Front Speed in the Burgers Equation with a Random Flux

We study the large-time asymptotic shock-front speed in an inviscid Burgers equation with a spatially random flux function. This equation is a prototype for a class of scalar conservation laws with spatial random coefficients such as the well-known Buckley–Leverett equation for two-phase flows, and the contaminant transport equation in groundwater flows. The initial condition is a shock located at the origin (the indicator function of the negative real line). We first regularize the equation by a special random viscous term so that the resulting equation can be solved explicitly by a Cole–Hopf formula. Using the invariance principle of the underlying random processes and the Laplace method, we prove that for large times the solutions behave like fronts moving at averaged constant speeds in the sense of distribution. However, the front locations are random, and we show explicitly the probability of observing the head or tail of the fronts. Finally, we pass to the inviscid limit, and establish the same results for the inviscid shock fronts.     

Propagation of fronts in cellular automata

The problem of propagation of fronts (traveling fronts) is investigated for two classes of two-dimensional cellular automata: simple totalistic automata with states 0,1, and Greenberg-Hastings automata that minic infection processes. These automata are investigated with analytic and with simulation methods. In the deterministic case the exact shapes of (anisotropic) fronts are determined as well as the propagation speed in several directions. In the stochastic case the fronts are investigated by simulation.     

Snell's law of refraction observed in thermal frontal polymerization

We demonstrate that Snell's law of refraction can be applied to thermal fronts propagating through a boundary between regions that support distinct frontal velocities. We use the free-radical frontal polymerization of a triacrylate with clay filler that allows for two domains containing two different concentrations of a peroxide initiator to be molded together. Because the polymerization reaction rates depend on the initiator concentration, the propagation speed is different in each domain. We study fronts propagating in two parallel strips in which the incident angle is 90 degrees. Our data fit Snell's law v(r)/v(i)=sin theta(r)/sin theta(i), where v(r) is the refracted velocity, v(i) is the incident velocity, theta(r) is the angle of refraction, and theta(i) is the incident angle. Further, we study circular fronts propagating radially from an initiation point in a high-velocity region into a low-velocity region (and vice versa). We demonstrate the close resemblance between the numerically simulated and experimentally observed thermal reaction fronts. By measuring the normal velocity and the angle of refraction of both simulated and experimental fronts, we establish that Snell's law holds for thermal frontal polymerization in our experimental system. Finally we discuss the regimes in which Snell's law may not be valid.     

Test of a conical lens using a two-beam shearing interferometer

We describe a two-beam shearing interferometric technique for testing refractive conical lenses. The optical configuration requires two mutually coherent plane wave fronts transmitted through the conical lens under test. The method can also be considered as an interferometric fringe projection technique in which a fringe pattern produced by the two interfering wave fronts is projected through the optical elements. We describe the principle of the method and present application of the technique for determining the angle formed by the flat surface and the conical surface of a refractive conical lens.     

Range resolution and the possible use of spectral information in the echolocating bat, Eptesicus fuscus

Individuals of the echolocating bat Eptesicus fuscus were trained to discriminate simulated two-wave-front targets with internal time delays of 0 to 100 microns between the wave fronts from a one-wave-front target. The ability of bats to discriminate between such targets can be referred to as range resolution. In Eptesicus fuscus, this ability is limited to distinct internal time delays (12, 32-40, and 52-100 microns) between the two wave fronts of a double-wave-front target. Analysis of the simulated two-wave-front echoes reveals periodic frequency minima in the spectrum. Position and separation of these spectral minima depend on the time delay between the two wave fronts. The occurrence of spectral minima within the frequency range of the first harmonic in the echo of the bats' echolocation call correlates to the bats' ability to discriminate a one-wave-front echo from two-wave-front echoes, suggesting that Eptesicus fuscus uses spectral differences within the first harmonic in echoes for range resolution.     

Isotropic compensation of diffraction-driven angular dispersion

We report on an optical arrangement capable of compensating angular dispersion of paraxial wave fields developed by diffractive optical elements (DOEs). Schematically, the system is a beam expander in which two phase-only zone plates have been inserted, remaining afocal the coupled system. The DOE, which induces a continuous set of dispersive tilted plane waves, is placed at a specific position within the proposed setup providing an output spectrum with achromatic angular deviation. A directional matching between phase fronts and pulse fronts of output wave packets is demonstrated.     

Spatial multistability and nonvariational effects

We investigate the phenomenon of spatial multistability of fronts in thin bistable systems and stress the important role played by the absence of a variational principle. Nonvariational effects allow, for instance, two different immobilized fronts to coexist. The morphological instability of the corresponding nucleating solution can then lead, even in the absence of any diffusive instability, to nontrivial patterns in the depth of one-side-fed reactors.     

The propagation of discontinuities in non-homogeneous thermoviscoelastic media

In this study, the propagation of plane, cylindrical and spherical dilatational waves in non-homogeneous thermoviscoelastic media is investigated by employing the notion of singular surfaces and the method of characteristics. The inhomogeneity of the medium is such that the material properties depend in an arbitrary manner on the co-ordinate coinciding with the direction of the propagation. An integral type constitutive equation is considered for the heat flux which permits a finite propagation speed for thermal disturbances. It is found that the application of a dynamic input on the boundary surface gives rise to two different wave fronts along which mechanical and thermal effects are coupled. The growth and decay equations describing the change of the strength of the discontinuities on these two wave fronts are then obtained. By integrating the growth and decay equations along the rays the solutions valid at the wave fronts are found. The solutions are then reduced to two special cases: in one the heat flux equation is taken as the so-called modified Fourier equation, and in the other as the classical Fourier equation. The effects of inhomogeneity, geometry of the wave front, thermomechanical coupling and material internal friction on the strength of the discontinuity are discussed.     

二次波面干涉的剪切散斑干涉计量术

提出了一种新的剪切散斑干涉方法─—二次波面干涉的剪切散斑干涉计量术．这一方法将被测物体变形前后波面的第一次干涉信息分别储存在两张全息干板上，通过光学信息处理实现波面的第二次干涉．两次波面干涉分别消除了位移和位移的一阶导数场对波面位相的影响，得到仅反映位移二阶导数场的条纹图．     

Fronts between rhythms: spatiotemporal dynamics of extended polyrhythmic media

We study the propagation of fronts in extended oscillatory reaction-diffusion systems that contain several coexisting limit cycles. In contrast with the variational behavior, fronts between regions oscillating in two different limit cycles are found to propagate not necessarily towards the region of the less stable limit cycle, but towards the regions of the largest amplitudes, provided that the frequency mismatch between the cycles is sufficiently large. In other words, the smaller oscillations can always be made to control the whole system.     

High-speed imaging of the ignition of ethanol at engine relevant conditions in a rapid compression machine

The rapid compression machine (RCM) is a great tool for investigating fuel properties under engine relevant conditions (high-pressures, low temperatures). The most common diagnostics is measuring the pressure over time and determining the ignition delay time (IDT). In this study, for the first time, the OH* luminescence of ethanol/air mixture is measured within an RCM experiment at 15 and 20?bar for Φ?=?0.5. Combining the common pressure measurements with the simultaneously recorded high-speed images (up to 74.5?kHz framerate) gives a first insight into understanding the ignition modes and the corresponding pressure traces. At 74.5?kHz, in contrast to findings in literature, the ethanol ignition did not show to be purely homogeneous. Four different propagating fronts of OH* luminescence have been recorded. Besides a flame kernel and a detonation-like ignition front two further fronts prior to main ignition have been observed. The propagating speeds of the fronts have been determined and depend on the overall IDT.     

Bound states of topological defects in parametrically excited capillary waves

Bound states of topological defects arising in a tetragonal lattice formed by two orthogonal standing parametrically excited capillary surface waves are investigated. Such bound states are shown to consist either of two topological charges of one sign (type 1) or of topological charges having opposite signs (type 2). It was found that bound states of type 1 move primarily along wave fronts, and type 2 bound states move at an angle of 45^○ to the wave fronts forming a tetragonal lattice. A system of four coupled Ginzburg–Landau equations is proposed to model bound states. Numerical modeling of this system gave solutions corresponding to type 1 bound states observed in experiment.     

One-dimensional dynamics for traveling fronts in coupled map lattices

Multistable coupled map lattices typically support traveling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile allows a reduction of the infinitely dimensional dynamics to a one-dimensional circle homeomorphism, whose rotation number gives the propagation velocity. The mode locking of the velocity with respect to the system parameters then typically follows. We study the behavior of fronts near the boundary of parametric stability, and we explain how the mode locking tends to disappear as we approach the continuum limit of an infinite density of sites.     

Stability of convective patterns in reaction fronts: a comparison of three models

Autocatalytic reaction fronts generate density gradients that may lead to convection. Fronts propagating in vertical tubes can be flat, axisymmetric, or nonaxisymmetric, depending on the diameter of the tube. In this paper, we study the transitions to convection as well as the stability of different types of fronts. We analyze the stability of the convective reaction fronts using three different models for front propagation. We use a model based on a reaction-diffusion-advection equation coupled to the Navier-Stokes equations to account for fluid flow. A second model replaces the reaction-diffusion equation with a thin front approximation where the front speed depends on the front curvature. We also introduce a new low-dimensional model based on a finite mode truncation. This model allows a complete analysis of all stable and unstable fronts.     

The effects of fluid motion on oscillatory and chaotic fronts

We study oscillatory and chaotic reaction fronts described by the Kuramoto-Sivashinsky equation coupled to different types of fluid motion. We first apply a Poiseuille flow on the fronts inside a two-dimensional slab. We show regions of period doubling transition to chaos for different values of the average speed of Poiseuille flow. We also analyze the effects of a convective flow due to a Rayleigh-Taylor instability. Here the front is a thin interface separating two fluids of different densities inside a two-dimensional vertical slab. Convection is caused by buoyancy forces across the front as the lighter fluid is under a heavier fluid. We first obtain oscillatory and chaotic solutions arising from instabilities intrinsic to the front. Then, we determine the changes on the solutions due to fluid motion.     

Nonlocal dynamics of spontaneous imbibition fronts

We have studied spontaneous imbibition fronts generated by capillary rise between two roughened glass plates, the separation d of which varied between 10 and 50 microm. Perfect agreement with Washburn's law was obtained. We have determined the roughness exponent chi of the fronts, and found chi=0.81+/-0.01 for small length scales. Above a certain crossover length xi, it reached chi=0.58+/-0.04, as predicted by the quenched noise Kardar-Parisi-Zhang equation. The crossover length is found to scale with the plate separation as sqrt[d], as predicted by recent models which properly include nonlocal dynamics effects on the front. We believe this to be the first clear identification of crossover from nonlocal to local dynamics.     

Out-of-equilibrium kondo effect in double quantum dots

We present results of high resolution experiments on kinetic roughening of slow combustion fronts in paper, focusing on short length and time scales. Using three different grades of paper, we find that the combustion fronts show apparent spatial and temporal multiscaling at short scales. The scaling exponents decrease as a function of the order of the corresponding correlation functions. The noise affecting the fronts reveals short range temporal and spatial correlations, and non-Gaussian noise amplitudes. Our results imply that the overall behavior of slow combustion fronts cannot be explained by standard theories of kinetic roughening.     

Experimental determination of KPZ height-fluctuation distributions

Height-fluctuation distributions of nonequilibrium interfaces were analyzed using slow-combustion fronts propagating in sheets of paper. All distributions measured were definitely non-Gaussian. The experimental distributions for transient and stationary regimes were well fitted by the theoretical distributions proposed by Prähofer and Spohn in reference [9]. Consistent with the Galilean invariance of the system, the same distributions were found for horizontal fronts and, when determined along the normal to the slope, for fronts with a non-zero average slope.     

Persistence of zero velocity fronts in reaction diffusion systems

Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control parameter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The experimental observation of fronts with a zero velocity over a finite interval of parameters, e.g., in catalytic experiments [Barelko et al., Chem. Eng. Sci., 33, 805 (1978)], therefore, seems paradoxical. We show that the velocity dependence on the control parameter may be such that velocity is very small over a finite interval, and much larger outside. This happens in a class of reaction diffusion systems with two components, with the extra assumptions that (i) the two diffusion coefficients are very different, and that (ii) the slowly diffusing variables has two stable states over a control parameter range. The ratio of the two velocity scales vanishes when the smallest diffusion coefficient goes to zero. A complete study of the effect is carried out in a model of catalytic reaction. (c) 2000 American Institute of Physics.