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This paper investigates an uncommon technique by using the influence of the random function (Weiner process function), on a two-temperature problem, at the free surface of the semiconducting medium, by using the photo-thermoelasticity theory. Using the Silicon material as an example of a semiconducting medium under the influence of a magnetic field, the novel model can be formulated. To make the problem more logical, the randomness of the Weiner process function is aged to the governing stochastic equation. A combining stochastic process with the boundary of the variables is studied. In this case, the stochastic and deterministic solutions were obtained for all physical quantities. The additional noise is regarded as white noise. The problem is investigated according to a two-dimensional (2D) deformation. The normal mode method can be used mathematically to obtain numerically the deterministic, stochastic, and variance solutions of all physical quantities. Three sample paths are obtained by making a comparison between the stochastic and deterministic distributions of the field variables. The impacts of adding randomization to the boundary conditions are highlighted. The numerical results are shown graphically and discussed in consideration of the two-temperature parameter effect.

In this study, an existing iterative least-squares (LS) method for determining ocean surface currents from X-band nautical radar images is modified for extracting ocean wave information from the same data. Within each iterative step, the image spectra samples are classified as containing contributions from fundamental, first-order and higher harmonic waves or noise. Based on the classification result, a new scheme is proposed to increase the robustness of current estimation. This involves automatically adjusting the first threshold that is used for obtaining an initial guess of the current velocity in the iterative LS method. The proposed wave algorithm directly uses the classified fundamental and first-order harmonic wave components for wave spectra and parameter retrieval. Unlike previous wave analysis techniques in which a bandpass filter is required to eliminate the non-wave contributions after the current velocity is obtained, the proposed algorithm simplifies the wave retrieval without such a bandpass filter. Algorithm verification is first conducted by using simulated radar images. Subsequently, the method is applied to field radar data and the results are compared with wave-buoy measurements. Wave parameters from both types of data show that the modified wave algorithm produces results that are close to those achieved using traditional algorithms.

We analyzed electrostatic electron cyclotron harmonic waves observed by the interferometry observation mode of the Arase satellite. It is found that the magnitude of the phase difference varies with the satellite spin. The spin dependence of this phase difference was investigated by examining the trend of the spin dependence for the 84 events of interferometry observation of ECH waves. We found that they are divided into two categories. One is that the phase difference tends to show sinusoidal variations as a function of the angle γ B between the ambient magnetic field projected on the spin plane and the electric field sensor. The other is that the phase difference is close to zero and does not depend on γ B . A numerical model of interferometry observation of single plane wave is constructed to explain the observed phase differences. We performed the numerical calculations when the background magnetic field was oriented in the direction often observed in the Arase satellite. The result of the calculations shows the wave vector direction relates to the spin angle with the maximum phase difference. Using this relation, we show that it may be possible to estimate the wave vector direction of ECH waves from one-dimensional interferometry data. This is expected to enable more accurate estimates of phase velocity. Graphical Abstract

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

Wave‐particle interactions are essential for energy transport in the magnetosphere. In this study, we investigated an event during which electrons interact simultaneously with waves in different scales, using data from the Magnetospheric Multiscale mission. At the macroscale (∼105 ${\\sim} 1{0}^{5}$ km), drift resonance between ultra‐low frequency (ULF) waves and 70–300 keV electrons is observed. At the microscale (∼100−101 ${\\sim} 1{0}^{0}-1{0}^{1}$ km), lower‐band chorus waves and electron cyclotron harmonic (ECH) waves are alternately generated, showing signatures of modulation by ULF waves. We found that compressional ULF waves affect the temperature anisotropy of 1–10 keV electrons, thereby periodically exciting chorus waves. Through linear instability analysis, we propose that ULF waves modulate ECH wave emissions by regulating the gradient of electron phase space density at the edge of the loss cone. Our results enhance the understanding of cross‐scale wave‐particle interactions, highlighting their importance in magnetospheric dynamics.

Two‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation. Plain Language Summary Recent studies have unveiled the generation of nonlinear second harmonics (SH) of electromagnetic ion cyclotron (EMIC) waves. The SH is nonlinearly driven by the fundamental wave (FW) and satisfies the necessary conditions: ω2 = 2ω1 and k2 = 2k1, where ω1 (ω2) and k1 (k2) are the frequency and the wave vector of the FW (SH), respectively. Previous studies have relied on one‐dimensional (1‐D) hybrid simulations to investigate the SH. However, 1‐D simulations allow waves to propagate along a single dimension and lack spatial variation of the field orthogonal to this dimension, which impedes the complete verification of the relation k2//k1. Thus, in this study, the SH generation is modeled by two‐dimensional (2‐D) hybrid codes. The simulated SH exhibits characteristics similar to typical EMIC waves with left‐hand polarization and small wave normal angle. The bicoherence index is utilized to reveal the phase coupling between the SH and FW. The necessary conditions, especially for the wave vector relation, are verified from a 2‐D perspective for the first time. Additionally, the amplitude ratios of the SH to the FW and their phase velocities are compared with theoretical results. The comprehensive analyses of this study provide substantial evidence for the SH generation mechanism. Key Points Two‐dimensional (2‐D) hybrid codes are developed to model the nonlinear second‐harmonic (SH) generation of electromagnetic ion cyclotron waves The necessary conditions required by the SH generation mechanism are verified from a 2‐D perspective The theoretical amplitude ratios between harmonics are only satisfied in the SH saturation stage

This work aims to create an ANN-based system for a musical improviser. An artificial improviser of \"hearing\" music will create a melody. The data supplied to the improviser is MIDItype musical data. This is the harmonic-rhythmic course, the background for improvisation, and the previously made melody notes. The harmonic run is fed into the system as the currently ongoing chord and the time to the next chord, while the supplied few dozen notes performed earlier will indirectly carry information about the entire run and the musical context and style. Improvisation training is carried out to check ANN as a correctlooking musical improvisation device. The improviser generates several hundred notes to be substituted for a looped rhythmicharmonic waveform and examined for quality.

Harmonic boundary excitation of localized oscillatory waves in a mass-in-mass metamaterial is studied. It is shown that switch-on/off of the boundary excitation gives rise to a formation of a sequence of such waves, which propagate keeping its form and velocity. The wave formation is achieved only outside the band gap interval of the excitation frequencies. The boundary reflection of the localized oscillatory waves is observed and analysed.

The Martian magnetotail current sheet serves as a critical pathway for ionospheric ion escape. Contrary to the conventional view that external magnetic pressure is balanced mainly by internal ion thermal pressure, we present novel observations from the Mars Atmosphere and Volatile Evolution spacecraft of an electron‐dominated pressure balance configuration. The current sheet electrons exhibit two distinct populations: a thermal core of ionospheric origin and a suprathermal shell of magnetosheath origin. Their bulk temperature reaches up to three times higher than that outside the current sheet. Based on linear instability analysis, we propose two candidate heating mechanisms: (a) Landau resonant or transit‐time heating by magnetosonic waves likely originating from the magnetosheath, and (b) Landau or cyclotron resonant heating by whistler and electron cyclotron harmonic waves generated spontaneously from the shell‐like electron velocity distribution. These results highlight the potentially significant role of plasma waves in sustaining the Martian atmospheric escape channels.

Bicoherence analysis is statistically performed for the oxygen ion cyclotron harmonic (OCH) waves observed by Van Allen Probes. While OCH waves and so‐called electromagnetic ion cyclotron harmonics have indistinguishable spectral characteristics in observation, they are believed to be excited by different mechanisms with the latter being suggested to arise from nonlinear wave‐wave coupling. Our result reveals that most of the OCH wave events have small bicoherence indices, so they are unlikely excited by wave‐wave coupling. The result is not much affected by the parameter choice in the bicoherence analysis, although increasing the subinterval length and/or reducing the subinterval overlap increases the chance of getting large bicoherence index values. Furthermore, the examination of two special events with large bicoherence indices shows that the observed phase relationship among different wave components does not align with the expectation from wave‐wave coupling. The events cannot be convincingly confirmed to be generated through wave‐wave coupling. Plain Language Summary This paper presents a statistical bicoherence analysis study of the oxygen ion cyclotron harmonic (OCH) waves observed by Van Allen Probes. OCH waves have apparent features similar to electromagnetic ion cyclotron (EMIC) harmonics in observation. Previous studies have suggested that OCH waves are excited through the oxygen ion Bernstein instability but EMIC harmonics are generated by nonlinear wave‐wave coupling. Bicoherence analysis is commonly employed for assessing wave‐wave coupling. The results of our bicoherence analysis indicate that most of the OCH events have bicoherence indices less than 0.5, so they are unlikely generated through wave‐wave coupling. The study also demonstrates that the parameter choice in bicoherence analysis affects the calculated index values, but the index values remain mostly less than 0.5 for the various reasonable parameter choices tested. In addition, a detailed analysis of the phase relationship among various electric and magnetic wave components in two specific OCH events reveals that, despite their large bicoherence indices, the observed phase relationship does not align with what would be expected if the waves are generated from wave‐wave coupling. This reminds us that having a large bicoherence index is a necessary but not sufficient condition to prove that waves are generated by wave‐wave coupling. Key Points Most of the oxygen ion cyclotron harmonic (OCH) waves observed by Van Allen Probes have small bicoherence indices Increasing the subinterval length and/or reducing the subinterval overlap increases the chance of getting large bicoherence index values Examination of two special OCH wave events with large bicoherence indices does not support them being generated from wave‐wave coupling