Localized Wave Packets Research Articles

Modal and absolute thermal instability in a vertical porous layer

The conduction regime in a vertical porous layer subject to a horizontal temperature gradient is studied. The boundaries are considered as isothermal, with different temperatures, and permeable to the external environment. The linear stability of this basic flow state is analysed by testing the dynamics of the normal modes of perturbation. The numerical solution of the stability eigenvalue problem leads to the determination of the neutral stability condition. Then, the evolution in time of localised wavepacket perturbations is investigated leading to the determination of the threshold to absolute instability.

Weak Alfvénic turbulence in relativistic plasmas. Part 2. current sheets and dissipation

Alfvén waves as excited in black hole accretion disks and neutron star magnetospheres are the building blocks of turbulence in relativistic, magnetized plasmas. A large reservoir of magnetic energy is available in these systems, such that the plasma can be heated significantly even in the weak turbulence regime. We perform high-resolution three-dimensional simulations of counter-propagating Alfvén waves, showing that an $E_{B_{\perp }}(k_{\perp }) \propto k_{\perp }^{-2}$ energy spectrum develops as a result of the weak turbulence cascade in relativistic magnetohydrodynamics and its infinitely magnetized (force-free) limit. The plasma turbulence ubiquitously generates current sheets, which act as locations where magnetic energy dissipates. We show that current sheets form as a natural result of nonlinear interactions between counter-propagating Alfvén waves. These current sheets form owing to the compression of elongated eddies, driven by the shear induced by growing higher-order modes, and undergo a thinning process until they break-up into small-scale turbulent structures. We explore the formation of current sheets both in overlapping waves and in localized wave packet collisions. The relativistic interaction of localized Alfvén waves induces both Alfvén waves and fast waves, and efficiently mediates the conversion and dissipation of electromagnetic energy in astrophysical systems. Plasma energization through reconnection in current sheets emerging during the interaction of Alfvén waves can potentially explain X-ray emission in black hole accretion coronae and neutron star magnetospheres.

Twist versus heterostrain control of optical properties of moiré exciton minibands

We investigate the optical properties of interlayer excitons in heterobilayer transition metal dichalcogenides where moiré pattern is introduced by heterostrain, in comparison with that introduced by twisting (and/or lattice mismatch). Besides being a cause of the moiré texture, strain also effectively introduces a constant gauge potential on either electron or hole, which shifts the dispersion of kinetic energy with respect to the excitonic crystal momenta in the moiré superlattices. This leads to distinct exciton mini-band dispersions and light coupling properties from the twisting induced moiré, even if the excitonic moiré superlattice potentials have the similar real-space profile for the two cases. For strain that breaks the three-fold rotational symmetry at the atomic scale, the exciton wave packets trapped at the superlattice potential minima have elliptically polarized valley optical selection rules, in contrast to the circularly polarized ones in the twisting moiré. We investigate the evolution of the excitonic mini-bands and the optical dipoles of the bright states inside the light cones with the decrease of the moiré periodicity, upon which the excitonic wave functions evolve from localized wave packets to the extended Bloch states. Furthermore, moiré exciton properties under the interplay of twisting and heterostrain are also discussed.

Optical nondiffractive and nondispersive dark-wave dynamics in hydrodynamic origin

The primary attention of this work focuses on finding rational and generalized rational solutions for the (2 + 1)-dimensional Kadomtsev–Petviashvili equation that can be used to describe nondispersive and nondiffractive localized wave packet in power law nonlinear media. Specifically, the (2 + 1)-dimensional nonlinear Schrödinger equation with power law nonlinearity is first transformed into the Kadomtsev–Petviashvili equation. Then, through the bilinear form and symbolic computation, we derive two hierarchies of multi-lump solitary waves, composing of three, six, and eight lump waves. The obtained solutions observe a specific ‘circularity structure’ that the lump waves sit at the same circular. In addition, we illustrate that these waves are stable during propagation.

Thermal gaussian wave packets

The notion of a thermal wave packet and the inferred spatial probability distribution are elucidated at the example of freely moving particles. Particle localisation and the use of localised Gaussian wave packets to describe a thermal state of the freely moving particle are critically assessed.

Interpretation of Multilobe Wavepackets in Spectral Proper Orthogonal Decomposition of Supersonic Jet

Spectral proper orthogonal decomposition (SPOD) is a major modal analysis that extracts a dominant structure at each frequency from complicated flow data, such as the wavepacket hidden under turbulent jets. This study investigated the physical interpretation of subdominant multilobe structures in the SPOD modes. A high-speed schlieren movie that exhibited multilobe structures in the SPOD was analyzed using a wavelet-based conditional sampling and averaging (WB-CSA) method. The results of WB-CSA showed spatiotemporally localized wavepackets, which were formed intermittently and convected downstream through growth and decay. Such intermittent convection causes multilobe structures in the SPOD, as illustrated by simple synthetic data that model the results of WB-CSA. Therefore, multilobe structures, together with the most dominant single-lobe wavepackets, can be interpreted as representing the intermittent convection of wavepackets.

Quantum dynamics of the isotropic universe in metric f(R) gravity

We analyse the canonical quantum dynamics of the isotropic universe, as emerging from the Hamiltonian formulation of a metric f(R) gravity, viewed in the Jordan frame. The canonical method of quantization is performed by solving the Hamiltonian constraint before quantizing and adopting like a relational time the non-minimally coupled scalar field emerging in the Jordan frame. The resulting Schr\"oedinger evolution is then investigated both in the vacuum and in the presence of a massless scalar field, though as the kinetic component of an inflaton. We show that, in vacuum, the morphology of localized wave packets is that of a non-spreading profile up to the cosmological singularity. When the external scalar field is included into the dynamics, we see that the wave packets acquire the surprising feature of increasing localization of the universe volume, as it expands. This result suggests that in the metric f(R) formulation of gravity, a spontaneous mechanism arises for the universe classicization. Actually, when the phase space of the scalar field is fully explored, such an increasing localization in the Universe volume is valid up to a given value of the time, i.e. of the non-minimally coupled mode after which the wave packets spread again. We conclude our analysis by inferring that before this critical transition age is reached, the inflationary phase could take place, here modelled via a cosmological constant. This point of view provides an interesting scenario for the transition from a Planckian Universe to a classical de-Sitter phase, which in the f(R) gravity appears more natural than in the Einsteinian picture.

Investigation of Hirota equation: Modified double Laplace decomposition method

In this article, the non-linear coupled Hirota equations are considered attributed to localized excitations. By employing a modified double Laplace transform decomposition method, we derived the general approximate solutions for the coupled Hirota and coupled Hirota Satsuma equations. It is observed that the proposed method is a systematic and powerful scheme for solving such nonlinear systems. The main advantage of the method is to calculate solutions in a series form without any linearization, discretization, or perturbation. Using convergence analysis, we observed that the proposed method is converging to the exact solution of the system. Numerical analysis for these solutions shows the confine carrier wave and ensures localized wave packets. A degree enhancement reduction in the dispersion nonlinearly coefficients alters both the spatial width and amplitude of the waves. At vanishingly small dispersion, internal oscillations in the pulse-shaped solitary waves reduced the wave breaking effect. We have noticed that the numerical solutions converge to the exact solutions, confirming the importance of the proposed technique.

Universal S-matrix correlations for complex scattering of wave packets in noninteracting many-body systems: Theory, simulation, and experiment.

We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of nonstationary many-body scattering of noninteracting indistinguishable particles where the incoming states are localized wave packets. Contrary to the stationary case, the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations, and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.

Propagation and overturning of three-dimensional Boussinesq wave packets with rotation

Simulations of fully localized internal gravity wave packets with their induced mean flow superimposed reveal that waves overturn even for initial amplitudes significantly lower than the critical amplitudes predicted by linear theory, in contrast with previous results of one- and two-dimensional wave packets without rotation.

Diverse solitary and Jacobian solutions in a continually laminated fluid with respect to shear flows through the Ostrovsky equation

In this paper, the generalized Jacobi elliptical functional (JEF) and modified Khater (MK) methods are employed to find the soliton, breather, kink, periodic kink, and lump wave solutions of the Ostrovsky equation. This model is considered as a mathematical modification model of the Korteweg-de Vries (KdV) equation with respect to the effects of background rotation. The solitary solutions of the well-known mathematical model (KdV equation) usually decay and are replaced by radiating inertia gravity waves. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. Many distinct solutions are obtained through the employed computational schemes. Moreover, some solutions are sketched in 2D, 3D, and contour plots. The effective and powerful of the two used computational schemes are tested. Furthermore, the accuracy of the obtained solutions is examined through a comparison between them and that had been obtained in previously published research.

Self-sustaining and propagating mechanism of localized wave packet in plane-Poiseuille flow

In this Letter, it is revealed that the convection velocity of a localized wave packet in two-dimensional plane-Poiseuille flow is determined by the solitary wave at the centerline of a vortex dipole, which is evinced by subtracting the base flow from the mean flow. The fluctuation component propagates obeying the local dispersion relation of the mean flow and oscillates with a global frequency selected by the upstream marginal absolute instability and, hence, is a traveling wave mode. The vortex dipole provides an unstable region for the fluctuation waves to grow up, and the Reynolds stress of the fluctuation waves leads to streaming components enhancing the vortex dipole. By applying localized initial disturbances, a nonzero wave-packet density is achieved at the threshold state, suggesting a first-order transition.

Pulsed Three-Dimensional Planar Caustic Beams

We present an algorithm for designing and manipulating pulsed caustic (accelerating) beams that propagate along a predefined planar curved beam-axis trajectory in free space. These pulsed beams are localized time-dependent wave packets. We evaluate the pulsed aperture field (source) distribution that radiates the beam along the desired trajectory. The aperture field is evaluated by setting its delay to form the caustic surface about the beam-axis skeleton and to control the lateral beamwidth, and the amplitude is chosen to form a uniform intensity profile of the beam along its axis. Numerical examples are included.

Eady edge waves, frontal wave-trains and type-B cyclogenesis

Eady edge waves (EEWs) propagate on surface baroclinic zones and they resemble synoptic and sub-synoptic scale frontal wave-trains. The wave-trains are frequently depicted on surface charts, and occur per se on a front with a local baroclinicity extremum. The possible linkage of EEWs to frontal waves is explored within the framework of so-called ‘surface quasi-geostrophic dynamics’ by establishing the properties of free and forced EEWs propagating on an ambient flow comprising a laterally confined baroclinic zone. It is shown that the dispersion properties of the free EEWs modes are influenced significantly both by the zone’s baroclinicity extremum and by key features that are akin to those of cold and warm fronts. In particular the larger-scale waves are nondispersive and a local wave-packet can retain coherency, the leading modes on a pseudo-cold front possess a phase speed related to the baroclinicity extremum, whereas waves on a pseudo-warm front propagate in the reverse direction. Also theoretical considerations demonstrate that forced modes can undergo resonant secular growth. It is further shown that transient or sustained forcing of a front by an upper-tropospheric potential vorticity anomaly (sic. short-wave trough) can serve to instigate features akin to frontal wave-trains and type-B cyclogenesis. More generally the study hints at the significance for NWP of a front’s structure and its dispersion properties, and that an element of predictability is introduced by the latter features due to dynamical scale selection.

Экспериментальные исследования влияния периодической модуляции течения на развитие возмущений в пограничном слое скользящего крыла при числе Маха 2,5

The results of experimental studies on the impact of periodic flow modulation on the development of natural disturbances and artificial localized wave packets in the boundary layer of a swept wing with a leading edge swept angle of 40 degrees at a Mach number M = 2.5 are presented. The boundary layer was modulated using periodic roughness on the model surface. Artificial wave packets were generated by a pulsed glow discharge. Hot-wire anemometer measurements showed that, according to the experimental conditions, periodic modulation of the boundary layer leads to the stabilization of the development of controlled localized disturbances and to an increase in the growth of natural disturbances.

Numerical simulations for the predator–prey model as a prototype of an excitable system

AbstractThis research paper investigates the numerical solutions of the predator–prey model through five recent numerical schemes (Adomian decomposition, El Kalla, cubic B‐spline, extended cubic B‐spline, exponential cubic B‐spline). We investigate the obtained computational solutions via the modified Khater methods. This model is considered as a well‐known bimathematical model to describe the prototype of an excitable system. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. The accuracy of the obtained numerical solutions is investigated by calculating the absolute error between the exact and numerical solutions. Many sketches are given to illustrate the matching between the exact and numerical solutions.

Buildup and decay dynamics of exponentially modulated quantum waves in resonant structures

We derive an exact analytic solution of time-dependent Schrödinger’s equation for cutoff quantum waves with exponential modulation to explore the dynamics along the internal region of a one-dimensional potential of arbitrary shape. The modulation of the wave packet is controlled by a single parameter given by its momentum distribution width, Δ, which allows to explore on the same footing the transient features of both cutoff spatially localized wave packets and extended plane waves. From the formal solution, we derive a simple and reliable formula that accurately describes both the buildup and decay of the probability density inside a resonant structure. The buildup-decay formula involves two exponential terms governed respectively by the resonance width Γ1 of the lowest resonance of the system and the width of a ‘virtual’ state induced by the incident wave packet. During the buildup process, we demonstrate that the contributions of both Γ1 and become essential. In the decay process, on the other hand, we find that there are two regimes characterized by a critical value Δc, such that for Δ > Δc the exponential decay is governed by Γ1, while for Δ < Δc the exponential decay is governed by . We also derive an analytic formula for a relevant timescale for the buildup-decay process, which depends in a simple fashion on the decay rates Γ1 and . Deviations from the exponential decay law at long times are also discussed.

Computational simulation for the (1 + 1)-dimensional Ito equation arising quantum mechanics and nonlinear optics

This research paper investigates the numerical solutions of the (1 + 1)-dimensional Ito equation through the extended simplest equation (ESE) method. This model is considered as well-known in quantum mechanics and nonlinear optics, which represents the height of the water’s free surface above a flat bottom. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. Diverse novel computational solutions are constructed and demonstrated through three distinct types of sketches. The stability of our obtained solutions is investigated by using Hamiltonian system’s characterizations. The novelty of our paper is explained by comparing our obtained solutions with the previously evaluated computational solutions with different computational schemes.

Time-evolved Schrödinger wave packets of a quantum mechanical system trapped in a deformed Coulombian potential

We study the properties of a quantum system confined in a shifted Coulomb potential using a direct analytical approach and the supersymmetric quantum mechanics analysis and then show concurrence of results of the two approaches. This analysis reveals an energy spectrum quite dependent of the shift distance and scaled down by the space deformation parameter. The spectral values are shown to generate a peculiar revival pattern on a localized wave packet that is discussed.

Quantum clocks observe classical and quantum time dilation

At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.