Related papers: Exactly solvable dynamical models with a minimal l…
We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…
We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicability that allow, among others, to replace in a canonical way…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
We present an analogy between natural oscillations of the standing wave type on a pool of liquid with an interface and a mechanical oscillator model. It is shown that the equations of motion governing both systems have qualitatively similar…
Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and…
We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…
In this work, the dynamics of the deformed one-dimensional harmonic oscillator with minimal length uncertainty is examined and the analytical solutions for time evolution of position and momentum operators are presented in which the rough…
Kramers problem for a dimer in a bistable piecewise linear potential is studied in the presence of correlated noise processes. The distribution of first passage times from one minima to the basin of attraction of the other minima is found…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose we consider the motion of a particle subjected to dry friction and coloured noise. The finite correlation time…
A new model of oscillators was suggested, in which an oscillating particle in the minimum energy state has a nonzero velocity. A system consisting of a point material particle and a scalar field described by the nonlinear Klein-Gordon…
Motion of a point particle sliding on a turntable is studied. The equations of motion are derived assuming that the table exerts frictional force on the particle, which is of constant magnitude and directed opposite to the direction of…
One dimensional systems are under intense investigation, both from theoretical and experimental points of view, since they have rather peculiar characteristics which are of both conceptual and technological interest. We analyze the…
History-dependent maximum static friction is investigated using simple models with two and three particles in one-dimensional periodic potentials. In some situations, these systems possess two values of the maximum static friction, with…
We consider the classical evolution of a lattice of non-linear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale $\ell_{nl}$, symmetry principles, causality and scaling arguments. Causality implies that the asymptotic linear-elastic fields…
Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…
Within the standard Lagrangian settings (i.e., the difference between kinetic and potential energies), we discuss and report isochronicity, linearizability and exact solubility of some $n$-dimensional nonlinear position-dependent mass (PDM)…