568 research outputs found
Dispersion of Waves in Relativistic Plasmas with Isotropic Particle Distributions
The dispersion laws of Langmuir and transverse waves are calculated in the
relativistic non-magnetized formalism for several isotropic particle
distributions: thermal, power-law, relativistic Lorentzian and hybrid
. For Langmuir waves the parameters of superluminal undamped, subluminal
damped principal and higher modes are determined for a range of distribution
parameters. The undamped and principal damped modes are found to match
smoothly. Principal damped and second damped modes are found not to match
smoothly. The presence of maximum wavenumber is discovered above that no
longitudinal modes formally exist. The higher damped modes are discovered to be
qualitatively different for thermal and certain non-thermal distributions.
Consistently with the known results, the Landau damping is calculated to be
stronger for non-thermal power-law-like distributions. The dispersion law is
obtained for the single undamped transverse mode. The analytic results for the
simplest distributions are provided.Comment: 8 pages, 12 figures, accepted by Physics of Plasma
Limit theorems for random point measures generated by cooperative sequential adsorption
We consider a finite sequence of random points in a finite domain of a
finite-dimensional Euclidean space. The points are sequentially allocated in
the domain according to a model of cooperative sequential adsorption. The main
peculiarity of the model is that the probability distribution of a point
depends on previously allocated points. We assume that the dependence vanishes
as the concentration of points tends to infinity. Under this assumption the law
of large numbers, the central limit theorem and Poisson approximation are
proved for the generated sequence of random point measures.Comment: 17 page
Stator current limiting in variable-frequency electrical drive with scalar control system
The problem of stator current limiting of asynchronous electrical drive under overload is reviewed. Task of research is stated. Mathematical model of simplest scalar control system with current limiter and results of mathematical modeling of electrical drives in stator limiting modes are included.Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ° ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΡ ΡΠΎΠΊΠ° ΡΡΠ°ΡΠΎΡΠ° Π°ΡΠΈΠ½Ρ
ΡΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΡΠΈΠ²ΠΎΠ΄Π° ΠΏΡΠΈ ΠΏΠ΅ΡΠ΅Π³ΡΡΠ·ΠΊΠ΅. ΠΠ°Π΅ΡΡΡ ΠΏΠΎΡΡΠ°Π½ΠΎΠ²ΠΊΠ° Π·Π°Π΄Π°ΡΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΏΡΠΎΡΡΠ΅ΠΉΡΠ΅ΠΉ ΡΠΊΠ°Π»ΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Ρ ΠΎΡΡΠ΅ΡΠΊΠΎΠΉ ΠΏΠΎ ΡΠΎΠΊΡ ΠΈ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² ΡΠ»Π΅ΠΊΡΡΠΎΠΏΡΠΈΠ²ΠΎΠ΄Π° Π² ΡΠ΅ΠΆΠΈΠΌΠ°Ρ
ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΡ ΡΠΎΠΊΠ° ΡΡΠ°ΡΠΎΡΠ°
Almost Periodic and Asymptotically Almost Periodic Solutions of LiΓ©nard Equations
The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the LiΒ΄enard equation
xβ²β² + f(x)xβ² + g(x) = F(t),
where F : T ! R (T = R+ or R) is an almost periodic or asymptotically almost periodic function and g : (a, b) ! R is a strictly decreasing function. We study also this problem for the vectorial LiΒ΄enard equation.
We analyze this problem in the framework of general non-autonomous dynamical systems (cocycles). We apply the general results obtained in our early papers [3, 7] to prove the existence of almost periodic (almost automorphic, recurrent, pseudo recurrent) and asymptotically almost periodic (asymptotically almost automorphic, asymptotically recurrent, asymptotically pseudo
recurrent) solutions of LiΒ΄enard equations (both scalar and vectorial)
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