Two-dimensional dynamics of a free molecular chain with a secondary structure

A simple two-dimensional ͑2D͒ model of an isolated (free) molecular chain with primary and secondary structures has been suggested and investigated both analytically and numerically. This model can be considered as the simplest generalization of the well-known Fermi-Pasta-Ulam model of an anharmonic chain in order to include transverse degrees of freedom of the chain molecules. Both the structures are provided by the first-and second-neighbor intermolecular bonds, respectively, resulting in a regular zig-zag (''2D helix'') chain on a plane. The set of two coupled nonlinear field equations with respect to the longitudinal and transverse displacements of the chain molecules has been derived. Two types of stable ͑nontopological͒ soliton solutions which describe either ͑i͒ a supersonic solitary wave of longitudinal stretching accompanied by transverse slendering or, as in the 1D model, ͑ii͒ supersonic pulses of longitudinal compression propagating together with localized transverse thickening (bulge) have been found. Some peculiar stability properties of these two-component soliton solutions have been discovered by using numerical techniques developed in this paper. ͓S1063-651X͑96͒10809-6

Soliton ratchets

The mechanism underlying the soliton ratchet, both in absence and in presence of noise, is investigated. We show the existence of an asymmetric internal mode on the soliton profile which couples, trough the damping in the system, to the soliton translational mode. Effective soliton transport is achieved when the internal mode and the external force are phase locked. We use as working model a generalized double sine-Gordon equation. The phenomenon is expected to be valid for generic soliton systems.Comment: 4 pages, 4 figure

Discrete breathers in polyethylene chain

The existence of discrete breathers (DBs), or intrinsic localized modes (localized periodic oscillations of transzigzag) is shown. In the localization region periodic contraction-extension of valence C-C bonds occurs which is accompanied by decrease-increase of valence angles. It is shown that the breathers present in thermalized chain and their contribution dependent on temperature has been revealed.Comment: 5 pages, 6 figure

On the nonlinear dynamics of topological solitons in DNA

Dynamics of topological solitons describing open states in the DNA double helix are studied in the frameworks of the model which takes into account asymmetry of the helix. It is shown that three types of topological solitons can occur in the DNA double chain. Interaction between the solitons, their interactions with the chain inhomogeneities and stability of the solitons with respect to thermal oscillations are investigated.Comment: 16 pages, 16 figure

Heat conduction in 1D lattices with on-site potential

The process of heat conduction in one-dimensional lattice with on-site potential is studied by means of numerical simulation. Using discrete Frenkel-Kontorova, $\phi$--4 and sinh-Gordon we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For models sin-Gordon and $\phi$--4 phonons are scattered at thermalized lattice of topological solitons; for sinh-Gordon and $\phi$--4 - models the phonons are scattered at localized high-frequency breathers (in the case of $\phi$--4 the scattering mechanism switches with the growth of the temperature).Comment: 26 pages, 18 figure

ХИРУРГИЧЕСКОЕ ЛЕЧЕНИЕ ДЕТЕЙ С НЕТРАВМАТИЧЕСКИМ ЗАСТАРЕЛЫМ АТЛАНТО-АКСИАЛЬНЫМ РОТАЦИОННЫМ БЛОКИРОВАНИЕМ

Atlanto-axial rotatory fixation (AORF) develops on the background of acute torticollis. Widely adopted terms such as C1 subluxation or atlantooccipital rotational subluxation do not reflect the core of this pathology and carry negative weight in the diagnostics and treatment of AORF. Retrospective analysis of the diagnostics and treatment outcome of 5 children with confirmed AORF diagnosis and literature review were performed. Clinical method, radiography and functional computer tomography were used to verify the diagnosis. De-rotational halo-traction and open correction with screw fixation were applied for treatment. Head position was managed to be improved in all patients. In one case the reduction was performed using correction in suboccipital segments and in other 4 cases the correction and fixation by Harms and de-rotational halo-traction allowed to correct torticollis. The pain syndrome had been arrested completely. Disease outcome resulted in formation of C1-C2 fibrous or bone fusion regardless the method of treatment. The patients with neglected AORF represent a great challenge for diagnostics and treatment. When conservative treatment fails it is necessary to involve de-rotational halo-traction with possible application of open reduction and posterior fusion. The purpose of treatment is to eliminate torticollis and pain using creation of proper C1-C2 alignment. The motions in atlantooccipital joint do not restore due to formation of the fibrous or bone fusion.Атланто-аксиальное ротационное блокирование (ААРБ) развивается на фоне синдрома острой кривошеи. Широко применяемые у нас термины «подвывих С1» или «атланто-аксиальный ротационный подвывих» не отражают сути данной патологии и вносят свою отрицательную лепту в диагностику и лечения ААРБ. Представлены ретроспективный анализ диагностики и результатов лечения 5 детей с подтвержденным диагнозом ААРБ, обзор литературы. Для подтверждения диагноза использовались клинический метод, рентгенография и функциональная компьютерная томография. В качестве методов лечения применялось деротационное halo-вытяжение, открытая коррекция с винтовой фиксацией. У всех пациентов удалось улучшить положение головы. В одном случае репозиция выполнена за счет коррекции в субаксиальных сегментах, у остальных 4 пациентов коррекция и фиксация по Harms и деротационное halo-вытяжение позволили устранить кривошею. Болевой синдром купирован полностью. Исходом заболевания вне зависимости от метода лечения являлось образование фиброзного или костного блока С1-С2. Пациенты с застарелым ААРБ представляют серьезную проблему для диагностики и лечения. При неэффективности консервативного лечения, необходимо перейти к деротационной halo-тракции с возможным использованием открытой коррекции и задней фиксации. Целью лечения является устранение кривошеи и болей за счет создания правильного соотношения С1-С2. Движения в атланто-аксиальном суставе не восстанавливаются из-за образования фиброзного или костного блока

Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

Peierls Instabilities in Quasi-One-Dimensional Quantum Double-Well Chains

Peierls-type instabilities in quarter-filled ($\bar{n}=1/2$) and half-filled ($\bar{n}=1$) quantum double-well hydrogen-bonded chain are investigated analytically in the framework of two-stage orientational-tunnelling model with additional inclusion of the interactions of protons with two different optical phonon branches. It is shown that when the energy of proton-phonon coupling becomes large, the system undergoes a transition to a various types of insulator states. The influence of two different transport amplitudes on ground states properties is studied. The results are compared with the pressure effect experimental investigations in superprotonic systems and hydrogen halides at low temperatures.Comment: 7 pages, RevTeX, 9 eps figure

Soliton ratchets induced by ac forces with harmonic mixing

The ratchet dynamics of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least bi-harmonic) of zero mean is studied. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point particle representation of the soliton. We find that first order perturbative calculations lead to incomplete descriptions, due to the important role played by the soliton-phonon interaction in establishing the phenomenon. The role played by the temporal symmetry of the system in establishing soliton ratchets is also emphasized. In particular, we show the existence of an asymmetric internal mode on the kink profile which couples to the kink translational mode through the damping in the system. Effective soliton transport is achieved when the internal mode and the external force get phase locked. We find that for kinks driven by bi-harmonic drivers consisting of the superposition of a fundamental driver with its first odd harmonic, the transport arises only due to this {\it internal mode} mechanism, while for bi-harmonic drivers with even harmonic superposition, also a point-particle contribution to the drift velocity is present. The phenomenon is robust enough to survive the presence of thermal noise in the system and can lead to several interesting physical applications.Comment: 9 pages, 13 figure