Related papers: Small oscillations of the pendulum, Euler's method…
We use the Liouville-von Neumann (LvN) approach to study the dynamics and the adiabaticity of a time-dependent driven anharmonic oscillator as an eample of non-equilibrium quantum dynamics. We show that the adiabaticity is minimally broken…
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
We consider the problem of finding the shortest possible period for an exactly periodic solution to some given autonomous ordinary differential equation. We show that, given a pair of Lyapunov-like observable functions defined over the…
The one-dimensional nonlinear oscillations of a magnet attached to a spring and interacting with a set of magnets are analyzed theoretically and experimentally. The equation of motion is solved numerically using the Euler method in a…
Using min-max inequality we investigate the existence of solutions and thier dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle…
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…
In a recent work Sideris constructed a finite-parameter family of compactly supported affine solutions to the three-dimensional isentropic compressible Euler equations satisfying the physical vacuum condition. The support of these solutions…
In this contribution, the relativistic quantum motions of the position-dependent mass (PDM) oscillator field with a scalar potential in the context of the Kaluza-Klein theory is investigated. Through a purely analytical analysis, the…
On a bounded smooth domain we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to the boundary of the domain. We derive global a priori bounds of the…
Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…
In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…
We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides,…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…
A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…
We investigate a class of fourth-order differential systems with instantaneous and non-instantaneous impulses. Our technical approach is mainly based on a variant of Clark's theorem without the global assumptions. Under locally subquadratic…
This paper investigates a two-dimensional Kemmer oscillator within relativistic quantum mechanics, incorporating minimal length and non-commutative phase space effects. We derive eigen solutions in configuration space $\{p\}$, examining the…
Far as we know there are not exact solutions to the equation of motion for a relativistic harmonic oscillator. In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is studied by…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We…