Breatherlike defects and their dynamics in the one-dimensional roll structure of twisted nematics

The dynamics of the nonsingular defects in the periodic structures of the rolls that appear in π/2-twisted nematic liquid crystals during electroconvection is studied experimentally and theoretically. The roll structures in twisted nematics are characterized by the presence of an axial component of the hydrodynamic flow velocity with opposite directions in neighboring rolls. The critical oscillation frequency of structural defects is quantitatively estimated using a nonlinear equation of motion for roll displacements. It is found that a pair of edge dislocations with topological charges of +1 and–1 nucleates and annihilates periodically during the oscillations of a defect with a nonsingular core. Oscillating defects with a zero topological charge is shown to correspond to the solution of the sine-Gordon equation in the form of standing breathers. Asymmetry is detected in the full oscillation cycle of a breather defect, and it is related to the twist symmetry of a twist nematic. This asymmetry is taken into account as effective anisotropic friction. The behavior of a breather on a trap, namely, a classical defect (dislocation), is investigated. Dislocation motion is shown to be anisotropic in the oscillation cycle: in one direction, a dislocation moves regularly; in the second phase, the transition into the initial state proceeds via the decay of the breather into a dipole pair of dislocations of opposite signs followed by their annihilation.     

Breathers in the one-dimensional roll structure of twisted nematics

The dynamics of nonsingular defects has been studied experimentally and theoretically in the periodic roll structures arising at electroconvection in nematic liquid crystals twisted by π/2. The presence of an axial component of the velocity of the hydrodynamic flow with the opposite direction in the neighboring rolls is characteristic of roll structures in twisted nematics. The quantitative estimates of the critical frequency of the oscillations of structural defects have been obtained on the basis of the nonlinear equation of motion for the roll displacement. It has been found that the periodic creation and annihilation of a pair of edge dislocations with the topological indices +1 and −1 occur in the process of oscillations of a defect with a nonsingular nucleus. It has been demonstrated that oscillating defects with zero topological indices correspond to the solution of the sine-Gordon equation in the form of standing breathers.     

Structure and dynamics of the Frenkel-Kontorova dislocations in electroconvection in liquid crystals

The Frenkel-Kontorova instability is studied in a 1D lattice of domains formed during electroconvection in nematic liquid crystals twisted by π/2. It is found that generation of defects by such instability can be observed in this model medium. Among other things, it is shown that several types of defects with singular and nonsingular cores, as well as with a extended core, are formed in the 1D domain structure above the electroconvective instability threshold. The extended cores of dislocations are dissociated into a line, and the entire structure is isomorphic to two partial dislocations spaced by a certain distance, which are not observed in free form. Defects with a nonsingular core (zero topological index) exist owing to spiral hydrodynamic flows in convective rolls and are not observed in layers with a homogeneous orientation of molecules. It is shown that the formation of both types of defects follows the scenario of decay of dislocations with extended cores via detachment of nonsingular defects (i.e., discretely); as a result, a dislocation with a singular core is left. “Breather” defects, which are the result of periodic creation and annihilation of dislocations with a topological index of ±1, are also observed. The effect of defects on the transition from the 1D to 2D structures is considered.     

Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of mobile breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a “symmetry breaking” can be observed, which we show to be an numerical artifact.     

Nonlinear dynamics of breathers in the spiral structures of magnets

The structure and properties of pulsating solitons (breathers) in the spiral structures of magnets are analyzed within the sine-Gordon model. The breather core pulsations are shown to be accompanied by local shifts and oscillations of the spiral structure with the formation of “precursors” and “tails” in the moving soliton. The possibilities for the observation and excitation of breathers in the spiral structures of magnets and multiferroics are discussed.     

Statistical mechanics of composite particles: I. General formulation using a projection technique for the fixed ion plasma model

This paper is concerned with the Statistical Mechanics of an hydrogenic plasma with randomly fixed ions. Starting from the “physical” problem we introduce an “ideal” problem (with an enlarged state space); the latter is defined in such a way that its dynamical evolution leads to the dynamical evolution of the former by means of a projection technique. The interesting features of the “ideal” problem are to be simpler than the “physical” one (usual commutation relations for the “ideal” creation and annihilation operators) and to have a two-particle hamiltonian (instead of an infinite number of particle-operators as in all previous works).     

Discrete nonlinear Schrödinger breathers in a phonon bath

We study the dynamics of the discrete nonlinear Schr?dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather. Received 21 January 1999 and Received in final form 20 September 1999     

Discrete moving breather collisions in a Klein-Gordon chain of oscillators

We study the collisions of moving breathers with the same frequency, traveling with opposite directions within a Klein-Gordon chain of oscillators. Two types of collisions have been analyzed: symmetric and non-symmetric, head-on collisions. For low enough frequency the outcome is strongly dependent of the dynamical states of the two colliding breathers just before the collision. For symmetric collisions, several results can be observed: breather generation, with the formation of a trapped breather and two new moving breathers; breather reflection; generation of two new moving breathers; and breather fusion bringing about a trapped breather. For non-symmetric collisions some possible results are: breather generation, with the formation of three new moving breathers; breather fusion, originating a new moving breather; breather trapping with breather reflection; generation of two new moving breathers; and two new moving breathers traveling as a bound state. Breather annihilation has never been observed.     

Three-dimensional simulation of irregular dynamics of topological solitons in moving magnetic domain walls

A three-dimensional computer simulation of dynamic processes occurring in a domain wall moving in a soft-magnetic uniaxial film with in-plane anisotropy has been performed based on the micromagnetic approach. It has been shown that the domain wall motion is accompanied by topological transformations of the magnetization distribution, or, more specifically, by “fast” processes associated with the creation and annihilation of vortices, antivortices, and singular (Bloch) points. The method used for visualizing the topological structure of magnetization distributions is based on the numerical determination of topological charges of two types by means of the integration over the contours and surfaces with variable geometry. The obtained data indicate that the choice of the initial configuration predetermines the dynamic scenario of topological transformations.     

Strongly interacting parton matter equilibration

We study the kinetic and chemical equilibration in “infinite” parton matter within the Parton-Hadron-String Dynamics transport approach. The “infinite” matter is simulated within a cubic box with periodic boundary conditions initialized at different energy densities. Particle abundances, kinetic energy distributions, and the detailed balance of the off-shell quarks and gluons in the strongly-interacting quarkgluon plasma are addressed and discussed.     

Neutral and charged quommutators with and without symmetries

We present two sets of qualgebras involving operators which generalize creation and annihilation operators. These two groups of operators satisfy separately quommutation relations rather than commutation or anticommutation relations. The quommutators of the creation and annihilation operators generate new “neutral operators” which themselves are subjected to quommutation relations. Two solutions are presented. In the second one, some new symmetry relations are added to the system. In a certain sense these extra relations, rather than imposing new constraints on the parameters, increase their freedom.     

The sine-gordon breather as a moving oscillator in the sense of de broglie

The breather solution of the sine-Gordon equation represents an extended oscillator moving as a whole with constant velocity. We investigate the properties of the breather solution in the context of de Broglie's basic concept of “moving oscillator”, which led to quantum mechanics. We show that the momentum of the breather is proportional to its wave vector, and its total energy is proportional to the oscillator frequency.     

Recombination of close frenkel defects in gold

The occurrence of close-vacancy-interstitial-pairs in electron-irradiated gold and the annealing temperature of this type of defect have been investigated by means of “sub-threshold” irradiations. Different samples have been irradiated with 3 MeV electrons at five different temperatures between 7.5°K and 36°K. These samples containing Frenkel defects have then been irradiated at 12°K with 1.2 MeV electrons. This energy is less than the threshold for defect production. During the sub-threshold irradiation, defect annihilation rates have been measured which depend strongly on the temperature at which the defects had been produced. For 7.5°K and 12°K they are of the same order of magnitude as were found in Al, Cu, Pt, and Ta, and were ascribed to recombination of closevacancy-interstitial-pairs. For defects produced at 22°K the annihilation rate is smaller by one order of magnitude and even smaller for defects produced at still higher temperatures. It is concluded from this that close-pairs become thermally unstable in gold between 12 and 22°K.     

On symmetric breather collisions in lattices with saturable nonlinearity

Symmetric collisions of two discrete breathers in the lattice with saturable nonlinearity are investigated. The strong correlation of the collision properties and the parameters of colliding breathers (power, velocity, and phase difference), lattice parameters and position of the collision point is found. This is related to the internal structure of the colliding breathers and energy exchange with the phonon background. The type of collision changes from elastic to the inelastic (the breathers merging, multi-bounce interactions, breather creation etc.) with the increasing of the colliding breather power. Collision of high power breathers always results in the breather fusion. The elastic and inelastic collisions are related to the periodic and quasi-periodic colliding breathers, respectively.     

Dynamics of localized waves with large amplitude in a weakly dispersive medium with a quadratic and positive cubic nonlinearity

The dynamics of localized waves is analyzed in the framework of a model described by the Korteweg-de Vries (KdV) equation with account made for the cubic positive nonlinearity (the Gardner equation). In particular, the interaction process of two solitons is considered, and the dynamics of a “breathing” wave packet (a breather) is discussed. It is shown that solitons of the same polarity interact as in the case of the Korteweg-de Vries equation or modified Korteweg-de Vries equation, whereas the interaction of solitons of different polarity is qualitatively different from the classical case. An example of “unpredictable” behavior of the breather of the Gardner equation is discussed.     

Multibreather solitons in the diffraction managed NLS equation

We study analytically and numerically localized breather solutions in the averaged discrete nonlinear Schrödinger equation (NLS) with diffraction management, a system that models coupled waveguide arrays with periodic diffraction management geometries. Localized breathers can be characterized as constrained critical points of the Hamiltonian of the averaged diffraction managed NLS. In addition to local extrema, we find numerically more general solutions that are saddle points of the constrained Hamiltonian. An interesting class of saddle points are “multi-bump” solutions that are close to superpositions of translates of simpler breathers. In the case of zero residual diffraction and small diffraction management, the existence of multibumps can be shown rigorously by a continuation argument.     

An approximate method of predicting the response of periodically supported beams subjected to random convected loading

The space-averaged response of an infinite, elastically supported, periodic beam subjected to convected random loading has been studied by using an approximate “assumed mode” method. The complex wave motion in the beam is represented by any number of suitably chosen complex modes. With a good, yet simple, choice of mode which satisfies certain boundary conditions on one periodic beam element, a “single mode approximation” can yield very accurate values of the average response. This has been verified for a wide range of the support stiffnesses and loading convection velocities. Consideration has also been given to the ratio of the maximum response in the beam to the space-averaged response. The method has been applied only to uniform beams in this paper, but it should be readily applicable to periodic systems consisting of non-uniform beam elements.     

分子空位缺陷对环三亚甲基三硝胺含能材料几何结构、电子结构及振动特性的影响

含能材料中的微观缺陷是导致“热点”形成并相继引发爆轰的重要因素. 然而, 由于目前人们对材料内部微观缺陷的认识不足, 限制了对含能材料中“热点”形成微观机理的理解, 进而阻碍了含能材料的发展和应用. 为了洞悉含能材料内部微观缺陷特性及探索缺陷引发“热点”的形成机理, 利用第一性原理方法研究了分子空位缺陷对环三亚甲基三硝胺(RDX) 含能材料的几何结构、电子结构及振动特性的影响, 探讨了微观缺陷对初始“热点”形成的基本机理. 采用周期性模型分析了分子空位缺陷对RDX几何结构、电子能带结构、电子态密度及前线分子轨道的影响. 采用团簇模型分析了分子空位缺陷对RDX振动特性的影响. 结果发现, 分子空位缺陷的存在使其附近的N–N键变长, 分子结构变得松弛; 使导带中很多简并的能级发生分离, 电子态密度减小, 并使由N-2p和O-2p轨道形成的导带底和价带顶均向费米面方向移动, 降低了能带隙值, 增加了体系活性. 前线分子轨道及红外振动光谱的计算分析表明, 分子缺陷使最高已占分子轨道电荷主要集中在缺陷附近的分子上, 且分子中C–H键和N–N键能减弱. 这些特性表明, 分子空位缺陷的存在使体系能带隙变小, 并使缺陷附近的分子结构松弛, 电荷分布增多, 反应活性增强; 在外界能量激发下, 缺陷附近分子将变得不稳定, 分子中的C–H键或N–N键较易先发生断裂, 发生化学反应释放能量, 进而成为形成“热点”的根源.