Running Wave Research Articles

Classes of exact solutions to the Teukolsky master equation

The Teukolsky master equation is the basic tool for the study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky radial equation and the Teukolsky angular equation. We present here a unified description of all classes of exact solutions to these equations in terms of the confluent Heun functions. Large classes of new exact solutions are found and classified with respect to their characteristic properties. Special attention is paid to the polynomial solutions which are singular ones and introduce collimated one-way running waves. It is shown that a proper linear combination of such solutions can present bounded one-way running waves. This type of waves may be suitable as models of the observed astrophysical jets.

Stationary drag photocurrent caused by strong effective running wave in quantum wires: Quantization of current

The stationary current induced by a strong running potential wave in one-dimensional system is studied. Such a wave can result from illumination of a straight quantum wire with special grating or spiral quantum wire by circular-polarized light. The wave drags electrons in the direction correlating with the direction of the system symmetry and polarization of light. In a pure system the wave induces minibands in the accompanied system of reference. We study the effect in the presence of impurity scattering. The current is an interplay between the wave drag and impurity braking. It was found that the drag current is quantized when the Fermi level gets into energy gaps.

Microwave device for liquid dielectrics diagnostics

It is developed a method for measuring of dielectric permittivity of liquid dielectrics. High accuracy and reliability of the method is provided by definite hardware realization; it is used resonance-bridge method; to provide high stability of measuring SHF-signal frequency there is used self-excited oscillator on a basis of active running wave resonator.

Running waves in the sunspot chromosphere

Running waves at the chromospheric level (Hα) in sunspots are studied. Propagating 3-min oscillations are shown to be typical of many spots. Presumably, they propagate along the vertical magnetic-field lines. Their propagation speed is measured. According to our analysis, the 5-min oscillations propagating in the penumbral chromosphere are not a continuation of the 3-min umbral oscillations. The wavelength and propagation speed of the running penumbral waves are determined.

Electrons in finite superlattices: soft and hard confinements

The properties of electrons in superlattices (SLs) of a finite length are described using standing waves resulting from the fixed boundary conditions (FBCs) at both ends. These electron properties are compared with those predicted by the standard treatments using running waves (Bloch states) resulting from the cyclic boundary conditions. It is shown that, while the total number of eigenenergies in a miniband is the same according to both treatments, the number of different energies is twice higher according to the FBCs. We differentiate between FBCs provided by infinitely high barriers (‘hard’ confinement), as used in the existing literature, and FBCs provided by finite-hight barriers (‘soft’ confinement) used in the present work. Using numerical solutions of the Schrödinger equation for an electron in an increasing number N of periodic quantum wells (beginning with N = 2), we investigate the formation of an energy miniband and of a Brillouin zone according to the two approaches. Calculating the Fourier transforms of the computed wavefunctions, we analyze their momentum structures. We show that the number of higher values of momentum involved in an eigenenergy state is twice higher for a standing wave than for a corresponding running Bloch wave. Experiments are proposed to observe the described properties of electrons in finite SLs.

Frequency stabilization in free-electron masers with 2D and 1D distributed feedback

We analyze the dynamics of free-electron masers (FEMs) with two-mirror hybrid Bragg resonators using the coupling between running and quasi-critical modes in the input mirror. Such a mirror may have the form of a 2D Bragg structure with coaxial geometry or a segment of a cylindrical waveguide with axisymmetric corrugation having a period close to the wavelength. The output mirror has the traditional Bragg structure coupling two counterpropagating running waves (the corrugation period is close to half the wavelength). It is shown that a stable unimodal lasing with a radiation frequency close to the cutoff frequency of the quasicritical mode excited in the input mirror can be attained using this scheme under optimal conditions. Such a regime is insensitive to variations of the electron beam parameters. Simulation of experimentally implemented FEMs and those being developed is carried out.

A 3D study of the photosphere of HD 99563 - I. Pulsation analysis

We have used high-speed spectroscopy of the rapidly oscillating Ap (roAp) star HD 99563 to study the pulsation amplitude and phase behaviour of elements in its stratified atmosphere over one 2.91-d rotation cycle. We identify spectral features related to patches in the surface distribution of chemical elements and study the pulsation amplitudes and phases as the patches move across the stellar disc. The variations are consistent with a distorted non-radial dipole pulsation mode. We measure a 1.6 km s−1 rotational variation in the mean radial velocities of Hα and argue that this is the first observation of Hα abundance spots caused by He settling through suppression of convection by the magnetic field on an oblique rotator, in support of a prime theory for the excitation mechanism of roAp star pulsation. We demonstrate that HD 99563 is the second roAp star to show aspect dependence of blue-to-red running wave line profile variations in Nd iii spots.

Forced oscillations of shells of revolution in a viscous fluid flow

The influence of mechanical properties of a large-sized shell on its forced oscillations in a flow of a viscous fluid is considered. As is known [1], the flow past a shell can be controlled by generating a wave that runs over the shell surface. Hydrodynamic calculations performed for only transverse running waves [2–6] show the potential possibility of significantly decreasing the drag, but conditions under which these running waves can be maintained in a shell of finite length had not been studied until now. The present paper considers the laws that govern a running wave generated in the front part of a shell of revolution occurring in a flow of a viscous fluid.

Running waves and dynamical chaos in active media: A numerical study

In the framework of a self-similar problem, we numerically analyze the onset of solutions in the form of running waves in excitable and oscillating active media. We show that the passage to the solution in the form of a running wave occurs through cascades of bifurcations responsible for the development of chaotic dynamics in nonlinear dissipative systems of differential equations.

The strontium-vapor laser pumping efficiency under running-wave excitation

The effect of the design features of the gas-discharge tube on the processes proceeding in the discharge circuit of a metal-vapor laser has been investigated. The position of electrodes in the gas-discharge tube has been found to significantly affect the processes at work in the discharge circuit and the energy characteristics of the laser. For instance, gas-discharge tubes with electrodes placed in the hot region of the discharge channel are typified by high metastable-population rates at the leading edge of the excitation pulse, whereas with electrodes positioned in cold buffer regions, the leading edge of the voltage pulse across the resistive component of the tube impedance is seen to peak. Conditions for running-wave generation in the active media of lasers on self-terminated transitions of metal atoms and the running-wave use efficiency for laser pumping are discussed, considering a strontium-vapor laser as an illustration. It is shown that the running wave is generated as the result of the breakdown in the anode end of the gas-discharge tube and is maintained by the energy stored in the capacitive component of the impedance of the gas-discharge tube. The lasing pulse duration under running-wave excitation corresponds to the time it takes an ionization wave to propagate from the anode to the cathode of the gas-discharge tube, with pumping efficiency being ~6-8% for a strontium-vapor laser. The average lasing power varies within 10-15% depending on whether the totally reflecting cavity mirror is placed near the anode or the cathode of the tube.

Arterial Wave Intensity and Ventricular-Arterial Coupling by Vascular Ultrasound: Rationale and Methods for the Automated Analysis of Forwards and Backwards Running Waves

Wave intensity (WI) in the circulation is estimated noninvasively as the product of instantaneous changes in pressure and velocity. We recorded diameter as a surrogate for pressure, and velocity in the right common carotid artery using an Aloka SSD-5500 ultrasound scanner. We developed automated software, applying the water hammer equation to obtain local wave speed from the slope of a pressure/velocity loop during early systole to separate net WI into individual forwards and backwards-running waves. A quality index was developed to test for noisy data. The timing, duration, peak amplitude and net energy of separated WI components were measured in healthy subjects with a wide age range. Age and arterial stiffness were independent predictors of local wave speed, whereas backwards-travelling waves correlated more strongly with ventricular systolic function than with age-related changes in arterial stiffness. Separated WI offers detailed insight into ventricular-arterial interactions that may be useful for assessing the relative contributions of ventricular and vascular function to wave travel. (E-mail: carlo.palombo@med.unipi.it)

Nanoliter liquid characterization by open whispering-gallery mode dielectric resonators at millimeter wave frequencies

We present an approach for identification and concentration determination of liquids of pico to nanoliter volumes at a frequency of 35 GHz based on a whispering-gallery mode (WGM) dielectric resonator technique. A quasioptical coupling scheme based on dielectric image waveguides was employed to excite high-Q running wave WGMs with uniform azimuthal field distribution in cylindrical sapphire disks with quality factors up to 4×105 at room temperature. Measurement of the liquid induced changes in the resonator quality factor and resonance frequency has been performed for droplets down to 90 pl volume spotted at different positions on the surface of the sapphire disk. We have employed our method for concentration determination of ethanol, glucose, and albumin dissolved in water. Solutions with concentration values well below 10% could be clearly separated from pure water. Our method is promising for the characterization of biological liquids.

Origin of Axially Running Waves in Liquid Bridges

A supercritical three-dimensional thermoconvective flow in a long non-isothermal liquid bridge with aspect ratio Γ = 1.8 is numerically investigated under terrestrial conditions. Study of the flow regimes shows that the instability sets in as an axially running wave with zero wave number, m = 0, which is a two-dimensional unsteady flow. Further increasing the applied temperature difference results in bifurcation of m = 1 wave traveling azimuthally with a slightly higher frequency. The two waves co-exist within a certain range of the temperature difference values, and finally the m = 0 wave is suppressed while the azimuthal one gets stronger.

Pulsed-periodic laser on RM helium and strontium transitions

Conditions of generation of a running excitation wave in the active medium of gas lasers and efficiency of the running wave application for pumping of the active medium are considered by the example of a strontium vapor laser. It is demonstrated that the running excitation wave is generated directly in the active laser medium and is supported by the energy stored in the capacitive component of the impedance of a gas-discharge tube. Generation on the self-limited (21P1-21S0) transition of the helium atom at λ = 2058 nm and simultaneous generation on RM transitions of the strontium ion and strontium and helium atoms and on a number of neon atom transitions is first excited.

On the superfluidity of classical liquid in nanotubes, I. Case of even number of neutrons

We show that the superfluidity effect in nanotubes arises in a classical liquid (regarded as the limit as h → 0 of the quantum liquid) and involves not only the Bogolyubov “running waves,” but also a “standing wave.” This is obtained from the variational equations in the context of ultrasecondary quantization. It is stressed that the “atomic” size of the nanotube plays a crucial role in the phenomena.

Single-wave approximation for a one-dimensional acoustic running wave in the viscous gas

The one-dimensional nonstationary disturbed flow about the equilibrium (stationary) compressible viscous gas state is considered. In the framework of the single-wave approximation an equation of disturbance propagation in gas is obtained. The solutions of the equation obtained are compared with the solutions of the Burgers equation to show the possibility of using this equation for simulation of smooth upward jumps.

Exact axially symmetric wave solutions of the Yang-Mills equations

We find a class of exact axially symmetric wave solutions of the Yang-Mills equations with SU(2) symmetry. The solutions in this class describe running waves propagating at the speed of light in a vacuum and contain two arbitrary differentiable functions of their phase. We consider properties of field sources that can generate such running waves.

Forces exerted on atoms by stochastic laser fields

We present analytical results and numerical simulations for the force exerted on moving atoms in the fields of two counterpropagating waves whose amplitudes or phases are described as stochastic processes. We assume that one field repeats the other with some delay, as would occur when the two fields derive from a common source through a beam splitter and mirrors. We show that, just as with the force exerted by the field of two counterpropagating sequences of π-pulses, or two counterpropagating bichromatic or frequency-modulated waves, the force on an atom in counterpropagating stochastic waves may considerably exceed the force exerted by the field of a single running wave. For comparison we also discuss the interaction of an atom with two counterpropagating waves when one of them is monochromatic and the other one has a stochastic phase. In this case the force substantially exceeds the force exerted by the field of a single running wave but appreciably smaller then the radiative force in the counterpropagating waves in which one field repeats the other with some delay.

The discovery of a new type of upper atmospheric variability in the rapidly oscillating Ap stars with VLT high-resolution spectroscopy★

In a high-resolution spectroscopic survey of rapidly oscillating Ap (roAp) stars with the Ultraviolet and Visual Echelle Spectrograph on the Very Large Telescope of the European Southern Observatory, we find that almost all stars show significant variation of the radial velocity amplitudes - on a time-scale of a few pulsation cycles - for lines of the rare earth ion Pr III and in the core of the Ha line. These variations in the radial velocity amplitudes are described by new frequencies in the amplitude spectra that are not seen in broad-band photometric studies of the same stars. The Pr III lines form high in the atmosphere of these stars at continuum optical depths of log τ 5000 < -5 and tend to be concentrated towards the magnetic poles in many stars, and the core of the Ha line forms at continuum optical depths -5 ≤ log τ 5000 ≤ -2, whereas the photometry samples the atmosphere on average at continuum optical depths closer to log τ 5000 = 0 and averages over the visible hemisphere of the star. Therefore, there are three possible explanations for the newly discovered frequencies: (1) there are modes with nodes near to the level where the photometry samples that can be easily detected at the higher level of formation of the Pr III lines; or (2) there are higher degree, l, non-radial oblique pulsation modes that are detectable in the spectroscopy because the Pr III is concentrated towards the magnetic poles where such modes have their highest amplitudes, but average out over the visible hemisphere in the photometry which samples the star's surface more uniformly; or (3) there is significant growth and decay of the principal mode amplitudes on a time-scale of just a few pulsation cycles at the high level of formation of the Pr III lines and core of the Ha line. The third hypothesis implies that this level is within the magneto-acoustic boundary layer where energy is being dissipated by both outward acoustic running waves and inward magnetic slow waves. We suggest observations that can distinguish among these three possibilities. We propose that strong changes in pulsation phase seen with atmospheric height in roAp stars, in some cases more than n rad from the top to the bottom of a single spectral line, strongly affect the pulsation phases seen in photometry in various bandpasses which explains why phase differences between bandpasses for roAp stars have never been explicable with standard theories that assume single spherical harmonics within the observable atmosphere. We also discuss the photometric amplitude variations as a function of bandpass, and suggest that these are primarily caused by continuum variations, rather than by variability in the rare earth element lines. We propose further tests of this suggestion.

Structure of the fronts of strong collisional shock waves in an ideal two-temperature electron-ion plasma with ions of arbitrary charge

Solutions in the form of plane running waves are investigated numerically in the framework of a two-temperature hydrodynamic model of a fully ionized ideal plasma with ions of arbitrary charge number Z0. Most simulations were carried out for simple boundary conditions corresponding to a cold immobile plasma at the front of a running wave. All the solutions obtained have a discontinuity in the form of an isoelectronic-thermal jump, whose parameters relax to their steady-state values in the course of calculation. The problem of finding numerical solutions in which all the quantities at infinity take on finite (equilibrium) values actually reduces to the problem of the front structure of a strong shock wave. For a plasma with singly changed ions (Z0 = 1), numerical solutions were found to coincide with the previously known solution. For a plasma with arbitrarily charged ions (Z0 > 1), numerical solutions were obtained for the first time on the basis of justified formulas for the electron thermal conductivity.