共查询到20条相似文献,搜索用时 109 毫秒
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G. A. Tirskiy 《Doklady Physics》2017,62(12):560-563
We have obtained an analytical solution of two simultaneous ordinary differential equations of the physical theory of meteors: the equation of motion for the center of mass of a meteoroid (deceleration equation), the thermal balance equation (ablation equation), the luminosity equation, and the ionization trail equation. The solution has been obtained by assuming a straight-line trajectory and a power-law dependence of the ablation parameter on the meteoroid velocity for an arbitrary atmosphere in the continuous flow regime. 相似文献
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The motion of the center of a soliton in a trap with oscillating walls is studied analytically and numerically for the case in which the intrinsic frequency of small soliton oscillations in the equilibrium state considerably exceeds the frequency of wall oscillations. this problem can be solved either by applying the gross–pitaevskii equation, which most exactly describes the behavior of the soliton in the trap, or by using the approximate, “mechanical,” equation of motion of the newtonian type for the center of the soliton. an approximate analytical solution of the mechanical equation is obtained and is compared with the numerical solution of the newton equation, while the latter solution is compared with the numerical solution of the gross–pitaevskii equation. good agreement between the first two solutions is revealed. it is also shown that there is a range of parameters in which the numerical solutions of the newton and gross–pitaevskii equations are closest to each other. the frequency-sweeping effect of soliton center oscillations is revealed. an approximate analytical formula for the limiting frequency of these oscillations is obtained and the numerical analysis of this phenomenon is performed. 相似文献
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We consider a generalized Kac equation without cutoff, with which we associate a non-standard nonlinear stochastic differential
equation. We adapt the techniques in Bichteler and Jacod [2] to prove that the law of a solution of the stochastic differential
equation has a density, which is a solution of the Kac equation. The initial law is very general: we only assume it has second
order moments and is not the Dirac mass at 0. We thus generalize the analytical results of existence of a solution of this
equation. If we furthermore assume existence of all moments for the initial law, we obtain as a corollary using the proof
in Desvillettes [6] that the density is smooth. We prove a slightly better regularity result under more stringent assumptions
using the stochastic calculus of variations, adapting the methods in [1].
Received: 15 July 1998 / Accepted: 4 March 1999 相似文献
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Within the framework of a Boltzmann-Lorentz equation, we analyze the dynamics of a granular rotor immersed in a bath of thermalized particles in the presence of a frictional torque on the axis. In numerical simulations of the equation, we observe two scaling regimes at low and high bath temperatures. In the large friction limit, we obtain the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation. In the limit of large rotor mass and small friction, we derive a Fokker-Planck equation for which the exact solution is also obtained. 相似文献
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In this paper, the generalized Langevin equation introduced by Kubo and Mori is formulated as a random integral equation. We consider (1) the existence and uniqueness of the solution, (2) moments of the solution process, (3) a comparison theorem for solution processes, and (4) the Cauchy polygonal approximation to the solution. 相似文献
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An asymptotic solving method for the periodic solution of a class of disturbed nonlinear evolution equation
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<正>A class of disturbed evolution equation is considered using a simple and valid technique.We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation.Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method.We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis. 相似文献
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Ricardo Cordero-Soto Raquel M. Lopez Erwin Suazo Sergei K. Suslov 《Letters in Mathematical Physics》2008,84(2-3):159-178
We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schrödinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schrödinger equation and some special and limiting cases are outlined. 相似文献
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E. Momoniat 《Physica A》2008,387(11):2427-2432
We consider a linear constant coefficient diffusion equation with a mixed derivative term that exhibits the same statistical properties as the phenomenological diffusion equation. The solution of this diffusion equation represents the time evolution of a probability distribution with oscillating tails. 相似文献
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P. Podio-Guidugli G. Tomassetti 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(2):191-198
A new derivation is presented of Walker's exact solution to Gilbert equation, a solution which mimicks the travelling-wave
motion of a flat domain wall at 180°. It is shown that a process during which the working of the applied magnetic field exactly compensates dissipation (the Walker
condition) exists both under the constitutive circumstances considered in the standard Gilbert equation and when either the
internal free-energy or the dissipation, or both, are generalized by the introduction of higher-gradient terms; but that such
a process cannot solve the generalized Gilbert equation. It is also shown that, when dry-friction dissipation is considered
and a suitable magnetic field is applied, the associated Gilbert equation has a Walker-type solution mimicking a flat wall,
at 90° this time, which however does not satisfy the Walker condition.
Received 16 November 2001 相似文献
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In this paper, Lie symmetry is investigated for a new integrable
coupled Korteweg--de Vries (KdV) equation system. Using some symmetry
subalgebra of the equation system, we obtain five types of the
significant similarity reductions. Abundant solutions of the coupled
KdV equation system, such as the solitary wave solution, exponential
solution, rational solution and polynomial solution, etc. are
obtained from the reduced equations. Especially, one type of
group-invariant solution of reduced equations can be acquired by
means of the Painlev\'e I transcendent function. 相似文献
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建立圆柱体任意两个截面间的一般黏弹性转动力学方程,讨论了相对转角的稳定性,由于此方程为变系数的二阶线性的非齐次常微分方程组,没有统一的求解方法.因此,针对其中的一类黏弹性系数求得其解.
关键词:
变系数方程的解
相对转角
稳定性 相似文献
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We present a solution of the dither equation in a ring laser gyro. This solution is based on an application of Floquet theory to the linear equation derived from the original dither equation. The circumvention of the zero locking band as well as the appearance of higher order locking zones are discussed. 相似文献
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介绍了回归分析计算原理,LINEST(known_y’s,known_x’s,const,stats)语法。通过补加一组方程,Excel回归分析可解多元线性方程,列举了解多元线性方程实例。 相似文献
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利用同伦映射方法研究了一类广义Sine-Gordon方程. 首先引入一个同伦变换. 然后构造了原方程解的迭代关系式. 最后得到了问题的解析解.
关键词:
孤子
扰动
同伦映射 相似文献