共查询到20条相似文献,搜索用时 15 毫秒
1.
Robinson JC 《Chaos (Woodbury, N.Y.)》1995,5(1):330-345
Dissipative partial differential equations have applications throughout the sciences: models of turbulence in fluids, chemical reactions, and morphogenesis in biology can all be written in a general form which allows them to be subjected to a unified analysis. Recent results on these equations show that in many cases they are not as complex as they initially appear, and can be converted into a set of ordinary differential equations. However, most of the relevant references present a bewildering array of terms which can obscure the simple underlying ideas. The main purpose of this paper is to introduce this terminology, motivated by several major results, slowly and by example. Detailed proofs are omitted, but it is hoped that this approach will give a good understanding of and intuitive feel for the subject without recourse to technicalities. Nevertheless, sufficient mathematical detail is included to allow application of these results to many examples. (c) 1995 American Institute of Physics. 相似文献
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Giovanni Riela 《Physics letters. A》1982,91(5):203-204
Numerical evidence is reported on the loss of differentiability of the flow on invariant tori near their disappearance in a dissipative dynamical system. 相似文献
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We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations. 相似文献
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《Physics letters. A》1999,259(2):135-139
Exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobi's elliptic function. The induced differential-difference equations are related to some soliton systems. 相似文献
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Here cell population dynamics in which there is simultaneous proliferation and maturation is considered. The resulting mathematical model is a nonlinear first-order partial differential equation for the cell density u(t,x) in which there is retardation in both temporal (t) and maturation variables (x), and contains three parameters. The solution behavior depends on the initial function varphi(x) and a three component parameter vector P=(delta,lambda,r). For strictly positive initial functions, varphi(0) greater, similar 0, there are three homogeneous solutions of biological (i.e., non-negative) importance: a trivial solution u(t) identical with 0, a positive stationary solution u(st), and a time periodic solution u(p)(t). For varphi(0)=0 there are a number of different solution types depending on P: the trivial solution u(t), a spatially inhomogeneous stationary solution u(nh)(x), a spatially homogeneous singular solution u(s), a traveling wave solution u(tw)(t,x), slow traveling waves u(stw)(t,x), and slow traveling chaotic waves u(scw)(t,x). The regions of parameter space in which these solutions exist and are locally stable are delineated and studied. 相似文献
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Krauss G Fehrenbacher D Brida D Riek C Sell A Huber R Leitenstorfer A 《Optics letters》2011,36(4):540-542
A passively phase-locked laser source based on compact femtosecond Er:fiber technology is introduced. The carrier-envelope offset frequency is set to zero via difference frequency generation between a soliton at a wavelength of 2?μm and a dispersive wave at 860?nm generated in the same highly nonlinear fiber. This process results in a broadband output centered at 1.55?μm. Subsequently, the 40?MHz pulse train seeds a second Er:fiber amplifier, which boosts the pulse energy up to 8?nJ at a duration of 125?fs. Excellent phase stability is demonstrated via f-to-2f spectral interferometry. 相似文献
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《Physics letters. A》1986,118(1):17-21
We study two bifurcations which, because of the piecewise linear nature of the system under consideration, occur at the same parameter value. The three orbits created in this compound bifurcation are the principal periodic orbits of a homoclinic bifurcation seen in the system. 相似文献
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《Physica D: Nonlinear Phenomena》2001,148(3-4):183-200
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K. Le Hur 《Annals of Physics》2008,323(9):2208-2240
The concept of entanglement entropy appears in multiple contexts, from black hole physics to quantum information theory, where it measures the entanglement of quantum states. We investigate the entanglement entropy in a simple model, the spin-boson model, which describes a qubit (two-level system) interacting with a collection of harmonic oscillators that models the environment responsible for decoherence and dissipation. The entanglement entropy allows to make a precise unification between entanglement of the spin with its environment, decoherence, and quantum phase transitions. We derive exact analytical results which are confirmed by Numerical Renormalization Group arguments both for an ohmic and a subohmic bosonic bath. The entanglement entropy obeys universal scalings. We make comparisons with entanglement properties in the quantum Ising model and in the Dicke model. We also emphasize the possibility of measuring this entropy using charge qubits subject to electromagnetic noise; such measurements would provide an empirical proof of the existence of entanglement entropy. 相似文献
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A. V. Fedin A. V. Gavrilov M. N. Ershkov S. N. Smetanin S. A. Solokhin 《Bulletin of the Russian Academy of Sciences: Physics》2012,76(6):637-642
The conditions leading to control over phase-locked oscillation in a set of three loop lasers containing self-pumped phase-conjugate gain-grating mirrors by using a LiF: F 2 ? passive Q-switch are studied both experimentally and theoretically. Cases of spatially uniform lamp pumping and high-efficiency spatially nonuniform transverse diode pumping are considered. 相似文献
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从质点系的牛顿动力学方程出发,引入系统的高阶速度能量,导出完整力学系统的高阶Lagrange方程、高阶Nielsen方程以及高阶Appell方程,并证明了完整系统三种形式的高阶运动微分方程是等价的.结果表明,完整系统高阶运动微分方程揭示了系统运动状态的改变与力的各阶变化率之间的联系,这是牛顿动力学方程以及传统分析力学方程不能直接反映的.因此,完整系统高阶运动微分方程是对牛顿动力学方程及传统Lagrange方程、Nielsen方程、Appell方程等二阶运动微分方程的进一步补充.
关键词:
高阶速度能量
高阶Lagrange方程
高阶 Nielsen方程
高阶Appell方程 相似文献
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Lie symmetry and conserved quantity of a system of first-order differential equations 总被引:5,自引:0,他引:5
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This paper focuses on studying the Lie symmetry and a conserved quantity of
a system of first-order differential equations. The determining equations of
the Lie symmetry for a system of first-order differential equations, from
which a kind of conserved quantity is deduced, are presented. And their
general conclusion is applied to a Hamilton system, a Birkhoff system and a
generalized Hamilton system. Two examples are given to illustrate
the application of the results. 相似文献
18.
Temperature effect on dissipative holographicscreening-photovoltaic solitons in a biased dissipative system
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In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic (DHSP) solitons. The results reveal that, the evolution and the self-deflection of the bright and dark DHSP solitons are influenced by the system temperature. At a given temperature, for a stable DHSP soliton originally formed in the dissipative system, it attempts to evolve into another DHSP soliton when the temperature change is appropriately small, whereas it will become unstable or break down if the temperature departure is large enough. Moreover, the self-deflection degree of the solitary beam centre increases as temperature rises in some range, while it is decided by the system parameters and is slight under small-signal condition. The system temperature can be adjusted to change the formation and the self-deflection of the solitary beam in order to gain certain optical ends. In a word, the system temperature plays a role for the DHSP solitons in the dissipative system. 相似文献
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Bifurcations of the complex homoclinic loops of an equilibrium saddle point in a Hamiltonian dynamical system with two degrees of freedom are studied. It arises to pick out the stationary solutions in a system of two coupled nonlinear Schrodinger equations. Their relation to bifurcations of hyperbolic and elliptic periodic orbits at the saddle level is studied for varying structural parameters of the system. Series of complex loops are described whose existence is related to periodic orbits. 相似文献
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A dissipative spin system, which is also considered to be a model for optical fluorescence, is investigated from the viewpoint of Brownian motion of spins. The most probable path and the fluctuations are determined by the quantum mechanical version of the system size expansion method. For the most probable path, the flow lines as well as the time evolutions are obtained exactly. This system exhibits a sort of nonequilibrium phase transition as the strength of an external field exceeds the dissipation. The fluctuations show unusual behaviour associated with the Volterra-like oscillations above threshold. 相似文献