Generic Wave Research Articles

Emergence of extreme events from randomly chirped condensate

We explore rogue wave emergence in generic wave systems governed by the nonlinear Schrödinger equation. We highlight the interplay between the stochastic focusing induced by a random chirp of a continuous wave condensate and modulation instability of the condensate to periodic and/or random perturbations. We show that regardless of its statistical properties, the random chirp of the condensate leads to a non-Gaussian, heavy-tailed probability density distribution of peak powers of the waves excited atop of the condensate, which is a statistical signature of rogue waves, or more broadly, extreme events in physics.

Families of exact similaritons with flexible modulations in N-coupled homogeneous and inhomogeneous systems

In this paper, a family of exact solutions to N-coupled nonlinear Schrödinger (N-CNLS) equations including bright and dark solitons, Akhmediev breathers, Kuznetsov-Ma breathers, and rogue waves are derived with the aid of a generic nonlinear wave assumption. As an application of the solutions, we present a scheme to realize amplitude coding in an identical waveguide system. Furthermore, by a general self-similar transformation method, exact controllable similaritons of N-coupled inhomogeneous NLS (N-CINLS) equations are constructed under relaxed compatibility conditions. Flexible modulations of similaritons are investigated in a typical inhomogeneous system. Based on the general self-similar transformation, we further study various and novel modulations of composite similariton of 2-CINLS regimes. The various similaritons presented here may be expected to find application in the control and transmission of nonlinear waves in realizable complex systems including those based on optical fibers and Bose-Einstein condensates.

Unveiling correlated two-dimensional topological insulators through fermionic tensor network states—classification, edge theories and variational wavefunctions

The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of electronic bands becomes obsolete, it has been established that topological insulator phases persist as stable phases, separate from the trivial insulators. However, due to the inability to express the ground states of such systems as Slater determinants, the formulation of generic variational wave functions for numerical simulations is highly desirable. In this paper, we tackle this challenge for two-dimensional topological insulators by developing a comprehensive framework for fermionic tensor network states. Starting from simple assumptions, we obtain possible sets of tensor equations for any given symmetry group, capturing consistent relations governing symmetry transformation rules on tensor legs. We then examine the connection between these tensor equations andnon-chiraltopological insulators by constructing edge theories and extracting quantum anomaly data from each set of tensor equations. By exhaustively exploring all possible sets of equations, we achieve a systematic classification of non-chiral topological insulator phases. Imposing the solutions of a given set of equations onto local tensors, we obtain generic variational wavefunctions for the corresponding topological insulator phases. Our methodology provides an important step toward simulating topological insulators in strongly correlated systems. We discuss the limitations and potential generalizations of our results, paving the way for further advancements in this field.

Nonresonant Scattering of Energetic Electrons by Electromagnetic Ion Cyclotron Waves: Spacecraft Observations and Theoretical Framework

AbstractElectromagnetic ion cyclotron (EMIC) waves lead to rapid scattering of relativistic electrons in Earth's radiation belts, due to their large amplitudes relative to other waves that interact with electrons of this energy range. A central feature of electron precipitation driven by EMIC waves is deeply elusive. That is, moderate precipitating fluxes at energies below the minimum resonance energy of EMIC waves occur concurrently with strong precipitating fluxes at resonance energies in low‐altitude spacecraft observations. This paper expands on a previously reported solution to this problem: nonresonant scattering due to wave packets. The quasi‐linear diffusion model is generalized to incorporate nonresonant scattering by a generic wave shape. The diffusion rate decays exponentially away from the resonance, where shorter packets lower decay rates and thus widen the energy range of significant scattering. Using realistic EMIC wave packets from δf particle‐in‐cell simulations, test particle simulations are performed to demonstrate that intense, short packets extend the energy of significant scattering well below the minimum resonance energy, consistent with our theoretical prediction. Finally, the calculated precipitating‐to‐trapped flux ratio of relativistic electrons is compared to ELFIN observations, and the wave power spectra is inferred based on the measured flux ratio. We demonstrate that even with a narrow wave spectrum, short EMIC wave packets can provide moderately intense precipitating fluxes well below the minimum resonance energy.

Reliable analysis for obtaining exact soliton solutions of (2+1)-dimensional Chaffee-Infante equation

<abstract><p>The (2+1)-dimensional Chaffee-Infante equation (CIE) is a significant model of the ion-acoustic waves in plasma. The primary objective of this paper was to establish and examine closed-form soliton solutions to the CIE using the modified extended direct algebraic method (m-EDAM), a mathematical technique. By using a variable transformation to convert CIE into a nonlinear ordinary differential equation (NODE), which was then reduced to a system of nonlinear algebraic equations with the assumption of a closed-form solution, the strategic m-EDAM was implemented. When the resulting problem was solved using the Maple tool, many soliton solutions in the shapes of rational, exponential, trigonometric, and hyperbolic functions were produced. By using illustrated 3D and density plots to evaluate several soliton solutions for the provided definite values of the parameters, it was possible to determine if the soliton solutions produced for CIE are cuspon or kink solitons. Additionally, it has been shown that the m-EDAM is a robust, useful, and user-friendly instrument that provides extra generic wave solutions for nonlinear models in mathematical physics and engineering.</p></abstract>

A deterministic approach to investigate nonlinear evolution equations for large balance numbers

When the balance number is greater than one, the modified simple equation (MSE) method typically fails to yield analytical wave solutions for nonlinear evolution equations (NLEEs) that appear in engineering and mathematical physics. We have addressed this shortcoming in this article and established a technique to implement the MSE approach to investigate NLEEs for balancing number two. Two NLEEs, namely, the regularized long wave and the Jimbo-Miwa equations, have been investigated in order to affirm the approach. Through this method, we found further generic wave solutions related to physical parameters, and when the parameters receive particular values, solitons emerge from the exact solutions. Graphs are used to investigate the solitary wave features of the attained solution functions, which illustrate the usefulness, validity, and compatibility of the scheme.

An Optimal Control Perspective on Classical and Quantum Physical Systems

This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.

Numerical and Experimental Characterization of Rotational Floating Body Drag

Hydrodynamic drag plays a significant role in the motions and response of floating bodies – whether it be a wave energy converter, floating wind structure, or offshore oil & gas platform. Existing literature provides significant overview of the methodologies (both experimental and numerical) to characterize translational drag, however, there is limited research on the contributions (and methods of application) for rotational drag.
 
 This paper will detail both numerical modelling and a physical experimental campaign to assess how rotational drag impacts floating body dynamics, and best practices for numerical model inclusion. Specific focus will be on 1) the variety of methods used to input rotational drag into numerical models; 2) processes and lessons learnt from the experimental derivation of rotational drag coefficients; and 3) how does weakly non-linear wave stretching methods influence rotational drag.
 
 The experimental campaign is currently underway to classify the significance of rotational drag coefficients in characterizing floating body behavior. Translational and rotational drag coefficients of a simplified, inertial property matched, 1:50 floating body is being determined through a series of calibration tests. Both traditional free decay tests and forced oscillation tests will be implemented to evaluate these coefficients across multiple degrees-of-freedom. The final paper will present an overview of the experimental campaign, the results and lesson learnt.
 
 On the numerical side, the floating body will be modelled in the open-source wave energy converter modelling tool, WEC-Sim, and validated against the experimental results. Numerical results will be presented to review general body responses, with and without rotational drag, and generic wave conditions plus those expected at the PacWave wave energy test site in Oregon, USA.
 
 The inclusion of rotational drag coefficients and weakly nonlinear hydrodynamics are expected to improve computational model results, especially in the nonlinear wave excitation range, providing a better understanding of floating body behavior.

Comprehensive geometric-shaped soliton solutions of the fractional regularized long wave equation in ocean engineering

The time-fractional regularized long wave equation is a significant model in the study of ocean engineering, plasma physics, and fluid dynamics. The fractional derivative is contemplated in the beta derivative sense, which is consistent with all the principles of derivative. In this article, the reliable and viable two-variable (G'/G,1/G)-expansion approaches is instigated to generate a variety of novel and generic wave outcomes. Consequently, the presented research provides abundant robust soliton solutions, including periodic soliton, bell-shaped soliton, W-shaped soliton, and some other type solitons. The effect of the fractional-order derivative has also been shown, and it is noticed that the fractional-order derivative has a significant impact on the wave profile. The physical conduct of the solitons has been demonstrated thoroughly via three- and two-dimensional and contour graphs. It can be noted that the new solutions obtained will provide greater convenience in the study of the phenomena described by the regular long-wave equation.

Practical power absorption assessment limits for generic wave energy converters

There lacks a generic representation of the wave power absorption of devices across dimensions, shapes, and resource conditions. A conventional resource assessment approach only evaluates the wave power based on wave characteristics, which is insufficient to capture the practical power absorption variations between WEC archetypes. In this paper, a novel WEC net power assessment (WNPA) method is proposed and is generally applicable to any arbitrary WECs design. Two theoretical upper bounds of wave power absorption are adopted and derived for different types of WECs. Numerical simulations are conducted to apply this novel technique to assess the net power available to different WECs at the Wave Energy Test Site (WETS), Hawaii and the PacWave site, Oregon over 11 years. By comparing the power potential for WECs oscillating in different degrees of freedom, the results indicate the surging mode may be the most energetic; regardless of shapes and ocean sites. When applied to three generic WECs (point absorber, terminator, and attenuator), the pitching terminator is shown to have lower absorption potential. Finally, the mean annual energy production (MAEP) of the three generic WECs at WETS and PacWave are compared, and a surging attenuator shows a significant wave power potential at PacWave.

Near-Field Behaviors of Internal Energy Flows of Free-Space Electromagnetic Waves Induced by Electric Point Dipoles

Both orbital and spin energy fluxes constitute the internal flows decomposed from a Poynting vector. For generic electromagnetic waves propagating through source-free media, these energy fluxes are quadratic in field variables so that their properties are not easily predictable. Notwithstanding, their near-field behaviors play important roles in nanoscale photonics. For time-oscillatory fields, we found two hitherto-overlooked distinctions between the two internal flows. The first is an unequal level between them because the vorticity of an orbital energy flux plays a role comparable to a spin energy flux itself. The second is regarding the electric-magnetic dual symmetry in handling the two internal flows, whence the reactive helicity plays a role as important as the electromagnetic helicity. By helicity conservation, an inter-electric-magnetic transport is possible for the spin angular momentum density, while the electric and magnetic constituents of orbital energy fluxes admit only respective intra-electric and intra-magnetic transports. We have tested the validities of all these claims by exemplarily taking the electromagnetic fields induced by an electric point dipole, either a linear or a circular one. We have thus made new contributions not only in deriving explicit forms of the internal energy flows but also in revealing the magnetic activities hidden under the electromagnetic waves induced by electric point dipoles.

Analysis of some new wave solutions of DNA-Peyrard–Bishop equation via mathematical method

The main goal of this paper is to extract the closed-form wave solutions by means of [Formula: see text]-expansion method to the DNA flow known as the Peyrard–Bishop model which describes the nonlinear interaction between neighboring displacements and hydrogen bonds. The aforementioned model is investigated for the time-fractional order and the fractional derivatives are used in the sense of conformable derivatives. The projected method provides additional generic and comprehensive wave solutions incorporated with physical parameters whose specific values reveal different shapes of the waveform such as periodic soliton, singular kink soliton, singular anti-kink soliton, and other different types of solitons. The obtained soliton solutions are novel, advanced, distinct, and relevant based on the available information in the literature which may be applied to more complex phenomena. The three-dimensional, two-dimensional, and contour plots of some of the attained results are sketched by assigning individual values of the parameters to scrutinize the dynamic behavior of the waves.

Near-Field Spatial Correlation for Extremely Large-Scale Array Communications

Extremely large-scale array (XL-array) communications correspond to systems whose antenna sizes are so large that the scatterers and/or users may no longer be located in the far-field region. By discarding the conventional far-field uniform plane wave (UPW) assumption, this letter studies the near-field spatial correlation of XL-array communications, by taking into account the more generic non-uniform spherical wave (NUSW) characteristics. It is revealed that different from the far-field channel spatial correlation which only depends on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">power angular spectrum</i> (PAS), the near-field spatial correlation depends on the scattered power distribution not just characterized by their arriving angles, but also by the scatterers’ distances, which is termed as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">power location spectrum</i> (PLS). A novel integral expression is derived for the near-field spatial correlation in terms of the scatterers’ location distribution, which includes the far-field spatial correlation as a special case. The result shows that different from the far-field case, the near-field spatial correlation no longer exhibits <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spatial stationarity</i> in general, since the correlation coefficient for each pair of antennas depends on their specific positions, rather than their relative distance only. To gain further insights, we consider a generalized one-ring model for scatterer distribution, where the ring center may be flexibly located. Numerical results are provided to show the necessity of the near-field spatial correlation modelling for XL-array communications.

Angular momentum eigenstates of the isotropic 3-D harmonic oscillator: Phase-space distributions and coalescence probabilities

The isotropic 3-dimensional harmonic oscillator potential can serve as an approximate description of many systems in atomic, solid state, nuclear, and particle physics. In particular, the question of 2 particles binding (or coalescing) into angular momentum eigenstates in such a potential has interesting applications. We compute the probabilities for coalescence of two distinguishable, non-relativistic particles into such a bound state, where the initial particles are represented by generic wave packets of given average positions and momenta. We use a phase-space formulation and hence need the Wigner distribution functions of angular momentum eigenstates in isotropic 3-dimensional harmonic oscillators. These distribution functions have been discussed in the literature before but we utilize an alternative approach to obtain these functions. Along the way, we derive a general formula that expands angular momentum eigenstates in terms of products of 1-dimensional harmonic oscillator eigenstates.

Efficient assessment for the pitchpoling risks of a generic wave energy converter based on first passage statistics

Of the rapidly emerging wave energy converter (WEC) designs, many can be essentially categorized as moored, floating, cylindrical structures. Their capsizing risks under random waves (i.e. dynamic instability) haven't been investigated adequately. The stochastic averaging proves to be an efficient approach providing quantitative assessments of dynamic instabilities. This study has adapted stochastic averaging to assess the pitchpoling risks of a generic moored floating WEC under random waves. Studies reveal that the statistics from stochastic averaging can be correlated reasonably with the statistics from the time domain simulations. Without requiring numerous simulations, the obtained first passage statistics could formulate a semi-analytical dynamic stability criterion for WEC designs. Sensitivity analysis have been performed with respect to various parameters, including wave period, mooring setup, initial condition and geometry modification.

Utilizing Gaussian mixture models in all-sky searches for short-duration gravitational wave bursts

Coherent WaveBurst is a generic, multidetector gravitational wave burst search based on the excess power approach. The coherent WaveBurst algorithm currently employed in the all-sky short-duration gravitational wave burst search uses a conditional approach on selected attributes in the multidimensional event attribute space to distinguish between noisy events from that of astrophysical origin. We have been developing a supervised machine learning approach based on the Gaussian mixture modeling to model the attribute space for signals as well as noise events to enhance the probability of burst detection [Gayathri et al.Phys. Rev. D 102, 104023 (2020)]. We further extend the GMM approach to the all-sky short-duration coherent WaveBurst search as a postprocessing step on events from the first half of the third observing run (O3a). We show an improvement in sensitivity to generic gravitational wave burst signal morphologies as well as the astrophysical source such as core-collapse supernova models due to the application of our Gaussian mixture model approach to coherent WaveBurst triggers. The Gaussian mixture model method recovers the gravitational wave signals from massive compact binary coalescences identified by coherent WaveBurst targeted for binary black holes in GWTC-2, with better significance than the all-sky coherent WaveBurst search. No additional significant gravitational wave bursts are observed.

Analysis of Beam Sweeping Techniques for Cell-Discovery in Millimeter Wave Systems

Cell discovery is the procedure in which a user equipment (UE) finds a suitable base station (BS) to establish a communication link. When beamforming with antenna arrays is done at both transmitter and receiver, cell discovery in mm wave systems also involves finding the correct angle of arrival – angle of departure alignment between the UE and the detected BS. First, we consider the single BS scenario and present the mathematical model for the cell discovery problem. We present the details of the beam sweepingbased techniques and explain the beam combining scheme to reduce the training overhead. We analytically characterize the performance of energy detector at the UE for both beam sweeping and beam combining methods under some channel assumptions. Further, we consider the multiple BS case where BSs transmit synchronization signals along with directional beamforming. We analyze the performance of the energy detector in this case as well. We finally present simulation studies with channels generated using generic mm wave channel emulators and draw inferences on the role of various parameters on the cell discovery performance.

Broadband X waves with orbital angular momentum

We describe the minimal diffraction-free and dispersion-free, superluminal wave packets (X-waves and generic superluminal localized waves) that can carry a given amount of units $m$ of orbital angular momentum (OAM) per photon. Even if their frequency spectrum is wide enough to synthesize a unipolar pulse, OAM imposes a temporal pulse shape with as many zeroes as units of OAM, and therefore $|m|/2$ temporal oscillations. All the frequencies in the broadband spectrum are displayed, like in a rainbow, from the bluer ones in the vicinity of the vortex to the redder ones in the wave periphery. At the same time, the whole wave paclet experiences a blue shift proportional to $|m|$. As a result of the radial red shift and the OAM blue shift, the colour of the brilliant ring around the central vortex is independent of OAM, and solely determined by the broadband source spectrum. Given the very peculiar properties of X-waves with OAM, their generation and use, instead of standard Laguerre-Gauss modes, could improve the performance of OAM-based communication and quantum cryptographic systems, as well as the efficiency of the generation of high harmonics and attosecond pulses with OAM.

The Prospect of Combining a Point Absorber Wave Energy Converter with a Floating Offshore Wind Turbine

With recent advances in offshore floating wind and wave energy technology, questions have emerged as to whether the two technologies can be combined to reduce their overall levelised cost of energy. In this paper, the potential for combining a floating offshore wind turbine to a point absorbing wave energy converter is investigated. The focus of the investigation is how much power might be produced by a combined floating wind and wave energy converter system, and the resultant changes in motion of the floating wind platform. A model for the combined wave and wind system is developed which uses the standardised NREL OC3 5 MW spar type wind turbine and a cylindrical buoyant actuator (BA), which is attached to the spar via a generic wave power take-off system (modelled as a spring-damper system). Modelling is conducted in the frequency domain and the tests span a wide range of parameters, such as wave conditions, BA sizes, and power take-off coupling arrangements. It is found that the optimal (with respect to power production) BA size is a draft and radius of approximately 14 m. It is found that this BA can theoretically produce power in the range of 0.3 to 0.5 MW for waves with a significant wave height of 2 m, and has the potential to produce power greater or near to 1 MW for waves with a significant wave height of at least 3 m. However, it is also found that, in terms of the relative capture width, significantly smaller BAs are optimal, and that these smaller BA sizes less significantly alter the motion of the floating wind platform.

Sensitivity Analysis of In Silico Fluid Simulations to Predict Thrombus Formation after Left Atrial Appendage Occlusion

Atrial fibrillation (AF) is nowadays the most common human arrhythmia and it is considered a marker of an increased risk of embolic stroke. It is known that 99% of AF-related thrombi are generated in the left atrial appendage (LAA), an anatomical structure located within the left atrium (LA). Left atrial appendage occlusion (LAAO) has become a good alternative for nonvalvular AF patients with contraindications to anticoagulants. However, there is a non-negligible number of device-related thrombus (DRT) events, created next to the device surface. In silico fluid simulations can be a powerful tool to better understand the relation between LA anatomy, haemodynamics, and the process of thrombus formation. Despite the increasing literature in LA fluid modelling, a consensus has not been reached yet in the community on the optimal modelling choices and boundary conditions for generating realistic simulations. In this line, we have performed a sensitivity analysis of several boundary conditions scenarios, varying inlet/outlet and LA wall movement configurations, using patient-specific imaging data of six LAAO patients (three of them with DRT at follow-up). Mesh and cardiac cycle convergence were also analysed. The boundary conditions scenario that better predicted DRT cases had echocardiography-based velocities at the mitral valve outlet, a generic pressure wave from an AF patient at the pulmonary vein inlets, and a dynamic mesh approach for LA wall deformation, emphasizing the need for patient-specific data for realistic simulations. The obtained promising results need to be further validated with larger cohorts, ideally with ground truth data, but they already offer unique insights on thrombogenic risk in the left atria.