Biomedical subjects

Y Zolotaryuk

Publications and source records attributed to Y Zolotaryuk.

11 recordsLinked to original sources

PubMed2004

Discrete kink dynamics in hydrogen-bonded chains: the two-component model.

We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion-proton interaction in the hydrogen bond, (ii) a harmonic coupling between the protons in adjacent hydrogen bonds, and (iii) a harmonic coupling between the nearest-neighbor heavy ions (an isolated diatomic chain with the lowest acoustic band) or instead a harmonic on-site potential for the heavy ions (a diatomic chain subject to a substrate with two optical bands), both providing a bistability of the hydrogen-bonded proton. Exact two-component (kink and antikink) discrete solutions for these models are found numerically. We compare the soliton solutions and their properties in both the one- (when the heavy ions are fixed) and two-component models. The effect of stability switchings, discovered previously for a class of one-component kink-bearing models, is shown to exist in these two-component models as well. However, the presence of the second component, i.e., the softness of the heavy-ion sublattice, brings principal differences, like a significant difference in the stability switchings behavior for the kinks and the antikinks. Water-filled carbon nanotubes are briefly discussed as possible realistic systems, where topological discrete (anti)kink states might exist.

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PubMed2004

Ratchetlike dynamics of fluxons in annular Josephson junctions driven by biharmonic microwave fields.

Experimental observation of the unidirectional motion of a topological soliton driven by a biharmonic ac force of zero mean is reported. The observation is made by measuring the current-voltage characteristics for a fluxon trapped in an annular Josephson junction that was placed into a microwave field. The dependence of the fluxon mean velocity at zero dc bias versus the phase shift between the first and second harmonic of the driving force is in qualitative agreement with theoretical expectations.

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PubMed2003

Discrete breathers in classical ferromagnetic lattices with easy-plane anisotropy.

Discrete breathers (nonlinear localized modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. This paper is devoted to the investigation of a classical d-dimensional ferromagnetic lattice with easy plane anisotropy. Its dynamics is described via the Heisenberg model. Discrete breathers exist in such a model and represent excitations with locally tilted magnetization. They possess energy thresholds and have no analogs in the continuum limit. We are going to review the previous results on such solutions and also to report new results. Among the new results we show the existence of a big variety of these breather solutions, depending on the respective orientation of the tilted spins. Floquet stability analysis has been used to classify the stable solutions depending on their spatial structure, their frequency, and other system parameters, such as exchange interaction and local (single-ion) anisotropy.

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PubMed2002

Discrete kink dynamics in hydrogen-bonded chains: 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 the 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 traveling-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).

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PubMed2002

Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response.

We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system.

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PubMed2002

Broken symmetries and directed collective energy transport in spatially extended systems.

We study the appearance of directed energy current in homogeneous spatially extended systems coupled to a heat bath in the presence of an external ac field E(t). The systems are described by nonlinear field equations. By making use of a symmetry analysis, we predict the right choice of E(t) and obtain directed energy transport for systems with a nonzero topological charge Q. We demonstrate that the symmetry properties of motion of topological solitons (kinks and antikinks) are equivalent to the ones for the energy current. Numerical simulations confirm the predictions of the symmetry analysis and, moreover, show that the directed energy current drastically increases as the dissipation parameter alpha reduces.

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PubMed2001

Ratchet due to broken friction symmetry.

A ratchet mechanism that occurs due to asymmetric dependence of the friction of a moving system on its velocity or a driving force is reported. For this kind of ratchet, instead of a particle moving in a periodic potential, the dynamics of which have broken space-time symmetry, the system must be provided with some internal structure realizing such a velocity- or force-friction dependence. For demonstration of a ratchet mechanism of this type, an experimental setup (gadget) that converts longitudinal oscillating or fluctuating motion into a unidirectional rotation has been built and experiments with it have been carried out. In this device, an asymmetry of friction dependence on an applied force appears, resulting in rectification of rotary motion. In experiments, our setup is observed to rotate only in one direction, which is in accordance with given theoretical arguments. Despite the setup being three dimensional, the ratchet rotary motion is proved to be described by one dynamical equation. This kind of motion is a result of the interplay of friction and inertia. We also consider a case with viscous friction, which is irrelevant to this gadget, but it can be a possible mechanism of rotary unidirectional motion of some swimming organisms in a liquid.

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PubMed2001

Breathers in Josephson junction ladders: resonances and electromagnetic wave spectroscopy.

We present a theoretical study of the resonant interaction between dynamical localized states (discrete breathers) and linear electromagnetic excitations (EE's) in Josephson junction ladders. By making use of direct numerical simulations we find that such an interaction manifests itself by resonant steps and various sharp switchings (voltage jumps) in the current-voltage characteristics. Moreover, the power of ac oscillations away from the breather center (the breather tail) displays singularities as the externally applied dc bias decreases. All these features may be mapped to the spectrum of EE's that has been derived analytically and numerically. Using an improved analysis of the breather tail, a spectroscopy of the EE's is developed. The nature of breather instability driven by localized EE's is established.

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PubMed2000

Directed current due to broken time-space symmetry

We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U(X) = U(X+2pi) under the influence of a time-periodic space-homogeneous external field E(t) = E(t+T). If E(t) is neither a symmetric function of t nor antisymmetric under time shifts E(t+/-T/2) not equal-E(t), an ensemble of trajectories with zero current at t = 0 yields a nonzero finite current as t-->infinity. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.

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PubMed2000

Observation of breathers in Josephson ladders.

We report on the observation of spatially localized excitations in a ladder of small Josephson junctions. The excitations are whirling states which persist under a spatially homogeneous force due to the bias current. These states of the ladder are visualized using a low temperature scanning laser microscopy. We also compute breather solutions with high accuracy in corresponding model equations. The stability analysis of these solutions is used to interpret the measured patterns in the I-V characteristics.

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PubMed1999

Moving lattice kinks and pulses: an inverse method.

We develop a general mapping from given kink or pulse shaped traveling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping-by definition an inverse method-to acoustic solitons in chains with nonlinear intersite interactions, nonlinear Klein-Gordon chains, reaction-diffusion equations, and discrete nonlinear Schrödinger systems. Potential functions can be found in a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least C2 functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.

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