Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by homogeneous linear differential equations that produce only oscillating terms. Here we extend quantum simulation algorithms to general inhomogeneous linear differential equations, which can include exponential terms as well as oscillating terms in their...

Domain wall type solution with oscillating thickness in a real, scalar field model is investigated with the help of a polynomial approximation. We propose a simple extension of the polynomial approximation method. In this approach we calculate higher order corrections to the planar domain wall solution, find that the domain wall with oscillating thickness radiates, and compute dumping of oscill...

The Higgs effective potential with temperature corrections is considered and different cases of scalar field symmetry state are discussed within gauge theories of gravity. It is shown that nonsingular oscillating solutions of cosmological equations exist for this model. PACS: 04.50, 98.80Cq

The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point t∗ and fast oscillating behavior after the point t∗. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve-1 equation and some elliptic equation with constant coefficient...

The non-singular, oscillating Friedman cosmology within the framework of General Relativity is considered. The general oscillatory solution given in terms of elliptic functions and the conditions for its existence are discussed. It is shown that the wall-like-matter and the small, but negative cosmological constant are required for oscillations. The oscillations can , in principle, be deep enou...

This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a fourier series analysis of the RayleighPlesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillations of a single bubble. This is used in the approximate solution of the oscillating wall problem and the re...

This paper deals with a design of a cost-effective protection circuits for a new developed high-power self-oscillating converter. The proposed solution provides a simple way to protect the converter and converterpowered circuits from the damage caused by possible fault modes of operation. It covers three typical failure events – short circuit at the output, overloading and overheating of the co...

oscillating reactions are one of the most interesting topics in chemistry and analytical chemistry. fluctuations in concentrations of one the reacting species (usually a reaction intermediate) create an oscillating chemical reaction. in oscillating systems, the reaction is far from thermodynamic equilibrium. in these systems, at least one autocatalytic step is required. developing an instinctiv...

This talk concerns numerical approximations of oscillating patterns in reaction-diffusion systems. Stability analysis on a test reactiondiffusion system with oscillating solution allows comparisons in terms of stability regions and stepsize restrictions of some time integrators. Moreover, a dissipation and dispersion analysis are also carried out, see [1]. We consider the well known and commonl...