Propagation Of Nonlinear Solitary Waves Research Articles

Localized Energy Absorbers in Hertzian Chains

Energy absorbers and energy-harvesting devices have been under the scope of scientists and engineers for decades to fulfill specific technological needs, mainly concerned with sound and vibration absorbers, and efficient mechanical energy converters. In this paper, as a proof of concept, we build a mass-in-mass device to study the response of a linear absorber immersed in one of the spheres composing a linear array of equal elastic spheres. Spheres barely touch one another and can thus sustain nonlinear solitary wave propagation only. The linear intruder absorbs a given amount of energy depending on the frequency content of the incident solitary wave. A numerical simulation is developed to account for the experimental finding. The validation of the numerical model allows for the theoretical study of the energy absorbed by any number of intruders, and to demonstrate that the former increases exponentially with the latter, indicating that only ten of the intruders is enough to absorb the system energy. A detailed study of the transmitted energy from an external source into the chain reveals that, due to nonlinearity, the array of spheres is able to convert almost any mechanical shock to a well-defined solitary or trains of solitary waves, whose frequency content is nearly independent on the excitation amplitude. This property leads to the design of a device, which is optimized to absorb energy over a broad frequency range.

Feasibility of the use of nonlinear solitary waves for the nondestructive measurement of Young's modulus of rocks and compacted materials

This article describes the development of a new device to measure the Young’s modulus of geomaterials. This device bases its operation on the propagation of nonlinear solitary waves along a chain full of spheres. The chain is placed vertically on the sample's surface, and then an incident wave is generated at its top. The pulse travels through the chain of spheres from top to bottom, generating a reflected wave as a result of the interaction between the last element and the material tested. The time-lapse between the incident and reflected waves, measured using a piezoelectric load cell inserted in the middle of the chain of spheres, allows the estimation of the Young's modulus of the sample through a numerical model. The usefulness of the device is demonstrated in control samples of known elastic properties, rocks, and compacted soils. Besides, this paper proposes a modification of the device, which consists of placing a metal cylinder instead of the last sphere of the chain; This modification improves the results obtained when analyzing soft soils. The results show that Young's moduli calculated by the developed device are equivalent to the modulus measured by alternative tests. This device could become a useful nondestructive test for measuring Young's modulus of subgrade materials.

Oblique Propagation of Nonlinear Solitary Waves in Magnetized Plasma with Nonextensive Electrons

In this paper, authors have studied the properties of obliquely propagating nonlinear solitary waves in a plasma system consisting of warm ions and nonextensively distributed electrons. The nonlinear Korteweg-de-Vries (KdV) equation and its solution have been derived using the standard reductive perturbation method. The effect of ion temperature on the propagation of solitary waves has been investigated numerically. The critical value of nonextensivity at which solitary structures transit from negative to positive potential is found to shift to the lower value under the effect of finite temperature. The numerical results are interpreted graphically. The results may be useful for understanding the wave propagation in laboratory and space plasmas where magnetic field is present.

New method for rekindling the nonlinear solitary waves in Maxwellian complex space plasma

Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main reason for this consideration is to exhibit the effects of dust charge fluctuations on acoustic modes evaluated by the use of a new method. A special method (G′/G) has been developed to yield the coherent features of nonlinear waves augmented through the derivation of a Korteweg-de Vries equation and found successfully the different nature of solitons recognized in space plasmas. Evolutions have shown with the input of appropriate typical plasma parameters to support our theoretical observations in space plasmas. All conclusions are in good accordance with the actual occurrences and could be of interest to further the investigations in experiments and satellite observations in space. In this paper, we present not only the model that exhibited nonlinear solitary wave propagation but also a new mathematical method to the execution.

Propagation of Nonlinear Solitary Waves in Nonuniform Dusty Plasmas with Two-Ion Temperature

The nonlinear properties of dust acoustic solitary waves in inhomogeneous dusty plasmas with two-ion temperature are investigated. By using the reductive perturbation theory, a modified variable coefficients Korteweg-de Vries (MKdV) equation is derived. The typical integral form of the Sagdeev potential is examined numerically. The numerical results show that the inhomogeneity, the two-ion temperature have strong influence on the nonlinear properties of dust acoustic solitary waves.

Numerical Simulation of Solitary Waves Using Smoothed Particle Hydrodynamics Method

Understanding shallow water wave propagation is of major concern in any coastal mitigation effort. Many times, a solitary wave replicates a shallow water wave in its extreme sense which includes a tsunami wave. It is mainly due to known physical characteristics of such waves. Therefore, the study of propagation of solitary waves in the near shore waters is of equal importance in the context of non linear water waves. Owing to the significant growth in computational technologies in the last few decades, a significant number of numerical methods have emerged and applied to simulate nonlinear solitary wave propagation. In this study, one such method, the Smoothed Particle Hydrodynamics (SPH) method has been described to simulate the solitary waves. The split-up of a single solitary wave while it crosses a continental kind of shelf has been simulated by the present model. Then SPH model is coupled with the Boussinesq model to predict the time interval between two successive solitary waves on landfall. It has also been shown to be equally efficient in simulating the wave breaking while a solitary wave propagates over a mild slope.

Highly nonlinear solitary wave propagation in Y-shaped granular crystals with variable branch angles

We study the propagation of highly nonlinear waves in a branched (Y-shaped) granular crystal composed of chains of spherical particles of different materials, arranged at variable branch angles. We experimentally test the dynamic behavior of a solitary pulse, or of a train of solitary waves, crossing the Y-junction interface, and splitting between the two branches. We describe the dependence of the split pulses' speed and amplitude on the branch angles. Analytic predictions based on the quasiparticle model and numerical simulations based on Hertzian interactions between the particles are found to be in excellent agreement with the experimental data.

Observations of internal bores and waves of elevation on the New England inner continental shelf during summer 2001

During July–August 2001, oceanographic variability on the New England inner continental shelf was investigated with an emphasis on temporal scales shorter than tidal periods. Mooring and ship survey data showed that subtidal variation of inner shelf stratification was in response to regional Ekman upwelling and downwelling wind driven dynamics. High‐frequency variability in the vertical structure of the water column at an offshore mooring site was linked to the baroclinic internal tide and the onshore propagation of nonlinear solitary waves of depression. Temperature, salinity, and velocity data measured at an inshore mooring detected a bottom bore that formed on the flood phase of the tide. During the ebb tide, a second bottom discontinuity and series of nonlinear internal waves of elevation (IWOE) formed when the water column became for a time under hydraulic control. A surface manifestation of these internal wave crests was also observed in aircraft remote sensing imagery. The coupling of IWOE formation to the offshore solitary waves packets was investigated through internal wave breaking criterion derived in earlier laboratory studies. Results suggested that the offshore solitons shoaled on the sloping shelf, and transformed from waves of depression to waves of elevation. The coupling of inshore bore formation to the offshore solitary waves and the possible impact of these periodic features on mixing on the inner shelf region are discussed.

On the propagation of nonlinear solitary waves in a distributed Schottky barrier diode transmission line

A nonlinear distributed Schottky barrier diode is analyzed and it is found to be similar to a 3-component quasi-neutral plasma consisting of negative ions and electrons that are neutralized with positive ions. In such a plasma, it has been shown that both KdV and mKdV solitons can exist. We obtain the criteria for the distributed Schottky barrier diode that will permit the propagation of both KdV and mKdV solitary waves.

The dispersion-managed soliton as a ground state of a macroscopic nonlinear quantum oscillator

Highfrequency nonlinear solitary wave propagation in media with strongly varying dispersion is considered. A dynamical model is proposed which allows us to determine the propagation characteristics...

Simulation of non-hydrostatic, density-stratified flow in irregular domains

A numerical model has been developed for simulating density-stratified flow in domains with irregular but simple topography. The model was designed for simulating strong interactions between internal gravity waves and topography, e.g. exchange flows in contracting channels, tidally or convectively driven flow over two-dimensional sills or waves propagating onto a shoaling bed. The model is based on the non-hydrostatic, Boussinesq equations of motion for a continuously stratified fluid in a rotating frame, subject to user-configurable boundary conditions. An orthogonal boundary fitting co-ordinate system is used for the numerical computations, which rely on a fourth-order compact differentiation scheme, a third-order explicit time stepping and a multi-grid based pressure projection algorithm. The numerical techniques are described and a suite of validation studies are presented. The validation studies include a pointwise comparison of numerical simulations with both analytical solutions and laboratory measurements of non-linear solitary wave propagation. Simulation results for flows lacking analytical or laboratory data are analysed a posteriori to demonstrate satisfaction of the potential energy balance. Computational results are compared with two-layer hydraulic predictions in the case of exchange flow through a contracting channel. Finally, a simulation of circulation driven by spatially non-uniform surface buoyancy flux in an irregular basin is discussed.

On the validity of Hertz contact law for granular material acoustics

We discuss the acoustical behavior of a 1D model of granular medium, which is a chain of identical spherical beads. In this geometry, we are able to test quantitatively alternative models to the Hertz theory of contact between elastic solids. We compare the predictions of the different models to experimental results that concern linear sound wave propagation in the chain submitted to a static force, and nonlinear solitary wave propagation in an unconstrained chain. We use elastic, elastic-plastic and brittle materials, the beads roughness extends on one order of magnitude, and we also use oxidized metallic beads. We demonstrate experimentally that at low static forces, for all types of beads, the linear acoustic waves propagate in the system as predicted by Hertz's theory. At larger forces, after onset of permanent plastic deformation at the contacts, the brass beads exhibit non Hertzian behavior, and hysteresis. Except in the case of brass beads, the nonlinear waves follow the predictions of Hertz theory.

Nonlinear waves in DNA and regulation of transcription

The transmission of conformational changes along the DNA double helix is interpreted as a propagation of nonlinear solitary waves. Experimental and theoretical data in favour of this approach are presented. The possible role of nonlinear waves in regulation of transcription is discussed.

On magnetohydrodynamic solitons in jets

Nonlinear solitary wave propagation in a compressible magnetic beam model of an extragalactic radio jet is examined and shown to lead to solitons of the Benjamin-Ono type. A number of similarities between such magnetic beam models of jets and models of solar photospheric flux tubes are pointed out and exploited. A single soliton has the appearance of a symmetric bulge on the jet which propagates faster than the jet's flow.