a parameter $\alpha$ whose range is determined by the coefficient of friction $\gamma$, that is, $0 \leq \alpha \leq \gamma$. For…
The paper concludes the cycle of investigations on the bifurcation diagrams of the system with three degrees of freedom which describes the motion of an axially symmetric top with the Kowalevski conditions in a double force field. The…
Beam tracking software for accelerators typically falls into two categories: fast envelope simulations limited to linear beam optics, and slower multiparticle simulations that can model nonlinear effects. To find a middle ground between…
The finite duration of collisions appear as time-nonlocality in the kinetic equation. Analyzing the corresponding quantum kinetic equation for dense interacting Fermi systems a delay differential equation is obtained which combines time…
Kinetic equations are analyzed for thermal degradation of polymers. The governing relations are based on the fragmentation-annihilation concept. Explicit solutions to these equations are derived in two particular cases of interest. For…
Sliding cable system with frictions is encountered in many engineering applications. Such system is typically characterized by existences of complex and varied motion states of different sliding nodes (pulleys), which leads to significant…
In this note we analyse the equations of motion of a minimally coupled Rarita-Schwinger field near the horizon of an anti-de Sitter-Schwarzschild geometry. We find that at special complex values of the frequency and momentum there exist two…
In this note we introduce a hierarchy of phase spaces for static friction, which give a graphical way to systematically quantify the directional dependence in static friction via subregions of the phase spaces. We experimentally plot these…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…