Propagation Of Localized Waves Research Articles

Source wavelet and local wave propagation effects on the amplitude-variation-with-offset response of thin-layer models: A physical modeling study

In target layers with thicknesses below the vertical seismic resolution as thin layers, the tuning effect/interference between the wave propagation modes may increase the challenge of doing amplitude-variation-with-offset (AVO) analysis because it is difficult to recover the primary PP amplitudes embedded in the data by further seismic data processing. Thus, we have investigated the importance of the primary PP reflections, locally P-SV converted waves, and internal multiple reflections in the amplitude response of two thin-layer seismic physical models. One model consists of a thin water layer embedded between two nylon plates, and another model with a thin acrylic layer surrounded by water. Numerical modeling using the reflectivity method was applied to analyze each wave propagation mode and the source waveform role in the experimental data. Before the experimental reflection data acquisition, we characterized two source and receiver piezoelectric transducer (PET) pairs: one with a circular plane face and the other with a semispherical face. We measured the source wavelet, its dominant frequency, and the PETs’ directivity pattern. Semispherical PETs were chosen to acquire common midpoint reflection data. Thereafter, a processing workflow was applied to remove linear events interfering with the target reflections and to correct amplitudes due to transmission losses, source/receiver directivity, and geometric spreading effects. Finally, we investigated the thin-layer targets near incidence angle amplitude and the AVO response. The results showed that the interference between the primary PP reflections and the locally converted shear waves may considerably affect the observed amplitude response. The source wavelet bandwidth appeared as a second-order effect, and the internal multiple reflections were practically negligible. These results suggested that in real data sets, it is important to investigate the wave propagation modes and source wavelet role in the amplitudes observed, before deciding the AVO analysis/inversion workflow that should be adopted.

MAVEN observations of tail current sheet flapping at Mars

AbstractThe Martian magnetotail is a complex regime through which atmospheric particles are lost to space. Our current understanding of Mars' tail continues to develop with the comprehensive particle and field data collected by Mars Atmosphere and Volatile EvolutioN (MAVEN). In this work, we identify periods when MAVEN encounters multiple current sheet crossings through a single tail traversal in order to understand tail dynamics. We apply an analysis technique that has been developed and validated by using multipoint measurements in order to separate the spatial and temporal properties associated with current sheet flapping. Events are classified into periods of steady flapping, due to a global motion of the current sheet, and kink‐like flapping, resulting from localized wave propagation along the tail current sheet. Out of 106 periods during which multiple current sheet crossings were observed, 20 were due to steady flapping and 10 from kink‐like flapping. A majority of the kink‐like events resulted from waves propagating in the opposite direction of the solar wind convection electric field, regardless of their location in the tail, unlike at Earth and Venus. This finding suggests that possible magnetosphere energy sources, whereby plasma is accelerated and removed from the Martian environment, are not located in the central magnetotail; rather, these waves may be driven by a source located at the tail flank based on the direction of the solar wind electric field. Therefore, by identifying potential sources of impulsive energy release in the tail, we may better understand mechanisms that drive atmospheric loss at Mars.

Propagation of localized waves in magnetized cold hadronic gas

Propagation of solitary waves and their stability conditions in a cold dense hadron gas as a non-relativistic fluid is investigated based on the ‘reductive perturbation method’, at the presence of sufficiently strong external magnetic field. We have shown that the magnetic field stabilizes breaking and shock waves into livelong solitonic profiles with small amplitudes which are governed by the Zakharov–Kuznetsov (ZK) equation. Our results show that the phase speed and amplitude of solitary waves corresponding to each kind of medium components are different. The effects of medium characters on the evolution of solitary profiles are investigated too.

A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multibody systems involving impact should consider the local plastic deformation and the strict requirements of the spatial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlinear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.

Colliding solitary waves in quark gluon plasmas

We study the head-on collision of propagating waves due to perturbations in quark gluon plasmas. We use the Massachusetts Institute of Technology bag model, hydrodynamics equation, and suitable equation of state for describing the time evolution of such localized waves. A nonlinear differential equation is derived for the propagation of small amplitude localized waves using the reductive perturbation method. We show that these waves are unstable and amplitude of the left-moving (right-moving) wave increases (decreases) after the collision, and so they reach the borders of a quark gluon plasma fireball with different amplitudes. Indeed we show that such arrangements are created because of the geometrical symmetries of the medium.

Control of localized non-linear strain waves in complex crystalline lattices

The distributed feedback control is developed to support propagation of localized non-linear waves for the double sine-Gordon equation and the dispersive sine-Gordon equation previously obtained for the description of dynamic processes in complex crystalline lattices. The control allows the propagation of both bell-shaped and kink-shaped waves with permanent shape and velocity, with a functional form which does not correspond to the known analytical solutions of the equations. The results might be used for choosing external loading providing desired strain localization or variations in the internal structure of the lattice.

Optimized double sweep Schwarz method by complete radiation boundary conditions

We present an optimized double sweep nonoverlapping Schwarz method for solving the Helmholtz equation in semi-infinite waveguides. The domain is decomposed into nonoverlapped layered subdomains along the axis of the waveguide and local wave propagation problems equipped with complete radiation conditions for high-order absorbing boundary conditions are solved forward and backward sequentially. For communication between subdomains, Neumann data of local solutions in one domain are transferred to the neighboring subdomain in the forward direction and Dirichlet data are exploited in the backward direction. The complete radiation boundary conditions enable us to not only minimize reflection coefficients for most important modes in an optimal way but also find Neumann data without introducing errors that would be produced if finite difference formulas were used for computing Neumann data. The convergence of the double sweep Schwarz method is proved and numerical experiments using it as a preconditioner are presented to confirm the convergence theory.

A generalized reconstruction framework for transient elastography

Ultrasound transient elastography has emerged as a promising imaging modality for noninvasive evaluation of tissue mechanical properties. Most of the established techniques, however, rely on a pointwise measurement of the induced shear wave speed based on a localized planar wave propagation assumption. This assumption is not always true as most tissues exhibit heterogamous characteristics. Complex interaction of different geometries, boundary conditions, and tissue composition limit the ability of these techniques such that additional spatial-temporal filtering and signal truncations are required. These signal conditionings might lead to improvement in elasticity estimation for some cases (e.g. certain geometries, material properties) but the fact that they do not stem from a comprehensive framework can lead to unrealistic mechanical properties in more complex scenarios. We present a generalized framework based on inverse solution of the elasto-dynamic equations which can simultaneously solve for material properties and geometries without requiring any prior knowledge of the wave types. The method is based on a modified error in constitutive equation (MECE) without requiring additional filtering. We present the results of standard phantom studies based on acoustic radiation force excitation and fast ultrasound tracking where MECE technique successfully estimated the elastic moduli and geometry. [Work supported by NIH grant CA174723.]

Localization of the sine-Gordon equation solutions

Localization of the waves of the sine-Gordon equation depends on the shape of the initial condition. It is shown how initially motionless Gaussian distribution may be modified to obtain propagation of localized waves in both directions. However, the resulting localized wave profile is described neither by an asymptotic envelope- wave solution to the sine-Gordon equation nor by its exact traveling breather solution. The distributed control algorithms are developed to achieve wave localization independent of the shape of the initial condition. It is shown that localization of the waves in both directions is achieved by means of a feedforward (nonfeedback) control. The waves are similar to the envelope wave solution. The feedback distributed algorithm is shown to provide both localized waves according to analytical solutions and their unidirectional propagation.

Исследование локализации пластической деформации электролитически насыщенного водородом алюминиевого сплава методом декорреляции цифровых спекл-изображений

The paper presents investigations of the effect of hydrogen embrittlement on the plastic flow. The studies are performed for test samples of aluminum alloy subjected to electrolytic hydrogenation in a three-electrode electrochemical cell at a controlled constant cathode potential using the Digital Image Correlation method. Diagrams of localized plasticity wave propagation through the length of the sample under deformation have been obtained. The deformation diagrams are examined for the deformed samples of the aluminum alloy and also main parameters of localized plasticity patterns are determined. Using the scanning electron microscopy method, the changes in the fracture surface are investigated.

A new method for shear wave speed estimation in shear wave elastography.

Visualization of mechanical properties of tissue can aid in noninvasive pathology diagnosis. Shear wave elastography (SWE) measures the elastic properties of soft tissues by estimation of local shear wave propagation speed. In this paper, a new robust method for estimation of shear wave speed is introduced which has the potential for simplifying continuous filtering and real-time elasticity processing. Shear waves were generated by external mechanical excitation and imaged at a high frame rate. Three homogeneous phantoms of varying elastic moduli and one inclusion phantom were imaged. Waves propagating in separate directions were filtered and shear wave speed was estimated by inversion of the 1-D first-order wave equation. Final 2-D shear wave speed maps were constructed by weighted averaging of estimates from opposite traveling directions. Shear wave speed results for phantoms with gelatin concentrations of 5%, 7%, and 9% were 1.52 ± 0.10 m/s, 1.86 ± 0.10 m/s, and 2.37 ± 0.15 m/s, respectively, which were consistent with estimates computed from three other conventional methods, as well as compression tests done with a commercial texture analyzer. The method was shown to be able to reconstruct a 2-D speed map of an inclusion phantom with good image quality and variance comparable to conventional methods. Suggestions for further work are given.

Energy Flux in the Cochlea: Evidence Against Power Amplification of the Traveling Wave.

Traveling waves in the inner ear exhibit an amplitude peak that shifts with frequency. The peaking is commonly believed to rely on motile processes that amplify the wave by inserting energy. We recorded the vibrations at adjacent positions on the basilar membrane in sensitive gerbil cochleae and tested the putative power amplification in two ways. First, we determined the energy flux of the traveling wave at its peak and compared it to the acoustic power entering the ear, thereby obtaining the net cochlear power gain. For soft sounds, the energy flux at the peak was 1 ± 0.6 dB less than the middle ear input power. For more intense sounds, increasingly smaller fractions of the acoustic power actually reached the peak region. Thus, we found no net power amplification of soft sounds and a strong net attenuation of intense sounds. Second, we analyzed local wave propagation on the basilar membrane. We found that the waves slowed down abruptly when approaching their peak, causing an energy densification that quantitatively matched the amplitude peaking, similar to the growth of sea waves approaching the beach. Thus, we found no local power amplification of soft sounds and strong local attenuation of intense sounds. The most parsimonious interpretation of these findings is that cochlear sensitivity is not realized by amplifying acoustic energy, but by spatially focusing it, and that dynamic compression is realized by adjusting the amount of dissipation to sound intensity.

Nonlinear-wave based analysis and modeling of heat integrated distillation column

The heat integrated distillation column (HIDiC) has a larger energy-saving potential but more complex dynamics stemming from thermal coupling. A nonlinear natural wave velocity for different stages of HIDiC is derived and reveals the local wave propagation dynamics. From the distribution of the natural wave velocity, the process of the disturbance propagation is observed clearly. Also, the coexistence of self-sharpening and non-sharpening waves can be easily understood. Then, a simplified nonlinear wave model from the perspective of the whole profile propagation is proposed, and clearly illustrates the nonlinear dynamic behaviors of HIDiC such as the dependence of response on the magnitudes and directions of disturbance, the asymmetric behavior of the transitions between two steady states, and the different dynamics between the rectifying and stripping columns.

Stable solitary waves in super dense plasmas at external magnetic fields

Propagation of localized waves in a Fermi-Dirac distributed super dense matter at the presence of strong external magnetic fields is studied using the reductive perturbation method. Previous works indicate that localized waves break down in unmagnetized super dense hadronic matter. We have shown that stable solitons can be created in such non-relativistic fluids in the presence of an external magnetic field. Such solitary waves are governed by the Zakharov-Kuznetsov (ZK) equation. Properties of solitonic solutions are studied in media with different values of back ground mass density and strength of magnetic field.

Nonlinear dynamic behavior of an impact damaged composite skin–stiffener structure

One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage. A wide range of technologies, comprising global vibration and local wave propagation methods, can be employed for health monitoring purposes. Traditional modal analysis based methods are linear methods. The effectiveness of these methods is sometimes limited since they rely on a stationary and linear description of the system. The nonlinear interaction between a low frequency wave field and a local impact induced damage in a composite skin–stiffener structure is experimentally demonstrated in this work. The different mechanisms linked to the distorted waveforms are separated with the help of phase portraits. The harmonic waveform distortions are concentrated at the damaged region and increased for higher excitation amplitudes. It is shown that linear damage identification methods are feasible for low excitation amplitudes, but that the presence of nonlinear dynamic effects cannot remain silent for higher amplitudes. Analyzing the damage induced nonlinear effects can provide useful information about the current state of the structure.

A mathematical model of calculating local tsunami wave source constraints and propagation

This paper presents a local tsunami simulation, including the initial displacement field model of tsunami source and tsunami wave propagation model. We deduced the tsunami wave equation; applied the matching of interior and exterior solutions method and water mass method to determine the initial displacement field in different bottom topography. Tsunami wave propagation model was based on the Boussinesq equation. Difference format was based on the ADI method which discretized in alternating direction in the form of implicit scheme. The open boundary of ADI had been revised considering the influence of wave propagation in the equation of motion. The local tsunami mathematical model was used in the simulation of 2011 Japan tsunami, and the results and the observation data match well.

Head on collision of shock and breaking waves in degenerate hadronic plasmas

Astronomical compact objects, like neutron stars, are made of Fermi-Dirac distributed hadronic matter which has a wide range of densities. In this work, non-relativistic dynamics of high density hadronic plasmas with shear and bulk viscosities are studied. The propagation of localized waves in media with hadronic gas equation of state is investigated. Initially, localized lumps are propagated as breaking and shock waves in inviscid media. It is shown that in the viscous case, the localized waves can travel longer distances before changing into shock or breaking profiles.

Guided Impact Mitigation in 2D and 3D Granular Crystals

We simulate the dynamics of impacts on 1D, 2D and 3D arrays of metallic spheres in order to design novel granular protection systems. The dynamics of these highly organized systems of spheres, commonly called granular crystals, are governed by the contact law that describes how each particle interacts with the others. We use our recently developed force-displacement model of the dynamic compression of elastic-plastic spheres as the building block to investigate the response of systems comprised of metallic spheres to an impact. We first provide preliminary experimental results using a drop tower as validation of our numerical approach for 2D and 3D systems. We then use simulations of large periodic granular crystals in order to determine which particle properties govern the velocity of stress waves in these materials. We show that the properties of 1D systems can be scaled to predict the behavior of more complex 2D and 3D granular crystals. Because we can choose the material properties of each of the constituent particles and design how the particles are geometrically packed, we can leverage the heterogeneity of the system to create materials with unique properties such as anisotropic local stiffnesses and wave propagation velocities. We show that these materials allow us to design the dispersion and dissipation properties within the material in order to influence the propagation of a stress wave. Using these materials, we can therefore design protection systems or armor that directs damage away from sensitive parts or localizes damage to an unimportant area after impact from a projectile or a blast.

Dynamic Ruptures on a Frictional Interface with Off-Fault Brittle Damage: Feedback Mechanisms and Effects on Slip and Near-Fault Motion

The spontaneous generation of brittle rock damage near and behind the tip of a propagating rupture can produce dynamic feedback mechanisms that modify significantly the rupture properties, seismic radiation, and generated fault zone structure. In this work, we study such feedback mechanisms for single rupture events and their consequences for earthquake physics and various possible observations. This is done through numerical simulations of in-plane dynamic ruptures on a frictional fault with bulk behavior governed by a brittle damage rheology that incorporates reduction of elastic moduli in off-fault yielding regions. The model simulations produce several features that modify key properties of the ruptures, local wave propagation, and fault zone damage. These include (1) dynamic generation of near-fault regions with lower elastic properties, (2) dynamic changes of normal stress on the fault, (3) rupture transition from crack-like to a detached pulse, (4) emergence of a rupture mode consisting of a train of pulses, (5) quasi-periodic modulation of slip rate on the fault, and (6) asymmetric near-fault ground motion with higher amplitude and longer duration on the side with reduced elastic moduli. The results can have significant implications to multiple topics ranging from rupture directivity and local amplification of seismic motion to near-fault tremor-like signals.

Gaussian solitary waves and compactons in Fermi-Pasta-Ulam lattices with Hertzian potentials.

We consider a class of fully nonlinear Fermi-Pasta-Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order α>1. This class of systems incorporates a classical Hertzian model describing acoustic wave propagation in chains of touching beads in the absence of precompression. We analyse the propagation of localized waves when α is close to unity. Solutions varying slowly in space and time are searched with an appropriate scaling, and two asymptotic models of the chain of particles are derived consistently. The first one is a logarithmic Korteweg-de Vries (KdV) equation and possesses linearly orbitally stable Gaussian solitary wave solutions. The second model consists of a generalized KdV equation with Hölder-continuous fractional power nonlinearity and admits compacton solutions, i.e. solitary waves with compact support. When [Formula: see text], we numerically establish the asymptotically Gaussian shape of exact FPU solitary waves with near-sonic speed and analytically check the pointwise convergence of compactons towards the limiting Gaussian profile.