Showing papers on "Wave propagation published in 1995"

A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

Abstract: Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlinearity is made, the equations can be applied to simulate strong wave interactions prior to wave breaking. A high-order numerical model based on the equations is developed and applied to the study of two canonical problems: solitary wave shoaling on slopes and undular bore propagation over a horizontal bed. Results of the Boussinesq model with and without strong nonlinearity are compared in detail to those of a boundary element solution of the fully nonlinear potential flow problem developed by Grilli et al. (1989). The fully nonlinear variant of the Boussinesq model is found to predict wave heights, phase speeds and particle kinematics more accurately than the standard approximation.

Chemical waves and patterns

Abstract: Spiral Waves. Lingering Mysteries about Organizing Centers in the Belousov-Zhabotinsky Medium and its Oregonator Model A. Winfree. Spiral Wave Dynamics S. Muller, T. Plesser. A Theory of Rotating Scroll Waves in Excitable Media J. Tyson, J. Keener. Spiral Waves in Weakly Excitable Media A.S. Mikhailov, V.S. Zykov. Spiral Meandering D. Barkley. Spiral and Target Waves in Finite and Discontinuous Media A.-A. Sepulchre, A. Babloyantz. Turing and Turing-like Patterns. Turing Patterns: from Myth to Reality J. Boissonade, E. Dulos, P. DeKepper. Onset and Beyond Turing Pattern Formation Q. Ouyang, H.L. Swinney. The Chemistry behind the First Experimental Chemical Examples of Turing Patterns I. Lengyel, I.R. Epstein. Turing Bifurcations and Pattern Selection P. Borckmans, G. Dewel, A. De Witt, D. Walgraef. The Differential Flow Instabilities M. Menzinger, A. Rovinsky. Chemical Wave Dynamics. Wave Propagation and Pattern Formation in Nonuniform Reaction-Diffusion Systems A. Zhabotinsky. Chemical Front Propagation: Initiation and Stability E. Mori, X. Chu, J. Ross. Pattern Formation on Catalytic Surfaces M. Eiswirth, G. Ertl. Simple and Complex Reaction-Diffusion Fronts S.K. Scott, K. Showalter. Modeling Front Pattern Formation and Intermittent Bursting Phenomena in the Couette Flow Reactor A. Arneodo, J. Elegaray. Fluctuations and Chemical Waves. Probabilistic Approach to Chemical Instabilities and Chaos G. Nicolis, F. Baras, P. Geysermans, P. Peeters. Internal Noise, Oscillations, Chaos and Chemical Patterns R. Kapral, X.-G. Wu. Index.

Time-Dependent Numerical Code for Extended Boussinesq Equations

Abstract: The extended Boussinesq equations derived by Nwogu (1993) significantly improve the linear dispersive properties of long-wave models in intermediate water depths, making it suitable to simulate wave propagation from relatively deep to shallow water. In this study, a numerical code based on Nwogu's equations is developed. The model uses a fourth-order predictor-corrector method to advance in time, and discretizes first-order spatial derivatives to fourth-order accuracy, thus reducing all truncation errors to a level smaller than the dispersive terms retained by the model. The basic numerical scheme and associated boundary conditions are described. The model is applied to several examples of wave propagation in variable depth, and computed solutions are compared with experimental data. These initial results indicate that the model is capable of simulating wave transformation from relatively deep water to shallow water, giving accurate predictions of the height and shape of shoaled waves in both regular and irregular wave experiments.

Microcrack-induced elastic wave anisotropy of brittle rocks

Abstract: The failure of brittle rocks during compression is preceded by the formation, growth, and coalescence of microcracks. Elastic wave velocities are reduced in the presence of open microcracks and fractures and may therefore be used to monitor the progressive damage of the rock. In general, these microcracks are not randomly oriented, and the rock displays an elastic anisotropy. The elastic anisotropy due to cracks can be expressed in terms of a second-rank and fourth-rank crack density tensor. For open cracks the contribution of the fourth-rank crack density tensor to the elastic wave velocities is small. These results are compared with recent measurements of the ultrasonic compressional and shear wave velocities for propagation parallel and perpendicular to an increasing axial stress applied at constant confining stress to Berea sandstone. Inversion of the velocity measurements indicates that the microcracks propagate parallel to the maximum compressive stress, in agreement with current rock mechanics theory. A reasonable fit to the data is obtained using only the second-rank crack density tensor even though, at high confining stress, the cracks are expected to be in partial contact along their length. This is consistent with the model of elastic wave propagation in a medium containing partially contacting fractures published by White. However, measurements of off-axis wave velocities are required to fully quantify the contribution of the fourth-rank crack density tensor.

Wave propagation in layered anisotropic media : with applications to composites

Abstract: Introduction - historical background. Part 1 Field equations and tensor analysis: the stiffness tensor material symmetry matrix forms of stiffness engineering constants transformed equations expanded field equations planes of symmetry. Part 2 Bulk waves: an overview the Christoffel equation material symmetry computer aided analysis group velocity energy flux. Part 3 Generalized Snell's law and interfaces: boundary conditions characterization of incident waves critical angles two fluid media two isotropic media. Part 4 Formal solutions: common form of solutions triclinic layer the monoclinic case higher symmetry materials formal solutions in fluid media the alpha-c relation and the Christoffel equation. Part 5 Scattered wave amplitudes: notation reflection from a free surface scattering from fluid-solid interfaces scattering from solid-solid interface. Part 6 Interface waves: surface waves pseudo-surface waves Scholte waves. Part 7 Free wave in plates: free waves in triclinic plates free waves in monoclinic plates higher symmetry material plates numerical computation strategy. Part 8 General layered media: geometric description of unit cell analysis properties of the transfer matrix free waves on the layered cell waves in a periodic medium bottom bounding solid substrate. Part 9 Propagation along axes of symmetry: geometry SH waves motion in the sagittal plane free waves on the layered cell waves in a periodic medium bottom bounding solid substrate. Part 10 Fluid-loaded solids: reflection from a substrate plates completely immersed in fluids higher symmetry cases leaky waves experimental technique. Part 11 Piezoelectric effects: basic relations of piezoelectric materials simplified field equations analysis formal solutions higher symmetric materials remarks on the monoclinic-m case reflection and transmission coefficients sample illustration remarks on layered piezoelectric media. Part 12 Transient waves: theoretical development source characterization integral transforms of formal solutions isotropic media anisotropic media Cagniard-de Hoop transformation semi-space media. Part 13 Scattering from layered cylinders: field equations formal solutions in isotropic cylinders characterization of incident waves formal solutions for a layer scattering amplitudes. Part 14 Elastic properties of composites: general description of fibrous composites the model the layered model the square fibrous case anisotropic fibre and matrix strain energy approach undulated fibre appendix.

Anisotropic wave propagation through finite‐difference grids

Abstract: An algorithm is presented to solve the elastic-wave equation by replacing the partial differentials with finite differences. It enables wave propagation to be simulated in three dimensions through generally anisotropic and heterogeneous models. The space derivatives are calculated using discrete convolution sums, while the time derivatives are replaced by a truncated Taylor expansion. A centered finite difference scheme in cartesian coordinates is used for the space derivatives leading to staggered grids. The use of finite difference approximations to the partial derivatives results in a frequency-dependent error in the group and phase velocities of waves. For anisotropic media, the use of staggered grids implies that some of the elements of the stress and strain tensors must be interpolated to calculate the Hook sum. This interpolation induces an additional error in the wave properties. The overall error depends on the precision of the derivative and interpolation operators, the anisotropic symmetry system, its orientation and the degree of anisotropy. The dispersion relation for the homogeneous case was derived for the proposed scheme. Since we use a general description of convolution sums to describe the finite difference operators, the numerical wave properties can be calculated for any space operator and an arbitrary homogeneous elastic model. In particular, phase and group velocities of the three wave types can be determined in any direction. We demonstrate that waves can be modeled accurately even through models with strong anisotropy when the operators are properly designed.

Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm.

Abstract: The structural elements in a rock are characterized by their density in Preisach-Mayergoyz space (PM space). This density is found for a Berea sandstone from stress-strain data and used to study the response of the sandstone to elaborate pressure protocols. Hysteresis with discrete memory, in agreement with experiment, is found. The relationship between strain, quasistatic modulus, and dynamic modulus is established. Nonlinear wave propagation, the production of copious harmonics, and nonlinear attenuation are demonstrated. PM space is shown to be the central construct in a new paradigm for the description of the elastic behavior of consolidated materials.

Order- N spectral method for electromagnetic waves

Abstract: We show that the eigenmodes for electromagnetic waves in an inhomogeneous dielectric medium can be obtained with an algorithm that scales linearly with the size of the system. The method employs discretization of the Maxwell equations in both the spatial and the time domain and the integration of the Maxwell equations in the time domain. The spectral intensity can then be obtained by a Fourier transform. We applied the method to a few problems of current interest, including the photonic band structure of a periodic dielectric structure, the effective dielectric constants of some three-dimensional and two-dimensional systems, and the defect states of a periodic dielectric structure with structural defects.

Metallic photonic band-gap materials

Abstract: We calculate the transmission and absorption of electromagnetic waves propagating in two-dimensional (2D) and 3D periodic metallic photonic band-gap (PBG) structures. For 2D systems, there is substantial difference between the {ital s}- and {ital p}-polarized waves. The {ital p}-polarized waves exhibit behavior similar to the dielectric PBG`s. But, the {ital s}-polarized waves have a cutoff frequency below which there are no propagating modes. For 3D systems, the results are qualitatively the same for both polarizations but there are important differences related to the topology of the structure. For 3D structures with isolated metallic scatterers (cermet topology), the behavior is similar to that of the dielectric PBG`s, while for 3D structures with the metal forming a continuous network (network topology), there is a cutoff frequency below which there are no propagating modes. The systems with the network topology may have some interesting applications for frequencies less than about 1 THz where the absorption can be neglected. We also study the role of the defects in the metallic structures.

Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation

Abstract: This tutorial paper proposes a subclass of cellular neural networks (CNN) having no inputs (i.e., autonomous) as a universal active substrate or medium for modeling and generating many pattern formation and nonlinear wave phenomena from numerous disciplines, including biology, chemistry, ecology, engineering, and physics. Each CNN is defined mathematically by its cell dynamics (e.g., state equations) and synaptic law, which specifies each cell's interaction with its neighbors. We focus on reaction-diffusion CNNs having a linear synaptic law that approximates a spatial Laplacian operator. Such a synaptic law can be realized by one or more layers of linear resistor couplings. An autonomous CNN made of third-order universal cells and coupled to each other by only one layer of linear resistors provides a unified active medium for generating trigger (autowave) waves, target (concentric) waves, spiral waves, and scroll waves. When a second layer of linear resistors is added to couple a second capacitor voltage in each cell to its neighboring cells, the resulting CNN can be used to generate various turing patterns. >

Modeling of Breaking and Nonbreaking Long-Wave Evolution and Runup Using VTCS-2

Abstract: We present a variable grid finite-differences approximation of the characteristic form of the shallow-water-wave equations without artificial viscosity or friction factors to model the propagation and runup of one-dimensional long waves, referred to as VTCS-2. We apply our method in the calculation of the evolution of breaking and nonbreaking waves on sloping beaches. We compare the computational results with analytical solutions, other numerical computations and with laboratory data for breaking and nonbreaking solitary waves. We find that the model describes the evolution and runup of nonbreaking waves very well, even when using a very small number of grid points per wavelength. Even though our method does not model the detailed surface profile of wave breaking well, it adequately predicts the runup of plunging solitary waves without ad-hoc assumptions about viscosity and friction. This appears to be a further manifestation of the well-documented but unexplained ability of the shallow water wave equatio...

Fundamentals of optical fibers

Abstract: Preface.Introduction.Chapter 1. Selected Topics in Electromagnetic Wave Propagation.1.1. Maxwell's Equations and the Fundamental Fields.1.2. Electromagnetic Wave Propagation in Sourceless Media.1.3. Power Transmission.1.4. Group Velocity.1.5. Reflection and Transmission of Waves at Plane Interfaces.1.6. Material Resonances and Their Effects on Wave Propagation.Problems.References.Chapter 2. Symmetric Dielectric Slab Waveguides.2.1. Ray Analysis of the Slab Waveguides.2.2. Field Analysis of the Slab Waveguides.2.3. Solutions of the Eigenvalue Equations.2.4. Power Transmission and Confinement.2.5. Leaky Waves.2.6. Radiation Modes.2.7. Wave Propagation in Curved Slab Waveguides.Problems.References.Chapter 3. Weakly-Guiding Fibers with Step Index Profiles.3.1. Rays and Fields in the Step Index Fiber.3.2. Field Analysis of the Weakly-Guiding Fiber.3.3. Eigenvalue Equation for LP Modes.3.4. LP Mode Characteristics.3.5. Single Mode Fiber Parameters.3.6. Derivation of the General Step Index Fiber Modes.Problems.References.Chapter 4. Loss Mechanisms in Silica Fiber.4.1. Basic Loss Effects in Transmission.4.2. Fabrication of Silica Fibers.4.3. Intrinsic Loss.4.4. Extrinsic Loss.4.5. Bending Loss.4.6. Source-to-Fiber Coupling.Problems.References.Chapter 5. Dispersion.5.1. Pulse Propagation in Media Possessing Quadratic Dispersion.5.2. Material Dispersion.5.3. Dispersion in Optical Fiber.5.4. Chromatic Dispersion Compensation.5.5. Polarization Dispersion.5.6. System Considerations and Dispersion Measurement.Problems.References.Chapter 6. Special Purpose Index Profiles.6.1. Multimode Graded Index Fiber.6.2. Special Index Profile Optimization.Problems.References.Chapter 7. Nonlinear Effects in Fibers I: Non-Resonant Processes.7.1. Nonlinear Optics Fundamentals.7.2. Nonlinear Phase Modulation on Pulses.7.3. The Nonlinear Schrodinger Equation.7.4. Additional Non-Resonant Processes.Problems.References.Chapter 8. Nonlinear Effects in Fibers II: Resonant Processes and Amplification.8.1. Raman Scattering.8.2. Stimulated Brillouin Scattering.8.3. Rare-Earth-Doped Fiber Amplifiers.Problems.References.Appendix A: Properties of Bessel Functions.Appendix B: Notation.Index.

A galerkin least-squares finite element method for the two-dimensional Helmholtz equation

Abstract: In this paper a Galerkin least-squares (GLS) finite element method, in which residuals in least-squares form are added to the standard Galerkin variational equation, is developed to solve the Helmholtz equation in two dimensions. An important feature of GLS methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes. Previous work has accomplished this for the one-dimensional Helmholtz equation using dispersion analysis. In this paper, the selection of the GLS mesh parameter for two dimensions is considered, and leads to elements that exhibit improved phase accuracy. For any given direction of wave propagation, an optimal GLS mesh parameter is determined using two-dimensional Fourier analysis. In general problems, the direction of wave propagation will not be known a priori. In this case, an optimal GLS parameter is found which reduces phase error for all possible wave vector orientations over elements. The optimal GLS parameters are derived for both consistent and lumped mass approximations. Several numerical examples are given and the results compared with those obtained from the Galerkin method. The extension of GLS to higher-order quadratic interpolations is also presented.

An Iterative Filtering Technique for the Analysis of Copolar Differential Phase and Dual-Frequency Radar Measurements

Abstract: Copolar differential phase is composed of two components, namely, differential propagation phase and differential backscatter phase. To estimate specific differential phase KDP, these two phase components must first be separated when significant differential backscatter phase is present. This paper presents an iterative range filtering technique that can separate these phase components under a wider variety of conditions than is possible with a simple range filter. This technique may also be used when estimating hail signals from range profiles of dual-frequency reflectivity ratios.

Linear and nonlinear modes in nonrelativistic electron-positron plasmas

Abstract: A comprehensive two-fluid model is developed for collective modes in a nonrelativistic electron-positron plasma. Longitudinal and transverse electrostatic and electromagnetic modes, both in the presence and absence of a magnetic field, are studied. Wave properties are discussed in terms of dispersion relations, wave normal surfaces, and cylindrical mirror analyzer clemmow-Mullaly-Allis diagrams. The results are extended to include the two-stream instability and ion acoustic solitary waves. For the two-stream instability, a similar result is found as in the electron-ion plasma. For ion acoustic solitary waves, only subsonic solutions are found to exist. Furthermore, their width is proportional to their amplitude, unlike the electron-ion plasma case, where the speed is proportional to the amplitude.

Wave propagation in heterogeneous, porous media: A velocity‐stress, finite‐difference method

Abstract: A particle velocity-stress, finite-difference method is developed for the simulation of wave propagation in 2-D heterogeneous poroelastic media. Instead of the prevailing second-order differential equations, we consider a first-order hyperbolic system that is equivalent to Biot's equations. The vector of unknowns in this system consists of the solid and fluid particle velocity components, the solid stress components, and the fluid pressure. A MacCormack finite-difference scheme that is fourth-order accurate in space and second-order accurate in time forms the basis of the numerical solutions for Biot's hyperbolic system. An original analytic solution for a P-wave line source in a uniform poroelastic medium is derived for the purposes of source implementation and algorithm testing. In simulations with a two-layer model, additional «slow» compressional incident, transmitted, and reflected phases are recorded when the damping coefficient is small. This «slow» compressional wave is highly attenuated in porous media saturated by a viscous fluid. From the simulation we also verified that the attenuation mechanism introduced in Biot's theory is of secondary importance for «fast» compressional and rotational waves. The existence of seismically observable differences caused by the presence of pores has been examined through synthetic experiments that indicate that amplitude variation with offset may be observed on receivers and could be diagnostic of the matrix and fluid parameters. This method was applied in simulating seismic wave propagation over an expanded steam-heated zone in Cold Lake, alberta in an area of enhanced oil recovery (EOR) processing. The results indicate that a seismic surface survey can be used to monitor thermal fronts

0n the dynamics of warped accretion disks

Abstract: We present some analyses of warping modes in inviscid near Keplerian disks taking the three-dimensional structure fully into account. The results of this investigation verify the validity of a vertical averaging approximation for thin disks when the radial wavelength is significantly longer than the disk thickness. They also indicate that long wavelength disturbances may persist for long times. Shorter wavelength disturbances in non-self gravitating disks are found to propagate with little dispersion at a speed related to the sound speed. When self-gravity becomes important, fast and slow waves are found which also propagate with little dispersion. When a small viscosity is included, the evolution of the disturbances becomes more diffusive in character.

Generation and propagation of infragravity waves

Abstract: The generation and propagation of infragravity waves (frequencies nominally 0.004–0.04 Hz) are investigated with data from a 24-element, coherent array of pressure sensors deployed for 9 months in 13-m depth, 2 km from shore. The high correlation between observed ratios of upcoast to downcoast energy fluxes in the infragravity (FupIG/FdownIG) and swell (Fupswell/Fdownswell) frequency bands indicates that the directional properties of infragravity waves are strongly dependent on incident swell propagation directions. However, FupIG/FdownIG is usually much closer to 1 (i.e., comparable upcoast and downcoast fluxes) than is Fupswell/Fdownswell, suggesting that upcoast propagating swell drives both upcoast and downcoast propagating infragravity waves. These observations agree well with predictions of a spectral WKB model based on the long-standing hypothesis that infragravity waves, forced by nonlinear interactions of nonbreaking, shoreward propagating swell, are released as free waves in the surf zone and subsequently reflect from the beach. The radiated free infragravity waves are predicted to be directionally broad and predominantly refractively trapped on a gently sloping shelf. The observed ratios FseaIG/FshoreIG of the seaward and shoreward infragravity energy fluxes are indeed scattered about the theoretical value 1 for trapped waves when the swell energy is moderate, but the ratios deviate significantly from 1 with both low- and high-energy swell. Directionally narrow, shoreward propagating infragravity waves, observed with low-energy swell, likely have a remote (possibly trans-oceanic) energy source. High values (up to 5) of FseaIG/FshoreIG, observed with high-energy swell, suggest that high-mode edge waves generated near the shore can be suppressed by nonlinear dissipation processes (e.g., bottom friction) on the shelf.

Complementary approximations to wave scattering by vertical barriers

Abstract: Scattering of waves by vertical barriers in infinite-depth water has received much attention due to the ability to solve many of these problems exactly. However, the same problems in finite depth require the use of approximation methods. In this paper we present an accurate method of solving these problems based on a Galerkin approximation. We will show how highly accurate complementary bounds can be computed with relative ease for many scattering problems involving vertical barriers in finite depth and also for a sloshing problem involving a vertical barrier in a rectangular tank.

Time Frequency Analysis of Dispersive Waves by Means of Wavelet Transform

Abstract: A new approach is presented for investigating the dispersive character of structural waves. The wavelet transform is applied to the time-frequency analysis of dispersive waves. The flexural wave induced in a beam by lateral impact is considered. It is shown that the wavelet transform using the Gabor wavelet effectively decomposes the strain response into its time-frequency components. In addition, the peaks of the time-frequency distribution indicate the arrival times of waves. By utilizing this fact, the dispersion relation of the group velocity can be accurately identified for a wide range of frequencies.

Optical propagation in non-Kolmogorov atmospheric turbulence

Abstract: Several observations of atmospheric turbulence statistics have been reported which do not obey Kolmogorov's power spectral density model. These observations have prompted the study of optical propagation through turbulence described by non-classical power spectra. This paper presents an analysis of optical propagation through turbulence which causes fluctuations in the index of refraction. The index fluctuations are assumed to have spatial power spectra that obey arbitrary power laws. The spherical and plane wave structure functions are derived using Mellin transform techniques. The wave structure function is used to compute the Strehl ratio of a focused plane wave propagating in turbulence as the power law for the spectrum of the index of refraction fluctuations is varied from -3 to -4. The relative contributions of the log amplitude and phase structure functions to the wave structure function are computed. At power laws close to -3, the magnitude of the log amplitude and phase perturbations are determined by the system Fresnel ratio. At power laws approaching -4, phase effects dominate in the form of random tilts.

Tropical instability wave kinematics: Observations from the Tropical Instability Wave Experiment

Abstract: The kinematics of planetary waves originating from instability of the nearsurface equatorial currents are reported on using velocity measurements from an array of acoustic Doppler current profilers deployed in the equatorial Pacific during the Tropical Instability Wave Experiment. A distinctive wave season was observed from August to December 1990, with wave energy confined primarily above the core of the Equatorial Undercurrent. Particle motions in the horizontal plane are described by eccentric ellipses oriented toward the north, but tilting into the cyclonic shear of the South Equatorial Current. The tilt is maximum near the surface just north of the equator and decreases to the south and with depth. The distribution of wave variance is narrowband in both frequency and zonal wavenumber, with central period, zonal wavelength, and westward directed phase propagation estimated to be 500 hours, 1060 km, and 59 cm s -1 , respectively. Neither the meridional nor the vertical wavenumber component is statistically different from zero. These results generally agree with previous findings on tropical instability waves from the Atlantic and Pacific Oceans, and, in the undersampled arena of geophysical measurements, they provide an example where statistical inference is supported by an ensemble of independent measurements

Three‐dimensional instabilities of film flows

Abstract: Two‐dimensional (2‐D) interfacial waves on flowing films are unstable with respect to both two‐ and three‐dimensional instabilities. In this paper, several distinct three‐dimensional instabilities that occur in different regions of the parameter space defined by the Reynolds numberR and the frequency f of forced two‐dimensional waves are discussed in detail. (a) A synchronous 3‐D instability, in which spanwise deformations of adjacent wave fronts have the same transverse phase, appears over a wide range of frequency. These transverse modulations occur mainly along the troughs of the primary waves and eventually develop into sharp and nearly isolated depressions. The instability involves many higher harmonics of the fundamental 2‐D waves. (b) A 3‐D surbharmonic instability occurs for frequencies close to the neutral curve f c (R). In this case, the transverse modulations are out of phase for successive wave fronts, and herringbone patterns result. It is shown that this weakly nonlinear instability is due to the resonant excitation of a triad of waves consisting of the fundamental two‐dimensional wave and two oblique waves. The evolution of wavy films after the onset of either of these 3‐D instabilities is complex. However, sufficiently far downstream, large‐amplitude solitary waves absorb the smaller waves and become dominant.

Logic gates in excitable media

Abstract: The interaction of chemical waves propagating through capillary tubes is studied experimentally and numerically. Certain combinations of two or more tubes give rise to logic gates based on input and output signals in the form of chemical waves and wave initiations. The geometrical configuration, the temporal synchronization of the waves, and the ratio of the tube radius to the critical radius of the excitable medium determine the features of the logic gates.

Biot model of sound propagation in water‐saturated sand

Abstract: Elastic theory of wave propagation and the measured speed of sound in sandy ocean sediments indicate that such sediments are impenetrable to high‐frequency sound at shallow grazing angles. The speed of sound in water‐saturated, unconsolidated sand is in the region of 1700 m/s which, under the elastic theory of wave propagation, gives it a critical grazing angle in the region of 28°. At shallower grazing angles, refraction is not permitted, and total internal reflection is predicted. Recent experimental measurements contradict this view. Biot’s theory of acoustic propagation in porous sediments is the most likely explanation. Biot’s theory of acoustic propagation, as it applies to water‐saturated sand, is reviewed. The speed of the slow wave is found to be higher than previously predicted. New input parameter values are deduced.

Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method

Abstract: The finite element approach has been previously used, with the help of the ATILA code, to model the scattering of acoustic waves by single or doubly periodic passive structures [A. C. Hladky‐Hennion et al., J. Acoust. Soc. Am. 90, 3356–3367 (1991)]. This paper presents a new extension of this technique to the analysis of the propagation of plane acoustic waves in passive periodic materials without losses and describes with particular emphasis its application to doubly periodic materials containing different types of inclusions. In the proposed approach, only the unit cell of the periodic material has to be meshed, thanks to Bloch–Floquet relations. The modeling of these materials provides dispersion curves from which results of physical interest can be easily extracted: identification of propagation modes, cutoff frequencies, passbands, stopbands, as well as effective homogeneous properties. In this paper, the general method is first described, and particularly the aspects related to the periodicity. Then a test example is given for which analytical results exist. This example is followed by detailed presentations of finite element results, in the case of periodic materials containing inclusions or cylindrical pores. The homogenized properties of porous materials are determined with the help of an anisotropic model, in the large wavelength limit. A validation has been carried out with periodically perforated plates, the resonance frequencies of which have been measured. The efficiency and the versatility of the method is thus clearly demonstrated.

Magnetosphere cyclotron maser: Backward wave oscillator generation regime

Abstract: A new generation regime of the magnetosphere cyclotron maser is considered, based on phase coherence effects in wave-particle systems with step-like deformations of electron velocity distribution functions. Such deformations appear during cyclotron interactions of noise-like whistler wave emissions and energetic electrons at the boundaries between resonant and nonresonant particles. The new regime is similar to the backward wave oscillator in laboratory electronic devices. This regime applies to the generation of chorus emissions and may explain the connection between chorus and hiss, their fast growth rates, and the temporal succession of chorus elements.