Three-dimensional Wave Packet Research Articles

Propagation of lump and traveling wave solutions to the (4 + 1)-dimensional Fokas equation arising in mathematical physics

In this paper, the [Formula: see text]-dimensional Fokas model is investigated analytically with extensive applications in nonlinear wave theory including the evolution of a three-dimensional wave packet in water with a finite depth, and surface waves and internal waves in straits or channels of varied depth and width. Applying the Hirota bilinear approach, the lump wave solitons and interaction of lump with periodic waves, the interactions of lump wave along single, double-kink solitons as well as the interactions of lump, periodic along double-kink solitons of the governing model are developed. Additionally, by using the extended tanh function technique, certain new traveling wave solitons are established. The physical nature of several solitons is illustrated by drawing the 3D, contours and 2D plots. Consequently, a set of periodic, bright, dark, rational as well as elliptic function solitons are constructed. The employed techniques seem to be more effective and well organized to build some interesting analytical wave solitons to several appealing nonlinear models.

Ortho-Para Conversion for H+ + H2 Collision in Low Temperature: A Fully Close-Coupled Time-Dependent Wave Packet Study.

The collision-induced rate coefficients of ortho-para conversion for the H+ + H2 reaction provide accurate information to probe the lifetime of cold environments in interstellar media. Rotationally resolved reaction probabilities are calculated at the low collision energy regime (0 < Ecol ≤ 0.3 eV) by employing the coupled three-dimensional (3D) time-dependent wave packet (TDWP) formalism in hyperspherical coordinates on a recently constructed ab initio ground adiabatic potential energy surface of H3+ [J. Chem. Phys. 2014, 141, 204306] for the process H+ + H2 (v = 0, j = 0-5) → H+ + H2 (v' = 0, j'). Cross-sections are then computed from the converged reaction probabilities as a function of total angular momentum (J) over the same energy regime and subsequently employed to obtain the rate constants for the ortho-to-para (O-P) and para-to-ortho (P-O) conversions and their ratio. The ratio of ortho-para conversion shows (a) appropriate convergence with the inclusion of a higher number of initial rotational states as well as a reasonable agreement with the results from a quantum statistical method and (b) a peak at lower temperature that could be due to the available collision energy for transitions involving lower rotational states (j = 0 → j' = 1).

Propagation of nonlinear ion-acoustic fluctuations in the mantle of Venus

Motivated by the observations of ion-acoustic fluctuations with the Parker Solar Probe (PSP) and earlier by the Pioneer Venus Orbiter (PVO) in the Venusian magnetosheath, we investigate the nature of ion-acoustic solitary and double-layer (DL) structures in the mantle. We employed a hydrodynamic description along with reductive perturbation theory to derive the nonlinear Zakharov—Kuznetsov equation that elucidates the dynamics of three-dimensional ion-acoustic wave packets. Using the spacecraft measurements of the plasma configuration at Venus, we carried out a parametric analysis of these structures, including the influence of the magnetic field strength and the relative densities and temperatures, considering two cases: quasi-parallel and oblique propagation. Moreover, we determined the structural characteristics of these waves, where oblique (quasi-parallel) solitary waves have a potential of 0.4 V (0.4 V) and a maximum electric field amplitude Em ~ 0.024 mV m−1 (8 m V m−1) across spatial and temporal widths of ~40–80 km (~140–200 m) and 0.4 s (1.6 ms). These waves produce low-frequency electrostatic activity in the frequency range of 1.6–10 Hz (630–3160 Hz). Quasi-parallel DLs have potential drops of (6.5–13) V and Em ~ (0.16–0.35) mV m−1 with a width and duration of (100–120) m and ~1 ms, and a frequency range of ~630–3980 Hz. These outcomes can explain the detected electrostatic fluctuations above the ionosphere via PVO in the frequency channels of 730 Hz and 5.4 kHz. Furthermore, the DL features estimated in this work are in line with the recent PSP measurements of the DLs propagating in the magnetosheath of Venus.

Quasi-classical motion of a particle in a bulk dissipative medium

A version of the quasi-classical approach is proposed, which makes it possible to describe the straight-line motion of a micro-particle in a bulk dissipative medium. From the side of the medium, the particle is acted upon by the force of viscous friction and the drag force, which are proportional to the velocity and the square of the velocity, respectively. In addition, an external conservative force is applied to the particle. The Green’s function of the particle and the quasi-classical coherent state in the form of a three-dimensional localized wave packet are found. It is shown that the translational motion of the wave packet is accompanied by a monotonic increase in the uncertainties of the particle coordinates up to certain maximum asymptotic values. Due to the drag force, these asymptotic uncertainties contain information about the corresponding initial uncertainties in the coordinates of the micro-particle, about its initial velocity, as well as about the external conservative force.

Coupled three-dimensional quantum mechanical wave packet study of proton transfer in H2+ + He collisions on accurate abinitio two-state diabatic potential energy surfaces.

We have carried out fully close-coupled three dimensional quantum mechanical wave packet dynamical calculations for the reaction He+H2+→HeH++H on the ground electronic adiabatic potential energy surface and on the lowest two electronic states of newly constructed abinitio calculated diabatic potential energy surfaces for the system [Naskar et al., J. Phys. Chem. A 127, 3832 (2023)]. With the reactant diatom (H2+) in its roto-vibrational ground state (v = 0, j = 0), the calculations have been carried out in hyperspherical coordinates to obtain the reaction attributes. Convergence profiles of the reaction probability with respect to the total angular momentum quantum number at different collision energies are presented for the title reaction. State-to-state as well as initial state selected integral reaction cross sections are calculated from the fully converged reaction probabilities over a range of collision energies. The integral cross section values computed using the two-state diabatic potential energy surfaces are significantly lower than those obtained using the ground electronic state adiabatic potential energy surface and are in much better agreement with the available experimental results than the latter for total energy greater than 1.1eV. Therefore, it becomes clear that it is important to include the nonadiabatic coupling terms for a quantitative prediction of the dynamical observables.

Transmission and reflection of three-dimensional Boussinesq internal gravity wave packets in nonuniform retrograde shear flow

Simulated fully localized internal gravity wave packets with moderately large initial amplitude exhibit finite transmission across a reflection level, due to the combined effects of the wave-induced shear locally cancelling the retrograde background shear, modulational instability, and the nonlinear generation and evolution of secondary wave packets.

Three-dimensional photoelectron holography with trichromatic polarization-tailored laser pulses

We present a three-dimensional (3D) photoelectron wave packet holography scheme based on polarization-tailored trichromatic femtosecond laser pulses for the determination of quantum phases in atomic multiphoton ionization (MPI). Experimentally, we combine supercontinuum polarization pulse shaping with photoelectron tomography for the reconstruction of the 3D photoelectron momentum distribution (PMD). To demonstrate the 3D photoelectron holography scheme, we superimpose a sculptured wave packet encoding a relative continuum phase with a reference wave packet. In particular, we create a sculptured angular momentum superposition wave packet by (2 + 1) resonance-enhanced MPI of potassium atoms using a counter-rotating circularly polarized bichromatic pulse sequence. The sculptured wave packet, consisting of states with different orbital angular momentum quantum numbers, interferes with the reference wave packet generated by direct three-photon ionization with a circularly polarized pulse of the third color. Depending on the circularity of the reference pulse, interference of both wave packets gives rise to 3D photoelectron holograms with c 2 or c 4 rotational symmetry in the laser polarization plane, i.e., in the azimuthal direction. In the polar direction, the azimuthal interference pattern undergoes a phase-shift revealing the relative quantum phase between the p- and f-type continuum partial waves in the sculptured wave packet. We determine the relative continuum phase by fitting the parameters of an analytical model of the hologram to the measured 3D PMD and confirm the result by direct extraction of the continuum phase difference from the polar-angle-dependent azimuthal phase-shift of the photoelectron angular distribution.

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface.

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H2/D2 reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H2 and D2) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H2 and F + D2 reactions are presented along with previous theoretical and experimental results.

Strong-field control by reverse engineering

Based on the idea of reverse engineering, we design an optimal laser pulse to control strong-field multiphoton atomic transitions. Starting from the time-dependent Schr\"odinger equation of the full system, we adiabatically eliminate the nonessential states and apply the rotating-wave approximation to arrive at an effective two-state representation that involves dynamic Stark shifts and multiphoton coupling. Solving this equation inversely for the field, we obtain an analytical laser pulse shape that is expected to induce the full system's evolution according to user-defined quantum pathways. In our procedure, the amplitude and phase of the laser pulse are engineered such that the dynamically shifted electronic states are resonantly coupled during the action of the pulse at each moment of time. As a result, the driven system evolves from an arbitrary initial population distribution to any desired final quantum state superposition at a predefined rate. The proposed scheme is demonstrated using the example of the $3s\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium. By solving the time-dependent Schr\"odinger equation of the single-active electron with two different methods, either propagating time-dependent coefficients of many field-free states or directly propagating the three-dimensional electronic wave packet on a grid, we demonstrate the robustness as well as the limitations of the presented reverse engineering scheme.

Boundary-Layer Instabilities in Supersonic Expansion Corner Flows

Experiments show that a sudden expansion of supersonic flow may strongly stabilize or even relaminarize the boundary layer. Only few theoretical studies addressed this effect considering evolution of small disturbances in cases of Mach number less than 4, where the first mode is most unstable. This paper addresses stability of a hypersonic (Mach 6) flow over the planar expansion corners of 0° (flat plate case), 5°, and 10°, where the Mack second mode is dominant. The linear analysis and direct numerical simulations of three-dimensional wave packets are performed to investigate details and understand mechanisms behind the stabilization effect. The theoretical and numerical results are compared demonstrating applicability of the linear stability theory to hypersonic expansion-corner configurations. No new modes of boundary layer are found over the expansion corners but the second Mack mode that is relevant to the flat plate boundary layer. Downstream the corner line, the second mode instability region shifts to lower frequencies due to an abrupt thickening of the boundary layer that causes the stabilization effect. The results of direct computations agree well with predictions of linear stability theory.

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.

On the breaking inception of unsteady water wave packets evolving in the presence of constant vorticity

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On receptivity of marginally separated flows

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Crest speeds of unsteady surface water waves

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Couplings between the temporal and orbital angular momentum degrees of freedom in ultrafast optical vortices

In any form of wave propagation, strong spatiotemporal coupling appears when non-elementary, three-dimensional wave-packets are composed by superimposing pure plane waves, or spontaneously generated by light-matter interaction and nonlinear processes. Ultrashort pulses with orbital angular momentum (OAM), or ultrashort vortices, furnish a critical paradigm in which the analysis of the spatiotemporal coupling in the form of temporal-OAM coupling can be carried out accurately by analytical tools. By generalizing and unifying previously reported results, we show that universal and spatially heterogeneous space-time correlations occur in propagation-invariant temporal pulses carrying OAM. In regions with high intensity, the pulse duration has a lower bound fixed by the topological charge of the vortex and such that the duration must increase with the topological charge. In regions with low intensity in the vicinity of the vortex, a large blue-shift of the carrier oscillations and an increase of the number of them is predicted for strongly twisted beams. We think that these very general findings highlight the existence of a structural coupling between space and time. These results have also applications in free-space communications, spectroscopy, and high-harmonic generation.

Experimental Study of the Formation of Three-Dimensional Waves from a Two-Dimensional Solitary Wave on Vertically Falling Liquid Films

The decay of a two-dimensional solitary wave into three-dimensional waves in film flow along a vertical plate has been studied using a high-speed laser-induced fluorescence technique that allows high spatial and temporal resolution measurements of the thickness of wave liquid films. It has been shown that the three-dimensional wave packet resulting from the decay of a two-dimensional solitary wave has a strong perturbing effect on the falling film and leads to the formation of rivulets on its surface.

Three-dimensional wave packet in a Mach 6 boundary layer on a flared cone

High-resolution direct numerical simulations (DNS) were carried out to investigate the nonlinear breakdown process of a three-dimensional wave packet initiated by a short-duration pulse in a flared cone boundary layer at Mach 6 and zero angle of attack. For these simulations the cone geometry of the flared cone experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University was considered. The computational domain covered a large extent of the cone in the azimuthal direction to allow for a wide range of azimuthal wavenumbers ( ) and to include shallow instability waves with small azimuthal wavenumbers. The simulation results indicated that the wave packet development was dominated by axisymmetric and shallow (small ) second-mode waves for a large downstream extent. Towards the downstream end of the computational domain a rapid broadening of the disturbance amplitude spectra was observed, which is an indication that the wave packet reached the strongly nonlinear stages. The disturbance spectra of the nonlinear regime, and the downstream amplitude development of the dominant disturbance wave components, provided conclusive evidence that the so-called fundamental breakdown was the dominant nonlinear mechanism. Furthermore, contours of the time-averaged Stanton number exhibited ‘hot’ streaks within the wave packet on the surface of the cone. Hot streaks have also been observed in the Purdue flared cone experiments using temperature sensitive paint (TSP) and in numerical investigations using DNS. The azimuthal streak spacing obtained from the wave packet simulation agrees well with that observed in the Purdue quiet tunnel experiments.

Robust Ultrashort Light Bullets in Strongly Twisted Waveguide Arrays.

We introduce a new class of stable light bullets that form in twisted waveguide arrays pumped with ultrashort pulses, where twisting offers a powerful knob to tune the properties of localized states. We find that, above a critical twist, three-dimensional wave packets are unambiguously stabilized, with no minimum energy threshold. As a consequence, when the higher-order perturbations that accompany ultrashort pulse propagation are at play, the bullets dynamically adjust and sweep along stable branches. Therefore, they are predicted to feature an unprecedented experimental robustness.

Molecular movie of ultrafast coherent rotational dynamics of OCS

Recording molecular movies on ultrafast timescales has been a longstanding goal for unravelling detailed information about molecular dynamics. Here we present the direct experimental recording of very-high-resolution and -fidelity molecular movies over more than one-and-a-half periods of the laser-induced rotational dynamics of carbonylsulfide (OCS) molecules. Utilising the combination of single quantum-state selection and an optimised two-pulse sequence to create a tailored rotational wavepacket, an unprecedented degree of field-free alignment, 〈cos2θ2D〉 = 0.96 (〈cos2θ〉 = 0.94) is achieved, exceeding the theoretical limit for single-pulse alignment. The very rich experimentally observed quantum dynamics is fully recovered by the angular probability distribution obtained from solutions of the time-dependent Schrödinger equation with parameters refined against the experiment. The populations and phases of rotational states in the retrieved time-dependent three-dimensional wavepacket rationalises the observed very high degree of alignment.

Three-dimensional localized Airy-Gaussian wave packets in a gradient-index medium

By solving the Schrödinger equation in spatial and temporal coordinates, the exact solution of the chirped Airy-Gaussian (CAiG) wave packets in a gradient-index medium is obtained. Based on that, we conduct a theoretical analysis about the properties of CAiG wave packets and discover that the chirp factor, the distribution factor, the initial velocity, as well as the propagation distance have an effect on the wave packets in both the propagation process and the spatiotemporal profiles. Among these, the Gaussian distribution factor, which is first added to the initial pulses, also alters the peculiarities of the Airy-Gaussian beams in the temporal domain and spatial domain. In addition, the investigation about the radiation force illuminates certain evolution properties of the CAiG wave packets well.