Two-Component Solitary Waves in Hydrogen-Bonded Molecular Systems

The dynamics of two-component solitary waves in hydrogen-bonded chains in an external force and damping is investigated. The influence of the motion and the optical mode of the heavy ion sublattice on the portion sublattice is discussed. It will increase the soliton width and decrease the soliton mobility. The general expression for the kink soliton soliton is obtained. The velocity, the mobility and conductivity of the kink soliton are calculated. The results are in good agreement with the experimental data.     

The inertia mode of uniformly driven kinks in damped multistable systems

Linear arrays of damped multistable systems in a constant driving fieldF are considered in the tight coupling limit. The existence of a localized relaxation mode (inertia mode) of the driven kinks is pointed out. This mode, whose frequency on the time scale of theL-system is a universal (model independent) quantity, describes the accomodation of the kink to a new shape and terminal velocity when the driving field is changed infinitestimally. In a chain without inertia the accommodation is instantaneous. Whence the name inertia mode (IM). The IM is generated by the translation invariance of the kink equation, in addition to the Goldstone mode (GM). In the absence of the driving force and dissipation, the IM becomes defectively degenerate with the GM and represents a pure algebraic mode of the free kink, describing another free kink moving with infinitesimally changed velocity.Work supported by the Swiss National Science Foundation.     

Kink velocity in nonstationary external fields for the sine-Gordon model with allowance for dissipation effects

With the help of energy analysis suggested by McLaughlin and Scott for the sine-Gordon equation, evolution of kink velocity modeling the propagation of a local conformational perturbation along the DNA molecule under the simultaneous action of dissipation effects and special nonstationary external fields is investigated. For a harmonically time-dependent external force, the kink velocity is characterized by oscillations about a rather monotonically decreasing trend expressed by an explicit analytical formula. The trend velocity coincides with the results of calculations of the kink velocity averaged over the period on different time intervals. Similar results are obtained for a nonstationary force in the form of a step function. A numerical analysis, in particular, demonstrates that the trend velocity changes its behavior for certain values of rectangular pulse duration. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 77–84, January, 2008.     

Criterion for the softening effect in crystalline materials under their doping

A dislocation model of the effect of softening (i.e., decrease in the microhardness or yield stress of the doped material as compared to the initial material) is developed. The motion of dislocations in metals with the body-centered cubic structure, semiconductors, and other materials in accordance with the kink mechanism is described taking into account the effect of impurity atoms creating the centers for benign generation of kink pairs and obstacles for propagation of kinks. The conditions under which the velocity of dislocations increases after the introduction of impurities are determined using the equation describing the kinetics of passage of dislocations through the Peierls barrier in the doped material.     

The study of stress induced effects on Mössbauer impurities forming the kink in dislocation in some crystals

The alternating external stress value required to move a dislocation together with Mössbauer impurities positioned at dislocation is calculated by using the kink model. The kinetic energy of the dislocation is calculated which leads to an energy shift in the γ-ray photon emitted by the atom moving with the dislocation. The critical stress values calculated at low temperatures are found to change with the mass and the Debye temperatures of the resonating atoms. The variation of mean square displacement, mean square velocity and the first moments for the Mössbauer impurity at low temperature are also evaluated. All the results are compared with the corresponding values obtained by using the string model.     

Dynamics of isolated twin boundary in (TMTSF)

Intermittent and irregular motion of isolated twin boundary (kink) in organic crystal (TMTSF)₂PF₆ was studied at room temperature. Both the local velocity and the time of intermission are determined not only by external stress and temperature but also by the time (t w) elapsed after the backward passage and before the following forward one. When the kink moves after longer t w, its velocity becomes smaller and the time of intermission longer. Both tend to saturate for t w longer than 10² s. This result indicates that some disorder is induced in the lattice by the backward motion and it is relaxed during t w. We also found that the effect of the backward motion of one kink on its following motion is equivalent quantitatively to that of the forward motion of the pair-created counterpart. Received: 14 April 1998 / Received in final form and Accepted: 1st September 1998     

Solitons molecules,lump and interaction solutions to a (2+1)-dimensional Sharma–Tasso–Olver–Burgers equation

Different resonance constraints enrich the behavior of soliton solutions. The soliton molecules, which are the bound states of solitons, can be set off by the velocity resonance. The lump waves, which are localized in all directions in space, are theoretically regarded as a limit form of soliton in some ways. In this paper, a (2+1)-dimensional Sharma–Tasso–Olver–Burgers (STOB) equation is investigated. Soliton (kink) molecule, half periodic kink(HPK) and HPK molecule are studied. Then the lump solution is obtained and the interactions between lump and kink molecule are discussed. The kink molecule-lump solutions exhibit a fusion phenomenon and a rogue (instanton) phenomenon, respectively.     

Kink dynamics in the highly discrete sine-Gordon system

We study kink dynamics in a very discrete sine-Gordon system where the kink width is of the order of the lattice spacing. Numerical simulations exhibit new properties of kinks in this case: they lose the memory of their initial velocity and propagate preferentially at well-defined velocities which correspond to quasi-steady states, while a kink moving at other velocities suffers relatively high rates of radiation of small amplitude oscillations. When a small external driving force is applied to the system, the same velocities appear as plateus in the strongly nonlinear mobility of the kink. The energy radiated by the kink is calculated for a simple model that preserves the discrete character of the system, and the preferential velocities for the kink are obtained to good accuracy. Similar results may be expected to be valid for other discrete systems manifesting topological solitons. The numerical simulations reveal also new stable “multiple-kink” excitations which can propagate almost freely in extremely discrete systems where “ordinary” simple kinks are pinned to the lattice by discreteness. The stability of the “multiple-kinks” is discussed.     

Comment on relativistic ideal soliton-gas approximations

We comment on the validity of using relativistic, ideal, Boltzmann-kink-gas phenomenology involving “bare” kinks for interpretation of experiments and molecular dynamics simulations. An improved velocity distribution is obtained for sine-Gordon and ?-four kink gases which incorporates the kink renormalization found to be essential in obtaining the correct total kink density. We argue, however, that even with this improvement, current ideal gas phenomenologies can only be trusted at low temperatures compared to the kink rest energy, where the majority of kinks have low velocity in any case.     

Twirling elastica: kinks, viscous drag, and torsional stress

Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state torsional stress and shape of a rotating rod with a kink. Drag deforms the rod, ultimately extending or folding it depending on the kink angle. For certain kink angles and kink locations, both states are possible at high rotation rates. The agreement between our macroscopic experiments and the theory is good, with no adjustable parameters.     

Dynamics of dislocation kink in the pinning center potential under influence of external forces

Dynamics of dislocation kink affected by external constant and variable forces in the pinning potential is considered for studying the point defects role in dislocation motion by the Peierls mechanism. Within the framework of perturbation theory, the linearization of equations of motion of the kink results in the linear oscillation equation for the kink velocity.     

托卡马克中宏观束-等离子体扭曲模不稳定性研究

本文主要研究了具有单一高能离子分量的托卡马克等离子体扭曲模宏观不稳定性。它基本上模拟了中性束平行注入经过电离和电荷交换后在本底等离子体中维持一个稳恒等离子体流的物理过程。高能和本底都用无碰撞的Vlasov等离子体,并取了低频、小拉莫尔半径极限。由于主要考虑束-等离子体无耗散宏观不稳定性,故可用能量原理来分析。结果表明,高能离子束对本底等离子体的外部模没有影响,只影响内部扭曲模的增长率和扰动振幅。对适当选择的速度剖面,束能够完全稳定体系n≥2,m=1模,与Dunlap线性理论结果相反而与目前实验观测一致。m/n=1/1内部扭曲模增长率在所取得模型下随注入能量β_b,注入功率P_bw,轴上安全因子q(0)和束速度的径向剖面分布参数S的不同而出现增稳、减稳及完全稳定的行为。适当选择S,在q(0)<0.924时,高能束能够稳定m/n=1/1模。 关键词：     

Approximately straight kink theories

A precise meaning is given to the idea of a kink theory approximating a vectoror vector-bundle-valued theory. It is shown that vector theories taking values in a vector bundle with groupSO(n- s,s;), acting naturally, do not approximate any kink theory. It is further shown that, where a kink theory is approximated by a vector bundle theory, the field equations in the vector theory can give rise to field equations in the kink theory. The theory of Skyrme and the sine-Gordon theory are of this form. An example is given of a nonlinear modification of electromagnetism having solitonlike solutions.     

Kink solutions of the classical transverse field Ising chain

We investigate stationary and travelling wave solutions of the classical one-dimensional transverse field Ising model. Results are given on the existence, shape and stability of kink solutions and periodic solutions. We review recent analytical results (e.g., the proof of existence of a one-parameter family of stationary kink solutions and the proof of existence of travelling wave kink solutions with nonzero velocity c≠ 0) and extend them by the use of numerical methods. Small oscillations arising in the tails of travelling kink solutions are investigated numerically. In the end, stability analysis puts some light on pinning effects. Received 23 February 2001 and Received in final form 4 October 2001     

铁电体中相界运动对压力的依赖性

在平均场理论的框架内研究了KNbO3 中的顺电—铁电相界在静水压的运动。纠缠解被用于不同压力下相界宽度和速度的计算。计算基于居里—外斯常数的实验数值和自由能的金兹堡—朗道展开式的参数。非经验性地研究了对静水压和三相点的响应。     

硅晶体中单个位错的运动

本文利用化学浸蚀方法,在400—900℃的温度范围内,在0.35—13kg·mm^{-2的应力条件下,测量了硅晶体中单个位错的运动速度。实验结果表明,位错运动速度V(τ,T)作为温度(T)和分解切应力(τ)的函数,满足如下方程:V(τ,T)=Aτme-Q/(KT)。式中m=1.02—1.49,Q=1.96—2.07eV。最后,把实验结果与扩展位错的弯结模型作了比较。 关键词：}     

Activated dynamics of semiflexible polymers on structured substrates

We study the thermally activated motion of semiflexible polymers in double-well potentials using field-theoretic methods. Shape, energy, and effective diffusion constant of kink excitations are calculated, and their dependence on the bending rigidity of the semiflexible polymer is determined. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. We consider both uniform and point-like driving forces. For the case of point-like forces the polymer crosses the potential barrier only if the force exceeds a critical value. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or of synthetic polyelectrolytes on structured substrates.     

Kink formation and motion in carbon nanotubes at high temperatures

We report that kink motion is a universal plastic deformation mode in all carbon nanotubes when being tensile loaded at high temperatures. The kink motion, observed inside a high-resolution transmission electron microscope, is reminiscent of dislocation motion in crystalline materials: namely, it dissociates and multiplies. The kinks are nucleated from vacancy creation and aggregation, and propagate in either a longitudinal or a spiral path along the nanotube walls. The kink motion is related to dislocation glide and climb influenced by external stress and high temperatures in carbon nanotubes.