Accelerating oscillatory fronts in a nonlinear sonic vacuum with strong nonlocal effects.

We describe and explore accelerating oscillatory fronts in sonic vacua with nonlocal interactions. As an example, a chain of particles oscillating in the plane and coupled by linear springs, with fixed ends, is considered. When one end of this system is harmonically excited in the transverse direction, one observes accelerated propagation of the excitation front, accompanied by an almost monochromatic oscillatory tail. Position of the front obeys the scaling law l(t) ∼ t(4/3). The frequency of the oscillatory tail remains constant, and the wavelength scales as λ ∼ t(1/3). These scaling laws result from the nonlocal effects; we derive them analytically (including the scaling coefficients) from a continuum approximation. Moreover, a certain threshold excitation amplitude is required in order to initiate the front propagation. The initiation threshold is evaluated on the basis of a simplified discrete model, further reduced to a completely integrable nonlinear system. Given their simplicity, nonlinear sonic vacua of the type considered herein should be common in periodic lattices.

Heat conduction in a chain of dissociating particles: Effect of dimensionality.

The paper considers heat conduction in a model chain of composite particles with hard core and elastic external shell. Such model mimics three main features of realistic interatomic potentials--hard repulsive core, quasilinear behavior in a ground state, and possibility of dissociation. It has become clear recently that this latter feature has crucial effect on convergence of the heat conduction coefficient in thermodynamic limit. We demonstrate that in one-dimensional chain of elastic particles with hard core the heat conduction coefficient also converges, as one could expect. Then we explore effect of dimensionality on the heat transport in this model. For this sake, longitudinal and transversal motions of the particles are allowed in a long narrow channel. With varying width of the channel, we observe sharp transition from "one-dimensional" to "two-dimensional" behavior. Namely, the heat conduction coefficient drops by about order of magnitude for relatively small widening of the channel. This transition is not unique for the considered system. Similar phenomenon of transition to quasi-1D behavior with growth of aspect ratio of the channel is observed also in a gas of densely packed hard (billiard) particles, both for two- and three-dimensional cases. It is the case despite the fact that the character of transition in these two systems is not similar, due to different convergence properties of the heat conductivity. In the billiard model, the divergence pattern of the heat conduction coefficient smoothly changes from logarithmic to power-like law with increase of the length.

Mechanical control of heat conductivity in molecular chains.

We discuss a possibility to control heat conductivity in molecular chains by means of external mechanical loads. To illustrate such possibilities we consider first well-studied one-dimensional chain with degenerate double-well potential of the nearest-neighbor interaction. We consider varying lengths of the chain with fixed number of particles. Number of possible energetically degenerate ground states strongly depends on the overall length of the chain, or, in other terms, on average length of the link between neighboring particles. These degenerate states correspond to mechanical equilibria; therefore, one can say that formation of such structures mimics a process of plastic deformation. We demonstrate that such modification of the chain length can lead to quite profound (almost fivefold) reduction of the heat conduction coefficient. Even more profound effect is revealed for a model with a single-well nonconvex potential. It is demonstrated that in a certain range of constant external forcing, this model becomes effectively double-well and has a multitude of possible states of equilibrium for fixed value of the external load. Due to this degeneracy, the heat-conduction coefficient can be reduced by two orders of magnitude. We suggest a mechanical model of a chain with periodic double-well potential, which allows control of the heat transport. The models considered may be useful for description of heat transfer in biological macromolecules and for control of the heat transport in microsystems. The possibility of the heat transport control in more realistic three-dimensional systems is illustrated by simulation of a three-dimensional model of polymer α-helix. In this model, the mechanical stretching also brings about the structural inhomogeneity and, in turn, to essential reduction of the heat conductivity.

Lattice stretching bistability and dynamic heterogeneity.

A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearest-neighbor interaction of a Morse-like potential (required to have a saturation branch) and a harmonic second-neighbor coupling. Under an external stretching applied to the chain ends, the intersite Morse-like potential results in the appearance of a double-well potential within each chain monomer, whereas the interaction between the second neighbors provides a homogeneous bistable (degenerate) ground state, at least within a certain part of the chain. As a result, different conformational changes occur in the chain under the external forcing. The transition regions between these conformations are described as topological solitons. With a strong second-neighbor interaction, the solitons describe the transition between the bistable ground states. However, the key point of the model is the appearance of a heterogenous structure, when the second-neighbor coupling is sufficiently weak. In this case, a part of the chain has short bonds with a single-well potential, whereas the complementary part admits strongly stretched bonds with a double-well potential. This case allows us to explain the existence of a plateau in the force-extension diagram for DNA and α-helix protein. Finally, the soliton dynamics are studied in detail.

Nonstationary heat conduction in one-dimensional models with substrate potential.

The paper investigates nonstationary heat conduction in one-dimensional models with substrate potential. To establish universal characteristic properties of the process, we explore three different models: Frenkel-Kontorova (FK), phi4+ (φ(4)+), and phi4- (φ(4)-). Direct numeric simulations reveal in all these models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with the parabolic Fourier equation of heat conduction and clearly demonstrates the necessity for hyperbolic corrections in the phenomenological description of the heat conduction process. The crossover wavelength decreases with an increase in the average temperature. The decay patterns of the temperature field almost do not depend on the amplitude of the perturbations, so the use of linear evolution equations for the temperature field is justified. In all models investigated, the relaxation of thermal perturbations is exponential, contrary to a linear chain, where it follows a power law. The most popular lowest-order hyperbolic generalization of the Fourier law, known as the Cattaneo-Vernotte or telegraph equation, is also not valid for the description of the observed behavior of the models with the substrate potential, since the characteristic relaxation time in an oscillatory regime strongly depends on the excitation wavelength. For some of the models, this dependence seems to obey a simple scaling law.

[New coarse-grained DNA model].

A new coarse-grained model of the DNA molecule has been proposed, which was elaborated on the basis of its all-atomic model analysis. The model has been shown to rather well reproduce the DNA structure under low and room temperatures. The Young's and torsion moduli calculated using the coarse-grained model are in close agreement with experimental data and the theoretical results of other authors. The model can be used for DNA fragments of several hundreds base pairs for rather long time scales (of the order of micros) and for simulating their interactions with other structures.

Wandering breathers and self-trapping in weakly coupled nonlinear chains: classical counterpart of macroscopic tunneling quantum dynamics.

We present analytical and numerical studies of the phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly moving: the periodic transverse translation (wandering) of the low-amplitude breather between the chains and the one-chain-localization of the high-amplitude breather. These two modes of coupled nonlinear excitations, which involve a large number of anharmonic oscillators, can be mapped onto two solutions of a single pendulum equation, detached by a separatrix mode. We also show that these two regimes of coupled phase-coherent breathers are similar and are described by a similar pair of equations to the two regimes in the nonlinear tunneling dynamics of two weakly linked interacting (nonideal) Bose-Einstein condensates. On the basis of this profound analogy, we predict a tunneling mode of two weakly coupled Bose-Einstein condensates in which their relative phase oscillates around pi/2 mod pi. We also show that the magnitude of the static displacements of the coupled chains with nonlinear localized excitation, induced by the cubic term in the intrachain anharmonic potential, scales approximately as the total vibrational energy of the excitation, either a one- or two-chain one, and does not depend on the interchain coupling. This feature is also valid for a narrow stripe of several parallel-coupled nonlinear chains. We also study two-chain breathers which can be considered as bound states of discrete breathers, with different symmetry and center locations in the coupled chains, and bifurcation of the antiphase two-chain breather into the one-chain one. Bound states of two breathers with different commensurate frequencies are found in the two-chain system. Merging of two breathers with different frequencies into one breather in two coupled chains is observed. Wandering of the low-amplitude breather in a system of several, up to five, coupled nonlinear chains is studied, and the dependence of the wandering period on the number of chains is analytically estimated and compared with numerical results. The delocalizing transition of a one-dimensional (1D) breather in the 2D system of a large number of parallel-coupled nonlinear oscillator chains is described, in which the breather, initially excited in a given chain, abruptly spreads its vibrational energy in the whole 2D system upon decreasing the breather frequency or amplitude below the threshold one. The threshold breather frequency is above the cutoff phonon frequency in the 2D system, and the threshold breather amplitude scales as the square root of the interchain coupling constant. The delocalizing transition of the discrete vibrational breather in 2D and 3D systems of parallel-coupled nonlinear oscillator chains has an analogy with the delocalizing transition for Bose-Einstein condensates in 2D and 3D optical lattices.

[High-performance liquid chromatographic method for the determination of dihydroquercetin in extracts of medicinal plants].

Determination of dihydroquercetin in extracts of medicinal plants by a high-performance liquid chromatography is presented. The method is simple, quick, highly reproducible and can be widely applied in phytopharmacology.

[Dynamics of the electrical activity in the form of a vortex with a straight filament in ground squirrel heart].

Attacks of tachysystolia have been studied, which were induced by premature stimuli (amplitude up to 4-5 diastolic thresholds, duration 4 ms) applied after a set of rectangular impulses (amplitude 2 diastolic thresholds, duration 4 ms, frequency 0.5 or 2 Hz). The spatial and temporal distribution of electrical potential throughout the surface of a thin (approximately 1 mm) preparation was registered by two multi-electrode arrays (32 unipolar electrodes each). One array recorded the distribution of electrical potential on the endocardial surface and the other, on the epicardial one. Wave isochronous pictures (maps) corresponding to spatial and temporal propagation of excitation on the surfaces of the preparation were reconstructed on the basis of electrograms registered on each of the surfaces. On the basis of these maps, the three-dimensional structure of scroll waves, including the location, direction and velocity of the shift of filament ends as well as the shape of the thread was analyzed. The analysis of the data obtained in our experiments allow one to conclude that, under tachysystolias caused by three-dimensional scroll wave with a straight filament, there occur the following kinds of wave thread movements: (1) the wave thread may change its location from turn to turn and on the whole be located at different angles to the preparation surfaces; (2) the wave thread may precess, when one of the filament end is "secured" on the surface and the other constantly changes its location on the opposite surface; (3) the wave thread may periodically intertwine (twisted filament) and untwine; (4) dimensions of the scroll wave kernels (sections of the filament on the surfaces) may change from turn to turn both simultaneously on both surfaces (endocardial and epicardial) and on one of them only; (5) the wave thread may curve when it goes within the wall from endocardial to epicardial surfaces; the curve may come rather close the surfaces of the myocardial tissue.

Heat conduction in a one-dimensional chain of hard disks with substrate potential.

Heat conduction in a one-dimensional chain of equivalent rigid particles in the field of the external on-site potential is considered. The zero diameters of the particles correspond to the integrable case with the divergent heat conduction coefficient. By means of a simple analytical model it is demonstrated that for any nonzero particle size the integrability is violated and the heat conduction coefficient converges. The result of the analytical computation is verified by means of numerical simulation in a plausible diapason of parameters, and good agreement is observed.

Heat conduction in one-dimensional lattices with on-site potential.

The process of heat conduction in one-dimensional lattices with on-site potential is studied by means of numerical simulation. Using the discrete Frenkel-Kontorova, phi(4), and sinh-Gordon models 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 the 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 sine-Gordon and phi(4) models, phonons are scattered at a dynamical lattice of topological solitons; for sinh-Gordon and for phi(4) in a different parameter regime 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).

Nonlinear dynamics of topological solitons in DNA.

Dynamics of topological solitons describing open states in the DNA double helix are studied in the framework of a model that 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.

Molecular gyroscopes and biological effects of weak extremely low-frequency magnetic fields.

Extremely low-frequency magnetic fields are known to affect biological systems. In many cases, biological effects display "windows" in biologically effective parameters of the magnetic fields: most dramatic is the fact that the relatively intense magnetic fields sometimes do not cause appreciable effect, while smaller fields of the order of 10-100 microT do. Linear resonant physical processes do not explain the frequency windows in this case. Amplitude window phenomena suggest a nonlinear physical mechanism. Such a nonlinear mechanism has been proposed recently to explain those "windows." It considers the quantum-interference effects on the protein-bound substrate ions. Magnetic fields cause an interference of ion quantum states and change the probability of ion-protein dissociation. This ion-interference mechanism predicts specific magnetic-field frequency and amplitude windows within which the biological effects occur. It agrees with a lot of experiments. However, according to the mechanism, the lifetime Gamma(-1) of ion quantum states within a protein cavity should be of unrealistic value, more than 0.01 s for frequency band 10-100 Hz. In this paper, a biophysical mechanism has been proposed, which (i) retains the attractive features of the ion interference mechanism, i.e., predicts physical characteristics that might be experimentally examined and (ii) uses the principles of gyroscopic motion and removes the necessity to postulate large lifetimes. The mechanism considers the dynamics of the density matrix of the molecular groups, which are attached to the walls of protein cavities by two covalent bonds, i.e., molecular gyroscopes. Numerical computations have shown almost free rotations of the molecular gyroscopes. The relaxation time due to van der Waals forces was about 0.01 s for the cavity size of 28 A.

Heat conduction in one-dimensional systems with hard-point interparticle interactions.

Results of extensive and accurate numerical studies on heat transfer in a system of particles with unequal masses, interacting through hard-point potentials with two types of symmetry, are reported. The particles are confined in a one-dimensional box with fixed ends coupled to heat reservoirs at different temperatures. The study aims to throw light upon recent controversial results on thermal conductivity in one-dimensional systems. When the particles interact through elastic hard-point collisions (a standard asymmetric case), the system is shown to have always infinite (anomalous) thermal conductivity as follows from the Prosen-Campbell theorem.

Solitons in spiral polymeric macromolecules.

The problem of the existence and stability of dynamical soliton regimes in a helix polymer is solved numerically. For the polytetrafluoroethylene macromolecule, within a model in which deformations of the valence and torsion angles and the valence bonds are taken into account, two types of soliton solutions are found. The first type describes the propagation of a solitary wave of torsional displacements of a helix chain. The twisting of the chain is a result of the compression of dihedral (torsion) angles. The second type describes the propagation of a solitary wave of longitudinal displacements of a helix chain. The longitudinal compression of the chain is a result of the compression of the valence angles and bonds. The solitons have a finite narrow spectrum of supersonic velocities: the soliton of torsion has a spectrum above the velocity of long-wavelength phonons of torsion while the spectrum of the solitons of compression lies above the velocity of long-wavelength phonons of longitudinal displacement. Numerical simulations of the soliton dynamics show their stability in the intervals of admissible velocities. The elasticity of soliton interactions under their collisions is demonstrated. The formation of solitons induced by deformation of end bonds of the helix chain has been modeled. It is shown that helicity of the macromolecule is the necessary condition for existence of torsional solitons.

Dependence of thermal conductivity on discrete breathers in lattices.

We study the properties of heat conduction in chains of coupled particles subjected to different anharmonic on-site potentials. Particular emphasis is placed on the role of breathers in saturation of the thermal conductivity for chains with hard anharmonicity. When the chain particles are subject to on-site potentials with soft anharmonicity, we find a characteristic temperature, below which the conductivity decreases but while above which it increases.

Homochirality and long-range transfer in biological systems.

It has been shown that the chiral purity of biomacromolecules has important biological significance not only from the standpoint of lock-and-key stereocomplementarity, but also as a basis for long-range communication in biosystems. An explicit demonstration is given for the case of proton transfer along the hydrogen-bonded chain that is formed by amino acids containing OH groups. It is found that the replacement of the L-amino acid residue by the D-isomer in a peptide chain suppresses proton transport through the hydrogen bond network.