Wave Form Research Articles

Analytical solutions of the Caudrey-Dodd-Gibbon equation using Khater II and variational iteration methods.

This study focuses on solving the Caudrey-Dodd-Gibbon ( ) equation using the Khater II ( ) method and the Variational Iteration ( ) method. The equation is a pivotal mathematical model in nonlinear wave dynamics, essential for understanding the evolution, interaction, and preservation of wave forms in dispersive media. Its applications span various fields, including fluid dynamics, nonlinear optics, and plasma physics, where it plays a crucial role in analyzing solitons and complex wave interactions. In this research, we meticulously implement the and methods to derive solutions for this nonlinear partial differential equation. Our findings reveal new aspects of the equation's behavior, offering deeper insights into nonlinear wave phenomena. The significance of this study lies in its contribution to advancing the understanding of these phenomena and their practical applications in the academic realm. The results underscore the effectiveness of the employed methods, their innovative contributions, and their relevance to applied mathematics.

Computational investigation on the formation of liquid-fueled oblique detonation waves

Utilizing a two-phase supersonic chemically reacting flow solver with the Eulerian-Lagrangian method implemented in OpenFOAM, this study computationally investigates the formation of liquid-fueled oblique detonation waves (ODWs) within a pre-injection oblique detonation wave engine operating at an altitude of 30 km and a velocity of Mach 9. The inflow undergoes two-stage 12.5° compression, followed by uniform mixing with randomly distributed n-heptane droplets before entering the combustor. The study examines the effects of droplet breakup models, gas-liquid ratios, and on-wedge strips on the ODW formation. Results indicate that under the pure-droplet condition, the ODW fails to form within the combustor, irrespective of the breakup models used. However, increasing the proportion of n-heptane vapor in the fuel/air mixture facilitates the ODW formation, because the n-heptane vapor rapidly participates in the gaseous reactions, producing heat and accelerating the transition from low- to intermediate-temperature chemistry. Additionally, the presence of on-wedge strips enhances ODW formation by inducing a bow shock wave within the combustor, which significantly increases the temperature, directly triggering intermediate-temperature chemistry and subsequent heat-release reactions, thereby facilitating the formation of ODW.

WISE J152614.95-111326.4, an Unusual Variable Star

ABSTRACT New time series photometry of WISE J152614.95-111326.4, an eclipsing binary candidate, has been obtained. Full cycles of variation were covered in five filters, ranging from B to z. Archival time series photometry is also available from several sources. The phased light curve shape changes from a double wave form in the red, to a single wave at shorter wavelengths. Analysis of the spectral energy distribution and SALT spectra shows the presence of a cool (∼ 7250−7900 K) white dwarf and an M6 star. The light curves can be explained by a hot spot on the opposing hemisphere of the white dwarf. The star may be in a pre-cataclysmic variable phase with a very low rate of mass flow from the red dwarf to the white dwarf, such that no flickering is evident. Evidence in favour of this hypothesis is that the period of the system (2.25 h) is in the cataclysmic variable period gap. It is speculated that a weak magnetic field associated with the white dwarf funnels accreted material onto a magnetic pole. Amplitudes of the W1 and W2 WISE light curves are anomalously large. The possibility is discussed that variability in this spectral region is primarily driven by electron cyclotron radiation.

Characterisation and synchronisation of a netted software defined radio radar

AbstractThe present work intends to characterise the combination of two netted software defined radios (SDR) and different radio frequency (RF) front‐ends installed in them, together with a two‐stratum time dissemination and synchronisation system. A modified implementation of the Network Time Protocol is used as coarse event synchronisation for either SDR back‐end. The White rabbit light embedded node implementation of the commonly known white rabbit synchronisation system (IEEE 1588 PTP‐2019) or arbitrary wave form generators are used as fine time dissemination system for either SDR. The resulting netted transceiver system is intended to compose a demonstrator for proof‐of‐concept experiments. The findings presented in this article show that the chosen combination of hardware and software is suitable for radar applications operating within L‐, S‐ and C‐bands. A channel coherency throughout the network with a relative modified Allan deviation of less than 80 fs for averaging intervals of 1 s, a phase noise better than −118 dBc/Hz at 10 Hz frequency offset and a fractional frequency lower than was measured. Within a single transceiver node, a fractional frequency lower than and phase noise of −124 dBc/Hz at 10 Hz frequency offset were measured as well. Multistatic radar systems exploit wide spatial diversity to enhance target detection and tracking, albeit with increased complexity when compared to a monostatic configuration. To exploit these benefits, all participating transceiver nodes within the netted radar need to synchronise to a common time base . The achieved synchronisation level increases the accuracy with which the chain of timed events at the transmitter and at the receiver side occur, intending to maximise the signal‐to‐noise ratio available at the receiver. The Universal software radio peripheral model X310 with two different daughterboard models as RF front‐end was used as SDR on either radar node. A network combining data and synchronisation purposes allowed the radar nodes under test to operate synchronously. The two‐stratum synchronisation system used glass fibres between 2 m and 5 km of length or coaxial cables with 2 m in length for network traffic, time and frequency dissemination purposes. The multiple RF front‐ends were stimulated by means of arbitrary waveform generators with calibrated traceability. Up‐chirp and sinusoid waveforms were used as stimuli for measuring the offset of either channel with regards of to ultimately estimate the achievable coherency limits of the system under test. Both analogue and digital evaluation methods were considered.

On the evolution of the shock waves systems created by the fan blades

Fan is one of the noise sources in a modern engine. The fan noise is especially noticeable during takeoff at high angular rotation speeds. In such operating modes, supersonic flow around the tips of the fan blades is realized, which leads to the formation of shock waves that propagate upstream until they exit of the engine channel. As a result, a specific noise is emitted into the front hemisphere, consisting of harmonics that are multiples of the fan rotation frequency. The paper analyzes the described effect based on a simple model of the propagation of a shock waves system. By using energy analysis, it is shown that the system of shock waves with equal amplitude decays faster than a system of shock waves with a spread in amplitude.

Nonlinear Perturbations and Weak Shock Waves in Isentropic Atmospheres

Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of part of the stellar envelope. While accurate analytic solutions to the fluid equations exist in the limits of low-amplitude waves or strong shocks, connecting these phases generally requires simulations. We address this problem using the fact that the plane-parallel Euler equations, in the presence of a constant gravitational field, admit exact Riemann invariants when the flow is isentropic. We obtain exact solutions for acoustic perturbations and show that after they steepen into shock waves, Whitham’s approximation can be used to solve for the shock’s dynamics in the weak to moderately strong regimes, using a simple ordinary differential equation. Numerical simulations show that our analytic shock approximation is accurate up to moderate (∼few–15) Mach numbers, where the accuracy increases with the adiabatic index.

General theory of diaphragm rupture in a shock tunnel

As the flow field starting device is in a shock tunnel, the rupture performance of the diaphragm directly influences the successful formation of the shock wave. The general theory of diaphragm rupture in shock tunnels is proposed first in this paper. The reasons for diaphragm rupture are explained fundamentally. The existing ideologies on diaphragm rupture are unified, and two hypotheses with corresponding methods are introduced. In the ideal diaphragm, diaphragm rupture pressure or rupture time can be predicted by considering the diaphragm opening as a throat through a diaphragm opening aperture. In the non-ideal diaphragm, the control of diaphragm rupture pressure can be realized by considering nominal rupture stress and grooved thickness. The correctness of the general theory of diaphragm rupture is proved through argumentation and based on experimental results of the literature. The general theory of diaphragm rupture can be used to predict the diaphragm rupture behavior of any shock tunnel worldwide and avoid the risk of shearing of petals on the diaphragm caused by the impact load. A new system of diaphragm rupture theory is constituted, and it is of significant importance for the efficient operation of shock tunnel equipment.

Solving Viscous Burgers’ Equation: Hybrid Approach Combining Boundary Layer Theory and Physics-Informed Neural Networks

In this paper, we develop a hybrid approach to solve the viscous Burgers’ equation by combining classical boundary layer theory with modern Physics-Informed Neural Networks (PINNs). The boundary layer theory provides an approximate analytical solution to the equation, particularly in regimes where viscosity dominates. PINNs, on the other hand, offer a data-driven framework that can address complex boundary and initial conditions more flexibly. We demonstrate that PINNs capture the key dynamics of the Burgers’ equation, such as shock wave formation and the smoothing effects of viscosity, and show how the combination of these methods provides a powerful tool for solving nonlinear partial differential equations.

Quantification of Sarcoplasmic Reticulum Ca2+ Release in Primary Ventricular Cardiomyocytes.

In the heart, ion channels generate electrical currents that signal muscle contraction through changes in intracellular calcium concentration, i.e., [Ca2+]. The cardiac ryanodine receptor type 2 (RyR2) is the predominant ion channel responsible for increasing intracellular [Ca2+] by releasing Ca2+ from the sarcoplasmic reticulum (SR). Timely Ca2+ release is necessary for appropriate cardiac function, and dysfunction can cause or contribute to life-threatening diseases such as arrhythmia. Quantification of SR-Ca2+ release in the form of sparks and waves can provide valuable insight into RyR2 opening, and factors that influence or regulate channel function. Here, we provide a series of protocols that outline processes for (1) obtaining high-quality isolated cardiomyocytes, (2) preparing samples for experimentally investigating factors that influence RyR2 function, and (3) data acquisition and analysis. Notably, our protocols leverage the potency of the recently developed myosin ATPase inhibitor, Mavacamten. This affords the opportunity to characterize the effects of small molecules or reconstituted proteins/enzymes on RyR2-Ca2+ release events across a range of [Ca2+]. © 2024 Wiley Periodicals LLC. Basic Protocol 1: Cardiomyocyte isolation from mouse Basic Protocol 2: Preparation of cardiomyocytes for Ca2+ imaging Basic Protocol 3: Confocal microscopy and quantitative Ca2+ analysis using SparkMaster 2.

Dynamic interface printing

Additive manufacturing is an expanding multidisciplinary field encompassing applications including medical devices1, aerospace components2, microfabrication strategies3,4 and artificial organs5. Among additive manufacturing approaches, light-based printing technologies, including two-photon polymerization6, projection micro stereolithography7,8 and volumetric printing9–14, have garnered significant attention due to their speed, resolution or potential applications for biofabrication. Here we introduce dynamic interface printing, a new 3D printing approach that leverages an acoustically modulated, constrained air–liquid boundary to rapidly generate centimetre-scale 3D structures within tens of seconds. Unlike volumetric approaches, this process eliminates the need for intricate feedback systems, specialized chemistry or complex optics while maintaining rapid printing speeds. We demonstrate the versatility of this technique across a broad array of materials and intricate geometries, including those that would be impossible to print with conventional layer-by-layer methods. In doing so, we demonstrate the rapid fabrication of complex structures in situ, overprinting, structural parallelization and biofabrication utility. Moreover, we show that the formation of surface waves at the air–liquid boundary enables enhanced mass transport, improves material flexibility and permits 3D particle patterning. We, therefore, anticipate that this approach will be invaluable for applications where high-resolution, scalable throughput and biocompatible printing is required.

Solitary wave form of reaction rate in graphite diffusive medium using different neutron absorbers

Abstract Graphite nuclear properties such as moderating power and absorption cross-section, are not as good as those of heavy water. But its pure form can be prepared. Its structural and thermal properties are good and it has a high thermal conductivity. The thermal neutron in graphite performs an average of 1,200 scattering collisions before it is absorbed. This very low absorption cross section makes graphite as an ideal material for applications in nuclear reactors. In the current research, graphite is assumed as a diffusive medium due to its low absorption cross-section (0.0035 b) and having a low mass close to the neutron mass. In this medium: Boron (10B), Cadmium (113Cd), Samarium (149Sm), Europium (151Eu), Hafnium (177Hf) and Gadolinium (157Gd), separately are also considered as neutron absorbers. The aim of this paper is obtaining the solitary wave form of reaction rate in graphite diffusive medium using these neutron absorbers.

Incoherence-to-coherence crossover observed in charge-density-wave material 1T-TiSe2

Analogous to the condensation of Cooper pairs in superconductors, the Bose–Einstein condensation (BEC) of electron–hole pairs in semiconductors and semimetals leads to an emergence of an exotic ground state — the excitonic insulator state. In this paper, we study the electronic structure of 1T-TiSe2 utilizing angle-resolved photoemission spectroscopy and alkali-metal deposition. Alkali-metal adatoms are deposited in-situ on the sample surface, doping the system with electrons. The conduction bands of 1T-TiSe2 are thereby pushed down below the Fermi energy, which enables us to characterize its temperature dependence with precision. We found that the formation of the charge density wave (CDW) in 1T-TiSe2 at ~ 205 K is accompanied by a significant increase of the band gap, supporting the existence of excitonic pairing in the CDW state of 1T-TiSe2. More importantly, by analyzing the linewidth of the single-particle excitation spectrum, we unveiled an incoherence-to-coherence crossover at 165 K, which could be attributed to a possible exciton condensation that occurs beneath the CDW transition in 1T-TiSe2. Our results not only explain the exotic transport properties of 1T-TiSe2, but also highlight the possible existence of an excitonic condensate in this semiconducting material.

Effects of internal intervention in tubes on shock wave attenuation, formation and propagation of flame during high-pressure hydrogen release

Experiments on the impacts of the combination of fin structure and expansion chamber on shock wave attenuation, hydrogen ignition, and flame characteristics during high-pressure hydrogen release were carried out. The fin is a four-edged platform hollowed out on all sides. The inflated upper and lower tube walls are located 85, 95, and 105 mm away from the nickel burst disk. With the incident shock wave traveling through the fin, the reflected shock and the superposition of multiple reflected shock waves appear, and the reflected shock wave intensity can equal that of the release pressure. The decrease of the incident shock wave intensity behind the fin leads to the decrease of the non-uniformity of the mixed layer temperature, further causing the decrease of the flame propagation velocity. The presence of fins increases the probability of ignition in the fin region and the critical release pressure for ignition is significantly lower than that in the barrier free tube, mainly because the fin inside intensifies the hydrogen/air mixture, resulting in a lower minimum ignition energy required for self-ignition. Furthermore, the decrease of flame propagation velocity leads to the increase of hydrogen consumption inside the tube and the decrease of shock overpressure outside.

EFFECT OF EXTERNAL HARMONIC VIBRATION ON THE FORMATION OF SOLITARY WAVES IN FALLING TWO-LAYER LIQUID FILMS

Abstract We study the influence of a low-frequency harmonic vibration on the formation of the two-dimensional rolling solitary waves in vertically co-flowing two-layer liquid films. The system consists of two adjacent layers of immiscible fluids with the first layer being sandwiched between a vertical solid plate and the second fluid layer. The solid plate oscillates harmonically in the horizontal direction inducing Faraday waves at the liquid–liquid and liquid–air interfaces. We use a reduced hydrodynamic model derived from the Navier–Stokes equations in the long-wave approximation. Linear stability of the base flow in a flat two-layer film is determined semi-analytically using Floquet theory. We consider sub-millimetre-thick films and focus on the competition between the long-wavelength gravity-driven and finite wavelength Faraday instabilities. In the linear regime, the range of unstable wave vectors associated with the gravity-driven instability broadens at low and shrinks at high vibration frequencies. In nonlinear regimes, we find multiple metastable states characterized by solitary-like travelling waves and short pulsating waves. In particular, we find the range of the vibration parameters at which the system is multistable. In this regime, depending on the initial conditions, the long-time dynamics is dominated either by the fully developed solitary-like waves or by the shorter pulsating Faraday waves.

Ignition and Combustion of Aluminum Hydride Dust Aerosols

ABSTRACT The results of comparative experimental studies of aluminum hydride AlH3 and aluminum Al particle aerosols, in particular, of the critical conditions for auto-ignition and the features of the flame propagation in low-volume (V ≈ 5.1·10−3 m3) and large clouds (volume is varied from 40 to 60 m3) are presented in this article. Experiments have shown that for aerosols of AlH3 particles, the auto-ignition temperature is much lower than for aluminum particles. This is due to the thermal decomposition of aluminum hydride into hydrogen and active aluminum. The laminar flame was studied in low-volume clouds. A two-frontal form of a laminar flame wave in AlH3 aerosol was found. Moreover, the visible flame propagation speeds for AlH3 correspond to those for finely dispersed Al and are two times higher compared to coarse Al. The turbulent flame in the large free clouds of aluminum hydride dusts has flame propagation speeds several times higher than those in the aluminum clouds and is characterized by the formation of a toroid vortex with a complex internal structure.

Mechanism of Spontaneous Acceleration of Slow Flame in Channel

This paper is devoted to the numerical analysis of the spontaneous acceleration of a slow flame in a semi-closed channel. In particular, the flow development in the channel ahead of the propagating flame is analyzed. The applied detailed numerical model allows the clear observation of all features intrinsic to the reacting flow evolution in the channel, including the formation of perturbations on the scale of the boundary layer and their further development. In all considered cases, perturbations of the boundary layer emerge in the early stages of flame acceleration and decay afterward. The flow stabilizes more rapidly in a narrow channel, where the velocity profile is close to the Poiseuille profile. At the same time, the compression waves generated in the reaction zone travel along the channel. The interaction between compression waves in the area of combustion products can lead to the formation of shock waves. The effect of shock waves on the flow in the fresh mixture causes an increase in the flame area and a corresponding flame acceleration. In addition, shock waves trigger boundary-layer instability in wide channels. The perturbations of the boundary layer grow and evolve into vortexes, while further vortex–flame interaction leads to significant flame acceleration.

Feasibility Assessment of Rapid Response EEG in the Identification of Nonconvulsive Seizures During Military Medical Air Transport.

Traumatic brain injury often requires neurologic care and specialized equipment, not often found downrange. Nonconvulsive seizures (NCSs) and nonconvulsive status epilepticus (NCSE) occur in up to 30% of patients with moderate or severe traumatic brain injury and is associated with a 39% morbidity and an 18% mortality. It remains difficult to identify at bedside because of the heterogeneous clinical manifestations. The primary diagnostic tool is an electroencephalogram (EEG) which is large, requires an external power source, and requires a specialized technician and neurologist to collect and interpret the data. Rapid response EEG (rr-EEG) is an FDA-approved device that is pocket sized and battery powered and uses a disposable 10-electrode headset. Prior studies have demonstrated the noninferiority of rr-EEG in the identification of NCSE and NCS as compared to conventional EEG in hospitals. An unanswered question is whether rr-EEG could be used in the identification of NCSE and NCS by medics. In conjunction with the Critical Care Air Transport (CCAT) team, a simulation was created and implemented on a CCAT training mission. The simulation team included a neurology resident, who oversaw the simulation, a pulmonary critical care fellow, an intensive care unit nurse, and a respiratory therapy. A survey was provided before and after the simulation. The team was expected to review the rr-EEG to make clinical decisions during ground transport, takeoff, and landing. The neurology resident monitored and recorded the team's ability to distinguish between NCS and a normal EEG. In between, the neurology resident monitored the quality of the EEG for potential interference and loss of quality. The CCAT team was able to efficiently set up the rr-EEG on a patient manikin, correctly identify visual EEG wave forms of a patient in NCS, and utilize the proprietary audio program of a simulated patient in NCS. The team reported that the device was easily set up in the environment, and the data were interpretable despite vibration, aircraft auditory and electrical noise, and the ergonomics of the aircraft medical section. This pilot study has validated a potentially revolutionary technology in medical transport. The rr-EEG technology is measurably user-friendly and will improve patient outcomes. This device and simulation can reduce time to an EEG by hours to days allowing for immediate treatment and intervention, which can significantly reduce morbidity and mortality.

Using Piezoelectric Elements to Convert Bio-Mechanical Pulsations into Electrical Energy for Energy Harvesting

On the Internet of Things (IoT) where all electronic devices are connected to the internet, a secure power supply is necessary. Energy harvesting technology is attracting attention as ”enabling technology” that expands the use and opportunities of IoT utilization. This technology harvests energy that dissipates around us, in the form of electromagnetic waves, heat, vibration, etc. and converts it into easy-to-use electric energy. Alternating current signals can be extracted from bio-mechanical pulsations using skin-attached piezoelectric elements with a protrusion, as we reported previously. However, we found that the maximum voltage of the extracted signal was unstable and low. This study demonstrates that piezoelectric elements can be stacked to stabilize and increase the maximum voltage, and that the extracted signal can be used to charge a capacitor, after rectification using a voltage-doubler rectifier circuit with Schottky barrier diodes.

Formation of a magnetized hybrid star with a purely toroidal field from phase-transition-induced collapse

ABSTRACT Strongly magnetized neutron stars are popular candidates for producing detectable electromagnetic and gravitational-wave signals. Gravitational collapses of neutron stars triggered by a phase transition from hadrons to deconfined quarks in the cores could also release a considerable amount of energy in the form of gravitational waves and neutrinos. Hence, the formation of a magnetized hybrid star from such a phase-transition-induced collapse is an interesting scenario for detecting all these signals. These detections may provide essential probes for the magnetic field and composition of such stars. Thus far, a dynamical study of the formation of a magnetized hybrid star from a phase-transition-induced collapse has yet to be realized. Here, we investigate the formation of a magnetized hybrid star with a purely toroidal field and its properties through dynamical simulations. We find that the maximum values of rest-mass density and magnetic field strength increase slightly and these two quantities are coupled in phase during the formation. We then demonstrate that all microscopic and macroscopic quantities of the resulting hybrid star vary drastically when the maximum magnetic field strength goes beyond a threshold of $\sim 5 \times 10^{17}$ G, but they are insensitive to the magnetic field below this threshold. Specifically, the magnetic deformation makes the rest-mass density drop significantly, suppressing the matter fraction in the mixed phase. These behaviours agree with those in the equilibrium models of previous studies. Therefore, this work provides a solid support for the magnetic effects on a hybrid star.

Self-induced transparency of long water waves over bathymetry: the dispersive shock mechanism

The shoreline hazard posed by ocean long waves such as tsunamis and meteotsunamis critically depends on the fraction of energy transmitted across the shallow near-shore shelf. In linear setting, bathymetric inhomogeneities of length comparable to the incident wavelength act as a protective high-pass filter, reflecting long waves and allowing only shorter waves to pass through. Here, we show that, for weakly nonlinear waves, the transmitted energy flux fraction can significantly depend on the amplitude of the incoming wave. The basis of this mechanism is the formation of dispersive shock waves (DSWs), a salient feature of nonlinear evolution of long water waves, often observed in tidal bores and tsunami/meteotsunami evolution. Within the framework of the Boussinesq equations, we show that the DSWs efficiently transfer wave energy into the high wavenumber band, where reflection is negligible. This is phenomenologically similar to self-induced transparency in nonlinear optics: small amplitude long waves are reflected by the bathymetric inhomogeneity, while larger amplitude waves that develop DSWs blueshift into the transparency regime and pass through. We investigate this mechanism in a simplified setting that retains only the key processes of DSW disintegration and reflection, while the effects such as bottom dissipation and breaking are ignored. The results suggests that the phenomenon is a robust, order-one effect. In contrast, the increased transmission due to the growth of bound harmonics associated with the steepening of the wave is weak. The results of the simplified modelling are validated by simulations with the FUNWAVE-TVD Boussinesq model.