Wave Trajectories Research Articles

Mapping of power deposition zone of electron Bernstein waves externally excited in tokamak plasmas

In toroidal plasmas, electron Bernstein (EB) waves mode-converted from X waves at the upper hybrid resonance (UHR) layer propagate toward the higher field side and are cyclotron-damped away at Doppler shifted frequency before arriving at the electron cyclotron resonance (ECR) layer. Resulting power deposition profile depends on local density, temperature and field profiles and is usually analyzed using the ray tracing technique for EB wave propagation and absorption in inhomogeneous magnetized plasmas. In axisymmetric tokamak plasmas, the ray tracing equation of EB waves can be cast into the form of equation of particle motion in a potential field. The particle trajectory and its momentum correspond to the wave trajectory and the refractive index, respectively. The potential field reflects the dispersion characteristics of EB waves, that is, the perpendicular refractive index strongly increases as the waves approach to the ECR layer from the lower field side, making a deep trench of potential along the ECR layer. Therefore the EB waves perpendicularly approach the ECR layer, which enable us to estimate the parallel refractive index and the parallel velocity of resonance electrons near the ECR layer. Thus, possible power deposition zone can be mapped and the associated current drive efficiency is roughly estimated directly from the information on wave frequency and plasma profiles without ray tracing calculations (direct mapping). The mapped zone, in the case of a moderately over dense plasma, is shown to be coincident with the ray tracing results for both XB and OXB schemes of mode conversion. In the cases of highly over dense, low safety factor and low aspect ratio plasmas, ω/Ωce is rather close to two at the UHR layer and the second harmonic cyclotron damping can take place along the ray trajectory just after OXB mode conversion, depending on the parameters. Here, ω is the wave frequency and Ωce is the local cyclotron frequency. It is shown that direct mapping also works in this case as well. The direct mapping technique is based on above picture of EB wave propagation and absorption, and is useful to guide the ray tracing analyses and cross-check the ray tracing results.

Self-similar Piston-Shock and CME

Based on a dimensional analysis, we discuss the existence conditions for one-dimensional self-similar solutions to the problem of a piston extending into an inhomogeneous plasma with magnetic field. In these solutions, the Mach number of a shock wave ahead of the piston is constant. As an application, we consider the SOL2010-06-13 solar eruptive event, where this property was found for a coronal wave at the formation stage of a coronal mass ejection (CME). Using a known wave trajectory in the distance–time plane, it is possible to follow the trajectory of an effective (virtual) piston that is a driver of the wave. The trajectory of the virtual piston originates in an eruptive filament during its impulsive acceleration and terminates at a rim bounding an apparent CME bubble in extreme-ultraviolet images, when the rim appears. The velocity of the rim at that time is approximately equal to the fast-mode speed at this place before the expansion onset, and the shock-front has a speed corresponding to a Mach number of about 1.5. We also discuss an analogy between the shock-wave propagation caused by the eruption of a solar magnetic flux-rope and the inverse-pinch effect as known from laboratory plasma physics.

An inverse method for the equation of state of detonation products from underwater explosion tests

Since the information of detonation product is transmitted outward in the form of compression wave during underwater explosion, the purpose of this paper is to explore how to determine the equation of state (EOS) of detonation products using underwater explosion tests. Compared with conventional cylinder test, underwater explosion test has the advantages of simpler equipment, lower cost, less limited charge size, and wider range of calibration pressures, which makes it more suitable for the on-site testing of large or non-ideal explosives. Based on the measurable shock wave trajectory and post-shock pressure history in general underwater explosion test, an inverse method of characteristics (inverse MOC) is proposed to recover the gas-water interface from the shock and post-shock data, and a genetic algorithm is developed to determine the EOS of detonation products by the gas-water interface. Compared with virtual experimental data extracted from underwater explosion simulations, it is found that the inverse MOC can properly reproduce the position and pressure of gas-water interface. The lower limit of pressure range is close to 2 MPa, which is far lower than that of 0.1 GPa in cylinder test. Based on the inversed results of gas-water interface, it is also confirmed that the genetic algorithm can also stably optimize the parameters of JWL equation because the isentrope pressure error of eight commonly used explosives is less than 3% in the range of detonation pressure 0.01 GPa. The results show that it is by the inverse MOC and genetic algorithm that the EOS of detonation products can be properly and stably determined by the underwater explosion test data.

Design and fabrication of a new piezoelectric paper feeder actuator without mechanical parts

A piezoelectric paper feeder actuator using Micro Virtual Roller (MVR) is proposed, designed, fabricated and tested. This actuator can drive a sheet of paper forward or backward without any mechanical parts, such as the costly and heavy rollers used in traditional paper feeders. In this paper feeder actuator, two vibrating stators which produce traveling waves are used to drive the paper. The vibrations of the stators are similar to those of piezoelectric motors and follow a similar procedure to move the paper. A feasibility study simulated the actuator in COMSOL Multiphysics Software. Traveling wave and elliptical trajectories were obtained and the dimensions of the stator were optimized using FEM so that the paper could move at top speed. Next, the eigenfrequencies of the actuator was determined. Experimental testing was done in order to validate the FEM results that revealed the relationships between speed and parameters such as frequency and voltage. Advantages of this new mechanism are the sharp decrease in power consumption and low maintenance.

A novel sub-epidemic modeling framework for short-term forecasting epidemic waves

BackgroundSimple phenomenological growth models can be useful for estimating transmission parameters and forecasting epidemic trajectories. However, most existing phenomenological growth models only support single-peak outbreak dynamics whereas real epidemics often display more complex transmission trajectories.MethodsWe develop and apply a novel sub-epidemic modeling framework that supports a diversity of epidemic trajectories including stable incidence patterns with sustained or damped oscillations to better understand and forecast epidemic outbreaks. We describe how to forecast an epidemic based on the premise that the observed coarse-scale incidence can be decomposed into overlapping sub-epidemics at finer scales. We evaluate our modeling framework using three outbreak datasets: Severe Acute Respiratory Syndrome (SARS) in Singapore, plague in Madagascar, and the ongoing Ebola outbreak in the Democratic Republic of Congo (DRC) and four performance metrics.ResultsThe sub-epidemic wave model outperforms simpler growth models in short-term forecasts based on performance metrics that account for the uncertainty of the predictions namely the mean interval score (MIS) and the coverage of the 95% prediction interval. For example, we demonstrate how the sub-epidemic wave model successfully captures the 2-peak pattern of the SARS outbreak in Singapore. Moreover, in short-term sequential forecasts, the sub-epidemic model was able to forecast the second surge in case incidence for this outbreak, which was not possible using the simple growth models. Furthermore, our findings support the view that the national incidence curve of the Ebola epidemic in DRC follows a stable incidence pattern with periodic behavior that can be decomposed into overlapping sub-epidemics.ConclusionsOur findings highlight how overlapping sub-epidemics can capture complex epidemic dynamics, including oscillatory behavior in the trajectory of the epidemic wave. This observation has significant implications for interpreting apparent noise in incidence data where the oscillations could be dismissed as a result of overdispersion, rather than an intrinsic part of the epidemic dynamics. Unless the oscillations are appropriately modeled, they could also give a false positive, or negative, impression of the impact from public health interventions. These preliminary results using sub-epidemic models can help guide future efforts to better understand the heterogenous spatial and social factors shaping sub-epidemic patterns for other infectious diseases.

Manipulating Elastic Waves with Conventional Isotropic Materials

Controlling the trajectory of general elastic waves with metamaterials is very difficult, because the classical elastic wave equations are not form-invariant. However, this study points out that the elastodynamic potential energy can nearly retain its form after conformal mapping, if the longitudinal wave velocity is much greater than the transverse. Based on this finding, an elastic-wave bender is designed and fabricated using two types of conventional rubber, and is verified as an efficient vibration isolator with a broad operating bandwidth. It even breaks the limit on damping ratios required by classical passive-vibration theory.

A model for the trajectory of the transverse detonation resulting from re-initiation of a diffracted detonation

A semi-analytical model is presented for predicting the trajectory of the transverse detonation during the re-initiation process of a diffracted cellular detonation wave from a channel. Numerical simulations based on the two-dimensional reactive Euler equations with a detailed hydrogen/oxygen chemistry model were first performed to observe key characteristics of cellular detonation wave diffraction and to obtain required input parameters for the model construction. The present numerical observations indicate that the transverse detonation stems from a location on the expansion wave front, and the horizontal distance from this initial location to the channel exit can be scaled by a constant multiplied by the detonation cell width for large deviation angles of the channel. The velocity of the transverse detonation basically equals the Chapman–Jouguet detonation wave velocity consisting of two orthogonal components: the expansion velocity of the diffracted wave front and the relative velocity to the diffracted wave front. The shape of the decoupled wave front is not affected by local explosion and thus can be predicted by the Chester–Chisnell–Whitham theory. Based on these numerical observations and the Chester–Chisnell–Whitham theory, a semi-analytical model is constructed to predict the wave trajectories as well as the distances of the wall reflection point for various deviation angles and initial pressures. The model prediction agrees with the corresponding numerical results. The model result shows that the distance of the wall reflection point varies from 15 to 20 multiples of the cell width with a minimal dependence on deviation angle, independent of the initial pressure. The trajectory calculated by the model is self-similar and determined by the horizontal distance of the initial location. The dimensionless trajectories divided by the horizontal distance are coincident for different initial pressures.

Complex-Periodic Spiral Waves Induced by Linearly Polarized Electric Field in the Excitable Medium

Complex-periodic spiral waves are investigated extensively in the oscillatory medium. In this paper, the linearly polarized electric field (LPEF) is employed to induce complex-periodic spiral waves in the excitable medium with abnormal dispersion. As the amplitude of LPEF is increased beyond a threshold, the simple-periodic spiral wave converts into an irregularly complex-periodic one, in which, the local dynamics exhibit several regular spikes followed by one missed spiking period. Furthermore, with the increase of the LPEF amplitude, the missed spiking period follows different numbers of regular spikes [so-called period-1 (P-1), period-2 (P-2), etc.], even a mix of different periods. Meanwhile, the wavelength of the spiral wave transits from a short to a longer one. The pure-periodic (from P-6 to P-2) spirals generally contain defect lines, across which the phase of local oscillation changes by [Formula: see text]. In contrast, there is no defect line in the mixed-periodic spiral waves. This finding indicates that the defect line is not a necessary feature for complex-periodic spiral waves. Moreover, three types of tip trajectories of pure-periodic spiral waves are identified depending on the periods. That is, the outward-petal meandering, the outward-petal meandering with slow modulation, and drifting tip motion, and the tip trajectories could be used to distinguish them from the complex-oscillatory spiral waves.

Modeling the HF Ray Trajectories and Vertical and Oblique Ionograms in the Artificially Disturbed Ionosphere Based on Radiotomographic Data

This paper presents the results of numerical simulation of the propagation of HF radio waves in the artificially disturbed ionosphere during launch of the Tsyklon-3 carrier rocket from the Plesetsk cosmodrome on December 18, 1991, and an industrial high-power explosion with a magnitude of M = 2.4 on the Kola Peninsula on April 8, 1990. A specially developed software package in Python programming language allows three-dimensional modeling of ray trajectories in the geometric optics approximation by solving a bicharacteristic system for the eikonal equation. The geomagnetic field is specified according to the IGRF model, and the ionospheric electron density distribution is specified according to radio tomography data. The ionogram modeling is performed using a three-dimensional shooting method based on the Nelder—Mead simplex minimization. It is shown that the artificial ionospheric irregularities that arise during the periods of the considered events are quasi-wave perturbations that have a significant effect on the ray trajectories of HF radio waves and ionograms of vertical and oblique sounding. This effect manifests itself in the form of characteristic peculiarities of ray trajectories with multiple reflections from the local maxima of the electron density and additional traces on ionograms caused by the passage of traveling ionospheric disturbances above the sounding system.

Design and Simulation of Robotic Arm PD Controller Based on PSO

This paper deals with design and simulation of Proportional plus Derivative (PD) controller for two links robotic arm. The PD controller was used to compute the required joint’s torque for tracking the desired trajectory. The Particle Swarm Optimization (PSO) algorithm has been used in order to tune the gains of the proportional and derivative parts of PD controller. Simulation results show an efficient and robust behavior of the proposed controller. Two cases of simulation tests were carried out. The first was tracking a sine wave trajectory while the second was tracking the same trajectory with the presence of disturbance torque on the dynamic model of the robotic arm. The simulation results were compared with the presence of disturbance torque on the dynamic model of the robotic arm. The simulation results were compared with the results obtained by other researchers, for similar robotic arm properties and same trajectory. The proposed controller offers a simple method for trajectory tracking problem with a satisfactory efficiency. A Mean Square Error (MSE) criterion was used to study the efficiency of the proposed controller in tracking the desired trajectory.

Two improved displacement shallow water equations and their solitary wave solutions

Two improved displacement shallow water equation (DSWE) are constructed by applying the Hamilton variational principle under the shallow water approximation. The first one is the extended DSWE (EDSWE), which contains a higher order nonlinear term omitted in the original DSWE; and the second one is the fully nonlinear DSWE (FNDSWE) which contains all the nonlinear terms. By using the exp-function method, the EDSWE is analyzed and different types of waves, including the regular solitary wave, the loop solitary wave, the solitary wave with a sharp peak, and the periodic wave, are obtained. The exact solitary wave solution of the FNDSWE is also obtained. It is proved that under the shallow water approximation, the particle trajectory of the solitary wave is a parabolic curve.

Evolution of a shock wave generated by underwater electrical explosion of a single wire

The results of an experimental, analytical, and numerical study of the cylindrical shock wave generated by the underwater electrical explosion of copper and aluminum wires are reported. Experiments were conducted using a microsecond timescale generator delivering ∼180 kA pulses with a 1.2 μs rise time. Shadow streak images were used to study the radial expansion of the exploding wire and the generated shock wave. It was found that the shock wave expansion velocity decreases to the velocity of sound in two stages: a fast stage and then a gradual stage. The fast stage occurs during ∼1.5 μs after the maximum of the resistive voltage is reached, and then, a gradual decrease occurs during several tens of microseconds. It was shown that the duration of the fast stage corresponds to the period of time when the main energy deposition into the wire occurs. Hydrodynamic simulations show that the fast decrease in the shock velocity is related to the evolution of the exploded wire's subsonic expansion, which leads to time/spatial compression of the adjacent water layer. For the gradual decrease stage of the shock wave velocity, we developed a simplified model, which considers uniform water density between the wire boundary and the shock wave front. The results of this model agree satisfactorily with the experimentally obtained shock wave trajectory and radial expansion of the wire.

Acoustic flat lensing using an indefinite medium

Acoustic flat lensing is achieved here by tuning a phononic array to have indefinite medium behaviour in a narrow frequency spectral region along the acoustic branch. This is confirmed by the occurrence of a flat band along an unusual path in the Brillouin zone and by interpreting the intersection point of isofrequency contours on the corresponding isofrequency surface; coherent directive beams are formed whose reflection from the array surfaces create lensing. Theoretical predictions are corroborated by time-domain experiments, airborne acoustic waves generated by a source with a frequency centered about $10.6$ kHz, placed at three different distances from one side of a finite phononic crystal slab, constructed from polymeric spheres, yield distinctive focal spots on the other side. These experiments evaluate the pressure field using optical feedback interferometry and demonstrate precise control of the three-dimensional wave trajectory through a sonic crystal.

Experimental investigation on turning characteristics of KVLCC2 tanker in regular waves

Manoeuvring performance of a ship in actual sea is significantly different from that in calm water due to wave loads. It is necessary to estimate the ship's manoeuvrabilities in waves at the early design stage for its safe operations. Several theoretical approaches have been attempted to estimate the manoeuvring performance of ships with considerations of wave loads in recent decades, but there are insufficient model test data for the validation of numerical results. In this study, free-running model tests are systematically performed for well-known KVLCC2 tanker. Model tests are carried out in a square basin, regular waves are generated with the variations of directions, lengths, and heights. In particular the wave lengths are selected at around the ship length. The number of propeller revolution is determined for the model speed corresponded to full-scale service speed in calm water, that rps is fixed in all runs. Therefore the loss of approach speed is observed depending on the encountered wave conditions. Encountered wave profiles are estimated by using relative wave heights data measured on the side of deck in real time, the rudder is always deflected at the moments when the wave crest passes on the midship of the model. The timing of rudder deflection has little influence on the low frequency manoeuvring motions of the model ship. Drifting distances of turning trajectories are relatively large when the wave lengths are below the ship length, and relative drifting angles between wave propagation direction and trajectory drifting direction are largest when the wave lengths equal to the ship length. Drifting distances and relative drifting angles increase with increasing wave heights. Although the trajectories at the early stage of turns are varied depending on encountered waves, drifting distance and angles during steady turns are similar if the wave height and length are identical. Based on the present test results, it is appropriate that the trajectory drifting distances and angles are defined as the magnitude and direction of a vector between two positions with the headings of 360° and 720°. Finally, the effects of velocity fluctuations on the trajectory drifts are analyzed in some cases.

Propagating, Evanescent, and Complex Wavenumber Guided Waves in High-Performance Composites.

The study of propagating, evanescent and complex wavenumbers of guided waves (GWs) in high-performance composites using a stable and robust semi-analytical finite element (SAFE) method is presented. To facilitate understanding of the wavenumber trajectories, an incremental material change study is performed moving gradually from isotropic aluminum alloy to carbon fiber reinforced polymer (CFRP) composites. The SAFE results for an isotropic aluminum alloy plate are compared with the exact analytical solutions, which shows that N = 20 SAFE elements across the thickness provides <0.5% error in the highest evanescent wavenumber for the given frequency-wavenumber range. The material change study reveals that reducing the transverse and shear moduli moves the wavenumber solution towards one similar to composite material. The comparison of the propagating, evanescent and complex wavenumber trajectories between composites and aluminum alloy show that antisymmetric imaginary Lamb wave modes always exist in composites although they may not exist in isotropic aluminum alloy at some frequencies. The wavenumber trajectories for a unidirectional CFRP plate show that the range of real wavenumber is much smaller than in the isotropic aluminum alloy. For laminated CFRP composite plates (e.g., unidirectional, off-axis, transverse, cross-ply and quasi-isotropic laminates), the quasi Lamb wave and shear horizontal (SH) wave trajectories are also identified and discussed. The imaginary SH wave trajectories in laminated composites are distorted due to the presence of ±45 plies. The convergence study of the SAFE method in various CFRP laminates indicates that sufficient accuracy can always be achieved by increasing the number of SAFE elements. Future work will address the stress-continuity between composite layers.

The influence of building interactions on seismic and elastic body waves

We outline some recent research advances on the control of elastic waves in thin and thick plates, that have occurred since the large scale experiment [S. Brûlé, Phys. Rev. Lett. 112, 133901 (2014)] that demonstrated significant interaction of surface seismic waves with holes structuring sedimentary soils at the meter scale. We further investigate the seismic wave trajectories of compressional body waves in soils structured with buildings. A significant substitution of soils by inclusions, acting as foundations, raises the question of the effective dynamic properties of these structured soils. Buildings, in the case of perfect elastic conditions for both soil and buildings, are shown to interact and strongly influence elastic body waves; such site-city seismic interactions were pointed out in [Guéguen et al., Bull. Seismol. Soc. Am. 92, 794–811 (2002)], and we investigate a variety of scenarios to illustrate the variety of behaviours possible.

Interface Liquid-Solid: Global Bifurcation Multiparameter of Flow Water Waves through Porous Compacted Granular by andldquo;Yakam Matrixandrdquo;

The construction of the tourbillon balls is fundamentally well known to Constatin and Strauss. In this work, we apply the flow of water through the compacted granular, in order to arrive at a model of passage in confinement and stagnation through the pores. An approach agrees of the advanced theory of water waves and the application of dynamics in microfluidics is discussed to improve “ASEAD Project water for everybody”. The approximation solution of nonlinear stochastic partial differential equation for only element of “Yakam Matrix” liquid-solid interface by simple understanding bifurcation behavior will follow the some trajectory of waves of water, granular compaction and dynamics of fluids at all scales, then we are still just at the beginning.

Acoustic scattering from a stiffened finite cylindrical shell with external rings

Studying the interaction of sound with cylindrical shells immersed in water is essential and helpful to improving underwater target detection and classification algorithms. Elastic cylindrical shells often occur as part of double-layered shell and have been widely used in marine and aerospace area. Acoustic waves are easy to be transmitted through the outer shell to the interior especially at low frequencies, thus directly being scattered by the inner shell and the rings in water between double-layered shells. Therefore, the externally ring-stiffened cylindrical shell is investigated in this paper. An experiment was conducted that measured the acoustic scattering. A hybrid 2-D/3-D finite-element modelling technique is employed to numerically calculate the scattering characteristics. Good qualitative agreement is found between numerical calculations and experimental measurement. An approximate analytical expression is given explicitly to identify the Bragg wave trajectories in the frequency-angle spectrum. It also has been shown that the rings not only affect the dynamic response of shell and indirectly influence the exterior scattered field, but also become direct acoustic scatterers in water and increase the target cross section especially at oblique incidence.

Scale-invariant structures of spiral waves

BackgroundSpiral waves are considered to be one of the potential mechanisms that maintain complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the organizing manifolds of information flow at multiple scales. MethodWe simulated spiral waves using a numerical model of cardiac excitation in a two-dimensional (2-D) lattice. We created a renormalization group by coarse graining and re-scaling the original time series in multiple spatiotemporal scales, and quantified the Lagrangian coherent structures (LCS) of the information flow underlying the spiral waves. To quantify the scale-invariant structures, we compared the value of the finite-time Lyapunov exponent between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale. ResultsBoth the repelling and the attracting LCS changed across the different spatial and temporal scales of the renormalization group. However, despite the change across the scales, some LCS were scale-invariant. The patterns of those scale-invariant structures were not obvious from the trajectory of the spiral waves based on voltage mapping of the lattice. ConclusionsSome Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales.

Effect of Long-Wavelength Magnetic Field Disturbances on the Generation of Auroral Kilometric Radiation

The effect of long-wavelength magnetic field disturbances typical of the Earth’s auroral region on the generation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron flow propagates against the background of cold low-density plasma is analyzed. The dynamics of the propagation and amplification of fluctuation waves with initial group velocities directed toward the higher magnetic field is considered in the geometrical optics approximation. Analysis of wave trajectories shows that the wave amplification coefficients depend on the magnetic field gradient in the reflection region. If the wave reflection point lies in the region where the gradient of the disturbed magnetic field is less than that of the undisturbed dipole field, then the wave amplification coefficients exceed those of waves propagating in the undisturbed field, and vice versa. Thus, the shape of the spectrum of generated waves changes in the presence of long-wavelength disturbances of the dipole magnetic field in such a way that segments with different curvatures can form in the spectrum.