Solitonlike and nonsoliton modes of interaction of taxis waves (illustrated with an example of bacterial population waves)

It was shown earlier that during collisions bacterial population waves may either penetrate one another or stop. In this communication, the mechanism of these two interaction modes is considered in detail. It is shown on the basis of theoretical and experimental results that this interaction is a graphic example confirming one of the characteristic properties of waves in cross-diffusion systems.     

Excitation of inertial Alfvén waves via modulational interaction with lower hybrid waves

The concept of modulational instability, which results from the coupling of waves modes of very different time and space scales, was introduced to plasma physics through an elegant paper by Vedenov and Rudakov in 1964 [1]. Our paper is devoted to the theory of modulational instability resulting from the interaction of lower hybrid waves and slow density perturbations associated with inertial Alfvén waves. The nonlinear set of equations describing the modulational coupling of these two types of waves is constructed. The lower hybrid wave trajectories are analyzed within predefined density structures and it is shown that these waves can be trapped in the vicinity of the density extremum. The density modulations, originally being associated with inertial Alfvén waves, deepen due to the trapping of lower hybrid waves; this leads to modulational instability. A dispersion relation describing the modulational instability is constructed and analyzed. The threshold intensity of the lower hybrid waves for the onset of instability is obtained and it is shown that instability can serve as an efficient mechanism for the excitation of inertial Alfvén waves in the auroral ionosphere.     

Structure of bound water and topological rearrangement waves

The evolutionary conception of bound water and the structure of liquid water has been briefly described. The function of the radial distribution of water molecules has been analyzed. The intermediate maxima at 0.35 nm of the function is shown to be described in the frame of the model of continuous hydrogen bond net without invoking the mixed and two-state models of liquid water. Using a simple extensive parametric structure, spiral 30/11, a model of topological rearrangement waves including bifurcate bonds is suggested. These waves can transmit the information on conformational transitions between cellular elements through the virtual spirals of bound water.     

Attenuation of Bragg backscattering of electromagnetic waves from density fluctuations near the region of polarization degeneracy in magnetoactive plasma

Specific features of Bragg backscattering under conditions of strong polarization degeneracy near the cutoff surface in an anisotropic medium are studied analytically and numerically. It is shown that the linear interaction of normal waves can substantially affect wave scattering by suppressing the amplification of Bragg backscattering near the cutoff region in the case of weak coupling between normal waves.     

Effect of parametric resonance on the formation of waves with a broad multiharmonic spectrum during the development of two-stream instability

A cubically nonlinear multiharmonic theory of two-stream instability in a two-velocity relativistic electron beam is constructed with allowance for parametric resonance between harmonics of longitudinal waves of different types, as well as between wave harmonics of the same type. The effect of these two kinds of parametric resonance interaction on the development of two-stream instability is investigated. It is shown that parametric resonance between different types of longitudinal waves excited in a two-velocity beam can substantially affect the development of physical processes in the system under study. It is proposed to use parametric resonance between longitudinal waves of different types to form waves with a prescribed broad multiharmonic spectrum.     

Biological effects of two successive shock waves focused on liver tissues and melanoma cells

A new generator of two successive shock waves focused to a common focal point has been developed. Cylindrical pressure waves created by multichannel electrical discharges on two cylindrical composite anodes are focused by a metallic parabolic reflector - cathode, and near the focus they are transformed to strong shock waves. Schlieren photos of the focal region have demonstrated that mutual interaction of the two waves results in generation of a large number of secondary short-wavelength shocks. Interaction of the focused shockwaves with liver tissues and cancer cell suspensions was investigated. Localized injury of rabbit liver induced by the shock waves was demonstrated by magnetic resonance imaging. Histological analysis of liver samples taken from the injured region revealed that the transition between the injured and the healthy tissues is sharp. Suspension of melanoma B16 cells was exposed and the number of the surviving cells rapidly decreased with increasing number of shocks and only 8 % of cells survived 350 shocks. Photographs of cells demonstrate that even small number of shocks results in perforation of cell membranes.     

Bright solitary waves as charge transport in DNA: A variational approximation

Modeling energy and charge transfer in DNA has been a challenging issue because of many conformations DNA can take. Due to its simplicity, we propose a discrete variational approach to study the charge transfer mechanism in DNA based on the Holstein-Su-Schrieffer-Heeger model. It is shown that bright solitary waves may propagate through the DNA and the variational approximation provides explicit relations between experimental parameters and important characteristics of the waves such as amplitude, width, chirp and homogenous phase, and energy. Our analytical predictions are confirmed by intensive numerical simulations with a good accuracy.     

Excitation of growing wake waves by an electron bunch in a plasma in an intense pump wave

A study is made of the excitation of wake waves by a one-dimensional electron bunch in an electron plasma in the presence of an intense monochromatic pump wave with circular polarization. In the main state (in the absence of a bunch), the interaction between a pump wave and a plasma is described by Maxwell's equations and the nonlinear relativistic hydrodynamic equations for a cold plasma. The excitation of linear waves by a one-dimensional bunch is investigated against a cold plasma background. It is shown that, in a certain range of parameter values of the bunch, pump wave, and plasma, the excitation is resonant in character and the amplitude of the excited wake waves increases with distance from the bunch.     

Dynamics of bacterial population waves as dependent on the type of the chemotactic response function

A study was made of the time of formation and the rate of propagation of bacterial population waves as dependent on substrate concentration. Experimentally and theoretically it is shown that the time of bacterial wave formation grows with increasing concentration of the nutritive component. At the same time, the wave propagation rate drops at relatively high concentrations of the nutritive component. In numerical experiments with a mathematical model, comparative analysis has been made of the dynamics of the behavior of bacterial waves at different chemotactic responses.     

Gene-culture waves of advance

Major genetic and cultural changes may have been coupled during hominid evolution. Since hominids have had a wide geographical distribution for about one million years, any mutant gene or cultural innovation that became established had to spread from its origin. A pair of nonlinear diffusion equations is derived which models the propagation of a mutant gene and a cultural innovation. Both are assumed to originate in the same locality along a linear habitat. The mutant gene and its allele are semidominant, and the two cultural choices are transmitted according to what I call the logistic attraction-repulsion model. The genes influence cultural choice, and the two interact to determine fitness. Of particular interest is the case in which mutant gene and cultural innovation are mutually dependent, neither being able to spread without the other. Each equation of the pair is similar in form to Fisher's equation, with a linear function of the other dependent variable replacing the constant coefficient in the reaction term. The partial differential equations are solved numerically to obtain the asymptotic speeds. Their form also suggests an heuristic argument which has proved useful, but I have been unable to obtain any analytic results. The waves of the system are shown to be of two types, synchronous and asynchronous. When genes and culture are mutually dependent, synchronous travelling waves can exist. However, their existence is dependent on initial conditions, and the speed of propagation is slow.     

Excitation of high-frequency azimuthal surface waves by an annular electron beam in a waveguide with a noncircular interface of the plasma column

An initial stage of the interaction of an electron beam ring rotating along Larmor orbits in a gap between the plasma column and a circular metal chamber of a cylindrical waveguide with extraordinarily polarized electromagnetic waves of the surface type is studied. These waves propagate along the azimuthal angle across an axial magnetic field in the range above the upper hybrid frequency. Using numerical analysis of the dispersion relation, it is shown that by the aid of an appropriate choice of the shape of the plasmavacuum interface one can achieve a significant increasing of growth rates of the resonant beam instability of these waves.     

Similarities and differences in the propagation of slow waves and peristaltic waves

The relationship between slow waves and peristaltic reflexes has not been well analyzed. In this study, we have recorded the electrical activity of slow waves together with that generated by spontaneous peristaltic contractions at 240 extracellular sites simultaneously. Recordings were made from five isolated tubular and six sheet segments of feline duodenum superfused in vitro. In all preparations, slow waves propagated as broad wave fronts along the longitudinal axis of the preparation in either the aborad or the orad direction. Electrical potentials recorded during peristalsis (peristaltic waves) also propagated as broad wave fronts in either directions. Peristaltic waves often spontaneously stopped conducting (46%), in contrast to slow waves that never did. Peristaltic waves propagated at a lower velocity than the slow waves (0.98 +/- 0.25 and 1.29 +/- 0.28 cm/s, respectively; P < 0.001; n = 24) and in a direction independent of the preceding slow wave direction (64% in the same direction, 46% in the opposite direction). In conclusion, slow waves and peristaltic waves in the isolated feline duodenum seem to constitute two separate electrical events that may drive two different mechanisms of contraction in the small intestine.     

Dissipative surface waves in plasma

Debatable aspects of the theory of nonpotential surface waves propagating along the boundary of a dissipative medium with frequency dispersion are discussed. On the basis of the known theoretical results and theoretical analysis carried out in this work, a theory of surface waves that is valid for any dissipation of the perturbation energy in the medium is developed. It is shown that, if dissipation is sufficiently strong, there can be surface waves the physical nature and dispersion law of which differ radically from those of ordinary surface waves. The damping rate of such waves is low even at large dissipation in the medium, and their group and phase velocities exceed the speed of light. In particular, surface waves on the interface between vacuum and cold collisional electron plasma are considered. The existence of such surface waves for different media of laboratory and natural origin is discussed.     

Traveling waves in a piecewise-linear reaction-diffusion model of excitable medium

One-dimensional autowaves (traveling waves) in excitable medium described by a piecewise-linear reaction-diffusion system have been investigated. Two main types of wave have been considered: a single pulse and a periodic sequence of pulses (wave trains). In a two-component system, oscillations are due to the second component of the reaction-diffusion system, while in a one-component system, they are caused by external periodic excitation (forcing). Using semianalytical solutions for the wave profile, the shape and velocity of autowaves have been found. It is shown that the dispersion relation for oscillating sequences of pulses has an anomalous character.     

Effect of a strong monochromatic electromagnetic wave with circular polarization on one-dimensional wake waves in plasma

A study is made of the excitation of wake waves by a one-dimensional bunch of charged particles in an electron plasma in the presence of an intense monochromatic pump wave with circular polarization. In the main state (in the absence of a bunch), the interaction between a pump wave and a plasma is described by the Maxwell equations and the nonlinear relativistic hydrodynamic equations for a cold plasma. The excitation of linear waves by a one-dimensional bunch is investigated against a cold plasma background. It is shown that, in a certain range of the parameter values of the bunch, pump wave, and plasma, the amplitude of the excited transverse waves grows as the energy of the bunch particles increases until the relativistic factor of the bunch reaches a certain threshold value above which the transverse wave amplitude becomes essentially independent of the bunch particle energy and grows as the intensity and frequency of the pump wave increase. The amplitude and wavelength of the longitudinal field, which is shown to depend weakly on the energy of the bunch particles, grows with increasing the pump wave intensity.     

Dichromatic Langmuir waves in degenerate quantum plasma

Langmuir waves in fully degenerate quantum plasma are considered. It is shown that, in the linear approximation, Langmuir waves are always dichromatic. The low-frequency component of the waves corresponds to classical Langmuir waves, while the high-frequency component, to free-electron quantum oscillations. The nonlinear problem on the profile of dichromatic Langmuir waves is solved. Solutions in the form of a superposition of waves and in the form of beatings of its components are obtained.     

Electron acceleration by Langmuir waves excited by a laser pulse in a semi-infinite plasma

Results are presented from a theoretical investigation of the acceleration of test electrons by a Langmuir wave excited by a short laser pulse at half the electron plasma frequency. Such a pulse penetrates into the plasma over a distance equal to the skin depth and efficiently excites Langmuir waves in the resonant interaction at the second harmonic of the laser frequency. It is shown that the beam of electrons accelerated by these waves is modulated into a train of electron bunches, but because of the initial thermal spread of the accelerated electrons, the bunches widen and begin to overlap, with the result that, at large distances, the electron beam becomes unmodulated.     

Propagation of shear waves in the muscle tissue

A mathematical model of the propagation of acoustic shear waves in muscle tissue is considered. The muscle is modelled by an incompressible transversely isotropic viscoelastic continuum with quasi-one-dimensional active tension. Two types of shear waves in an infinite medium have been established. The waves of the second type (transverse) propagate without attenuation even when myofibril viscosity is taken into account. A problem of standing transverse waves in a rectangular layer has been investigated numerically. The values of the problem parameters have been found for which the active tension or muscle tonus is easily estimated from the characteristics of standing waves. This value is informative for the diagnosis of muscle state.     

Oscillations and waves in the models of interactive neural populations

The dynamics of activity in interactive neural populations is simulated by the networks of Wilson-Cowan oscillators. Two extreme cases of connection architectures in the networks are considered: (1) 1D and 2D regular and homogeneous grids with local connections and (2) sparse random coupling. Propagating waves in the network have been found under the stationary external input and the regime of partial synchronization has been obtained for the periodic input. It has been shown that in the case of random coupling about 60% of neural populations demonstrate oscillatory activity and some of these oscillations are synchronous. The role of different types of dynamics in information processing is discussed. In particular, we discuss the regime of partial synchronization in the context of cortical microcircuits.     

Oscillations and waves in the models of interactive neural populations

The dynamics of activity in interactive neural populations is simulated by the networks of Wilson–Cowan oscillators. Two extreme cases of connection architectures in the networks are considered: (1) 1D and 2D regular and homogeneous grids with local connections and (2) sparse random coupling. Propagating waves in the network have been found under the stationary external input and the regime of partial synchronization has been obtained for the periodic input. It has been shown that in the case of random coupling about 60% of neural populations demonstrate oscillatory activity and some of these oscillations are synchronous. The role of different types of dynamics in information processing is discussed. In particular, we discuss the regime of partial synchronization in the context of cortical microcircuits.