Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Dispersal probability distributions and the wave-front speed problem

The speed and width of front solutions to reaction-dispersal models are analyzed both analytically and numerically. We perform our analysis for Laplace and Gaussian distribution kernels, both for delayed and nondelayed models. The results are discussed in terms of the characteristic parameters of the models

Reconstruction of Fresnel Holograms using partial wave front information

n this work we analyze the behavior of complex information in Fresnel domain taking into account the limited capability to display complex transmittance values of current liquid crystal devices, when used as holographic displays. In order to do this analysis we compute the reconstruction of Fresnel holograms at several distances using the different parts of the complex distribution (real and imaginary parts, amplitude and phase) as well as using the full complex information adjusted with a method that combines two configurations of the devices in an adding architecture. The RMS error between the amplitude of these reconstructions and the original amplitude is used to evaluate the quality of the information displayed. The results of the error analysis show different behavior for the reconstructions using the different parts of the complex distribution and using the combined method of two devices. Better reconstructions are obtained when using two devices whose configurations densely cover the complex plane when they are added. Simulated and experimental results are also presented.

Low Mass Calibration Target for MM-Wave Remote Sensing Instruments

The reliability of millimeter and sub-millimeter wave radiometer measurements is dependent on the accuracy of the loads they employ as calibration targets. In the recent past on-board calibration loads have been developed for a variety of satellite remote sensing instruments. Unfortunately some of these have suffered from calibration inaccuracies which had poor thermal performance of the calibration target as the root cause. Stringent performance parameters of the calibration target such as low reflectivity, high temperature uniformity, low mass and low power consumption combined with low volumetric requirements remain a challenge for the space instrument developer. In this paper we present a novel multi-layer absorber concept for a calibration load which offers an excellent compromise between very good radiometric performance and temperature uniformity and the mass and volumetric constraints required by space-borne calibration targets.

Two-wavelength whole-field interferometry setup for thermal lens study

In this paper we present a new approach for thermal lens analysis using a two-wavelength DSPI (Digital Speckle Pattern Interferometry) setup for wavefront sensing. The employed geometry enables the sensor to detect wavefronts with small phase differences and inherent aberrations found in induced lenses. The wavefronts was reconstructed by four-stepping fringe evaluation and branch-cut unwrapping from fringes formed onto a diffusive glass. Real-time single-exposure contour interferograms could be obtained in order to get discernible and low-spacial frequency contour fringes and obtain low-noise measurements. In our experiments we studied the thermal lens effect in a 4% Er-doped CaO-Al2O3 glass sample. The diode lasers were tuned to have a contour interval of around 120 μm. The incident pump power was longitudinally and collinearly oriented with the probe beams. Each interferogram described a spherical-like wavefront. Using the ABCD matrix formalism we obtained the induced lens dioptric power from the thermal effect for different values of absorbed pump power. © 2012 Copyright SPIE.

Pulse-front tilt for short-wavelength lasing by means of traveling-wave plasma-excitation

Generation of coherent short-wavelength radiation across a plasma column is dramatically improved under traveling-wave excitation (TWE). The latter is optimized when its propagation is close to the speed of light, which implies small-angle target-irradiation. Yet, short-wavelength lasing needs large irradiation angles in order to increase the optical penetration of the pump into the plasma core. Pulse-front back-tilt is considered to overcome such trade-off. In fact, the TWE speed depends on the pulse-front slope (envelope of amplitude), whereas the optical penetration depth depends on the wave-front slope (envelope of phase). Pulse-front tilt by means of compressor misalignment was found effective only if coupled with a high-magnification front-end imaging/focusing component. It is concluded that speed matching should be accomplished with minimal compressor misalignment and maximal imaging magnification.

A simple solution of the laminar dam break wave

The sudden release of a mass of fluid in a channel generates a highly unsteady flow motion, called dam break wave. While industrial fluids exhibit sometimes non-Newtonian behaviours, the viscous fluid flow assumption remains a useful approximation for simplified analyses. In this study, new solutions of laminar dam break wave are proposed for a semi-infinite reservoir based upon the method of characteristics. The solutions yield simple explicit expressions of the wave front location, wave front celerity and instantaneous free-surface profiles that compare favourably with experimental observations. Both horizontal and sloping channel configurations are treated. The simplicity of the equations may allow future extension to more complicated fluid flows.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.

Long period gratings in multimode optical fibers: application in chemical sensing

We propose and demonstrate a new technique for evanescent wave chemical sensing by writing long period gratings in a bare multimode plastic clad silica fiber. The sensing length of the present sensor is only 10 mm, but is as sensitive as a conventional unclad evanescent wave sensor having about 100 mm sensing length. The minimum measurable concentration of the sensor reported here is 10 nmol/l and the operating range is more than 4 orders of magnitude. Moreover, the detection is carried out in two independent detection configurations viz., bright field detection scheme that detects the core-mode power and dark field detection scheme that detects the cladding mode power. The use of such a double detection scheme definitely enhances the reliability and accuracy of the results. Furthermore, the cladding of the present fiber need not be removed as done in conventional evanescent wave fiber sensors.

Wave optics analysis by phase-shifting real-time holographic interferometry

The purpose of this work is to study the potentialities in the phase-shifting real-time holographic interferometry using photorefractive crystals as the recording medium for wave-optics analysis in optical elements and non-linear optical materials. This technique was used for obtaining quantitative measurements from the phase distributions of the wave front of lens and lens systems along the propagation direction with in situ visualization, monitoring and analysis in real time. (C) 2008 Elsevier GmbH. All rights reserved.

Dissipative three-wave structures in stimulated backscattering. I. A subluminous solitary attractor

We present a solitary solution of the three-wave nonlinear partial differential equation (PDE) model - governing resonant space-time stimulated Brillouin or Raman backscattering - in the presence of a cw pump and dissipative material and Stokes waves. The study is motivated by pulse formation in optical fiber experiments. As a result of the instability any initial bounded Stokes signal is amplified and evolves to a subluminous backscattered Stokes pulse whose shape and velocity are uniquely determined by the damping coefficients and the cw-pump level. This asymptotically stable solitary three-wave structure is an attractor for any initial conditions in a compact support, in contrast to the known superluminous dissipative soliton solution which calls for an unbounded support. The linear asymptotic theory based on the Kolmogorov-Petrovskii-Piskunov assertion allows us to determine analytically the wave-front slope and the subluminous velocity, which are in remarkable agreement with the numerical computation of the nonlinear PDE model when the dynamics attains the asymptotic steady regime. © 1997 The American Physical Society.

Full correction for spatially distributed speed-of-sound in echo ultrasound based on measuring aberration delays via transmit beam steering

Aberrations of the acoustic wave front, caused by spatial variations of the speed-of-sound, are a main limiting factor to the diagnostic power of medical ultrasound imaging. If not accounted for, aberrations result in low resolution and increased side lobe level, over all reducing contrast in deep tissue imaging. Various techniques have been proposed for quantifying aberrations by analysing the arrival time of coherent echoes from so-called guide stars or beacons. In situations where a guide star is missing, aperture-based techniques may give ambiguous results. Moreover, they are conceptually focused on aberrators that can be approximated as a phase screen in front of the probe. We propose a novel technique, where the effect of aberration is detected in the reconstructed image as opposed to the aperture data. The varying local echo phase when changing the transmit beam steering angle directly reflects the varying arrival time of the transmit wave front. This allows sensing the angle-dependent aberration delay in a spatially resolved way, and thus aberration correction for a spatially distributed volume aberrator. In phantoms containing a cylindrical aberrator, we achieved location-independent diffraction-limited resolution as well as accurate display of echo location based on reconstructing the speed-of-sound spatially resolved. First successful volunteer results confirm the clinical potential of the proposed technique.

Magnetic resonance imaging of the manipulation of a chemical wave using an inhomogeneous magnetic field

The effects of applied magnetic fields on the traveling wave formed by the reaction of (ethylenediaminetetraacetato)cobalt(II) (Co(II)EDTA2-) and hydrogen peroxide have been studied using magnetic resonance imaging (MRI). It was found that the wave could be manipulated by applying pulsed magnetic field gradients to a sample contained in a vertical cylindrical tube in the 7.0 T magnetic field of the spectrometer. Transverse field gradients decelerated the propagation of the wave down the high-field side of the tube and accelerated it down the low-field side. This control of the wave propagation eventually promoted the formation of a finger on the low-field side of the tube and allowed the wave to be maneuvered within the sample tube. The origin of these effects is rationalized by considering the Maxwell stress arising from the combined homogeneous and inhomogeneous magnetic fields and the magnetic susceptibility gradient across the wave front.