Traveling Plane Wave Research Articles

Phase reorganization leads to transient β-LFP spatial wave patterns in motor cortex during steady-state movement preparation.

Previous studies on the origin and properties of spatial patterns in motor cortex β-local field potential (β-LFP) oscillations have focused on planar traveling waves. However, it is unclear 1) whether β-LFP waves are limited to plane waves, or even 2) whether they are propagating waves of excito-excitatory activity, i.e., primarily traveling waves in excitable media; they could reflect, instead, reorganization in the relative phases of transient oscillations at different spatial sites. We addressed these two problems in β-LFPs recorded via microelectrode arrays implanted in three adjacent motor cortex areas of nonhuman primates during steady-state movement preparation. Our findings are fourfold: 1) β-LFP wave patterns emerged as transient events, despite stable firing rates of single neurons concurrently recorded during the same periods. 2) β-LFP waves showed a richer variety of spatial dynamics, including rotating and complex waves. 3) β-LFP wave patterns showed no characteristic wavelength, presenting instead a range of scales with global zero-lag phase synchrony as a limiting case, features surprising for purely excito-excitatory waves but consistent with waves in coupled oscillator systems. 4) Furthermore, excito-excitatory traveling waves induced by optogenetic stimulation in motor cortex showed, in contrast, a characteristic wavelength and reduced phase synchrony. Overall, β-LFP wave statistics differed from those of induced traveling waves in excitable media recorded under the same microelectrode array setup. Our findings suggest phase reorganization in neural coupled oscillators contribute significantly to the origin of transient β-LFP spatial dynamics during preparatory steady states and outline important constraints for spatially extended models of β-LFP dynamics in motor cortex. NEW & NOTEWORTHY We show that a rich variety of transient β-local field potential (β-LFP) wave patterns emerge in motor cortex during preparatory steady states, despite stable neuronal firing rates. Furthermore, unlike optogenetically induced traveling waves, β-LFP waves showed no characteristic wavelength, presenting instead a range of scales with global phase synchrony as a limiting case. Overall, our statistical analyses suggest that transient phase reorganization in neural coupled oscillators, beyond purely excito-excitatory traveling waves, contribute significantly to the origin of motor cortex β-LFP wave patterns.

A finite volume method for undercompressive shock waves in two space dimensions

Undercompressive shock waves arise in many physical processes which involve multiple phases. We propose a Finite Volume method in two space dimensions to approximate weak solutions of systems of hyperbolic or hyperbolic-elliptic conservation laws that contain undercompressive shock waves. The method can be seen as a generalization of the spatially one-dimensional and scalar approach in [C. Chalons, P. Engel and C. Rohde, SIAM J. Numer. Anal. 52 (2014) 554–579]. It relies on a moving mesh ansatz such that the undercompressive wave is represented as a sharp interface without any artificial smearing. It is proven that the method is locally conservative and recovers planar traveling wave solutions exactly. To demonstrate the efficiency and reliability of the new scheme we test it on scalar model problems and as an application on compressible liquid-vapour flow in two space dimensions.

Traveling Waves in a Reaction-Diffusion System Describing Smoldering Combustion

Combustion is a fast oxidation process and exhibits diverse behaviors according to experimental conditions. When there is no natural convection of air, such as in experiments aboard a space shuttle or in a vertically confined system, an unexpected finger-like smoldering combustion develops. In this paper, a reaction-diffusion-advection system that describes smoldering combustion is studied from the viewpoint of computer-aided analysis. In particular, we focus on the traveling wave solutions of the system, which represent the characteristic propagation of combustion. It is revealed that the existence or nonexistence of stable traveling wave solutions determines whether or not a combustion front propagates in a self-sustained way in one space dimension. In two space dimensions, we numerically suggest the existence of a traveling spot solution in which the flow rate is too low to support planar traveling wave solutions. Moreover, we discuss reflection phenomena of a combustion wave when it reaches the bounda...

Traveling wave solutions for bistable fractional Allen–Cahn equations with a pyramidal front

Using the method of sub-super-solution, we construct a solution of (−Δ)su−cuz−f(u)=0 on R3 of pyramidal shape. Here (−Δ)s is the fractional Laplacian of sub-critical order 1/2<s<1 and f is a bistable nonlinearity. Hence, the existence of a traveling wave solution for the parabolic fractional Allen–Cahn equation with pyramidal front is asserted.The maximum of planar traveling wave solutions in various directions gives a sub-solution. A super-solution is roughly defined as the one-dimensional profile composed with the signed distance to a rescaled mollified pyramid. In the main estimate we use an expansion of the fractional Laplacian in the Fermi coordinates.

An experimental and theoretical study of two-dimensional traveling waves in plates

The present work explores the generation of two-dimensional steady-state flexural waves that are non-reflective on a thin rectangular plate with free boundary conditions when excited by two macro-fiber composites (MFCs). The voltage signals to the MFCs have a frequency lying halfway between two adjacent resonant frequencies with a phase difference of [Formula: see text]. Locations of MFCs and frequencies of actuation are varied to study the response of the plate due to these forces. A finite element plate model is developed and updated based on experimental modal tests on the plate. This model is able to predict up to the 40th damped eigenvalue with a maximum error of 2.5% and match mode shapes accurately, with a lowest Modal Assurance Criterion value of 0.92. Numerical simulations of traveling waves have been carried out and are compared with experimental results. Preliminary results show that the location of the MFCs and the frequency of excitation have an effect on the type and the quality of the traveling waves. These results shall lay the foundation for an exhaustive analysis of planar traveling waves in plates.

Traveling Internal Plane-wave Synthesis (TIPS) for uniform B1 in high field MRI

A new target-field approach to generating uniform radio frequency (RF) fields within the human body for high field MRI is described. The method involves producing a set of external fields which, after interaction with a dielectric object, superimpose to produce a traveling plane wave, exposing all spins to the same RF amplitude (B1) over a cycle of the harmonic field. Conceptually this is similar to conventional RF shimming, but uses a different RF source design, input data, and objective function. The method requires a detailed knowledge of the coupling between exterior field modes, produced by an array of RF sources, and field modes within the body. Given an estimate of the coupling matrix, the linear superposition of external modes that produces a desired internal target field can be determined. The new method is termed Traveling Internal Plane-wave Synthesis (TIPS). A simple design of a coil array is described that can, in principle, generate the required field modes. Simulations demonstrate that radio frequency magnetic fields of nearly uniform (<1% variation) magnitude can be produced within dielectric objects larger than a wavelength in size. If the dielectric medium has non-zero conductivity, traveling waves are attenuated as they traverse the object, but field uniformity within planar slices is preserved. For general 3D imaging, a superposition of plane waves can provide field focusing to balance conductive losses, thereby achieving nearly uniform-magnitude B1+ magnetic fields over a volume of interest.

A helical-structured acoustic metamaterial

Here, we would like to present a helical-structured acoustic metamaterial that can effectively decelerate sound propagation. Unlike currently avaliable solutions which are mostly dispersive due to the requirement of local resonators., this non-dispersive helical-structured metamaterials is able to provide high effective refractive index. By adjusting the helicity of the acoustic metamaterial structures, we can further modify such refractive index. The performance of this helical-structured acoustic metamaterial has been numerically and experimentally verified. We even designed a lens base on multiple inhomogeneous helical-structured acoustic metamaterial unit cells. This lens can turn normally travelling plane wave into a self-accelerating beam.

Neutral core-shell particles under acoustic radiation force

We theoretically analyze how a core-shell small particle can become nonresponsive under the acoustic radiation force in an ideal fluid. The particle is composed by a fluid core cloaked by an elastic or viscoelastic solid shell with considering its outer radius much smaller than the wavelength, e.g., the so-called Rayleigh scattering limit. By suitably choosing the core volume fraction (the core-to-shell volume ratio) one may suppress the radiation force. In case of a traveling plane wave, radiation force neutrality is related to scattering cancellation by the cloaking shell. However, neutrality is not achieved for absorptive cloaks. The somehow “intuitive” connection between scattering cancellation and radiation force suppression does not happen for a standing plane wave. Also, shell absorption does not change neutrality in this case. It is worth to mention that standing wave is the leit motiv of particle handling in different microfluidics applications. Several examples of radiation force neutrality are ...

Chaotic behavior of collective ion dynamics in the presence of an external static magnetic field

The two-dimensional nonlinear collective ion dynamics in the presence of external magnetic field in an electron-ion plasma is investigated. The analysis is performed for traveling plane waves to elucidate the various aspects of the phase-space dynamics. The presence of magnetic field makes the dynamics of the nonlinear wave complex with a complicated phase-space behavior. Thus, the nonlinear wave supports a wide class of nonlinear structures viz., single soliton, multi-soliton, periodic, and quasi-periodic oscillations depending on the values of M (Mach number) and Ω (the ratio of ion gyro-frequency to the ion plasma frequency). The computational results predict the chaotic behavior of the nonlinear wave and the transition to chaos takes place when Ω≳0.35 depending on the direction of propagation and the value of M. The amplitude of the wave depends on the obliqueness of the propagation and Mach number, whereas the magnetic field changes the dispersion properties of the wave.

Acoustic radiation force and torque exerted on a small viscoelastic particle in an ideal fluid

We provide a detailed analysis on the acoustic radiation force and torque exerted on a homogeneous viscoelastic particle in the long-wave limit (i.e. the particle radius is much smaller than the incident wavelength) by an arbitrary wave. We assume that the particle behaves as a linear viscoelastic solid, which obeys the fractional Kelvin–Voigt model. Simple analytical expressions for the radiation force and torque are obtained. The developed theory is used to describe the interaction of acoustic waves (traveling and standing plane waves, and zero- and first-order Bessel beams) in the MHz-range with polymeric particles, namely lexan, low-density (LDPE) and high-density (HDPE) polyethylene. We found that particle absorption is chiefly the cause of the radiation force due to a traveling plane wave and zero-order Bessel beam when the frequency is smaller than 5MHz (HDPE), 3.9MHz (LDPE), and 0.9MHz (lexan). Whereas in a standing wave field, the radiation force is mildly changed due to dispersion inside the particle. We also show that the radiation torque caused by a first-order Bessel beam varies nearly quadratic with frequency. These findings may enable new possibilities of particle handling in acoustophoretic techniques.

Electronically Steerable and Fixed-Beam Frequency-Tunable Planar Traveling-Wave Antenna

The design of an electronically steerable wideband planar traveling-wave antenna is presented. The proposed antenna has a very simple structure based on a microstrip line loaded with several radiating elements and phase shifters between them. The phase shifters are based on tunable capacitances, in order to perform a continuous phase shift between the radiating elements and control the main beam direction. The radiating elements are complementary strip slots that have a very broad impedance bandwidth, thus allowing the antenna to have two different modes of operation: maintaining the main lobe direction over a significant bandwidth, 1.71–2.17 GHz, and performing a main beam scanning over this bandwidth with a maximum angle range of $-45^{\circ}$ to 45° at 2 GHz.

Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation

We prove the multidimensional stability of planar traveling waves for scalar nonlocal Allen-Cahn equations using semigroup estimates. We show that if the traveling wave is spectrally stable in one space dimension, then it is stable in $n$-space dimension, $n\geq 2$, with perturbations of the traveling wave decaying like $t^{-(n-1)/4}$ as $t\rightarrow +\infty$ in $H^k(\mathbb{R}^n)$ for $k\geq \left[\frac{n+1}{2}\right]$.

Induced radiation force and torque on a viscoelastic particle in an ideal fluid

The interaction of an acoustic wave with a suspended particle may produce radiation force and torque on the particle through linear and angular momentum transfer. Theoretical analysis of the radiation force exerted on a rigid, compressible fluid, elastic solid, and layered spherical particle is abundantly found in the literature. Nevertheless, less attention has been devoted to cases involving a homogeneous viscoelastic particle, even though viscoelastic materials are ubiquitous. Here, the radiation force and torque exerted on this kind of particle is studied in detail using the fractional Kelvin-Voigt viscoelastic model. Analytical expressions are obtained in the monopole-dipole approximation to a small particle in the long-wave limit. Considering a traveling plane wave interacting with a high-density polyethylene (HDPE) particle, we found that the axial radiation force is negative, i.e., the force and the wave propagation are in opposite directions. For a first-order Bessel vortex beam, a full 3D tractor beam develops on the HDPE particle placed in the beam's axis. Furthermore, negative axial radiation torque also appears on the particle, i.e., the torque and the beam's angular momentum are contrariwise. In addition, possible implications of this method to the advancement of acoustophoretic techniques will be outlined.

Role of heat generation and thermal diffusion during frontal photopolymerization

Frontal photopolymerization (FPP) is a rapid and versatile solidification process that can be used to fabricate complex three-dimensional structures by selectively exposing a photosensitive monomer-rich bath to light. A characteristic feature of FPP is the appearance of a sharp polymerization front that propagates into the bath as a planar traveling wave. In this paper, we introduce a theoretical model to determine how heat generation during photopolymerization influences the kinetics of wave propagation as well as the monomer-to-polymer conversion profile, both of which are relevant for FPP applications and experimentally measurable. When thermal diffusion is sufficiently fast relative to the rate of polymerization, the system evolves as if it were isothermal. However, when thermal diffusion is slow, a thermal wavefront develops and propagates at the same rate as the polymerization front. This leads to an accumulation of heat behind the polymerization front which can result in a significant sharpening of the conversion profile and acceleration of the growth of the solid. Our results also suggest that a novel way to tailor the dynamics of FPP is by imposing a temperature gradient along the growth direction.

Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping

We theoretically analyze a discrete Schr\"odinger chain with hopping to the first and second neighbors, as can be realized with zigzag arrangements of optical waveguides or lattice sites for cold atoms. Already at moderate values, the second-neighbor hopping has a strong impact on the band structure, leading to the emergence of a new extremum located inside the band, accompanied by a van Hove singularity in the density of states. The energy band is then divided into a subcritical regime with the usual unique correspondence between wave number and energy of the travelling waves, and a supercritical regime, in which waves of different wave number are degenerate in energy. We study the consequences of these features in a scattering setup, introducing a defect that locally breaks the translational invariance. The notion of a local probability current is generalized beyond the nearest-neighbor approximation and bound states with energies outside the band are discussed. At subcritical energies inside the band, an evanescent mode coexists with the travelling plane wave, giving rise to resonance phenomena in scattering. At weak coupling to the defect, we identify a prototypical Fano-Feshbach resonance of tunable shape and provide analytical expressions for its profile parameters. At supercritical energies, we observe coupling of the degenerate travelling waves, leading to an intricate wave packet fragmentation dynamics. The corresponding branching ratios are analyzed.

The acoustic radiation impedance of a rectangular panel

This paper extends the definition of the one sided radiation impedance of a panel mounted in an infinite rigid baffle which was previously used by the authors so that it can be applied to all transverse velocity wave types on the panel rather than just to the possibly forced travelling plane transverse velocity waves considered previously by the authors. For the case of travelling plane waves on a rectangular panel with anechoic edge conditions, and for the case of standing waves on a rectangular panel with simply supported edge conditions, the equations resulting from one of the standard reductions from quadruple to double integrals are given. These double integral equations can be reduced to single integral equations, but the versions of these equations given in the literature did not always converge when used with adaptive integral routines and were sometimes slower than the double integral versions. This is because the terms in the integrands in the existing equations have singularities. Although these singularities cancel, they caused problems for the adaptive integral routines. This paper rewrites these equations in a form which removes the singularities and enables the integrals in these equations to be evaluated with adaptive integral routines. Approximate equations for the azimuthally averaged one sided radiation impedance of a rectangular panel mounted in an infinite baffle are given for all the cases considered in this paper and the values produced by these equations are compared with numerical calculations.

Acoustic interaction forces between small particles in an ideal fluid.

We present a theoretical expression for the acoustic interaction force between small spherical particles suspended in an ideal fluid exposed to an external acoustic wave. The acoustic interaction force is the part of the acoustic radiation force on one given particle involving the scattered waves from the other particles. The particles, either compressible liquid droplets or elastic microspheres, are considered to be much smaller than the acoustic wavelength. In this so-called Rayleigh limit, the acoustic interaction forces between the particles are well approximated by gradients of pair-interaction potentials with no restriction on the interparticle distance. The theory is applied to studies of the acoustic interaction force on a particle suspension in either standing or traveling plane waves. The results show aggregation regions along the wave propagation direction, while particles may attract or repel each other in the transverse direction. In addition, a mean-field approximation is developed to describe the acoustic interaction force in an emulsion of oil droplets in water.

Alternans and Spiral Breakup in an Excitable Reaction-Diffusion System: A Simulation Study.

The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced.

Derivation and experimental validation of Lamb wave equations for an n-layered anisotropic composite laminate

Lamb waves are ultrasonic guided waves that propagate between two parallel free surfaces and their use for damage detection has been widely explored and demonstrated. Damage in materials/structures can be detected by analyzing the difference between the phase/group velocity and the loss of amplitude of Lamb waves on damaged and un-damaged specimens. The propagation characteristics of Lamb waves are described in the form of dispersion curves, which are plots of phase/group velocities versus the product of frequency-thickness generated by solving the Lamb wave equations. Lamb waves’ dispersion behaviors for isotropic materials are well established in the literature; however, such is not the case for the laminated composites. The most common methods for solving the Lamb wave equations in composites consist of using laminated plate theory or 3D linear elasticity by assuming an orthotropic and/or higher symmetry. This assumption may not be true, if the actuators and sensors in an orthotropic or transversely isotropic laminates are installed in a non-principle direction or the layup is symmetric but not balanced.This paper presents a full derivation of Lamb wave equations for n-layered monoclinic composite laminates based on linear 3D elasticity by considering the displacement fields in all three directions using the partial wave technique in combination with the Global Matrix (GM) approach. In the partial wave technique, the principle of superposition of three upward and three downward travelling plane waves are assumed in order to satisfy the associated boundary conditions. The bounded upper and lower surfaces reflect the waves and the combination of these reflections going towards the upper or lower interfaces results in the propagating guided waves. The GM approach is used to assemble all the equations from each layer to form a global, unified matrix that describes the displacement and stress fields along the entire laminate associated with the wave propagation. A robust method for numerically solving the Lamb wave equations is also presented.The presented method was verified experimentally by analyzing the propagation of Lamb waves in two different composite panels constructed out of unidirectional carbon-fiber epoxy prepreg and fiber-metal laminate (GLARE 3-3/4). The panels were instrumented with lead zirconate titanate (PZT) piezoelectric sensors, which were excited at different frequencies ranging from 20kHz to 500kHz to generate and acquire the waves. The waves were excited and gathered at three different propagation angles of 0°, 45°, and 90° for the carbon-fiber epoxy laminate panel and at six different angles of 0°, 20°, 45°, 70° and 90° for the fiber-metal laminates (GLARE). The phase and group velocities of the fundamental symmetric (So) and anti-symmetric (Ao) Lamb waves were extracted by tracking the peaks of each individual wave phase and the wave envelope respectively using an in-house code developed in MATLAB. It was found that the presented 3D linear elasticity model followed the experimental data closely for both symmetric and anti-symmetric Lamb modes. The analytical method presented in this paper was able to predict the Lamb wave dispersion for both the carbon-fiber epoxy laminate and the hybrid fiber-metal laminate proving the robustness and versatility of the solution method.

Acoustic radiation force due to a diverging wave: Demonstration and theory

A radiation force is the time-averaged force exerted by any kind of wave on a body. In the case of a divergent traveling acoustic wave, it is known that a relatively small rigid body can experience a radiation force that is directed toward the source. We show that this effect can be readily demonstrated with a styrofoam sphere pendulum near a horizontally directed loudspeaker that is emitting sound of sufficiently high amplitude and low frequency. The attraction is surprising because repulsive forces are exerted by a traveling plane wave and by an outward jetting or “wind” from the loudspeaker. We argue that the attractive force near a source that is small compared to the wavelength can be roughly understood and calculated as a time-averaged Bernoulli effect, if scattering is ignored. The result is within a factor of two of rigorous published results based on scattering calculations, when these results are specialized to the case of a rigid body whose average density is much greater than the density of the fluid. However, repulsion occurs when the average density of the body is less than the density of the fluid, in which case our Bernoulli result completely fails.