High-frequency instability of wave fronts

Experimental evidence is presented that a lateral instability of a wave front, as described earlier in a chemically active medium with the Belousov-Zhabotinsky reaction with decreased excitability, can also occur in a medium with any degree of excitability provided that a high-frequency wave train travels through the medium. The interaction of chemical waves with the boundary of the medium can result in the appearance of wave breaks and spiral waves.     

Dissipation of the excitation wave fronts

An excitation wave in cardiac tissue will fail to propagate if the transmembrane voltage at its front rises too slowly and does not excite the tissue ahead of it. Then the sharp voltage profile of the front will dissipate, and the subsequent spread of voltage will be purely diffusive. This mechanism is impossible in FitzHugh-Nagumo type systems. Here a simplified mathematical model for this mechanism is suggested. The model has exact traveling front solutions, and gives conditions for the front dissipation. In particular, a front will dissipate if it is not allowed to propagate faster than a certain nonzero speed. This critical speed depends only on the properties of the fast sodium current.     

High focal depth with fractional-power wave fronts

We explore the use of phase profiles with fractional power for tailoring modulation transfer functions with high focal depth at high pupil apertures. We present numerical simulations of the images that can be obtained with certain fractional-power profiles.     

Speckle statistics in partially corrected wave fronts

Wave fronts distorted by the atmosphere preserve high-spatial-frequency information. This information can be retrieved by use of adaptive optics systems to correct the incoming wave front. This correction should be as nearly complete as possible. In experiments performed in the visible, only partial compensation is attainable. We provide a theoretical model to predict the intensity statistics of the light in the image center as a function of the number of Zernike polynomials corrected.     

Existence and stability of steady fronts in bistable coupled map lattices

We prove the existence and we study the stability of the kinklike fixed points in a simple coupled map lattice (CML) for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value of the coupling parameter where a (multi) generalized saddle-node bifurcation occurs and destroys these solutions. An extension of the results to other CMLs in the same class is also displayed. Finally, we emphasize the property of spatial chaos for small coupling.     

Nonlinear hydrodynamic corrections to supersonic F-KPP wave fronts

We study the hydrodynamic corrections to the dynamics and structure of an exothermic chemical wave front of Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) type which travels in a one-dimensional gaseous medium. We show in particular that its long time dynamics, cut-off sensitivity and leading edge behavior are almost entirely controlled by the hydrodynamic front speed correction δU_h which characterizes the pushed nature of the front. Reducing the problem to an effective comoving heterogeneous F-KPP equation, we determine two analytical expressions for δU_h: an accurate one, derived from a variational method, and an approximate one, from which one can assess the δU_h sensitivity to the shear viscosity and heat conductivity of the fluid of interest.     

Spatiotemporal growing wave fronts in spatially stable boundary layers

In fluid dynamical systems, it is not known a priori whether disturbances grow either in space or in time or as spatiotemporal structures. For a zero pressure gradient boundary layer (also known as the Blasius boundary layer), it is customary to treat it as a spatial problem, and some limited comparison between prediction and laboratory experiments exist. In the present work, the two-dimensional receptivity problem of a Blasius boundary layer excited by a localized harmonic source is investigated under the general spatiotemporal framework, by using the Bromwich contour integral method. While this approach is seen to be equivalent to the spatial study for unstable systems, here we show for the first time how spatially stable systems show spatiotemporally growing wave fronts.     

On the velocity of electromagnetic and gravitational wave fronts

It is shown that, in the space of the general theory of relativity, the velocity of an electromagnetic wave front in a non-inertial frame of reference, and of electromagnetic and gravitational wave fronts in a synchronous frame of reference, is constant and equal to the fundamental velocity. It is noted that the concept of a wave front is meaningful in synchronous frames of reference, of which inertial systems in a Minkowski world are a special case.     

Frequency-locking phenomena of propagating wave fronts in reaction-diffusion systems

We observe N:(N-1)(N>/=2) frequency-locking phenomena of propagating wave fronts when increasing the light intensity in a spatially extended system. The experiments were carried out using the light-sensitive form of the Belousov-Zhabotinsky reaction with Ru(bpy)(2+)3 as a catalyst. By constructing a mapping function, the characteristic devil's staircase can be reproduced when plotting wave period versus light intensity, in agreement with the experimental data.     

Method for the generation of arbitrary complex vector wave fronts

We describe an extremely versatile method that permits the accurate generation of arbitrary complex vector wave fields. We implement the scheme using a reconfigurable binary optical element that also permits additional fine tuning, such as aberration correction, to be performed. As examples we demonstrate the generation of both azimuthally and radially polarized beams.     

Generalized pencils of rays in statistical wave optics

The recently introduced generalized pencil of Sudarshan which gives an exact ray picture of wave optics is analysed in some situations of interest to wave optics. A relationship between ray dispersion and statistical inhomogeneity of the field is obtained. A paraxial approximation which preserves the rectilinear propagation character of the generalized pencils is presented. Under this approximation the pencils can be computed directly from the field conditions on a plane, without the necessity to compute the cross-spectral density function in the entire space as an intermediate quantity. The paraxial results are illustrated with examples. The pencils are shown to exhibit an interesting scaling behaviour in the far-zone. This scaling leads to a natural generalization of the Fraunhofer range criterion and of the classical van Cittert-Zernike theorem to planar sources of arbitrary state of coherence. The recently derived results of radiometry with partially coherent sources are shown to be simple consequences of this scaling.     

Patterns of spiral wave attenuation by low-frequency periodic planar fronts

There is evidence that spiral waves and their breakup underlie mechanisms related to a wide spectrum of phenomena ranging from spatially extended chemical reactions to fatal cardiac arrhythmias [A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 2001); J. Schutze, O. Steinbock, and S. C. Muller, Nature 356, 45 (1992); S. Sawai, P. A. Thomason, and E. C. Cox, Nature 433, 323 (2005); L. Glass and M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988); R. A. Gray et al., Science 270, 1222 (1995); F. X. Witkowski et al., Nature 392, 78 (1998)]. Once initiated, spiral waves cannot be suppressed by periodic planar fronts, since the domains of the spiral waves grow at the expense of the fronts [A. N. Zaikin and A. M. Zhabotinsky, Nature 225, 535 (1970); A. T. Stamp, G. V. Osipov, and J. J. Collins, Chaos 12, 931 (2002); I. Aranson, H. Levine, and L. Tsimring, Phys. Rev. Lett. 76, 1170 (1996); K. J. Lee, Phys. Rev. Lett. 79, 2907 (1997); F. Xie, Z. Qu, J. N. Weiss, and A. Garfinkel, Phys. Rev. E 59, 2203 (1999)]. Here, we show that introducing periodic planar waves with long excitation duration and a period longer than the rotational period of the spiral can lead to spiral attenuation. The attenuation is not due to spiral drift and occurs periodically over cycles of several fronts, forming a variety of complex spatiotemporal patterns, which fall into two distinct general classes. Further, we find that these attenuation patterns only occur at specific phases of the descending fronts relative to the rotational phase of the spiral. We demonstrate these dynamics of phase-dependent spiral attenuation by performing numerical simulations of wave propagation in the excitable medium of myocardial cells. The effect of phase-dependent spiral attenuation we observe can lead to a general approach to spiral control in physical and biological systems with relevance for medical applications.     

Problems of interpretation of holographic interferograms near shock wave fronts

A method of avoiding ambiguity in the interpretation of interferograms near a shock wave front is proposed. The method is based on combining the double-exposure schlieren method and holographic interferometry. Relations for calculating, on the basis of data obtained by analyzing double-exposure schlieren photographs, both the density at the shock wave front and the gradient of the density directly behind the front, which is necessary for calculating the shifts of the interference fringes near the shock wave front, are presented. Zh. Tekh. Fiz. 68, 88–91 (September 1998)     

反应扩散系统中波传播的锁频现象

在空间延展系统中,当增强外部光强时,作者观察到波传播的N∶N-1(N≥2)锁频现象.此现象是在光敏BZ反应实验中观察到的.通过构建一个映射函数,发现在波周期和外部光强的关系中存在魔鬼阶梯,并且此阶梯与实验数据相吻合.     

Fluctuations of cosmic rays and interplanetary magnetic field in the vicinity of interplanetary shock fronts

The spectral characteristic of fluctuations of cosmic rays (CRs) and the interplanetary magnetic field in the prefront region of interplanetary shock waves, where coherent CR fluctuations with energies from ～10 keV to ～1 GeV are often observed, have been studied. It is concluded that the spectrum of CR fluctuations is subjected to modulation by fast magnetosonic waves generated by low-energy CRs reflected and/or accelerated at the shock fronts.     

Accurate eikonal-curvature relation for wave fronts in locally anisotropic reaction-diffusion systems

The dependency of wave velocity in reaction-diffusion (RD) systems on the local front curvature determines not only the stability of wave propagation, but also the fundamental properties of other spatial configurations such as vortices. This Letter gives the first derivation of a covariant eikonal-curvature relation applicable to general RD systems with spatially varying anisotropic diffusion properties, such as cardiac tissue. The theoretical prediction that waves which seem planar can nevertheless possess a nonvanishing geometrical curvature induced by local anisotropy is confirmed by numerical simulations, which reveal deviations up to 20% from the nominal plane wave speed.     

A relativistic fluid in which shock fronts are also wave surfaces

The equation of state which characterizes the fluid has a corresponding non-relativistic form. The fronts of all shocks that occur in the fluid are characteristics surfaces of the field equations.     

Theoretical model of terahertz radiation generation by laser pulses with tilted wave fronts

A theoretical model is proposed for terahertz radiation generation by femtosecond laser pulses with tilted wave fronts. Self-consistent evolution of the optical and terahertz pulses is investigated. The red shift of the pumping pulse spectrum and the formation of short-long-wave quasi-solitons are examined.     

Rerouting end-face-TIR capable rays to significantly increase evanescent wave signal power

The critical findings associated with end-face total internal reflection (TIR) phenomemon we proved before are reported.In particular,these findings reveal that the end-face-TIR capable rays experience enormous mode mixing when encountering a roughened end face.As a result,94% of the overall detectable power is contributed by this effect.With a smooth fiber end face,this figure is mere 52%.We interpret the mechanism behind these unusual phenomena and its significance for the performance enhancement of fiber optic evanescent wave sensor.     

New method for calculating reflected wave fronts of acute retroreflectors with tuned dihedral angle

An acute retroreflector having dihedral angles of 45, 60 and 90 deg exactly reflects incident rays in the opposite direction. Beam pattern or wave front of the reflected light of the acute retroreflector can be controlled by tuning dihedral angles. We present here a new method for calculating the reflected wave front of the acute retroreflector, in which the wave front is calculated with high accuracy and in a shorter calculation time than by the conventional ray trace method.