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International audience; In the current work, we study the role of chirality and non-centrosymmetry on the nonlinear wave propagation characteristics of periodic architectured media. The considered nonlinearities arise from the higher-order inner element kinematics of the periodic media and are therefore directly related to its structural pattern. Regarding centrosymmetric designs, the frequency corrections obtained -in the context of the Lindstedt-Poincare method- suggest that chiral architectures are more sensitive to inner kinematic nonlinearities than well-known, achiral lattice designs. In particular, for hexachiral lattice designs, non-negligible frequency corrections are obtained, not only for the primal eigenmode, but also for higher-order modes, extensively modifying the linear band diagram structure. To the contrary, for achiral, triangular and square lattice designs, inner kinematic nonlinearities mainly influence the primal, lowest eigenmode, with the higher-order modes to remain practically unaffected. Non-centrosymmetric inner designs modify the linear and nonlinear wave propagation material attributes both for chiral and achiral lattice patterns. However, the frequency ranges affected are strongly lattice dependent, with hexachiral and triangular lattices to be primarily influenced in their high frequency range, contrary to square lattices, which are mainly affected in their low frequency region.

The present work deals with wave generation in fully nonlinear numerical wave tanks (NWT). As an alternative to modelling a moving (physical) wavemaker, a two-dimensional (2D) potential-flow NWT is coupled with an external spectral wave data (SWD) application programming interface (API). The NWT uses the harmonic polynomial cell (HPC) method to solve the governing Laplace equations for the velocity potential and its time derivative, and has previously been extensively validated and verified for numerous nonlinear wave-propagation problems using traditional wave-generation mechanisms. Periodic waves of different steepness generated with a stream-function theory as reference solution in the SWD API are first considered to investigate the method’s numerical accuracy. Thereafter, with a higher-order spectral method (HOSM) as the SWD API solution, irregular waves with different wave heights and water depths relevant for e.g. aquaculture and offshore structures are simulated. Differences between the HPC and HOSM solutions in and near steep crests are investigated. The study aims to demonstrate a robust method to generate and propagate general wave fields for further studies of nonlinear waves and wave-body interaction in both two and three dimensions.

We experimentally demonstrate a simple approach to enhance second-harmonic generation (SHG) from multilayer Gallium Selenide by encapsulating with an optimized thickness of low-index dielectric layers. 46-times enhancement is observed showing good agreement with nonlinear wave propagation simulation.

The Haar wavelet method (HWM) is adapted for solving 2D nonlinear wave propagation problems. The 2D Burgers equation is considered as a model equation here. The 2D wavelet expansion is employed for the spatial derivatives and standard ordinary differential equation solvers are used for the temporal derivative. The aim of the study is to validate HWM in multi- dimensional case. The numerical results obtained are found to be in good agreement with analytical solution.

Various behaviours of nonlinear wave propagation and competition have been discussed and investigated extensively and meticulously, especially when the media are homogeneous. However, corresponding studies in heterogeneous media are much scarcer. In this paper, spontaneously generated waves from one-dimensional heterogeneous oscillatory media, modelled by complex Ginzburg–Landau equations with spatially varied controlling parameters, are investigated. An unexpected homogeneous wave train clearly emerges under certain conditions. With the theory of interface-selected waves, we can theoretically predict the frequencies and wavenumbers under several conditions. This kind of wave train can be found in a wide region of parameter space. These phenomena are robust when parameters are varied nonlinearly or linearly with fluctuation. Moreover, this kind of homogeneous wave plays an important role in wave competition and affects wave propagation in spatially heterogeneous nonlinear systems, which will bring new applications of heterogeneity and provide new ideas for wave control.

Different from elastic waves in linear periodic structures, those in phononic crystals (PCs) with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot accurately predict band-gap variations under finite-amplitude wave motions; creating nonlinear PCs remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like systems; most studies only consider weakly nonlinear regimes and cannot accurately obtain some relations between wave propagation characteristics and general nonlinearities. This paper presents propagation characteristics of longitudinal elastic waves in a thin rod and coupled longitudinal and transverse waves in an Euler–Bernoulli beam using their exact Green–Lagrange strain relations. We derive band structure relations for a periodic rod and beam and predict their nonlinear wave propagation characteristics using the B-spline wavelet on the interval (BSWI) finite element method. Influences of nonlinearities on wave propagation characteristics are discussed. Numerical examples show that the proposed method is more effective for nonlinear static and band structure problems than the traditional finite element method and illustrate that nonlinearities can cause band-gap width and location changes, which is similar to results reported in the literature for discrete systems. The proposed methodology is not restricted to weakly nonlinear systems and can be used to accurately predict wave propagation characteristics of nonlinear structures. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear PCs.

A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. The most fascinating concept is the breaking of replica symmetry: identical copies of the randomly interacting system that manifest completely different dynamics. Replica symmetry breaking has been predicted in nonlinear wave propagation, including Bose-Einstein condensates and optics, but never observed. Here, we report the experimental evidence of replica symmetry breaking in optical wave propagation The findings demonstrate that nonlinear propagation can manifest features typical of spin-glasses and provide a novel platform for testing so-far unexplored fundamental physical theories for complex systems.

Spatially periodic and stationary localized solutions arising from the dynamics of chains of linearly coupled mechanical oscillators characterized by on site cubic nonlinearity are addressed aiming to explore their relationship with the underlying nonlinear wave propagation regions. Softening and hardening nonlinearities are considered, and regions of occurrence of discrete breathers and multibreathers associated with homoclinic or heteroclinic connections are identified.

Recent results on parametric spatial solitary waves arising from multiple resonances in purely nonlinear 2-D lattices are presented. Theory and experiments highlight new possibilities for light self-confinement and steering via engineered planar nonlinear structures in periodically poled materials.

Numerical simulations demonstrate mesh dependency problems which can change the response of the model, especially when localization phenomena emerge. The use of a regularization method, called first gradient of dilation, is evaluated for the analysis of shear bands under dynamic conditions. It aims to eliminate the mesh dependency of the results by taking into account an enriched kinematic approach. While under static loading this method provides satisfactory results, under dynamic conditions it introduces a noise. An analytical solution of coupled S–P wave propagation in nonlinear micromorphic media and numerical simulations describe the irregular dynamic response of regularized media.

We investigate nonlinear wave propagation in multilayered structures containing left-handed layers. A delta-function description is used for the dielectric function of the structure. This model enables us to calculate the transmission coefficient of the structure using a 2-dimensional map. The special characteristics of wave propagation emerging from the inclusion of nonlinear left-handed layers in multilayered structures are elaborated by plotting global transmission diagrams. Optical bistability is studied both in the case of self-focusing and defocussing nonlinearity.

The present paper faces the problem of heat conduction within the framework of thermodynamics with internal state variables. A model, in which the heat flux vector depends both on the gradient of the absolute temperature and the gradient of a scalar internal variable, is proposed. Such a model leads to a diffusive-hyperbolic system which in general is parabolic, but also allows to shift to the hyperbolic regime. In the hyperbolic case the propagation of weak discontinuity waves is investigated. The Rankine-Hugoniot and Lax conditions for the propagation of strong shock waves are analyzed as well.

Nonlinear wave propagation in a 1D photonic crystal containing single-negative layers is investigated using the multiple-scale method. In this approach, the electric field is decomposed into a slowly varying envelope function and a fast Bloch-like function to obtain the analytic expressions of the effective parameters of an equivalent medium. The periodic structure has an equivalent left-handed medium for the envelope function. Gap soliton formation is discussed and compared with that associated with the Bragg gap.

In this paper, we present an algorithm that solves a time-domain nonlinear coupled system arising in nonlinear optics. The algorithm is an explicit nonlinear finite-difference method (NFDM) based on the exact solution of the nonlinear discrete equations. It enables simulations that preserve the characteristics of nonlinearity as well as coupling, and can be extended to arbitrary input waveform conditions.

This paper presents the structure and use of Dr. Layer, a computer program designed to provide students a simulation/visualization environment for studying linear and nonlinear wave propagation behavior in layered soil media. To support student-based exploration, Dr. Layer uses “live” modeling, i.e., modeling in which computation, interaction, and visualization occur simultaneously. © 2002 Wiley Periodicals, Inc. Comput Appl Eng Educ 9: 248–258, 2001; Published online in Wiley InterScience (www.interscience.wiley.com.); DOI 10.1002/cae.10003

Nonlinear wave propagation through a 2D lattice is investigated. Using reductive perturbation method, we show that this can be described by Kadomtsev–Petviashvili (KP) equation for quadratic nonlinearity and modified KP equation for cubic nonlinearity, respectively. With quadratic and cubic nonlinearities together, the system is governed by an integro-differential equation. We have also checked the integrability of these equations using singularity analysis and obtained solitary wave solutions.

which is identical to the governing equation of WAVEWATCH2 and represents an extension of the governing equation of WAM. The left side of this equation represents the effects of wave propagation as dictated by the dispersion relation and is inherently linear. The right side represents source and sink functions, including several effects of nonlinear wave propagation. Focusing on kinematic aspects of wave propagation, LH assume S [ 0 throughout the paper. In WAM and WAVEWATCH purely linear propagation is considered, and the characteristic velocities cg

It is well known that a velocity perturbation can travel through a mass spring chain with strongly nonlinear interactions as a solitary and antisolitary wave pair. In recent years, nonlinear wave propagation in 2D structures have also been explored. Here we first consider the propagation of such a velocity perturbation for cases where the system has a 2D "Y"-shaped structure. Here each of the three pieces that make up the "Y" are made of a small mass spring chain. In addition, we consider a case where multiple "Y"-shaped structures are used to generate a "tree." We explore the early time dynamical behavior associated with the propagation of a velocity perturbation initiated at the trunk and at the extremities for both cases. We are looking for the energy transmission properties from one branch to another of these "Y"-shaped structures. Our dynamical simulations suggest the following broad observations: (i) for strongly nonlinear interactions, mechanical energy propagation resembles pulse propagation with the energy propagation being dispersive in the linear case; (ii) for strong nonlinear interactions, the tree-like structure acts as an energy gate showing preference for large perturbations in the system while the behavior of the linear case shows no such preference, thereby suggesting that such structures can possibly act as switches that activate at sufficiently high energies. The study aspires to develop insights into the nature of nonlinear wave propagation through a network of linear chains.

The procedure of simulating linear and nonlinear wave propagation using the recently developed SimulinkTM software that has been incorporated into the MATLAB© program is described. Examples of wave propagation on linear transmission lines and soliton propagation on nonlinear transmission lines using this technique are given.

Wave propagation in weakly inhomogenious media is discussed. An approximate equation of shallow water waves propagating on a layer with both weakly and gently uneven bottom is derived from an exact system of equations. This type of equation has previously obtained by the present author for a rather wide class of systems. Based on the approximate equation thus derived, the effect of randomness on the propagation of the Burgers shock wave is studied.

International audience; The nonlinear parabolic equation (NPE) is a time-domain method widely used in underwater sound propagation applications. It allows simulation of weakly nonlinear sound propagation within an inhomogeneous medium. So that this method can be used for outdoor sound propagation applications it must account for the effects of an absorbing ground surface. The NPE being formulated in the time domain, complex impedances cannot be used and, hence, the ground layer is included in the computational system with the help of a second NPE based on the Zwikker-Kosten model. A two-way coupling between these two layers (air and ground) is required for the whole system to behave correctly. Coupling equations are derived from linearized Euler's equations. In the frame of a parabolic model, this two-way coupling only involves spatial derivatives, making its numerical implementation straightforward. Several propagation examples, both linear or nonlinear, are then presented. The method is shown to give satisfactory results for a wide range of ground characteristics. Finally, the problem of including Forchheimer's nonlinearities in the two-way coupling is addressed and an approximate solution is proposed.

Nonlinear wave propagation was investigated experimentally in coupled waveguides by means of the cascaded nonlinearity in quasi-phase-matched second-harmonic generation. With a specially designed wave-vector-mismatch distribution along the propagation axis, cascading was optimized for low fundamental depletion. High-contrast, ultrafast all-optical switching with switching powers of tens of watts was observed.

Waves propagating along the basilar membrane are amplified by an active nonlinear process. The general aspects of the active amplification of periodic signals can be discussed in the framework of critical oscillators. Here, we show how the concepts of a traveling wave and of critical oscillators can be combined to describe the main features of nonlinear wave propagation, energy flow and reflections in the cochlea.

We have studied the propagation of non-linear waves across a random medium, using the nonlinear Schrodinger equation with a random potential as a model. By simulating a scattering experiment, we show that non-linearity leads to an improvement of the transmission only when it contributes to create pulses. The propagation properties of these pulses can be described by an equivalent particle theory. Numerical experiments show that this is an approximation: two situations are presented depending on the two ratios of the amplitude and velocity to the perturbation. Concluding remarks link the time-dependent and time-independent regimes.

The transmission-line-matrix (TLM)-based finite-difference time-domain (FDTD) method has been generalized recently to incorporate graded mesh and anisotropic media. The method is equivalent to the three-dimensional TLM symmetrical condensed node, but is formulated and computed in a FDTD fashion. Therefore, it retains certain features of both the TLM and FDTD methods. The authors report recent progress in modeling with the TLM-based FDTD method, namely, successful implementation of the perfectly matched layer (PML) and simulation of nonlinear wave propagation.

In the Xenopus laevis oocyte, calcium ion channels are clustered in a thin shell. Motivated by this morphology, we study a general class of reaction-diffusion systems that include most of the well-known models that support wave propagation but restricting excitability to a “sheet” of codimension 1. We find waves that undergo propagation failure with increasing diffusion coefficient and a scaling regime in which the wave speed is independent of it. © 2003 The American Physical Society. Fil: Pando, Bernardo. Universidad de Buenos Aires; Argentina Fil: Pearson, John E.. Los Alamos National Laboratory; Estados Unidos Fil: Ponce Dawson, Silvina Martha. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

Quadratically nonlinear waveguides are studied in the presence of a Bragg grating resonant with one of the involved frequencies. In the case of second-harmonic generation and distributed feedback at the fundamental, we investigate the existence and features of two-color gap-solitary waves, focusing on controlling their propagation speed. This leads to the conception of optically controlled delay lines and retiming schemes for pulse streams in communication systems.

We demonstrate an important role of the process of optical rectification in the theory of nonlinear wave propagation in quadratically nonlinear [or $\chi^{(2)}$ ] periodic optical media. We derive a novel physical model for gap solitons in $\chi^{(2)}$ nonlinear Bragg gratings., Comment: 3.5 pages, double-column, no figures; submitted to Physical Review E

Electromagnetic wave propagation through cold collision free plasma is studied using the nonlinear perturbation method. It is found that the equations can be reduced to the modified Kortweg-de Vries equation.

Nonlinear wave propagation in an asymmetric converging Y junction, which consists of a nonlinear cladding, a linear film, and a linear substrate, is studied. The nonlinear dispersion curves of the successive sections of the Y junction are calculated to be used to illustrate the evolutions of the eigenmodes. The field incident from the nonlinear thinner branch can evolve into the symmetric mode of the stem with a high coupling efficiency. An insertion coupler for a time-multiplexed loop is suggested.

Recently, there has been interest in linear and nonlinear wave propagation in periodic and random potential fields. Studies of such effects using surface waves in adsorbed superfluid helium, which should show strong local nonlinear behavior, have begun. While there has been considerable theoretical attention given to nonlinear effects for these waves, there have been no systematic experimental studies. Research with a variety of experiments, including studies of linear and nonlinear propagation of these waves in uniform as well as periodic one‐dimensional media, has begun. Measurements have been made with drive levels varying over five orders of magnitude. The results have been found to exhibit nonlinear effects including a velocity of propagation dependent on drive level. [Work supported by NSF DMR 9000549 and the Office of Naval Research.]

Nonlinear wave propagation in inhomogeneous media is studied analytically in the model of the nonlinear Schrodinger equation. Exact solutions in the form of multisolitons, accelerated in the nonuniform medium, are obtained. (AIP)

A variational principle developed recently for constrained vector fields is applied to nonlinear waves and to unsteady, transonic flow. The mathematical conditions on the admissible functional form of the speed of propagation is compatible with physical considerations for the first systems and the treatment of the mixed derivative is indicative for a proper way to discretize the second for numerical calculations. The variational formulation provides a framework for stability analysis and finite element approximations for the nonlinear systems considered.

The problem of finite amplitude wave propagation in a viscoelastic semi-infinite and finite rod is treated. The rod is made of a material having a constitutive equation taken from Schapery's thermodynamic constitutive theory. The end of the rod is disturbed by a time-dependent input. A numerical method which is able to treat shocks is used and the linearly elastic, viscoclastic and nonlinearly elastic cases are obtained as special cases. The accuracy of the numerical procedure is checked by comparison with some special cases in which analytical conclusions could be drawn.

The wave propagation in an infinite one-dimensional anharmonic lattice is studied under the influence of an anharmonic potential and a weak dislocation potential. It is found that the equation for the nonlinear wave propagation has N -kink solution. The properties of one and two kink solutions are discussed in detail. It is also found that there exists the critical eigenvalue due to the competition between the above two kinds of potentials . A few conservation laws are obtained.

Waves nonlinear propagation in fluids due to convection, reviewing various solution methods

Several special methods including implicit separation of variables, explicit and implicit generalized traveling waves are introduced and employed to obtain solutions for nonlinear equations. Certain nonlinear wave propagation problems are shown to yield to implicit separation while generalized traveling wave concepts are applied in diffusion, fluid mechanics and wave propagation.

Several properties of solitary waves were measured on a nonlinear transmission line. These include the transition from a linear dispersive response into a solitary wave response as the amplitude of a narrow voltage impulse is increased, and an observation of the recurrence phenomena of solitary waves.

The topics studied in the program on nonlinear process included: Model systems in quantum optics; Nonlinear wave propagation in crystal lattices; Basic studies in nonlinear dynamics; Wave propagation in a Navier-Stokes fluid. This report lists publications resulting from the program.