0000000000114782
AUTHOR
Andrejs Reinfelds
Numerical Simulation of the Problem Arising in the Gyrotron Theory
Numerical aspects for solving of certain problem arising in gyrotron theory are discussed. Particularly, finite-difference schemes using quasistationarization and method of lines were applied and the relevant results analyzed.
A nonstandard Volterra integral equation on time scales
Abstract This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.
Stability of impulsive differential systems
The asymptotic phase property and reduction principle for stability of a trivial solution is generalized to the case of the noninvertible impulsive differential equations in Banach spaces whose linear parts split into two parts and satisfy the condition of separation.
Asymptotic Equivalence of Difference Equations in Banach Space
Conjugacy technique is applied to analysis asymptotic equivalence of nonautonomous linear and semilinear difference equations in Banach space.
Numerical experiments with single mode gyrotron equations
Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process is described by the system of two complex differential equations: nonlinear first order ordinary differential equation with parameter (averaged equation of electron motion) and second order partial differential equation for high frequency field (RF field) in resonator (Schrödinger type equation for the wave amplitude). The stationary problem of the single mode gyrotron equation in short time interval with real initial conditions was numerically examined in our earlier work. In this paper we consider the stationary and nonstationary …
Non-Isothermal Mathematical Model of Wood and Paper Drying
A mathematical model of wood or paper drying based on a detailed consideration of both heat and moisture transport phenomena is proposed. By averaging we express the model as a sequence of initial value problems for systems of two first order nonlinear ordinary differential equations. This mathematical model makes it possible to efficiently investigate the drying process of a thin wood plate or paper sheet for varying temperature and humidity conditions in the surroundings. In particular, we have considered the optimization of the heat regime over a series of steam-heated cylinders in a papermaking machine.
Hyers-Ulam Stability of a Nonlinear Volterra Integral Equation on Time Scales
We study Hyers-Ulam stability of a nonlinear Volterra integral equation on unbounded time scales. Sufficient conditions are obtained based on the Banach fixed point theorem and Bielecki type norm.
On constrained Volterra cubic stochastic operators
We consider constrained Volterra cubic stochastic operators and construct several Lyapunov functions for the constrained Volterra cubic stochastic operators. We prove that such kind operators do no...
Dynamical equivalence of impulsive quasilinear equations
Abstract Using Green type map we can find sufficient conditions under which an impulsive quasilinear equation is dynamically equivalent to its corresponding linear equation. This result extends Grobman Hartman theorem for equations without ordinary dichotomy.
Analysis of equations arising in gyrotron theory
The gyrotron is a microwave source whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. Powerful gyrotrons can be used to heat nuclear fusion plasma. In addition, they have found a wide utility in plasma diagnostics, plasma chemistry, radars, extra-high-resolution spectroscopy, high-temperature processing of materials, medicine, etc. However, the main application of gyrotrons is in electron cyclotron resonance heating in tokamaks and stellarators. Equations describing gyrotron operation are ordinary differential equations and Schrödinger type partial differential equations. The present paper provides a survey of the analytical a…
Nonstationary oscillations in gyrotrons
The onset of stochastic oscillations in gyrotrons is studied by means of the self-consistent theory describing nonstationary processes. Complicated alternating sequences of regions of stationary, automodulation, and chaotic oscillations are found in the plane of the generalized gyrotron variables: cyclotron resonance mismatch and dimensionless current. The results of the investigations are important in connection with attempts to increase the output power of gyrotrons by raising the current.
Numerical investigations of single mode gyrotron equation
A stationary problem with the integral boundary condition arising in the mathematical modelling of a gyrotron is numerically investigated. The Chebyshev's polynomials of the second kind are used as the tool of calculations. The main result with physical meaning is the possibility to determine the maximal value of electrons efficiency. First published online: 14 Oct 2010