Form Of Wave Packets Research Articles

Dynamics and lifetimes of resonant phonons in the quasiparticle and nonquasiparticle regimes

The dynamics and lifetimes of a phonon with model resonant interactions from the quasiparticle to nonquasiparticle regime were investigated employing Green's function and the Green-Kubo method. In the weak-coupling case, the dynamics of the resonant phonon are analogous to a damped harmonic oscillator and its lifetime $\ensuremath{\tau}$ is in accordance with the standard phonon transport theory $\ensuremath{\tau}=\frac{1}{2\mathrm{\ensuremath{\Gamma}}}$ ($\mathrm{\ensuremath{\Gamma}}$ being the imaginary part of phonon self-energy). In the strong-coupling nonquasiparticle regime, however, the resonant phonon ``propagates'' in a complex form of wave packets and the actual phonon lifetime ${\ensuremath{\tau}}_{\mathrm{GK}}$ as determined from the Green-Kubo formula significantly deviates from the standard $\ensuremath{\tau}=\frac{1}{2\mathrm{\ensuremath{\Gamma}}}$ relation. Taking the four-phonon resonant ${\mathrm{AgCrSe}}_{2}$ and three-phonon resonant PbSe model systems as examples, the phonon nonquasiparticle dynamics and their lifetimes in real materials are further investigated by first-principle calculations. Substantial discrepancies between ${\ensuremath{\tau}}_{\mathrm{GK}}$ and $\ensuremath{\tau}$ are found for the strongly resonant phonons at high-symmetrical points in both materials. Meanwhile, the lifetime ${\ensuremath{\tau}}_{\mathrm{GK}}$ of the phonons that are not subjected to resonant phonon interactions almost recovers to the conventional theoretical result $\ensuremath{\tau}$ despite the non-Lorentzian spectral feature of these phonons. It is suggested that $\ensuremath{\omega}{\ensuremath{\tau}}_{\mathrm{GK}}$, instead of the conventional $\ensuremath{\omega}\ensuremath{\tau}$, can be applied as a criterion to distinguish phonon quasiparticles and nonquasiparticles in addition to the phonon spectral functions.

Unsteady flow behaviors and noise source identification of a ducted orifice using detached-eddy simulation

In the present study, turbulent flow through a ducted orifice is numerically modeled using dynamic delayed detached-eddy simulations (dynamic delayed detached-eddy simulation) to clarify their unsteady flow behaviors and noise generation mechanisms. To this end, a total of four orifices with different thickness-to-diameter ratios (t/d = 0.5, 2, and 4) and porosities (orifice hole area to pipe area ratio, β= 20% and 31%) were chosen for comparison at a Reynolds number of 10 000. Characteristics of the unsteady turbulent flow are first examined in terms of time-mean and statistical flow quantities as well as wall pressure fluctuations. Subsequently, the coherent flow structures in the form of wavepackets are effectively evaluated through spectral proper orthogonal decomposition (SPOD) analysis. The main noise sources are identified as alternatively energetic acoustic dipoles on the orifice's leading and trailing faces, dominated by the intermittent interaction between the unsteady flow and the orifice plate, particularly at the inner edges. Comparisons of different orifice thicknesses at the same porosity (β = 31%) showed that the noise source in the thin configuration (t/d = 0.5) is alternatively dominated by the shedding and flapping behaviors of the vortical structures in the low-frequency range, while Kelvin–Helmholtz-type wavepackets result from the Kelvin–Helmholtz shear layer instability at higher frequencies. For thicker configurations (t/d = 2 and 4), reattachment of the separated shear layer occurs within the orifice throat region; the resultant SPOD modes reveal double-wavepacket structures issuing from the leading and trailing edges, with distinctly different behaviors captured at higher frequencies. Furthermore, for the thin orifice (t/d = 0.5), similar flow structures are found with different porosities (β= 20% and 31%), with intensified noise levels observed at the lower porosity.

Wave-Shape-Tolerant Photonic Quantum Gates.

Photons, acting as "flying qubits" in propagation geometries such as waveguides, appear unavoidably in the form of wave packets (pulses). The actual shape of the photonic wave packet as well as possible temporal and spectral correlations between the photons play a critical role in successful scalable computation. Currently, unentangled indistinguishable photons are considered a suitable resource for scalable photonic circuits. Here we show that using so-called coherent photon conversion, it is possible to construct flying-qubit gates which are not only insensitive to wave shapes of the photons and temporal and spectral correlations between them but which also fully preserve these wave shapes and correlations upon the processing. This allows the use of photons with correlations and purity in a very broad range for a scalable computation. Moreover, such gates can process entangled photonic wave packets even more effectively than unentangled ones.

The Role of Latent Heating Anomalies in Exciting the Summertime Eurasian Circulation Trend Pattern and High Surface Temperature

AbstractDynamical mechanisms for the summer Eurasian circulation trend pattern are investigated by analyzing reanalysis data and conducting numerical model simulations. The daily circulations that resemble the Eurasian circulation trend pattern are identified and categorized into two groups based on surface warming signal over central and eastern Europe. In the group with large warm anomaly, the upper-level circulation takes on a wave packet form over Eurasia, and there are enhanced latent heating anomalies centered over the North Sea and suppressed latent heating anomalies over the Caspian Sea. The numerical model calculations indicate that these latent heating anomalies can excite an upper-level circulation response that resembles the Eurasian circulation trend pattern. Additional analysis indicates that trends of these two latent heating centers contribute to the long-term circulation trend. In the weak warm anomaly group, the circulation pattern takes on a circumglobal teleconnection (CGT) pattern, and there is no heating signal that reinforces the circulation. These results indicate that not all CGT-like patterns excite temperature anomalies that are persistent and in phase with the trend pattern, and that quasi-stationary forcings, such as the latent heating anomalies, play an important role in driving the boreal summer circulation anomaly that accompanies the strong and persistent surface temperature signal.

Lepton pair production in ultraperipheral collisions

The lepton pair production in ultraperipheral collisions is studied in the classical field approximation. We derive a general form of the cross section in terms of photon distributions that depend on the transverse momentum and coordinate based on the wave packet form of nuclear wave functions. Such a general form of the cross section in the classical field approximation contains the results of the generalized equivalent photon approximation (EPA) as well as the corrections beyond EPA in the Born approximation. By rewriting the general form of the cross section in light-cone coordinates, we find a good connection with the transverse momentum dependent distribution factorization formalism in the Born approximation. Our numerical results are consistent with current experimental data.

Using Desmos to Understand the Difference Between Phase and Group Velocity

An individual harmonic wave (i.e., having a single frequency and wavelength over all time and space) traveling in a loss-free medium has a single constant speed, which is equal to the magnitude of the phase velocity of the wave. However, when a set of different harmonic waves are traveling in the same direction, they interfere to form wave packets. In general, the peak of a wave packet travels at a speed equal to the magnitude of the group velocity that can be vastly different than the phase speeds of the component harmonic waves, even if the entire set of harmonic waves only differ among themselves slightly in frequency and wavelength. It is difficult for students to understand the origin of this difference from verbal descriptions and static graphs of wave functions at successive instants in times, such as are typically presented in textbooks. However, considerable insight is possible using the free online software Desmos.

Study on characteristics of internal solitary waves in the Malacca Strait based on Sentinel-1 and GF-3 satellite SAR data

The study of the characteristics of internal solitary waves happened in the Malacca Strait is an urgent problem for submarine, ship navigation and marine engineering. Based on SAR remote sensing data obtained from the high spatial resolution Sentinel-1 and GF-3, the internal solitary wave characteristics of the Malacca Strait are investigated. By use of 20 Sentinel-1 SAR images from June 2015 to December 2016 and 24 GF-3 images from April 2018 to March 2019, the spatial distribution characteristics of internal solitary wave s are statistically analyzed. It is found that the internal solitary waves are usually in the form of wave packets and single solitary waves, and the maximum crest length of the leading wave can reach 39 km. The amplitude and group velocity of internal solitary wave s can be calculated by the inversion model of high-order nonlinear Schrodinger (NLS) equation, and the calculated amplitude of the internal solitary wave s and the propagation group velocity of the wave packets range from 4.7 m to 23.9 m and 0.12 m/s to 0.40 m/s, respectively. The range of phase velocity of single internal solitary waves obtained by KdV equation is 0.26 m/s to 0.60 m/s. In general, the amplitude and the velocity of internal solitary wave s in Malacca strait are related to the topography.

Global linear instability of rotating-cone boundary layers in a quiescent medium

The global linear stability of the family of infinite rotating-cone boundary layers in an otherwise still fluid is investigated using a velocity-vorticity form of the linearized Navier-Stokes equations. The formulation is separable with respect to the azimuthal direction. Thus, disturbance development is simulated for a single azimuthal mode number. Numerical simulations are conducted for an extensive range of cone half-angles (ψ∈[20∘:80∘]) and stability parameters (Reynolds number, azimuthal mode number), where conditions are taken to be near those specifications necessary for the onset of absolute instability. A localized impulsive wall forcing is implemented that excites disturbances that form wave packets. This allows the disturbance evolution to be traced in the spatial-temporal plane. When a homogeneous flow approximation is utilised that neglects the spatial variation of the basic state, linear perturbations display characteristics consistent with local stability theory. For disturbances to the genuine spatially dependent inhomogeneous flow, global linear instability characterized by a faster than exponential temporal growth arises for azimuthal mode numbers greater than the conditions for critical absolute instability. Furthermore, a reasonable prediction for the azimuthal mode number needed to bring about a change in global behavior is achieved by coupling solutions of the Ginzburg-Landau equation with local stability properties. Thus, the local-global stability behavior is qualitatively similar to that found in the infinite rotating-disk boundary layer and many other globally unstable flows.

Discharge Oscillations in Morozov’s Stationary Plasma Thruster as a Manifestation of Large-Scale Modes of Gradient Drift Instability

The phenomenon of large-scale discharge oscillations in Morozov’s stationary plasma thruster (SPT) is physically interpreted by analyzing global modes of gradient drift instability. The problem is solved using an ideal two-fluid hydrodynamic plasma model that includes the effects of stationary electron flow, electron inertia, and spatial inhomogeneities of the magnetic field and plasma density along the accelerating channel. The frequencies and axial structure of unstable eigenmodes are calculated for typical parameters of the SPT-100 thruster. The obtained spectrum is characterized by a finite set of long-wavelength azimuthal modes in the lower hybrid frequency range, which are predominantly localized in the near-anode region of the thruster. It is shown that the eigenmodes can form wave packets the main characteristics of which in the linear stage of instability coincide with the parameters of the experimentally observed large-scale azimuthal spoke-like structures. The influence of the thruster geometry (the length and width of the accelerating channel) on the frequency characteristics of oscillations and formation of beatings is investigated.

The non-modal onset of the tearing instability

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number$S$increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the$L_{2}$-norm, for the classical set-up of current sheets unstable to the TI, scales as$O(S^{1/4})$on time scales of$O(S^{1/4})$for$S\gg 1$. This behaviour is much faster than the time scale$O(S^{1/2})$when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

Energy-Dynamics Resulting in Turbulent and Acoustic Phenomena in an Underexpanded Jet

Underexpanded jets exhibit interactions between turbulent shear layers and shock-cell trains that yield complex phenomena that are absent in the more commonly studied perfectly expanded jets. We quantitatively analyze these mechanisms by considering the interplay between hydrodynamic (turbulence) and acoustic modes, using a validated large-eddy simulation. Using momentum potential theory (MPT) to achieve energy segregation, the following observations are made. The sharp gradients in fluctuations introduced by the shock-cell structure are captured mostly in the hydrodynamic mode, whose amplitude is an order of magnitude larger than the acoustic mode. The acoustic mode has a relatively smoother distribution, exhibiting a compact wavepacket form. Proper orthogonal decomposition (POD) identifies the third-to-sixth cells as the most dynamic structures. The imprint of shock cells is discernible in the nearfield of the acoustic mode, primarily along the sideline direction. Energy interactions that feed the acoustic mode remain compact in nature, facilitating a simple propagation technique for farfield noise prediction. The farfield sound spectra show peak directivity at 30 ∘ to the downstream axis. The POD modes of the acoustic component also identify two main energetic components in the wavepacket: one representative of the periodic internal structure and the other of intermittent downstream lobes. The latter component occurs at exactly the same frequency as, and displays high correlation with, the farfield peak noise spectra, making the acoustic mode a better predictor of the dynamics than velocity fluctuations.

Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow

The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.

Sparse and Dispersion-Based Matching Pursuit for Minimizing the Dispersion Effect Occurring when Using Guided Wave for Pipe Inspection.

Ultrasonic guided wave is an effective tool for structural health monitoring of structures for detecting defects. In practice, guided wave signals are dispersive and contain multiple modes and noise. In the presence of overlapped wave-packets/modes and noise together with dispersion, extracting meaningful information from these signals is a challenging task. Handling such challenge requires an advanced signal processing tool. The aim of this study is to develop an effective and robust signal processing tool to deal with the complexity of guided wave signals for non-destructive testing (NDT) purpose. To achieve this goal, Sparse Representation with Dispersion Based Matching Pursuit (SDMP) is proposed. Addressing the three abovementioned facts that complicate signal interpretation, SDMP separates overlapped modes and demonstrates good performance against noise with maximum sparsity. With the dispersion taken into account, an overc-omplete and redundant dictionary of basic atoms based on a narrowband excitation signal is designed. As Finite Element Method (FEM) was used to predict the form of wave packets propagating along structures, these atoms have the maximum resemblance with real guided wave signals. SDMP operates in two stages. In the first stage, similar to Matching Pursuit (MP), the approximation improves by adding, a single atom to the solution set at each iteration. However, atom selection criterion of SDMP utilizes the time localization of guided wave reflections that makes a portion of overlapped wave-packets to be composed mainly of a single echo. In the second stage of the algorithm, the selected atoms that have frequency inconsistency with the excitation signal are discarded. This increases the sparsity of the final representation. Meanwhile, leading to accurate approximation, as discarded atoms are not representing guided wave reflections, it simplifies extracting physical meanings for defect detection purpose. To verify the effectiveness of SDMP for damage detection results from numerical simulations and experiments on steel pipes are presented.

Nonparaxial Near-Nondiffracting Accelerating Optical Beams

We show that new families of accelerating and almost nondiffracting beams (solutions) for Maxwell's equations can be constructed. These are complex geometrical optics (CGO) solutions to Maxwell's equations with nonlinear limiting Carleman weights. They have the form of wave packets that propagate along circular trajectories while almost preserving a transverse intensity profile. We also show similar waves constructed using the approach combining CGO solutions and the Kelvin transform.

Femtosecond plasmon and photon wave packets excited by a high-energy electron on a metal or dielectric surface

Swift electrons generate coherent transition radiation (TR) when crossing a material surface, as well as surface plasmon polaritons (SPPs) when the material is metallic. We present analytical and numerical calculations that describe the time- and space-dependent electric fields of TR and SPPs induced by 30--300 keV electrons on a Drude metal surface. The generated SPPs form wave packets a few-hundred femtoseconds in duration, depending on the material permittivity. High-frequency components close to the plasmon resonance are strongly damped, causing the wave packets to shift to lower frequencies as they propagate further. TR is emitted to the far field as ultrashort wave packets consisting of just a few optical cycles, with an intensity and angle dependence that is determined by the material permittivity. The excitation reaches its peak amplitude within a few femtoseconds and then drops off strongly for longer times. From a correlation between material permittivity and the calculated emission behavior, we determine qualitative predictions of the TR evolution for any given material. The results presented here provide key insights into the mechanisms enabling swift electrons to serve as nanoscale optical excitation sources.

Parametric excitation of azimuthally non-symmetric surface waves propagating in metal waveguides filled with isotropic plasma

The paper is devoted to developing the theory of parametric excitation of electromagnetic waves propagating across the axis of symmetry in cylindrical waveguides partially filled with isotropic plasma. The problem is studied theoretically in the fluid approximation and expressions for the wave fields are derived from Maxwell’s equations. The azimuthally non-symmetric electromagnetic waves propagate in the form of wave packets which are approximately described by the main azimuthal harmonic and two nearest satellite temporal harmonics. The boundary condition, which is cast in a nonlinear form, describes the flowing of a surface current on the plasma interface. This condition allows one to derive an infinite set of equations for harmonics of the tangential electric field of azimuthally non-symmetric surface waves. The dependence of the growth rate of the parametric instability of these waves on parameters of the plasma-filled waveguide and alternating electric field is studied both analytically and numerically.

AZIMUTHALLY NON-SYMMETRIC SURFACE WAVES PROPAGATING IN METAL WAVEGUIDES FILLED WITH ISOTROPIC PLASMA

The paper is devoted to the theory of eigen electromagnetic waves propagating across the axis of symmetry in waveguides with a non-circular cross-section. The case of waveguides filled with isotropic cold plasma is studied theoretically. Plasma particles motion is described in fluid approximation; expressions for the waves' fields are derived from Maxwell equations. Cross-section of the studied waveguide is modeled by Fourier series with coefficients, which values are less than unity. This allows one to apply method of successive approximations for analytical research of this problem. Boundary conditions, which are formulated in non-linear form over the small parameters of the problem have been applied for derivation the dispersion equations, which determine frequency spectrum of these surface waves for waveguides of different constructions. Studied eigen electromagnetic waves propagate in the form of wave packets, which are approximately described by the main azimuthal harmonic and two nearest satellite spatial harmonics. Represented results have been obtained both analytically and numerically. Possible spheres of the studied eigen waves are discussed.

Creation of neutral fermions with anomalous magnetic moments from a vacuum by inhomogeneous magnetic fields

A consistent nonperturbative approach (based on QFT) to neutral fermion creation (due to their magnetic moments) in strong inhomogeneous magnetic fields is considered. It is demonstrated that quantization in terms of neutral particles and antiparticles is possible in terms of the states with well-defined spin polarization. Such states are localizable and can form wave packets in a given asymptotic region. In this case, the problem can be technically reduced to the problem of charged-particle creation by an electric step. In particular, the relation to the Schwinger method of an effective action is established. As an example, we calculate neutral fermion creation from the vacuum by a linearly growing magnetic field. We show that the total number and the vacuum-to-vacuum transition probability of created pairs depend only on the gradient of the magnetic field, but not on its strength, and this fact does not depend on the spacetime dimension. We show that the created flux aimed in one of the directions is formed from fluxes of particles and antiparticles of equal intensity and with the same magnetic moments parallel to the external field. In such a flux, particle and antiparticle velocities that are perpendicular to the plane of the magnetic moment and flux direction are essentially depressed. The creation of neutral fermions with anomalous magnetic moments leads to a smoothing of the initial magnetic field, which in turn prevents the appearance of superstrong constant magnetic fields. Our estimations show that the vacuum instability with respect to the creation of neutrinos and even neutrons in strong magnetic fields of the magnetars and fields generated during a supernova explosion has to be taken into account in the astrophysics. In particular, it may be of significance for dark matter studies.

“Electron ping-pong” on a one-dimensional lattice: Wave packet motion up to the first reflection

We consider the time evolution of the electron wave function on a one-dimensional lattice consisting of N identical sites and a single impurity site that differs from the rest of the lattice by the on-site energy and the hopping integral. At the initial instant, the wave function is entirely localized at the impurity site. With time, a localized wave packet forms, which moves over the lattice and reflects from its end. The process of reflection from the ends repeats many times and is called “electron ping-pong.” We obtain analytic expressions for the propagation of the wave packet front at different values of the problem parameters. The analytic expressions agree perfectly with numerical simulation results.

NONLINEAR PROPAGATION OF SOUND EMITTED BY HIGH SPEED WAVE PACKETS

Jet's sound-field emitted by a large scale source modeled as a wave packet is considered. Attention is given to nonlinear propagation effects caused by the source's supersonic Mach number and high amplitude. The approach of the Westervelt equation is adapted to derive a new set of weakly nonlinear sound propagation equations. An optimized Lax–Wendorff scheme is proposed for the newly derived equations. It is shown that these equations can be simulated using a time step close to the CFL limit even for high amplitudes unlike the conventional finite-difference simulation approach of the Westervelt equation. Two- and three-dimensional sound propagations were simulated for symmetric and asymmetric supersonic wave packets. It is seen that nonlinearity in the sound field is affected by the wave packet form, an effect that cannot be captured by a 1D propagation equation. High skewness in the pressure fluctuation and its time derivative were found near the Mach direction, showing crackle-like features. Pressure time history and frequency spectra are also investigated.