Thermal coherence tomography using match filter binary phase coded diffusion waves

Energy transport in diffusion-wave fields is gradient-driven and therefore diffuse, yielding depth-integrated responses with poor axial resolution. Using matched-filter principles, we propose a methodology enabling these parabolic diffusion-wave energy fields to exhibit energy localization akin to propagating hyperbolic wave fields. This not only improves axial resolution but also allows for deconvolution of individual responses of superposed axially discrete sources, opening a new field of depth-resolved subsurface thermal coherence tomography using diffusion waves.     

Brane-induced-gravity shock waves

We construct exact gravitational field solutions for a relativistic particle localized on a tensional brane in brane-induced gravity. They are a generalization of gravitational shock waves in 4D de Sitter space. We provide the metrics for both the normal branch and the self-inflating branch Dvali-Gabadadze-Porrati brane worlds, and compare them to the 4D Einstein gravity solution and to the case when gravity resides only in the 5D bulk, without any brane-localized curvature terms. At short distances the wave profile looks the same as in four dimensions. The corrections appear only far from the source, where they differ from the long distance corrections in 4D de Sitter space. We also discover a new nonperturbative channel for energy emission into the bulk from the self-inflating [corrected] branch, when gravity is modified at the de Sitter radius.     

Gravitational shock waves

This paper reports on and summarizes some recent progress on gravitational shocks, i.e., discontinuities in the Riemann curvature tensor. It is shown how the constraint equations play a crucial rôle in determining the nature and propagation of the shocks. Existence results are stated and are illustrated by some examples from numerical relativity.     

On gravitational shock waves

The discontinuity planes of the Riemann curvature tensorR _klm ⁱ in the Einsteinian vacuumR _kl =0 are isotropic hypersurfaces. These surfaces are to be conceived as being constructed of lightlike geodesics, which form, in the eikonal approximation, gravitational radiation. The discontinuity planes themselves describe the wave fronts of disturbances of the metricg _ik , propagating with the velocity of light. By successively applying continuity conditions for the derivatives of theg _ik that follow from Einstein's equations, we obtain the universal expression of gravitational wave fields in space-time strips (or representations) of arbitrarily selected Einstein spaces.     

Turbulence in argon shock waves

Irregular density fluctuations with turbulent-like behaviors are found in ionizing shock fronts produced by our arc driven shock tube. We use electric probes as the primary diagnostic. Spectral analyses show statistical patterns which seem frozen-in and characterizable by a dominant mode and its harmonics.     

Stationary one-dimensional dispersive shock waves

We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defects in defocusing media with linear gain and two-photon absorption. We found that, in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from a defect or generating beam, the competition between gain and two-photon absorption in a dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed a certain critical value.     

Converging shock waves in metals

Study of propagation of a spherically converging shock wave has been carried out by Whitham’s method. The variation of shock velocity and pressure along the radius of curvature has been calculated numerically for a number of metals. Attempt has also been made to compare the experimental results of velocity of detonation wave with those reported elsewhere by the application of Whitham’s method. A good agreement between experimental and theoretical results has been obtained in this study.     

Gene–culture shock waves

A hyperbolic model is presented which generalises Aoki?s parabolic system for the combined propagation of a mutant gene together with a cultural innovation. It is shown that this model allows for the propagation of a shock wave and the shock amplitude is calculated numerically. Particular attention is paid to the case where the shock moves into a region where the frequencies of the mutant gene and of the individuals adopting the innovation are zero.     

Interactions of dispersive shock waves

Collisions and interactions of dispersive shock waves in defocusing (repulsive) nonlinear Schrödinger type systems are investigated analytically and numerically. Two canonical cases are considered. In one case, two counterpropagating dispersive shock waves experience a head-on collision, interact and eventually exit the interaction region with larger amplitudes and altered speeds. In the other case, a fast dispersive shock overtakes a slower one, giving rise to an interaction. Eventually the two merge into a single dispersive shock wave. In both cases, the interaction region is described by a modulated, quasi-periodic two-phase solution of the nonlinear Schrödinger equation. The boundaries between the background density, dispersive shock waves and their interaction region are calculated by solving the Whitham modulation equations. These asymptotic results are in excellent agreement with full numerical simulations. It is further shown that the interactions of two dispersive shock waves have some qualitative similarities to the interactions of two classical shock waves.     

Reaction–diffusion waves in biology

The theory of reaction–diffusion waves begins in the 1930s with the works in population dynamics, combustion theory and chemical kinetics. At the present time, it is a well developed area of research which includes qualitative properties of travelling waves for the scalar reaction–diffusion equation and for system of equations, complex nonlinear dynamics, numerous applications in physics, chemistry, biology, medicine. This paper reviews biological applications of reaction–diffusion waves.     

Elastic-plastic phenomena in ultrashort shock waves

A physical model of shock-wave phenomena in metals irradiated by a femtosecond laser pulse has been developed. The use of the experimental results (reported in S.I. Ashitkov et al., Pis’ma Zh. Eksp. Teor. Fiz. 92, 568 (2010) [JETP Lett. 92, 516 (2010)] together with the molecular dynamics simulation makes it possible to study the elastic properties of aluminum crystals at extreme shear stresses comparable in amplitude with the shear modulus. As a result, the elastic Hugoniot adiabat has been continued to the region of metastable elastic states at very high pressures, which are one or two orders of magnitude higher than the commonly accepted values for the dynamic elastic limit. It has been shown that the ultrashort elastic shock wave of superhigh pressure precedes the formation of the known split-shock wave structure consisting of an elastic precursor and a plastic shock wave.     

Focusing of noncircular self-similar shock waves

We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.     

Dispersive shock waves with nonlocal nonlinearity

We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.     

Simulations of shock waves in solids

Molecular dynamic shock wave simulations have been carried out for face centered cubic (f.c.c.) and body centered cubic (b.c.c.) solids using Lennard-Jones and Morse potentials for the interatomic interactions. The Hugoniot conservation relations were accurately obeyed in all of these calculations. The shock wave profiles may vary with the interatomic potential and the crystal structure, effects most clearly shown by the temperature profile near the shock front. The Lennard-Jones solids are intensitive to a change in structure but the Morse solids appear sensitive to crystal structure, at least in comparing b.c.c. with f.c.c. It was shown that the average shock wave temperature can be calculated from a combination of the Hugoniot conservation relations and the Mie-Grüneisen equation of state. The temperature calculated this way is in good agreement with the average shock wave temperature obtained in the computer simulations.     

Electron kinetics in collisionless shock waves

We study the kinetic model of the formation of the energy spectrum of nonthermal electrons near the front of a quasilongitudinal, supercritical, collisionless shock wave. Nonresonant interactions of the electrons and the fluctuations generated by kinetic instabilities of the ions in the transition region inside the shock front play the main role in the heating and preacceleration of electrons. We calculate the electron energy spectrum in the vicinity of the shock wave and show that the heating and preacceleration of electrons occur on a scale of the order of several hundred ion inertial lengths in the vicinity of the viscous discontinuity. Although the electron distribution function is significantly nonequilibrium near the shock front, its low-energy part can be approximated by a Maxwellian distribution. The effective electron temperature T _eff ² behind the front, obtained in this manner, increases with the Mach number of the shock wave slower than it would if it followed the Hugoniot adiabat. We determine the condition under which the electron heating is ineffective but the electrons are effectively accelerated to high energies. The high-energy asymptotic behavior of the distribution function is that of a power law, with the exponent determined by the total compression ratio of the plasma, as in the case of acceleration by the first-order Fermi mechanism. The model is used to describe the case (important for applications) of acceleration of electrons by shock waves with large total Mach numbers, with the structure of these waves modified by the nonlinear interaction of nonthermal ions and consisting of an extended prefront with a smooth variation of the macroscopic parameters and a viscous discontinuity in speed with a moderate value of the Mach number. Zh. éksp. Teor. Fiz. 115, 846–864 (March 1999)     

Ignition of cyclopropane in shock waves

The values of the ignition delay time of cyclopropane–oxygen–argon (cyclo-C₃H₆–O₂–Ar) mixtures of different compositions (φ = 0.333, 1, and 3) behind reflected shock waves at temperatures of 1200–1640 K and a pressure of (0.55 ± 0.05) MPa are measured. A kinetic mechanism of cyclopropane ignition using the known rate constants for the most important elementary reactions is developed. The mechanism closely describes both our own and published experimental data on the delay time of ignition of cyclopropane in shock waves over wide ranges of temperature (1200–2100 K), pressure (0.1–0.55 MPa), cyclopropane concentrations (0.05–11 vol %), and oxygen concentrations (0.25–21 vol %). It is shown that, with increasing fraction of diluent gas in the mixture, the dependence of the ignition delay time on the fuel-to-oxidizer equivalence ratio changes.