Search

Motivated by problems arising in the piecewise construction of physically relevant solutions to models of shallow water fluid flows, we study the initial value problem for quasilinear hyperbolic systems of conservation laws in 1 + 1 dimensions when the initial data are continuous with "corners," i.e., derivative discontinuities. While it is well known that generically such discontinuities propagate along characteristics, under which conditions the initial corner points may fission into several ones, and which characteristics they end up following during their time evolution, seems to be less understood; this study aims at filling this knowledge gap. To this end, a distributional approach to moving singularities is constructed, and criteria for selecting the corner-propagating characteristics are identified. The extreme case of initial corners occurring with at least a one-sided infinite derivative is special. Generically, these gradient catastrophe initial conditions for hyperbolic systems (or their parabolic limits) can be expected to evolve instantaneously into either shock discontinuities or rarefaction waves. It is shown that when genuine nonlinearity does not hold uniformly and fails at such singular points, the solutions' continuity along with their infinite derivatives persist for finite times. All the results are demonstrated in the context of explicit solutions of problems emerging from applications to fluid flows. [ABSTRACT FROM AUTHOR]

A modified incremental harmonic balance (IHB) method is used to determine periodic solutions of wave propagation in discrete, strongly nonlinear, periodic structures, and solutions are found to be in a two-dimensional hyperplane. A novel method based on the Hill's method is developed to analyze stability and bifurcations of periodic solutions. A simplified model of wave propagation in a strongly nonlinear monatomic chain is examined in detail. The study reveals the amplitude-dependent property of nonlinear wave propagation in the structure and relationships among the frequency, the amplitude, the propagation constant, and the nonlinear stiffness. Numerous bifurcations are identified for the strongly nonlinear chain. Attenuation zones for wave propagation that are determined using an analysis of results from the modified IHB method and directly using the modified IHB method are in excellent agreement. Two frequency formulae for weakly and strongly nonlinear monatomic chains are obtained by a fitting method for results from the modified IHB method, and the one for a weakly nonlinear monatomic chain is consistent with the result from a perturbation method in the literature. [ABSTRACT FROM AUTHOR]

Abstract This study investigates the nonlinear Pochhammer–Chree equation, a model crucial for understanding wave propagation in elastic rods, through the application of the Khater III method. The research aims to derive precise analytical solutions and validate them using He’s variational iteration method (VIM). The Pochhammer–Chree equation’s relationship to other nonlinear evolution equations, such as the Korteweg-de Vries and nonlinear Schrödinger equations, underscores its significance in the field of nonlinear wave dynamics. The methodology employs the Khater III method for deriving analytical solutions, while He’s VIM serves as a numerical validation tool, ensuring the accuracy and stability of the obtained results. This dual approach not only yields novel solutions but also provides a robust framework for analyzing complex wave phenomena in elastic media. The findings of this study have significant implications for material science and engineering applications, offering new insights into the behavior of waves in elastic rods. By bridging the gap between theoretical models and practical applications, this research contributes to the advancement of both mathematical theory and physical understanding of nonlinear wave dynamics. Situated within the domain of applied mathematics, with a focus on nonlinear wave equations, this work exemplifies the interdisciplinary nature of contemporary research in mathematical physics. The results presented herein open new avenues for future investigations in related fields and highlight the potential for innovative applications in material science and engineering.

AbstractThis study investigates the nonlinear wave propagation in nanoclay composites reinforced concrete shell structures under external loading. The analysis is conducted using Hamilton’s principle and the Von-Karman strain-displacement relationship, which account for the geometrical nonlinearity inherent in such structures. The inclusion of nanoclay composites enhances the mechanical properties of the concrete shell, leading to improved wave resistance and stability. To solve the resulting nonlinear equations of motion, the Runge–Kutta method is employed, providing an efficient and accurate numerical approach for capturing the complex dynamic behavior of the structure. The findings offer valuable insights into the design and optimization of nanoclay composites reinforced concrete shells, particularly in applications where external dynamic loading and wave propagation are critical. After obtaining the results of mathematical modeling simulation, deep neural networks (DNNs) is used to estimate the nonlinear wave propagation in nanoclay composites reinforced concrete shell structures under complex situation. This study presents a method for estimating nonlinear phase velocity using deep neural networks trained on mathematical modeling datasets. By leveraging DNNs, the approach efficiently captures complex nonlinear relationships in wave propagation, enabling accurate predictions of phase velocity in various physical systems, enhancing modeling precision in engineering applications. This research contributes to the understanding of the interplay between material composition, structural geometry, and dynamic responses, paving the way for advanced engineering applications in construction and infrastructure. [ABSTRACT FROM AUTHOR]

The most common source of transformer failure is in the insulation, and the most prevalent warning signal for insulation weakness is partial discharge (PD). Locating the positions of these partial discharges would help repair the transformer to prevent failures. This work investigates algorithms that could be deployed to locate the position of a PD event using data from ultra-high frequency (UHF) sensors inside the transformer. These algorithms typically proceed in two steps: first determining the signal arrival time, and then locating the position based on time differences. This paper reviews available methods for each task and then propose new algorithms: a convolutional iterative filter with thresholding (CIFT) to determine the signal arrival time and a reference table of travel times to resolve the source location. The effectiveness of these algorithms are tested with a set of laboratory-triggered PD events and two sets of simulated PD events inside transformers in production use. Tests show the new approach provides more accurate locations than the best-known data analysis algorithms, and the difference is particularly large, 3.7X, when the signal sources are far from sensors.

• A novel model for nonlinear wave propagation in tri-directional functionally graded nanoplates coupled with an NEMS patch is established. • COMSOL multi-physics simulation and physics-informed deep neural networks are presented to verify the results of current work. • For coupling the composite structure with the piezoelectric patch, compatibility conditions are considered. • The effects of various geometrical and physical factors on the nonlinear phase velocity are discussed in detail. The nonlinear phase velocities analysis of tri-directional functionally graded (FG) nanoplates is crucial for optimizing their performance as nano-electro-mechanical systems (NEMS). By understanding the nonlinear phase velocities of various wave modes within the nanoplate, engineers can accurately predict and enhance the efficiency of NEMS. This analysis allows for the precise tuning of the piezoelectric patches to capture vibrational energy more effectively, ensuring maximum energy conversion efficiency. Moreover, it helps in identifying the optimal placement and orientation of the piezoelectric patches, minimizing energy loss and enhancing the reliability and durability of the NEMS. Ultimately, this leads to more efficient utilization of ambient vibrations in airplanes, providing a sustainable power source for various onboard sensors and monitoring systems, contributing to reduced reliance on external power sources, and improved overall energy management. For this issue, for the first time, nonlinear phase velocity in the tri-directional functionally graded nanoplate coupled with a piezoelectric patch via COMSOL multi-physics simulation, physics-informed deep neural networks (PIDNNs), and mathematics simulation are presented. In the mathematics simulation domain, nonlocal strain gradient theory for modeling both the hardening and softening behavior of the current nanoplate is presented. The electromechanical coupling effect and the abrupt change in material properties at the interfaces will have a major influence on the mechanical performance of tri-directional functionally graded (TD-FG) nanoplate coupled with a piezoelectric patch if transverse shear deformations cannot be well modeled. Thereby, in the current simulation, a quasi-3D refined theory with 10 variables is presented. Also, for coupling the composite structure with the piezoelectric patch, compatibility conditions are considered. An analytical solution procedure is presented for solving the nonlinear partial differential equations of the current electrical system. [ABSTRACT FROM AUTHOR]

In the present study, the quintic-septic nonlinear modulation of a longitudinal wave propagating to contribute the dispersive and higher-order nonlinear effects in a generalized cubically nonlinear elastic medium is considered. In recent work, for the modulation of a longitudinal wave, a cubic nonlinear Schrödinger equation with a third-order dispersive term is obtained by using a multi-scale expansion of quasi-monochromatic wave solutions. The third- quintic-septic longitudinal wave, by choosing specific values of material constants and wave number for which some coefficients of nonlinear terms are disappeared. In this case, a new perturbation expansion is needed to balance nonlinear effects with dispersive effects. As a result, a quintic-septic nonlinear Schrödinger equation with a third-order dispersion term is obtained as a new model that balances quintic-septic nonlinearity with a third-order dispersion term.

In this paper we develop two new approaches for directly assessing stability of nonlinear wave-based solutions, with application to jointed elastic bars. In the first stability approach, we strain a stiffness parameter and construct analytical stability boundaries using a wave-based method. Not only does this accurately determine stability of the periodic solutions found in the example case of two bars connected by a nonlinear joint, but it directly governs the response and stability of parametrically forced continuous systems without resorting to discretization, a new development in of itself. In the second stability approach, we pose a perturbation eigenproblem residue (PER) and show that changes in the sign of the PER locate critical points where stability changes from stable to unstable, and vice-versa. Lastly, we discuss follow-on research using the developed stability approaches. In particular, we identify an opportunity to study stability around internal resonance, and then identify a need to further develop and interpret the PER approach to directly predict stability. [ABSTRACT FROM AUTHOR]

In this paper, we develop two wave-based approaches for predicting the nonlinear periodic response of jointed elastic bars. First, we present a nonlinear wave-based vibration approach (WBVA) for studying jointed systems informed by re-usable, perturbation-derived scattering functions. This analytical approach can be used to predict the steady-state, forced response of jointed elastic bar structures incorporating any number and variety of nonlinear joints. As a second method, we present a nonlinear Plane-Wave Expansion (PWE) approach for analyzing periodic response in the same jointed bar structures. Both wave-based approaches have advantages and disadvantages when compared side-by-side. The WBVA results in a minimal set of equations and is re-usable following determination of the reflection and transmission functions, while the PWE formulation can be easily applied to new joint models and maintains solution accuracy to higher levels of nonlinearity. For example cases of two and three bars connected by linearly damped joints with linear and cubic stiffness, the two wave-based approaches accurately predict the expected Duffing-like behavior in which multiple periodic responses occur in the near-resonant regime, in close agreement with reference finite element simulations. Lastly, we discuss extensions of the work to jointed structures composed of beam-like members, and propose follow-on studies addressing opportunities identified in the application of the methods presented. [ABSTRACT FROM AUTHOR]

The cellular microstructure of periodic architected materials can be enriched by local intracellular mechanisms providing innovative distributed functionalities. Specifically, high-performing mechanical metamaterials can be realized by coupling the low-dissipative cellular microstructure with a periodic distribution of tunable damped oscillators, or resonators, vibrating at relatively high amplitudes. The benefit is the actual possibility of combining the design of wave-stopping bands with enhanced energy dissipation properties. This paper investigates the nonlinear dispersion properties of an archetypal mechanical metamaterial, represented by a one-dimensional lattice model characterized by a diatomic periodic cell. The intracellular interatomic interactions feature geometric and constitutive nonlinearities, which determine cubic coupling between the lattice and the resonators. The non-dissipative part of the coupling can be designed to exhibit a softening or a hardening behavior, by independently tuning the geometric and elastic stiffnesses. The nonlinear wavefrequencies and waveforms away from internal resonances are analytically determined by adopting a perturbation technique. The employed approach makes use of tools borrowed from Hamiltonian perturbation theory, together with techniques often used in the context of nearly-integrable Hamiltonian systems.The dispersion spectra are determined in closed, asymptotically approximate, form as a nonlinear function of the time-dependent decreasing amplitude decrement. The invariant manifolds defined by the harmonic periodic motions are also analytically determined. The asymptotic results are further validated numerically. [ABSTRACT FROM AUTHOR]

In this paper, nonlinearity associated with intense ultrasound is studied by using the one-dimensional motion of nonlinear shock wave in an ideal fluid. In nonlinear acoustics, the wave speed of different segments of a waveform is different, which causes distortion in the waveform and can result in the formation of a shock (discontinuity). Acoustic pressure of high-intensity waves causes particles in the ideal fluid to vibrate forward and backward, and this disturbance is of relatively large magnitude due to high-intensities, which leads to nonlinearity in the waveform. In this research, this vibration of fluid due to the intense ultrasonic wave is modeled as a fluid pushed by one complete cycle of piston. In a piston cycle, as it moves forward, it causes fluid particles to compress, which may lead to the formation of a shock (discontinuity). Then as the piston retracts, a forward-moving rarefaction, a smooth fan zone of continuously changing pressure, density, and velocity is generated. When the piston stops at the end of the cycle, another shock is sent forward into the medium. The variation in wave speed over the entire waveform is calculated by solving a Riemann problem. This study examined the interaction of shocks with a rarefaction. The flow field resulting from these interactions shows that the shock waves are attenuated to a Mach wave, and the pressure distribution within the flow field shows the initial wave is dissipated. The developed theory is applied to waves generated by 20 KHz, 500 KHz, and 2 MHz transducers with 50, 150, 500, and 1500 W power levels to explore the effect of frequency and power on the generation and decay of shock waves. This work enhances the understanding of the interactions of high-intensity ultrasonic waves with fluids.

This present manuscript studies a nonlinear hyperbolic model in fractional form which generalizes the nonlinear Klein–Gordon system. The equation under investigation includes the presence of a time-fractional operator of the Caputo type. A space-fractional form of that equation with integer-order temporal derivative has been previously investigated to elucidate the existence of localized wave transmission in relativistic wave equations. Here, we employ numerical techniques to estimate the solution of the fractional equation. The method has consistency of fourth order in space. Meanwhile, the temporal order of consistency is equal to 3−α. We considered herein a sinusoidal perturbation of the medium. The simulations show the existence of the transmission of localized nonlinear modes in some complex fractional media governed by hyperbolic models. Physically, the present work investigates the phenomenon of nonlinear supratransmission in a continuous generalization of linear chains of harmonic oscillators with memory effects. In particular, the present work corroborates the presence of this nonlinear phenomenon in chains of pendula with memory and arrays of Josephson junctions attached through superconducting wires and memory effects.

Intermodal nonlinear signal distortions in a graded-index three-mode fiber are experimentally investigated in a recirculating loop transmission over distances up to 684 km. Transmitting a 24.5 GBaud 16-quadrature-amplitude-modulated spatial super channel as channel under test together with an interfering channel band that is swept by more than 20 nm across the C-band, we find a Q-factor penalty of 1 dB for the signals in the LP01 mode when the interfering channels are approximately 17 nm separated from the channel under test. We find that the wavelength separation between strongest interacting spectral components is independent of the transmission distance. [ABSTRACT FROM AUTHOR]

From claims of roughly 3 % efficiency in 2009 to over 25 % efficiency now, perovskite solar cells have made amazing developments in recent years. Perovskite solar cells have quickly increased their efficiency, but there are still a number of obstacles to overcome before they can be considered a viable commercial technology. So, improving the stability of the perovskite solar cells and obtaining the mechanical properties of this kind of structure using computer simulation to decrease the computational cost is a challenging issue for designers. In this work, instead of a metal layer in the fabrication of solar cells, a functionally graded (FG) layer in which the material properties in this layer change in each direction. For the first time in the current report, the nonlinear phase velocity of the 3D-FG solar cells via mathematical simulation is presented. For solving the nonlinear partial differential equations (PDEs) of the perovskite solar cells, an analytical method is used. After doing some mathematical manipulation using the analytical method, a multiple scales method for solving the nonlinear equations in the time domain is presented. In order to compensate for the absence of a dataset suitable for deep neural networks (DNN), a mathematical simulation is conducted to acquire the nonlinear phase velocity characteristics of enhanced solar cells. The DNN method is used to forecast the nonlinear phase velocity characteristics of the present study, after the completion of training, testing, and validation processes. This approach has the advantage of cheap computing expense. Finally, the results show that when the panels tend to be too concave or convex, the nonlinear phase velocity is unstable. As an amazing outcome for related industries, the nonlinear phase velocity is very sensitive to the values of K x , K y , and R x / a , and all designers according to their purposes should consider the amount of these parameters. The current results' outcomes can be used in future building of the perovskite solar cell knowing about nonlinear dynamics features of 3D-FG perovskite solar cells. [ABSTRACT FROM AUTHOR]

The propagation of elastic waves in a circular cylinder and cylindrical annulus for two types of power-law constitutive equations is investigated. These power-law constitutive equations can describe elastic responses where the linearised strain and stress are nonlinearly related. These constitutive equations are a subclass of the more general class of implicit constitutive equations and are characterised by expressing the strain as a non-invertible function of the stress. Pseudo-solitary stress wave solutions for both types of constitutive equations in the circular cylinder and cylindrical annulus are derived. We find that for the power-law constitutive equation of Type I, a shock front will develop at the back of the wave while for the power-law constitutive equation of Type II, a shock front will develop at the front of the wave. Estimates of the times at which the shock front will develop are given. Standing wave solutions for both types of constitutive equations in the circular cylinder and cylindrical annulus are also obtained and the periods of oscillation are compared. [ABSTRACT FROM AUTHOR]

Excitation of nonlinear upper hybrid waves by O-mode HF heater in the ionospheric heating experiments was explored via HAARP digisonde operated in a fast mode. The observations are manifested by a bump in the virtual spread, which expands the ionogram echoes upward as much as 140 km and is located below the upper hybrid resonance frequency. The bump is similar to that, occurring in daytime ionograms, caused by the cusp at the E-F2 layer transition, indicating that there is a small ledge in the density profile similar to E-F2 layer transitions. The ionograms also show that the virtual height spread, which exceeds 50 km over a significant frequency range below the upper hybrid resonance frequency, is downward, rather than upward as observed in a natural Spread-F situation. It indicates that density irregularities along the geomagnetic field, rather than field-aligned, were generated. Theory shows that the upper hybrid waves excited by the parametric instabilities evolve into nonlinear periodic and solitary waves that enhance downward virtual height spread and generate density cavity to explain the experimental observations. [ABSTRACT FROM AUTHOR]

A rigid-walled semi-infinite circular cylindrical waveguide enclosing a weakly nonlinear fluid is considered. A quadratic nonlinear interaction is assumed as a model. A flat rigid piston generates an axisymmetric harmonic pressure that is prescribed as the input at the finite end of the waveguide. The objective is to study the modal interactions of waves. A regular perturbation method is used to separate the linear (primary) and the quasilinear (second harmonic) equations. First, linear solutions are established. Their quasilinear interactions then lead to modal interactions. Typically, the linear wavenumbers at the quasilinear order generate homogenous wavenumbers. Intersections of both these wavenumbers in the wavenumber-frequency plane are considered as resonances since the resulting pressure grows in amplitude in the axial propagating direction. The conditions under which the solutions become resonant or non-resonant are presented. In this last case, a beating phenomenon occurs with distance. It is found that the resonances are rare, except for the plane wave. Generally, the forced linear wavenumbers and the quasilinear generated wavenumbers acquire numerical values close to each other and create the beating phenomenon. • Modeled a rigid cylindrical nonlinear acoustic waveguide. • Used the perturbation method to find solutions at linear and quasilinear order. • Used the Bessel-Fourier series to represent second order inhomogeneous terms. • Obtained criteria for cross-mode resonances. • Obtained parameters that govern the beating phenomena. [ABSTRACT FROM AUTHOR]

A profound analysis of pressure and flow wave propagation in cardiovascular systems is the key in noninvasive assessment of hemodynamic parameters. Pulse transit time (PTT), which closely relates to the physical properties of the cardiovascular system, can be linked to variations of blood pressure and stroke volume to provide information for patient-specific clinical diagnostics. In this work, we present mathematical and numerical tools, capable of accurately predicting the PTT, local pulse wave velocity, vessel compliance, and pressure/flow waveforms, in a viscous hyperelastic cardiovascular network. A new one-dimensional framework, entitled cardiovascular flow analysis (CardioFAN), is presented to describe the pulsatile fluid–structure interaction in the hyperelastic arteries, where pertaining hyperbolic equations are solved using a high-resolution total variation diminishing Lax–Wendroff method. The computational algorithm is validated against well-known numerical, in vitro and in vivo data for networks of main human arteries with 55, 37 and 26 segments, respectively. PTT prediction is improved by accounting for hyperelastic nonlinear waves between two arbitrary sections of the arterial tree. Consequently, arterial compliance assignments at each segment are improved in a personalized model of the human aorta and supra-aortic branches with 26 segments, where prior in vivo data were available for comparison. This resulted in a 1.5% improvement in overall predictions of the waveforms, or average relative errors of 5.5% in predicting flow, luminal area and pressure waveforms compared to prior in vivo measurements. The open source software, CardioFAN, can be calibrated for arbitrary patient-specific vascular networks to conduct noninvasive diagnostics. [ABSTRACT FROM AUTHOR]

Abstract This study presents higher-order multiple scales analysis aimed at revealing angle- and amplitude-dependent invariant waveforms, and plane-wave stability, in two-dimensional periodic media. Multi-harmonic invariant waves arise from successive orders of particular solutions appearing in the multiple scales analysis. Simulations of nonlinear shear lattices confirm that inclusion of higher-order terms in the injected waveforms significantly reduce the ensuing growth of higher harmonics. These simulations also confirm the predicted directional-dependence of harmonic coefficients. In addition, the study assesses plane-wave stability using a local fixed-point analysis applied to the evolution equations, revealing angle-dependence in the stability characteristics. Based on the directional dependence uncovered, the study concludes with implications for encryption strategies and damage detection using weakly nonlinear lattices. [ABSTRACT FROM AUTHOR]

We present a theoretical model and experimental evidence of the long‐time relaxation process (slow dynamics) in rocks and other geomaterials following a dynamic wave excitation, at scales ranging from the laboratory to the Earth. The model is based on the slow recovery of an ensemble of grain contacts and asperities broken by a mechanical impact. It includes an Arrhenius‐type equation for recovery of the metastable, broken contacts. The model provides a characteristic size of the broken contacts (order 10−9 m) and predicts that their number increases with impact amplitude. Theoretical results are in good agreement with the laboratory and field data in that they predict both the logarithmic law of recovery rate and deviations from this law. Key Points: Many geomaterials are characterized by strong hysteretic nonlinearity and the long‐time relaxation after an impact (slow time)Laboratory experiments and seismic measurements reveal a typical logarithmic law of recovery of elastic moduli of rock in timeThe suggested theory explains such behavior for a broad range of geomaterials at scales from the laboratory to Earth [ABSTRACT FROM AUTHOR]

The acceleration of rotating plasma flow in crossed magnetic fields produced momentum transfer between the macroscopic degrees of freedom for a plasma flow was investigated. Results implied a concept for acceleration of plasma flow containing the charged macroscopic particles. Here, the case is treated when the plasma flow consists of electrons, protons, and heavy, multiply charged negative dust particles only. The analysis shows that these charged macroscopic particles have been trapped and, then, accelerated in the main plasma flow. As a result, such complex plasma flow can be accelerated in one axial direction to increase the thrust. It suggests that such complex plasma flow produced, for example, from cosmic dust medium may be used as a propellant and a work body for plasma thrusters. [ABSTRACT FROM AUTHOR]

A numerical solution is presented for a one-dimensional, nonlinear boundary-value problem of thermoelasticity with variable volume force and heat supply in a slab. One surface of the body is subjected to a given periodic displacement and Robin thermal condition, while the other is kept fixed and at zero temperature. Other conditions may be equally treated as well. The volume force and bulk heating simulate the effect of a beam of hot particles infiltrating the medium. The present study is a continuation of previous work by the same authors for the half-space [1]. The presented Figures display the process of propagation and reflection of the coupled nonlinear thermoelastic waves in the slab. They also show the effects of volume force and heat supply on the distributions of the mechanical displacements and temperature inside the medium. The propagation of beats provides evidence for sufficiently large time values.

Abstract We investigate the existence of solitary waves in a nonlinear square spring–mass lattice. In the lattice, the masses interact with their neighbors through linear springs, and are connected to the ground by a nonlinear spring whose force is expressed as a polynomial function of the masses out-of-plane displacement. The low-order Taylor series expansions of the discrete equations lead to a continuum representation that holds in the long wavelength limit. Under this assumption, solitary wave solutions are sought within the long wavelength approximation, and the subsequent application of multiple scales to the resulting nonlinear continuum equations. The study focuses on weak nonlinearities of the ground stiffness and reveals the existence of 3 types of solitons, namely a 'bright', a 'dark', and a 'vortex' soliton. These solitons result from the balance of dispersive and nonlinear effects in the lattice, setting aside other relevant phenomena in 2D waves such as diffraction that may lead to a field that does not change during propagation in nonlinear media. For equal constants of the in-plane springs, the governing equation reduces to the Klein–Gordon type, for which bright and dark solitons replicate solutions for one-dimensional lattices. However, unequal constants of the in-plane springs aligned with the two principal lattice directions lead to conditions in which the soliton propagation direction, defined by the group velocity, differs from the wave vector direction, which is unique to two-dimensional assemblies. Furthermore, vortex solitons are obtained for isotropic lattices, which shows similarities with results previously found in optics, thermal media and quantum plasmas. The paper describes the main parameters defining the existence of these solitary waves, and verifies the analytical predictions through numerical simulations. Results show the validity of obtained solutions and illustrate the main characteristics of the solitary waves found in the considered nonlinear mechanical lattice. The study provides an analysis of the physics of waves in nonlinear systems, and may lead to novel designs of devices that can be used for high-performance waveguides. [ABSTRACT FROM AUTHOR]

Many precursor-like anomaly observations prior to the Wenchuan earthquake were reported and analyzed, especially the abnormal strain pulses observed at the Guza station, but there are few discussions of the causes. Stick-slip motion is the basis for description of a great variety of phenomena characterized by the presence of sliding friction. In this article, perturbed Sine-Gordon (SG) equation is established from Bykov’s unsteady-state slip model. Stable solitary solutions of displacement and strain dimension are obtained and nonlinear pulse propagation is simulated using finite-difference modeling, while numerical stability is obtained by the flux-corrected transport method. Considering the solution of SG equation as initial source, a comparison between the modeling results and actual data at the Guza station gives one possible interpretation for this anomaly. During the seismogenic process of the Wenchuan earthquake, faults may likely occur as stick-slip tectonic movements which might be described by SG equation and would generate solitary wave signal. This kind of pulse experiences a forward tilting distortion due to nonlinear effect of the Earth and is received by the borehole strainmeter. Two kinds of nonlinear effects could lead to these special pulses. One is the nonlinear effects in the wave propagation process, and the other is effects of friction and stress in the process of unsteady-state slip. Because of the convergence effect of pulse, the wave would be collapsed at a certain time due to an excessive increase in the tilt angle. Hence, this kind of pulse cannot propagate for a long distance. [ABSTRACT FROM AUTHOR]

This article is aimed to investigate the geometrically nonlinear wave propagation of nano-beams on the basis of the most comprehensive size-dependent elasticity theory. To this end, the integral model of nonlocal elasticity theory in the most general form without any simplification in conjunction with the modified strain gradient theory is implemented in the analysis. Also, the Timoshenko beam model is utilized in the presented nonlocal strain gradient elasticity theory. By Hamilton’s principle, the governing integro-partial differential equations of motion are derived. Employing numerical integration and an efficient method called as periodic grid technique, a semi-analytical approach is presented for the solution procedure. To detect the impacts of nonlocality and small scale effects on the nonlinear wave propagation characteristics of beams at nanoscale, adequate numerical examples and comparison studies are presented. [ABSTRACT FROM AUTHOR]

We present a theoretical and experimental investigation of inter-modal four-wave mixing (FWM). After analyzing the phase-matching condition as the fundamental condition for efficient FWM, we show the impact of the individual mode’s propagation characteristics, such as differential mode delay and chromatic dispersion on the power of the generated idler. We verify the theoretical analysis with experimental measurements of intermodal FWM. We conclude that efficient broadband intermodal FWM can only be achieved for one specific FWM process and requires very close values of chromatic dispersion in all interacting fiber modes. [ABSTRACT FROM AUTHOR]

Plasma-based microwave power limitation is experimentally investigated in a microstrip transmission line integrating a direct current (dc) plasma discharge for preionization. Steady state and transient high-power microwave measurements demonstrate that the preionization by the dc plasma discharge helps in reducing limiting power thresholds and time responses to about 30 dBm and tens to few microsecond, respectively. Besides, optical diagnostics also exhibit interesting behaviors of the plasma discharge such as diffusion and parasitic breakdowns. Finally, the effect of plasma confinement is discussed, and it is shown that reducing the volume devoted to plasma expansion leads to a decrease in the dynamic range of the microwave power limitation. [ABSTRACT FROM AUTHOR]

Abstract: The Cauchy's problem of the generalized Poisson‐Nernst‐Planck‐Navier‐Stokes model in dimension three is considered. First, after dividing the physical domain into two parts: finite Mach number region and outside finite Mach number region, we give pointwise estimates of the Green's function by using long‐wave short‐wave decomposition and weighted energy estimate method in each region separately. Then from Duhamel's principle and some estimates on the nonlinear interactions between different wave patterns, we give the pointwise estimates of the solution for the nonlinear problem – , which exhibit generalized Huygens' principle for mass density, macroscopic momentum, negative charge distribution and positive charge distribution. As a byproduct, we find that the decay rates in L p ( R 3 ) ( 2 < p ≤ ∞) for both negative charge distribution and positive charge distribution are faster than those for the mass density ρ and the macroscopic momentum. More importantly, we obtained both electrostatic potential and the difference between negative charge distribution and positive charge distribution have the exponential decay rate in L p‐norm when p ≥ 1. [ABSTRACT FROM AUTHOR]

Infrasound waves are observed in the ionosphere relatively rarely, in contrast to atmospheric gravity waves. Infrasound waves excited by two distinguished sources as seismic waves from strong earthquakes ( M > 7) and severe tropospheric weather systems (typhoons) are discussed and analyzed. Examples of observation by an international network of continuous Doppler sounders are presented. It is documented that the co-seismic infrasound is generated by vertical movement of the ground surface caused by seismic waves propagating at supersonic speeds. The coseismic infrasound propagates nearly vertically and has usually periods of several tens of seconds far away from the epicenter. However, in the vicinity of the epicenter (up to distance about 1000–1500 km), the large amplitudes might lead to nonlinear formation of N-shaped pulse in the upper atmosphere with much longer dominant period, e.g. around 2 min. The experimental observation is in good agreement with numerical modeling. The spectral content can also be nonlinearly changed at intermediate distances (around 3000–4000 km), though the N-shaped pulse is not obvious. Infrasound waves associated with seven typhoons that passed over Taiwan in 2014–2016 were investigated. The infrasound waves were observed at heights approximately from 200 to 300 km. Their spectra differed during the individual events and event from event and covered roughly the spectral range 3.5–20 mHz. The peak of spectral density was usually around 5 mHz. The observed spectra exhibited fine structures that likely resulted from modal resonances. The infrasound was recorded during several hours for strong events, especially for two typhoons in September 2016. [ABSTRACT FROM AUTHOR]

Objectives: Recent advances in the field of acoustics and piezoelectric and ultrasound transducers have led to new approaches to the diagnosis and treatment of certain diseases. One method of treatment with ultrasonic waves is high‐intensity focused ultrasound (HIFU) treatment, which is a thermal therapeutic method used to treat malignant tumors. Although a variety of treatment‐planning strategies using ultrasonic waves have been investigated, little clinical success has been achieved. Computational modeling is a powerful tool for predicting device performance. Methods: The heating induced by a concave transducer with operating powers of 85 and 135 W was studied, and the experimental results presented in this article verify its applicability. Numerical simulations of the nonlinear acoustic field were performed by using the Westervelt and Khokhlov‐Zabolotskaya‐Kuznetsov equations. Heat transfer was measured for the 2 operational powers, and the results were compared with ex vivo experimental results. In addition, thermal dose contours for both the simulation and experimental results were calculated to investigate the ablated area. Results: Good agreement was found between the experimental and numerical results. The results show that the average temperature deviations calculated at the focal point were 12.8% and 4.3% for transducer powers of 85 and 135 W, respectively. Conclusions: This study provides guidance to HIFU practitioners in determining lesion size and identifying nonlinear effects that should be considered in HIFU procedures. [ABSTRACT FROM AUTHOR]

Wave propagation in metamaterial honeycombs endowed with periodically distributed nonlinear resonators is addressed. The linear and nonlinear dispersion properties of the metamaterial are investigated. The nonlinear wave propagation equations obtained via a projection method and the Floquet–Bloch theorem are attacked by the method of multiple scales to obtain in closed form the nonlinear manifolds parametrized by the amplitudes, the frequency, and the wave numbers. The effects of the nonlinearity on the frequency bandgaps are thoroughly investigated and the optimization problem of the resonators nonlinearity towards increased bandgap size is tackled to provide a significant practical framework for the design of nonlinear metamaterials. • Nonlinear dispersion functions of metamaterials hosting nonlinear resonators. • The nonlinear dispersion functions obtained via the method of multiple scales. • Optimization of the resonators nonlinearity towards increased bandgaps. • Validation of the bandgap behavior via time domain simulations. [ABSTRACT FROM AUTHOR]

Charged particle acceleration is a fundamental issue in many fields ranging from particle physics to spacecraft propulsion. In this paper, the interaction between electromagnetic waves and relativistic electrons is numerically studied. The effect of the initial gyrophase in a dipole magnetic field on electron acceleration by wave--particle interaction is found in a test particle code with various wave amplitudes. It is indicated that the initial gyrophase of the electrons plays a crucial role in the acceleration process. [ABSTRACT FROM AUTHOR]

We introduce a self-consistent approach for the description of the nonlinear light propagation in InAs/InGaAs quantum-dot semiconductor optical amplifiers and, using it, numerically analyze the four-wave mixing conversion efficiency in such amplifiers. This approach is based on a delay-differential equation for the optical field propagating through the amplifier and additional equations describing the microscopically calculated charge-carrier dynamics in the quantum-dot states and the surrounding quantum well reservoir. Here, we draw our attention to the studies of the hierarchy of the nonlinear effects involved in the four-wave-mixing processes We observe that the spectral hole burning is the most important effect to drive the four-wave mixing The charge-carrier density pulsation appearing together with the spectral hole burning constitutes the second most important effect, while the charge-carrier heating turned out to be negligible. Furthermore, we found that the four-wave mixing conversion efficiency can be effectively increased when higher device pump current or higher device temperature is used, provided that the frequencies of the injected light sources are adjusted to the temperature-dependent gain maximum. [ABSTRACT FROM PUBLISHER]

In the previous investigations, an intermode exchange was used to demonstrate the transfer of energy and momentum into using different kinematic degrees of freedom. This paper examines using a hydrodynamic approach using a cold, neutral flow in a rotating cylindrical plasma column using crossed magnetic fields. Results show that the twirling plasma flow in a cylindrical vortex can be accelerated in an axial direction, thereby resulting an energy/momentum transfer in the axial direction. These results are analogous to the creation of a plasma thruster using this effect. [ABSTRACT FROM PUBLISHER]