Spatiotemporal Wave Research Articles

Nonlinear Airy Light Bullets in a 3D Self‐Defocusing Medium

AbstractThe (3+1)‐dimensional [(3+1)D] nonlinear Schrödinger (NLS) equation is investigated, describing the propagation of nonlinear spatiotemporal wave packets in a self‐defocusing medium, and a new type of Airy spatiotemporal solutions is presented. By using the reductive perturbation method, the (3+1)D NLS equation is reduced to the spherical Kortewegde Vries (SKdV) equation. Based on the Hirota's bilinear method, the bilinear form of the SKdV equation is constructed and Airy light bullet (LB) solutions of different orders are obtained, which depend on the sets of two free constants associated with the amplitude and initial phase. The results show that these Airy LBs can exist in the self‐defocusing medium and their intensities can be controlled by selecting the suitable free parameters along the propagation distance. As examples, three types of low‐order approximate LB solutions are presented and their intensity profiles numerically discussed. The obtained results are helpful in exploring nonlinear phenomena in a self‐defocusing medium and providing a new approach for possible experimental verification of LBs.

Nature, diffraction-free propagation via space-time correlations, and nonlinear generation of time-diffracting light beams

We investigate on the properties of the recently introduced time-diffracting (TD) beams in free space. They are shown to be paraxial and quasi-monochromatic realizations of localized waves, spatiotemporal localized waves travelling undistorted at arbitrary speeds. The paraxial and quasi-monochromatic regime is shown to be necessary to observe what can properly be named diffraction in time. TD beams of finite energy travelling at quasi-luminal velocities are seen to form substantially longer foci or needles of light than the so-called abruptly focusing and defocusing needle of light, or limiting TD beam of infinite speed. Exploring the properties of TD beams under Lorentz transformations and transformation by paraxial optical systems, we realize that the relativistically moving nonlinear polarization of material media induced by a strongly localized fundamental pump wave generates a TD beam at its second harmonic, whose diffraction-free behavior as a needle of light in free space can be optimized with a standard $4f$-imager system.

Spatiotemporal Airy Ince\u2013Gaussian wave packets in strongly nonlocal nonlinear media

The self-accelerating Airy Ince–Gaussian (AiIG) and Airy helical Ince–Gaussian (AihIG) wave packets in strongly nonlocal nonlinear media (SNNM) are obtained by solving the strongly nonlocal nonlinear Schrödinger equation. For the first time, the propagation properties of three dimensional localized AiIG and AihIG breathers and solitons in the SNNM are demonstrated, these spatiotemporal wave packets maintain the self-accelerating and approximately non-dispersion properties in temporal dimension, periodically oscillating (breather state) or steady (soliton state) in spatial dimension. In particular, their numerical experiments of spatial intensity distribution, numerical simulations of spatiotemporal distribution, as well as the transverse energy flow and the angular momentum in SNNM are presented. Typical examples of the obtained solutions are based on the ratio between the input power and the critical power, the ellipticity and the strong nonlocality parameter. The comparisons of analytical solutions with numerical simulations and numerical experiments of the AiIG and AihIG optical solitons show that the numerical results agree well with the analytical solutions in the case of strong nonlocality.

Intra-operative high-resolution mapping of slow wave propagation in the human jejunum: Feasibility and initial results.

Bioelectrical slow waves are a coordinating mechanism of small intestine motility, but extracellular human studies have been restricted to a limited number of sparse electrode recordings. High-resolution (HR) mapping has offered substantial insights into spatiotemporal intestinal slow wave dynamics, but has been limited to animal studies to date. This study aimed to translate intra-operative HR mapping to define pacemaking and conduction profiles in the human small intestine. Immediately following laparotomy, flexible-printed-circuit arrays were applied around the serosa of the proximal jejunum (128-256 electrodes; 4-5.2mm spacing; 28-59cm2 ). Slow wave propagation patterns were mapped, and frequencies, amplitudes, downstroke widths, and velocities were calculated. Pacemaking and propagation patterns were defined. Analysis comprised nine patients with mean recording duration of 7.6±2.8minutes. Slow waves occurred at a frequency of 9.8±0.4cpm, amplitude 0.3±0.04mV, downstroke width 0.5±0.1seconds, and with faster circumferential velocity than longitudinal (10.1±0.8 vs 9.0±0.7mm/s; P=.001). Focal pacemakers were identified and mapped (n=4; mean frequency 9.9±0.2cpm). Disordered slow wave propagation was observed, including wavefront collisions, conduction blocks, and breakout and entrainment of pacemakers. This study introduces HR mapping of human intestinal slow waves, and provides first descriptions of intestinal pacemaker sites and velocity anisotropy. Future translation to other intestinal regions, disease states, and postsurgical dysmotility holds potential for improving the basic and clinical understanding of small intestine pathophysiology.

Stereo imaging and X-band radar wave data fusion: An assessment

The use of spatial and spatio-temporal data is rapidly changing the paradigm of wind wave observations, which have been traditionally restricted to time series from single-point measurements (e.g. from buoys, wave gauges). Active and passive 2D remote sensors mounted on platforms, ships, airplanes and satellites are now becoming standards in the oceanographic community and industry. Given the covered area ranging from centimeters to kilometers, such sensors are now a valuable tool for ocean and coastal observations. In this paper, we intercompare spatio-temporal wind wave data acquired with two state-of-the-art techniques, namely the stereo wave imaging and the X-band marine radar. The comparison was performed by operating the two instruments on an oceanographic research platform during a crossing-sea condition. We analyzed the statistical properties of the wave field, and its directional and omni-directional energy distributions. From our analysis, we suggest that stereo data can be exploited to find the best radar Modulation Transfer Function and scale factor needed to estimate wave parameters. Moreover, the fusion of the two systems will allow to broaden the scales covered by any one measurement, and to retrieve reliable directional wave spectra from short (∼1 m) to mid-wavelengths (∼100 m).

Role of Indian fluxes in the Intraseasonal 10-30 Days Variability of the African Monsoon

This study focused on the influence of Indian monsoon on the 10-30 days variability of the West African monsoon. One relies on the 500-300 hPa moisture fluxes calculated from specific wind and moisture fields from the ERAInterim reanalysis over the 1998-2008 period. These fluxes carry a signal of a spatio-temporal Rossby wave structure propagating westward from India. In the active phase of high convection of this wave, 500-300 hPa fluxes are Easterly. This high-tropospheric Rossby wave signal from the Indian monsoon area would modulate the dynamics over the Sahel.

Hydromechanics and Kinematics in Preferential Flow

Preferential flow covers macropore flow, nonequilibrium flow, and finger flow that are here exclusively approached with gravity-driven viscous flow. The basic unit is a water content wave whose two parameters are the waveʼs film thickness and its mainly vertical contact area per unit soil volume. The spatiotemporal wave properties depend on soil structure and on the intensity and duration of water input to the surface. Kinematic wave theory provides the mathematical tool for solving the analytical expressions. Three cases are the basic building blocks for approaching preferential flow: (a) single pulse, (b) a faster pulse trails a slower pulse, and (c) a faster pulse overtakes a slower pulse. Analytical procedures are presented for each case, and the potential of their applications is discussed. The analytical expressions and the superfluous representative elementary volume greatly facilitate preferential flow modeling.

Spatio-temporal scaling effects on longshore sediment transport pattern along the nearshore zone

A measure of uncertainties, entropy has been employed in such different applications as coastal engineering probability inferences. Entropy sediment transport integration theories present novel visions in coastal analyses/modeling the application and development of which are still far-reaching. Effort has been made in the present paper to propose a method that needs an entropy-power index for spatio-temporal patterns analyses. Results have shown that the index is suitable for marine/hydrological ecosystem components analyses based on a beach area case study. The method makes use of six Makran Coastal monthly data (1970–2015) and studies variables such as spatio-temporal patterns, LSTR (long-shore sediment transport rate), wind speed, and wave height all of which are time-dependent and play considerable roles in terrestrial coastal investigations; the mentioned variables show meaningful spatio-temporal variability most of the time, but explanation of their combined performance is not easy. Accordingly, the use of an entropy-power index can show considerable signals that facilitate the evaluation of water resources and will provide an insight regarding hydrological parameters’ interactions at scales as large as beach areas. Results have revealed that an STDDPI (entropy based spatio-temporal disorder dynamics power index) can simulate wave, long-shore sediment transport rate, and wind when granulometry, concentration, and flow conditions vary.

Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type.

We investigate the dynamics of spatiotemporal optical waves with one transverse dimension obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different types of conic sections (elliptic, parabolic, and hyperbolic) can lead to optical waves of the Bessel, Airy, and modified Bessel types, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.

Impulse response and spatio-temporal wave-packets: The common feature of rogue waves, tsunami, and transition to turbulence

Here, we present the impulse response of the canonical zero pressure gradient boundary layer from the dynamical system approach. The fundamental physical mechanism of the impulse response is in creation of a spatio-temporal wave-front (STWF) by a localized, time-impulsive wall excitation of the boundary layer. The present research is undertaken to explain the unit process of diverse phenomena in geophysical fluid flows and basic hydrodynamics. Creation of a tsunami has been attributed to localized events in the ocean-bed caused by earthquakes, landslides, or volcanic eruptions, whose manifestation is in the run up to the coast by surface waves of massive amplitude but of very finite fetch. Similarly rogue waves have often been noted; a coherent account of the same is yet to appear, although some explanations have been proposed. Our studies in both two- and three-dimensional frameworks in Sengupta and Bhaumik [“Onset of turbulence from the receptivity stage of fluid flows,” Phys. Rev. Lett. 107(15), 154501 (2011)] and Bhaumik and Sengupta [“Precursor of transition to turbulence: Spatiotemporal wave front,” Phys. Rev. E 89(4), 043018 (2014)] have shown that the STWF provides the central role for causing transition to turbulence by reproducing carefully conducted transition experiments. Here, we furthermore relax the condition of time behavior and use a Dirac-delta wall excitation for the impulse response. The present approach is not based on any simplification of the governing Navier-Stokes equation (NSE), which is unlike solving a nonlinear shallow water equation and/or nonlinear Schrödinger equation. The full nonlinear Navier-Stokes equation (NSE) is solved here using high accuracy dispersion relation preserving numerical schemes and using appropriate formulation of the NSE which minimizes error. The adopted numerical methods and formulation have been extensively validated with respect to various external and internal 2D and 3D flow problems. We also present results from the Orr-Sommerfeld equation to show that the origin of the STWF is via a linear mechanism. Nonlinearity and nonparallelism play the central role in causing these phenomena of geophysics and transition to turbulence.

Bloch oscillations and resonant radiation of light propagating in arrays of nonlinear fibers with high-order dispersion

Bloch oscillations of spatio-temporal light wave packets in arrays of nonlinear fibers with high-order dispersion are studied. The light wave experiences discrete spatial diffraction along the waveguide array coordinate together with continuous temporal dispersion including higher order terms. When a gradient in the waveguide light confinement strength is considered, the wave packet features robust long-lived Bloch oscillations with temporal and spatial spreading in the presence of a Kerr nonlinearity. The effect of the spatial Bloch oscillations on the emission of the dispersive radiation by the solitary wave is studied. It is shown that Bloch oscillations result in the generation of new frequencies. The condition of resonant emission of dispersive waves is derived and it is demonstrated that it matches very well with the results of direct numerical simulations.

Noise Equalization for Ultrafast Plane Wave Microvessel Imaging.

Ultrafast plane wave microvessel imaging significantly improves ultrasound Doppler sensitivity by increasing the number of Doppler ensembles that can be collected within a short period of time. The rich spatiotemporal plane wave data also enable more robust clutter filtering based on singular value decomposition. However, due to the lack of transmit focusing, plane wave microvessel imaging is very susceptible to noise. This paper was designed to: 1) study the relationship between ultrasound system noise (primarily time gain compensation induced) and microvessel blood flow signal and 2) propose an adaptive and computationally cost-effective noise equalization method that is independent of hardware or software imaging settings to improve microvessel image quality.

Receptivity to Harmonic Excitation Following Nonimpulsive Start for Boundary-Layer Flows

It has been shown in recent times that transition to turbulence occurs following two- and three-dimensional routes primarily by what is called the spatiotemporal wave front, for the canonical problem of a zero-pressure gradient boundary layer excited harmonically at the wall following an impulsive start. This paper shows that this onset process of disturbance growth continues also for a varying range of nonimpulsive wall excitation onset that is switched on smoothly. This is important because this will dispel any idea that a spatiotemporal wave front is totally due to impulsive start of wall excitation. This paper distinguishes between high- and low-frequency excitation cases to follow qualitatively different transition routes.

WASS: An open-source pipeline for 3D stereo reconstruction of ocean waves

Stereo 3D reconstruction of ocean waves is gaining more and more popularity in the oceanographic community and industry. Indeed, recent advances of both computer vision algorithms and computer processing power now allow the study of the spatio-temporal wave field with unprecedented accuracy, especially at small scales. Even if simple in theory, multiple details are difficult to be mastered for a practitioner, so that the implementation of a sea-waves 3D reconstruction pipeline is in general considered a complex task. For instance, camera calibration, reliable stereo feature matching and mean sea-plane estimation are all factors for which a well designed implementation can make the difference to obtain valuable results. For this reason, we believe that the open availability of a well tested software package that automates the reconstruction process from stereo images to a 3D point cloud would be a valuable addition for future researches in this area.We present WASS (http://www.dais.unive.it/wass), an Open-Source stereo processing pipeline for sea waves 3D reconstruction. Our tool completely automates all the steps required to estimate dense point clouds from stereo images. Namely, it computes the extrinsic parameters of the stereo rig so that no delicate calibration has to be performed on the field. It implements a fast 3D dense stereo reconstruction procedure based on the consolidated OpenCV library and, lastly, it includes set of filtering techniques both on the disparity map and the produced point cloud to remove the vast majority of erroneous points that can naturally arise while analyzing the optically complex nature of the water surface.In this paper, we describe the architecture of WASS and the internal algorithms involved. The pipeline workflow is shown step-by-step and demonstrated on real datasets acquired at sea.

Few-cycle spatiotemporal optical solitons in waveguide arrays

We consider the propagation of Gaussian spatiotemporal wave packets in arrays of parallel optical waveguides, assuming linear and nondispersive coupling between the adjacent guides. The numerical analysis is based on a discrete version of the modified Korteweg--de Vries equation that adequately describes the propagation of ultrashort (few-cycle) spatiotemporal solitons in waveguide arrays. Two kinds of such discrete-continuous localized wave forms, which are discrete solitons in the transverse direction, and few-cycle solitons in the longitudinal one, are put forward, namely breathing solitons and single-humped ones. The conditions of formation of these localized spatiotemporal structures, their time duration and spatial width, as well as their energies, are also investigated.

Numerical treatment of the spatio-temporal electromagnetic beam-wave packet

Abstract Propagation of a two-dimensional spatio-temporal electromagnetic beam wave is analysed. In parabolic (paraxial) approximation the exact analytical results for a spatio-temporal Gaussian impulse can be obtained. For solution of the full wave equation the numerical simulation has to be used. The various facets of this simulation are discussed here.

Optical-fluid dark line and X solitary waves in Kerr media

AbstractWe consider the existence and propagation of nondiffractive and nondispersive spatiotemporal optical wavepackets in nonlinear Kerr media. We report analytically and confirm numerically the properties of spatiotemporal dark line solitary wave solutions of the (2 + 1)D nonlinear Schrödinger equation (NLSE). Dark lines represent holes of light on a continuous wave background. Moreover, we consider non-trivial web patterns generated under interactions of dark line solitary waves,which give birth to dark X solitary waves. These solitary waves are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the (2 + 1)D type II Kadomtsev-Petviashvili (KP-II) equation. This finding opens a novel path for the excitation and control of optical solitary waves, of hydrodynamic nature.

Ultraefficient reduced model for countercurrent two-layer flows

A reduced two-phase model suitable for industrial uptake is introduced to predict the onset of flow reversal in falling films under countercurrent flow. Analysis of spatiotemporal stability and wave topology shows that vortex distribution plays a crucial role in the incipience of flow reversal.

Cover of coastal vegetation as an indicator of eutrophication along environmental gradients.

Coastal vegetation communities are important for primary production, biodiversity, coastal protection, carbon and nutrient cycling which, in combination with their sensitivity to eutrophication, render them potential indicators of environmental status for environmental policies like the EU Water and Marine Strategy Framework Directives. We evaluated one potential indicator for coastal vegetation, the cumulative cover at depths where the vegetation is light limited, by investigating its response to eutrophication along gradients in natural conditions. We used a large data set covering the Swedish coastline, spanning broad gradients in nutrient level, water clarity, seabed substrate, physical exposure and climate in addition to a salinity gradient from 0.5 to 30.5. Macroalgal cover increased significantly along gradients of declining nutrient concentration and increasing water clarity when we had accounted for diver effects, spatio-temporal sampling variability, salinity gradients, wave exposure and latitude. The developed empirical model explained 79% of the variation in algal cover across 130 areas. Based on this, we identified macroalgal cover as a promising indicator across the Baltic Sea, Kattegat and Skagerrak. A parallel analysis of soft-substrate macrophytes similarly identified significant increases in cover with decreasing concentrations of total nitrogen and increasing salinity, but the resulting empirical model explained only 52% of the variation in cover, probably due to the spatially more variable nature of soft-substrate vegetation. The identified general responses of vegetation cover to gradients of eutrophication across wide ranges in environmental settings may be useful for monitoring and management of marine vegetation in areas with strong environmental gradients.Electronic supplementary materialThe online version of this article (doi:10.1007/s00227-016-3032-6) contains supplementary material, which is available to authorized users.

Dark spatiotemporal optical solitary waves in self-defocusing nonlinear media

Dark three-dimensional spatiotemporal solitons or the “dark light bullets” in the self-defocusing nonlinear media with equal diffraction and dispersion lengths are demonstrated analytically. Our results show that the main characteristic of the dark light bullets can be described by the cylindrical Korteweg–de Vries (CKdV) equation. The dark wave packets are composed of the single-layer and multilayer toroidal rings. For the multilayer rings, there exist small inner rings enclosed in a large ring-shaped toroidal structure, when one chooses different orders of the soliton solutions of the CKdV equation. The radius of dark ring solitons increases with the propagation distance. Present results provide a feasible method for controlling the fundamental structure of these beams in the self-defocusing nonlinear media.