Local Wave Research Articles

Wave Downscaling Approach with TCN model, Case Study in Bengkulu, Indonesia

When conducting marine operations that rely on wave conditions, such as maritime trade, the fishing industry, and ocean energy, accurate wave downscaling is important, especially in coastal locations with complicated geometries. Traditional approaches for wave downscaling are usually obtained by performing nested simulations on a high-resolution local grid from global grid information. However, this approach requires high computation resources. In this paper, to downscale global wave height data into a high-resolution local wave height with less computation resources, we propose a machine learning-based approach to downscaling using the Temporal Convolutional Network (TCN) model. To train the model, we obtain the wave dataset using the SWAN model in a local domain. The global datasets are taken from the ECMWF Reanalysis (ERA-5) and used to train the model. We choose the coastal area of Bengkulu, Indonesia, as a case study. The results of TCN are also compared with other models such as LSTM and Transformers. It showed that TCN demonstrated superior performance with a CC of 0.984, RMSE of 0.077, and MAPE of 4.638, outperforming the other models in terms of accuracy and computational efficiency. It proves that our TCN model can be alternative model to downscale in Bengkulu’s coastal area.

On the stability of fully nonlinear hydraulic-fall solutions to the forced water wave problem

Two-dimensional free-surface flow over localised topography is examined, with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a dip, respectively. Steady hydraulic-fall solutions to the full incompressible, irrotational Euler equations are computed, and their linear and nonlinear stability is analysed by computing eigenspectra of the pertinent linearised operator and by solving an initial value problem. The computations are carried out numerically using a specially developed computational framework based on the finite-element method. The Hamiltonian structure of the problem is demonstrated, and stability is determined by computing eigenspectra of the pertinent linearised operator. It is found that a hydraulic-fall flow over a bump is spectrally stable. The corresponding flow over a dip is found to be linearly unstable. In the latter case, time-dependent simulations show that ultimately, the flow settles into a time-periodic motion that corresponds to an invariant solution in an appropriately defined phase space. Physically, the solution consists of a localised large-amplitude wave that pulsates above the dip while simultaneously emitting nonlinear cnoidal waves in the upstream direction and multi-harmonic linear waves in the downstream direction.

The Riemann Hilbert dressing method and wave breaking for two (2 + 1)-dimensional integrable equations

Abstract In this article, we present a method for generating (2 + 1)-dimensional integrable equations, resulting in the generalized Pavlov equation and dispersionless Kadomtsev–Petviashvili (dKP) equation, which can further be reduced to the standard Pavlov equation and dKP equation. Inspired by the inverse spectral transform presented in existing literature, we introduce the Riemann–Hilbert (RH) dressing method to construct the formal solutions of the Cauchy problems for the generalized Pavlov equation and dKP equation, providing a spectral representation of the solutions. Subsequently, we also extensively investigate the longtime behavior of solutions to these two equations in specific space regions. In particular, for the generalized dKP equation, we conduct a dedicated study on its implicit solutions expressed by arbitrary differential function through linearizing their RH problems. In the final section, we elaborate in detail on the analytic aspects of the wave breaking of a localized two-dimensional wave evolving according to the Hopf equation. With the assistance of a transformation, the longtime breaking of solutions to the generalized dKP equation can then be further characterized.

Mixed localized waves and their interaction structures for a spatial discrete Hirota equation

Mixed localized wave solutions and interactions are of great significance in nonlinear physical systems. This paper aims to investigating the generalized (m,N-m)-fold Darboux transformation and the mixed localized wave solutions of a spatial discrete Hirota equation. First, we construct the generalized (m,N-m)-fold Darboux transformation for the spatial discrete Hirota equation, which can produce the interactions between the breathers, degenerate breathers and rogue waves. For the Darboux transformation formula, we discuss the above order-1,2,3 localized wave solutions, as well as their dynamics by choosing the number of m = 1. We plot some specific examples such as the spatial (time)-periodic breather, second-order and third-order degenerate breathers and higher-order rogue waves with novel patterns. Furthermore, when m > 1, we give several kinds of mixed interaction solutions between the first-order rogue waves and first (second)-order (degenerate) breathers, between the first-order breather and second-order degenerate breathers, between second-order rogue waves and first-order breathers. At last, we also sum up the various mathematical features of the degenerate breathers and the mixed localized wave solutions.

Dynamical behaviors of vector localized wave solutions for the coupled modified Korteweg-de Vries equations

Dynamical behaviors of vector localized wave solutions for the coupled modified Korteweg-de Vries equations

On the Effect of Two-Dimensional Plasma Inhomogeneity in a Magnetic Island on the Parametric Excitation Threshold of Trapped Upper Hybrid Waves and the Level of Anomalous Absorption in ECRH Experiments

The effect of two-dimensional localization of an upper hybrid (UH) wave in a magnetic island is found. The influence of this effect on the threshold and saturation level of the absolute parametric decay instability of an extraordinary wave, which results in the excitation of two two-dimensional localized UH waves, is investigated.

Systematic soliton shape modulation by engineering superposed plane wave and soliton parameters.

We investigate the linear interference of a plane wave with different localized waves using the coupled Fokas-Lenells equation (FLE) with four-wave mixing term. We obtain the localized wave solution of the coupled FLE by linear superposition of two distinctly independent wave solutions, namely, the plane wave and one soliton solution and the plane wave and two soliton solution. We obtain several nonlinear profiles depending on the relative phase induced by soliton parameters. We present a systematic analysis of the linear interference profile under four different conditions on the spatial and temporal phase coefficients of interfering waves. We further investigate the interaction of two soliton solution and a plane wave. In this case, we find that, asymptotically, two soliton profiles may be similar or different from each other depending on the choices of soliton parameters in the two cases. The present analysis may also be applied to study the linear interference pattern of other localized waves. We believe that the results obtained by us shall be useful in soliton control, all-optical switching, and optical computing.

Free Infragravity Waves on the Inner Shelf: Observations and Parameterizations at Two Southern California Beaches

AbstractNumerical predictions of nearshore waves and shoreline runup are usually initialized on the inner shelf, seaward of the surfzone, with sea‐swell (SS) waves from local wave buoys or regional wave models. Lower frequency infragravity (IG) waves are not reliably measured by buoys or included in regional models. Here, co‐located pressure and velocity observations are used to characterize IG waves in 10–15 m depth in southern California. Shoreward propagating IG waves are often dominated by free waves, with the boundwave energy fraction <30% for moderate and low energy incident SS waves. Only 5% of records, with energetic long swell, show primarily bound waves. The shoreline slope of concave beaches increases by ∼3 between spring high and low tides, and free seaward and shoreward IG energy in 10–15 m vary tidally. The observed linear dependency of free IG energy on SS energy and period is consistent with Ardhuin et al. (2014, https://doi.org/10.1016/j.ocemod.2014.02.006)'s parameterization (R2 = 0.71). Including the tide level as a proxy for beach slope and modifying the SS frequency dependency increases R2 to 0.91. The ratio of free seaward to shoreward propagating IG energy suggests between 50 and 100% of the energy radiated seaward in depths of 10–15 m is trapped offshore and redirected shoreward. Free (random phase) and bound (phase‐coupled) IG waves are combined to initialize the SWASH numerical model. SWASH predicted runup is only weakly influenced by waves at the offshore boundary. Nonlinear IG generation and dissipation in the shoaling and surfzone overwhelm the effects of shoreward propagating waves observed at the offshore boundary.

Quantum Physics, Digital Computers, and Life from a Holistic Perspective

Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily modular hierarchical structures, with a number of key features. Firstly, they cannot be described by a single wave function: only local wave functions can exist, rather than a single wave function for a living cell, a cat, or a brain. Secondly, the quantum to classical transition is characterised by contextual wave-function collapse shaped by macroscopic elements that can be described classically. Thirdly, downward causation occurs in the physical hierarchy in two key ways: by the downward influence of time dependent constraints, and by creation, modification, or deletion of lower level elements. Fourthly, there are also logical modular hierarchical structures supported by the physical ones, such as algorithms and computer programs, They are able to support arbitrary logical operations, which can influence physical outcomes as in computer aided design and 3-d printing. Finally, complex systems are necessarily open systems, with heat baths playing a key role in their dynamics and providing local arrows of time that agree with the cosmological direction of time that is established by the evolution of the universe.

Pseudo grid-based physics-informed convolutional-recurrent network solving the integrable nonlinear lattice equations

Traditional discrete learning methods involve discretizing continuous equations using difference schemes, necessitating considerations of stability and convergence. Integrable nonlinear lattice equations possess a profound mathematical structure that enables them to revert to continuous integrable equations in the continuous limit, particularly retaining integrable properties such as conservation laws, Hamiltonian structure, and multiple soliton solutions. The pseudo grid-based physics-informed convolutional-recurrent network (PG-PhyCRNet) is proposed to investigate the localized wave solutions of integrable lattice equations, which significantly enhances the model’s extrapolation capability to lattice points beyond the temporal domain. We conduct a comparative analysis of PG-PhyCRNet with and without pseudo grid by investigating the multi-soliton solutions and rational solitons of the Toda lattice and self-dual network equation. The results indicate that the PG-PhyCRNet excels in capturing long-term evolution and enhances the model’s extrapolation capability for solitons, particularly those with steep waveforms and high wave speeds. Finally, the robustness of the PG-PhyCRNet method and its effect on the prediction of solutions in different scenarios are confirmed through repeated experiments involving pseudo grid partitioning.

Local conditions modulated the effects of marine heatwaves on coral bleaching in subtropical Hong Kong waters

A mass coral bleaching event occurred in the summer of 2022 in subtropical Hong Kong, driven by two marine heatwaves (MHWs) with high intensities of 1.56 and 0.86 °C above a mean climate condition, both MHWs 7 days with a short gap of 4 days during the strong La Niña year. A transect survey was conducted at nine study sites in three regions, which revealed widespread coral bleaching with bleached coral cover ranging from 2.4 to 70.3%. In situ environmental data revealed the presence of a thermocline and halocline. Local conditions, including depth and wave exposure, significantly influenced the bleaching response. Shallow-water (2–4 m) corals were primarily affected, particularly in sheltered and moderately sheltered sites that exhibited higher levels of bleached coral cover (42.97 ± 15.4% and 44.93 ± 29.4%, respectively) compared to the exposed sites (31.8 ± 5.2%). Bleaching in deep waters (4–6 m) was minimal, with only a few colonies of Goniopora at two of the three sheltered sites exhibiting bleaching (1.7 ± 1.5%). Heat stress resistance differed between coral genera. Recovery rate for four common coral genera is low for Acropora tumida. Additionally, a minor hypoxia event was found to cause mortality of non-coral benthos at a sheltered site (Sharp Island). These findings highlight the alarming impact of extreme heatwaves on subtropical coral communities and underscore the importance of monitoring coral bleaching.

Acoustic black hole ultrasonic scalpel

Ultrasonic scalpels (USs), as the preferred energy instruments, are facing a growing need to exhibit enhanced performance with the diversification of modern surgical challenges. Hence, we proposed an acoustic black hole ultrasonic scalpel (ABHUS) in longitudinal-bending coupled vibration for efficient surgical cutting. By incorporating an acoustic black hole profile, the local bending wave velocity is reduced and the amplitude is amplified cumulatively, thus creating a high-energy region near the blade tip to enhance the cutting performance of the ABHUS. The precise physical analysis model is established for systematic design of the ABHUS and quick estimation of its frequency characteristics. The vibration simulation and experiments demonstrate that compared with the conventional ultrasonic scalpel (CUS), the output amplitude of the ABHUS significantly increases, particularly a 425% increase in bending vibration displacement. The in-vitro cutting experiment confirms that ABHUS exhibits superior cutting performance. Our design presents vast possibilities and potential for the development of high-performance ultrasonic surgical instruments, serving as an innovative supplement with extraordinary significance for application of acoustic black holes.

Generalized [formula omitted]-fold Darboux transformation and localized waves for an integrable reduced spin Hirota-Maxwell-Bloch system in an erbium doped fiber

In this paper, under investigation is an integrable reduced spin Hirota-Maxwell-Bloch (rsHMB) system, which describes the transmission of the femtosecond pulses in an erbium doped fiber. Based on the existing N-fold Darboux transformation, we establish a generalized (n,N−n)-fold Darboux transformation for the rsHMB system, where n and N are the positive integers (n≤N). The Nth-order degenerate soliton and Nth-order rogue-wave solutions for the rsHMB system are obtained via the generalized (1,N−1)-fold Darboux transformation. By means of the generalized (2,N−2)-fold Darboux transformation, we derive the Nth-order hybrid wave solutions describing the interaction between the (N−1)th-order rogue wave and the first-order breather. The above solutions are discussed graphically, which exhibit the diverse wave structures including the triangle and pentagon, among others.

Rogue and solitary waves of a system of coupled nonlinear Schrödinger equations in a left-handed transmission line with second-neighbors coupling

The effects of the second-order neighbor interaction have been effective on the coherent localized waves and modulation instability spectrum. A coupled nonlinear Schrödinger equation is derived in the nonlinear left-handed electrical lattice, and the linear stability is used to formulate the modulation instability spectrum expression. Unstable modes are displayed to show symmetric lobes and increasing bandwidths under the influence of the neighbor coupling. The Benjamin-Feir instability has prospered in the network, and for weak perturbed wave numbers, the unstable modes increase. The numerical simulation is used to develop localized waves, including rogue waves with one crest and two humps, Akhmediev breathers, and other modulated structures. We notice that, for strong values of the perturbed wave number, an exponential growth of the continuous wave arises to confirm the fact that the nonlinear left-handed electrical lattice with coupling strength is opened to coherent localized waves. The long-lived nature of the obtained structures has also been demonstrated for specific times of propagation.

Emergent effects of synaptic connectivity on the dynamics of global and local slow waves in a large-scale thalamocortical network model of the human brain.

Slow-wave sleep (SWS), characterized by slow oscillations (SOs, <1Hz) of alternating active and silent states in the thalamocortical network, is a primary brain state during Non-Rapid Eye Movement (NREM) sleep. In the last two decades, the traditional view of SWS as a global and uniform whole-brain state has been challenged by a growing body of evidence indicating that SO can be local and can coexist with wake-like activity. However, the mechanisms by which global and local SOs arise from micro-scale neuronal dynamics and network connectivity remain poorly understood. We developed a multi-scale, biophysically realistic human whole-brain thalamocortical network model capable of transitioning between the awake state and SWS, and we investigated the role of connectivity in the spatio-temporal dynamics of sleep SO. We found that the overall strength and a relative balance between long and short-range synaptic connections determined the network state. Importantly, for a range of synaptic strengths, the model demonstrated complex mixed SO states, where periods of synchronized global slow-wave activity were intermittent with the periods of asynchronous local slow-waves. An increase in the overall synaptic strength led to synchronized global SO, while a decrease in synaptic connectivity produced only local slow-waves that would not propagate beyond local areas. These results were compared to human data to validate probable models of biophysically realistic SO. The model producing mixed states provided the best match to the spatial coherence profile and the functional connectivity estimated from human subjects. These findings shed light on how the spatio-temporal properties of SO emerge from local and global cortical connectivity and provide a framework for further exploring the mechanisms and functions of SWS in health and disease.

Dynamics of fractional solitonic profiles to multicomponent Gross–Pitaevskii system

The fractional multicomponent Gross-Pitaevskii system arising in the Bose-Einestein condensate is under consideration. The Gross-Pitaevskii equation plays a significant role in Bose-Einstein condensation and engineering, where it characterizes the dynamics of the condensate wave function. Superfluidity and superconductivity are two characteristics of the low-temperature phenomenon that are linked to the Bose–Einstein condensate, which is generated by a diluted atomic gas. The investigation of multi-component equations has garnered considerable attention because of their capacity to clarify intricate physical phenomena and reveal the dynamic configurations of localized wave solutions. A variety of solutions have been secured in various forms, including bright, dark, singular, and combo solitons, in addition to solutions of hyperbolic, periodic, and exponential functions. For the purpose of ensuring the solutions, recently developed integration tools called the modified Sardar subequation method and enhanced modified extended tanh-expansion method have been implemented. In nonlinear dispersive media, solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. The proposed approaches are certainly the most direct, efficient, and valuable method for dealing with multiple nonlinear models that arise in applied physics and mathematics, with the purpose of generating various types of exact solutions. In addition, 3D, 2D, contour, and density plots have been utilized to visually represent the obtained results, facilitating a greater understanding of the physical effects of the derived solutions. The solutions attained are of great importance with regard to their applicability across a wide range of quantum systems.

Comment on “Integrability, modulational instability and mixed localized wave solutions for the generalized nonlinear Schrödinger equation”

Comment on “Integrability, modulational instability and mixed localized wave solutions for the generalized nonlinear Schrödinger equation”

Investigating Asymmetry Development from SiO to H2O Maser Regions in VX Sagittarii

Simultaneous very-long-baseline interferometry monitoring observations of H2O and SiO masers toward VX Sagittarii were conducted from 2014 February to 2019 January. Thirty epochs of observations revealed that the H2O and SiO masers had asymmetric and ring-like structures, respectively. However, from 2017 September to 2018 March, the SiO maser transformed from a ring-like structure to a northeast–southwest (NE–SW) extension, and the 43.1 and 86.2 GHz SiO maser components had velocities of 39.48 and 10.65 km s−1 in the NE–SW direction, suggesting a possible localized strong shock wave. The H2O maser had a double-sided structure oriented in the NE–SW direction with near-stellar velocity components, which aligned with the extended direction of the SiO maser. The nonregular optical brightness and maser intensity variations were speculated to be related to the morphological evolution of the SiO maser. During the stable states attained by regular pulsations, the SiO maser region was presumed to experience radial acceleration, which reverted the SiO maser to a ring-like structure. However, the H2O maser region, where the acceleration almost terminates, retained its asymmetric morphology due to the prior influence of external forces. The results suggest that substantial energy transfer can alter the dynamics of the SiO maser and surrounding atmosphere, leading to an asymmetric distribution in the H2O maser region.

Reference values of carotid intima-media thickness and arterial stiffness in Chinese adults based on ultrasound radio frequency signal: A nationwide, multicenter study.

Carotid intima-media thickness (IMT) and diameter, stiffness, and wave reflections, are independent and important clinical biomarkers and risk predictors for cardiovascular diseases. The purpose of the present study was to establish nationwide reference values of carotid properties for healthy Chinese adults and to explore potential clinical determinants. A total of 3053 healthy Han Chinese adults (1922 women) aged 18-79years were enrolled at 28 collaborating tertiary centers throughout China between April 2021 and July 2022. The real-time tracking of common carotid artery walls was achieved by the radio frequency (RF) ultrasound system. The IMT, diameter, compliance coefficient, β stiffness, local pulse wave velocity (PWV), local systolic blood pressure, augmented pressure (AP), and augmentation index (AIx) were then automatically measured and reported. Data were stratified by age groups and sex. The relationships between age and carotid property parameters were analyzed by Jonckheere-Terpstra test and simple linear regressions. The major clinical determinants of carotid properties were identified by Pearson's correlation, multiple linear regression, and analyses of covariance. All the parameters of carotid properties demonstrated significantly age-related trajectories. Women showed thinner IMT, smaller carotid diameter, larger AP, and AIx than men. The β stiffness and PWV were significantly higher in men than women before forties, but the differences reversed after that. The increase rate of carotid IMT (5.5μm/year in women and 5.8μm/year in men) and diameter (0.03mm/year in both men and women) were similar between men and women. For the stiffness and wave reflections, women showed significantly larger age-related variations than men as demonstrated by steeper regression slopes (all P for age by sex interaction <0.05). The blood pressures, body mass index (BMI), and triglyceride levels were identified as major clinical determinants of carotid properties with adjustment of age and sex. The age- and sex-specific reference values of carotid properties measured by RF ultrasound for healthy Chinese adults were established. The blood pressures, BMI, and triglyceride levels should be considered for clinical application of corresponding reference values.

Local field potential sharp waves with diversified impact on cortical neuronal encoding of haptic input

Cortical sensory processing is greatly impacted by internally generated activity. But controlling for that activity is difficult since the thalamocortical network is a high-dimensional system with rapid state changes. Therefore, to unwind the cortical computational architecture there is a need for physiological ‘landmarks’ that can be used as frames of reference for computational state. Here we use a waveshape transform method to identify conspicuous local field potential sharp waves (LFP-SPWs) in the somatosensory cortex (S1). LFP-SPW events triggered short-lasting but massive neuronal activation in all recorded neurons with a subset of neurons initiating their activation up to 20 ms before the LFP-SPW onset. In contrast, LFP-SPWs differentially impacted the neuronal spike responses to ensuing tactile inputs, depressing the tactile responses in some neurons and enhancing them in others. When LFP-SPWs coactivated with more distant cortical surface (ECoG)-SPWs, suggesting an involvement of these SPWs in global cortical signaling, the impact of the LFP-SPW on the neuronal tactile response could change substantially, including inverting its impact to the opposite. These cortical SPWs shared many signal fingerprint characteristics as reported for hippocampal SPWs and may be a biomarker for a particular type of state change that is possibly shared byboth hippocampus and neocortex.