Photon dynamics in plasma waves

In this Letter the evolution of a single photon and collective effect of a photon system in background plasma waves are uniformly described in the framework of photon dynamics. In a small-amplitude plasma wave the modulation of photon dynamical behavior by the plasma wave can be treated as perturbation, and photon acceleration effect and photon Landau damping are investigated in linear theory. In an arbitrary-amplitude plasma wave, photon evolution trajectories in phase space are obtained by solving dynamical equations, and photon trapping effect and motion equations in the given plasma wave are also discussed.     

Nonlinear dynamics of two unstable waves

The dynamics of two interacting unstable waves is investigated. Possible stationary, homogeneous solutions for the amplitudes and their stability relative to the modulations are studied in the approximation of small, slowly changing amplitudes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 5–8, April, 1990.     

Mechanism and dynamics of the disintegration calcite shock waves

Luminescence spectra associated with calcite disintegration under the action of an electric-discharge-induced shock wave and under friction have been obtained. It has been found that, in these cases, the destruction mechanisms differ. Under the action of the wave, the crystal lattice of calcite decomposes into positively charged calcium, carbon, and oxygen ions. During friction, calcite disintegrates due to microcrack accumulation. The fraction of the volume that decomposes into ions depends on the electrical discharge energy. The percentage of decomposed calcite exceeds 60% when the energy is roughly equal to 80 J and is no higher than several fractions of a percent when the energy equals 0.2 J. In the latter case, disintegration localizes at grain boundaries, as follows from the time-resolved luminescence study (a time resolution of 2 ns).     

Gravitational waves from mesoscopic dynamics of the extra dimensions

Recent models which describe our world as a brane embedded in a higher dimensional space introduce new geometrical degrees of freedom, associated with spatial variations in the position of the brane and the size of the extra dimensions, that can be coherently excited by symmetry breaking in the early universe even on "mesoscopic" scales as large as 1 mm. The characteristic frequency and intensity of resulting gravitational radiation backgrounds are estimated. Extra dimensions with scale between 10(-14) and 1 mm can produce detectable backgrounds at frequencies f approximately 10(3) to 10(-4) Hz.     

Nearly linear dynamics of nonlinear dispersive waves

Dispersive averaging effects are used to show that the Korteweg-de Vries (KdV) equation with periodic boundary conditions possesses high frequency solutions, which behave nearly linearly. Numerical simulations are presented, which indicate the high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.     

Effects of abnormal excitation on the dynamics of spiral waves

The effect of physiological and pathological abnormal excitation of a myocyte on the spiral waves is investigated based on the cellular automaton model. When the excitability of the medium is high enough, the physiological abnormal excitation causes the spiral wave to meander irregularly and slowly. When the excitability of the medium is low enough,the physiological abnormal excitation leads to a new stable spiral wave. On the other hand, the pathological abnormal excitation destroys the spiral wave and results in the spatiotemporal chaos, which agrees with the clinical conclusion that the early after depolarization is the pro-arrhythmic mechanism of some anti-arrhythmic drugs. The mechanisms underlying these phenomena are analyzed.     

New relativistic effects in the dynamics of nonlinear hydrodynamical waves

In Newtonian and relativistic hydrodynamics the Riemann problem determines the evolution of a fluid which is initially characterized by two states having different rest-mass density, pressure, and velocity. When the fluid is allowed to relax, one of three possible wave patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a relativistic Riemann problem when velocities tangential to the initial discontinuity are present. A smooth transition from one wave pattern to another can be produced by varying the initial tangential velocities while maintaining the initial states unmodified. These special relativistic effects are produced by the Lorentz factors and do not have a Newtonian counterpart.     

On the dynamics of internal waves interacting with the equatorial undercurrent

The interaction of the nonlinear internal waves with a nonuniform current with a speci?c form, characteristic for the equatorial undercurrent, is studied. The current has no vorticity in the layer, where the internal wave motion takes place. We show that the nonzero vorticity that might be occuring in other layers of the current does not affect the wave motion. The equations of motion are formulated as a Hamiltonian system.     

Spiral magneto-electron waves in interstellar gas dynamics

We discuss possible observational consequences resulting from the propagation of transverse magneto-electron waves in the interstellar medium. We briefly describe a magnetohydrodynamic model for the cyclotron waves with emphasis on their analogy with hydrodynamic inertial waves. It is shown that the cyclotron waves are heavily damped in the interstellar medium and, therefore, cannot affect the gas dynamics of star-forming molecular clouds. We developed an analytical model of the helicoidal magneto-electron waves based on the electromagnetic induction equation for the magnetic flux density driven by the Hall and Ohmic components of the electric field generated by flows of thermal electrons. It is established that the helicons can propagate in the interstellar medium without any noticeable attenuation. The presented numerical estimates for the group velocity of the intercloud helicons suggest that spiral circularly polarized magneto-electron waves of this type can be responsible for the broadening of molecular lines detected from dark interstellar clouds.     

Nonlinear ship waves and computational fluid dynamics

Research works undertaken in the first author’s laboratory at the University of Tokyo over the past 30 years are highlighted. Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design. Based on these findings, a multitude of the Computational Fluid Dynamic (CFD) techniques have been developed over this period, and are highlighted in this paper. The TUMMAC code has been developed for wave problems, based on a rectangular grid system, while the WISDAM code treats both wave and viscous flow problems in the framework of a boundary-fitted grid system. These two techniques are able to cope with almost all fluid dynamical problems relating to ships, including the resistance, ship’s motion and ride-comfort issues. Consequently, the two codes have contributed significantly to the progress in the technology of ship design, and now form an integral part of the ship-designing process.     

Solitary waves in helicoidal models of DNA dynamics

Abstract

We analyze travelling solitary wave solutions in the Barbi-Cocco-Peyrard and in a simplified version of the Cocco-Monasson models of nonlinear DNA dynamics. We identify conditions to be satisfied by parameters for such solutions to exist, and provide first order ODEs whose solutions give the required solitary waves; these are not solvable in analytical terms, but are easily integrated numerically.     

Analytical investigation of Rossby waves in atmospheric dynamics

The (2+1)-dimensional nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane is analyzed by using the classical Lie group approach. Using the group theory, some types of general exact Rossby wave solutions can be obtained whence a special Rossby wave solution is known. Especially, it is found that the only effect of the time-dependent background basic wind on the Rossby waves is the accumulate motion in the zonal direction. Some types of exact explicit similarity Rossby wave solutions with both nonconstant linear and nonlinear shears are also given.     

The effect of cellular aging on the dynamics of spiral waves

Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg–Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves,the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly.     

Complex dynamics and chaos in the parametric coupling of counter-propagating waves

We study the dynamics of a distributed self-oscillating system of three parametrically coupled waves, one of which is propagating counter to the other two. We show that an infinite number of natural modes are self-excited as the bifurcation parameter, which has the meaning of the pump amplitude, increases without bound. Exact solutions describing steady-state oscillation regimes are found. We present the results of computer simulation, which show that for moderate pump amplitudes the transient process terminates when a stationary state corresponding to the fundamental mode sets in. As supercriticality increases, the oscillations become chaotic, with the transition to chaos being rapid. We note an analogy that exists between the dynamics of such a system and the dynamics of a Lorentz system. Zh. éksp. Teor. Fiz. 116, 1871–1881 (November 1999)     

Crack front waves and the dynamics of a rapidly moving crack

Crack front waves are nonlinear localized waves that propagate along the leading edge of a crack. They are generated by both the interaction of a crack with a localized material inhomogeneity and the intrinsic formation of microbranches. Front waves are shown to transport energy, generate surface structure, and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to microbranch formation, yields both inhomogeneity and scaling behavior within the fracture surface structure.