Ring Waves Research Articles

Effects of geometrical and loading parameters on wave propagation in a circular ring

A theoretical investigation into the transient elastic response of a circular ring under radial impact is undertaken. The effects of ring curvature, cross-section geometry and impact duration on the resulting shear force, axial force and bending moment distributions and ring deformation are examined. This extends an earlier effort (Shim, Quah, J. Appl. Mech. 65 (1998) 569–579) which employed classical Timoshenko beam theory, coupled with the method of characteristics, to analyse propagation of flexural waves in rings. The present study shows that curvature and ring cross-sectional geometry do not significantly affect the development of bending moments and shear forces but influence axial forces induced and the deformed shape. It is found that for a given impulse, propagation of generalised forces and the deformation geometry depend on impact duration. Wave speeds relating to different deformation modes are governed primarily by curvature and cross-sectional geometry.

Possible detection of high frequency gravitational waves in storage rings: speculation on future applications

The effects induced by the interaction of gravitational waves (GWs) with ultra-relativistic bunches of particles in storage rings are analysed. Using a system of high precision beam monitors, each individual bunch of particles can be monitored and its oscillations, at relatively high frequencies, measured. We speculate on the possible use of storage rings equipped with refined monitors to be used as GW detectors. The noise induced by ground motion at low frequencies limits the possibility to measure any effect for GW frequencies bellow 100 Hz, where the ground motion spectral power density is too high; however, the level of ground motion noise is low at high frequencies, increasing the signal to noise ratio and the possibility to detect a cosmic background of gravitational radiation.

Reaction–diffusion waves of actin filament polymerization/depolymerization in Dictyostelium pseudopodium extension and cell locomotion

Cell surface movements and the intracellular spatial patterns and dynamics of actin filament (F-actin) were investigated in living and formalin-fixed cells of Dictyostelium discoideum by confocal microscopy. Excitation waves of F-actin assembly developed and propagated several micrometers at up to 26 μm/min in cells which had been intracellularly loaded with fluorescently labeled actin monomer. Wave propagation and extinction corresponded with the initiation and attenuation of pseudopodium extension and cell advance, respectively. The identification of chemical waves was supported by the ring, sphere, spiral and scroll wave patterns, which were observed in the extensions of fixed cells stained with phalloidin-rhodamine, and by the similar, asymmetrical [F-actin] distribution in wavefronts in living and fixed cells. These F-actin patterns and dynamics in Dictyostelium provide evidence for a new supramolecular state of actin, which propagates as a self-organized, reaction–diffusion wave of reversible F-actin assembly and affects pseudopodium extension. Actin’s properties of oscillation and self-organization might also fundamentally determine the nature of the eukaryotic cell’s reactions of adaptation, timing and signal response.

Detection of gravitational waves in storage rings: Speculation on future applications

The effects induced by the interaction of gravitational waves (GWs) with ultra-relativistic bunches of particles in storage rings are analysed. Using a system of high precision beam monitors, each individual bunch of particles can be monitored and its oscillations, at relatively high frequencies measured. The noise induced by ground motion at low frequencies limits the possibility to measure any effect for GW frequencies bellow 100 Hz, where the ground motion spectral power density is too high, however, the level of ground motion noise is low at high frequencies, increasing the signal to noise ratio and the possibility to detect a cosmic background of gravitational radiation.

Chemical Abundance Gradients in the Star‐forming Ring Galaxies

Ring waves of star formation, propagating outward in the galactic disks, leave chemical abundance gradients in their wakes. We show that the relative (Fe/O) abundance gradients in ring galaxies can be used as a tool for determining the role of the SN Ia explosions in their chemical enrichment. We con- sider two mechanismsa self-induced wave and a density wavethat can create outwardly propagating star-forming rings in a purely gaseous disk and demonstrate that the radial distribution of the relative (Fe/O) abundance gradients depends neither on the particular mechanism of the wave formation anor on the parameters of the star-forming process. We show that the (Fe/O) pro—le is determined by the velocity of the wave, the initial mass function, and the initial chemical composition of the star-forming gas. If the role of SN Ia explosions is negligible in the chemical enrichment, the ratio (Fe/O) remains constant throughout the galactic disk with a steep gradient at the wave front. If SN Ia stars are impor- tant in the production of cosmic iron, the (Fe/O) ratio has a gradient in the wake of the star-forming wave with the value depending on the frequency of SN Ia explosions. Subject headings: galaxies: abundancesgalaxies: ISMgalaxies: structure

Aharonov-Anandan effect induced by spin-orbit interaction and charge-density waves in mesoscopic rings

We study the spin-dependent geometric phase effect in mesoscopic rings of charge-density-wave(CDW) materials. When electron spin is explicitly taken into account, we show that the spin-dependent Aharonov-Casher phase can have a pronounced frustration effects on such CDW materials with appropriate electron filling. We show that this frustration has observable consequences for transport experiment. We identify a phase transition from a Peierls insulator to metal, which is induced by spin-dependent phase interference effects. Mesoscopic CDW materials and spin-dependent geometric phase effects, and their interplay, are becoming attractive opportunities for exploitation with the rapid development of modern fabrication technology.

Investigation of multifrequency/multipolarization radar signatures of rain cells over the ocean using SIR‐C/X‐SAR data

Radar signatures of rain cells are investigated using multifrequency/multipolarization synthetic aperture radar (SAR) images acquired from the space shuttle Endeavour during the spaceborne imaging radar‐C/X‐band SAR (SIR‐C/X‐SAR) missions in April and October 1994. In SIR‐C/X‐SAR images, radar signatures of rain cells over the ocean usually consist of irregularly shaped bright and dark patches that strongly depend on radar frequency and polarization. The radar signatures of rain cells observed in SIR‐C/X‐SAR imagery of the ocean originate from (1) the scattering and attenuation of the microwaves by raindrops and ice particles in the atmosphere and (2) the modification of the sea surface roughness induced by the impact of raindrops and by wind gusts associated with rain cells. Raindrops impinging on the sea surface generate ring waves, which enhance the sea surface roughness, but they also generate turbulence in the upper water layer, which reduces the sea surface roughness. Depending on the radar wavelength, ocean areas struck by rain can have higher or lower normalized radar cross section (NRCS) than the surrounding rain‐free area; in ocean areas where heavy rain is impinging on the sea surface, the X‐ and C‐band NRCS is usually enhanced, and the L‐band NRCS is reduced. From the phase difference between the horizontally and vertically copolarized signals, estimates of the rain rate are obtained. The present analysis shows further that the presently used wind speed retrieval algorithms for the scatterometers aboard the ERS and ADEOS satellites may yield biased wind fields if several rain cells lie within a scatterometer resolution cell.

Rotating waves in rings of coupled oscillators

In this paper we discuss the types of stable oscillation created via Hopf bifurcations for a ring of identical nonlinear oscillators, each of which is diffusively and symmetrically coupled to both its neighbours, and which, when uncoupled, undergo a supercritical Hopf bifurcation creating a stable periodic orbit as a parameter, λ is increased. We show that for small enough coupling, the only stable rotating waves produced are either one or a conjugate pair, depending on the parity of the number of oscillators in the ring and the sign of the coupling constant, and that the magnitude of the phase difference between neighbouring oscillators for these rotating waves is either zero (i.e. the oscillators are synchronized) or the maximum possible, depending on the sign of the coupling constant. These brances of rotating waves are produced supercritically.

Doppler radar backscatter from ring waves

The effects of rain falling on the sea surface have been investigated using a 3 GHz Doppler radar. In the absence of wind, the field measurements of radar backscatter show an enhancement of surface roughness due to a 4 mm hr 1 rainfall, which is equivalent to a light wind of several m s 1, but without the azimuthal variation characteristic of wind generated roughness. The radar Doppler spectra are dominated by dual peaks corresponding to scatterers both approaching and receding from the radar at the phase velocity of the resonant Bragg wave. This indicates that the dominant backscatter mechanism from this rain-roughened sea was resonant Bragg scatter from ring-waves expanding outward from the sites of droplet impacts. A secondary feature of the Doppler spectra which may be backscatter from stalks, is characterized by intermittent, weaker returns at velocities that are approximately stationary relative to the water surface. The Doppler spectral widths indicate that ring-wave lifetimes exceed 300ms.

Effect of rainfall on sea-surface microwave thermal emission

The results of radiometric experiments on the effect of rainfall on sea-surface microwave thermal emission are considered. The sea surface is described as a multitude of independent ring waves, perturbed by rain, and characterized by a power spectrum determined by rain parameters. This description allows us to explain the increase of the brightness temperature of a perturbed sea surface as the result of the resonance phenomenon in thermal emission.

Directional Wave Characteristics of Multi-Directional Wave Generator based on Numerical Simulation

Many experiments had been carried out in the long experimental towing tank in Yokohama National University (YNU) with generating directional spectrum waves by segmented and independent wave makers and using side-wall reflections positively. It is important to make more accurate generation of the directional spectrum waves considering the increasing demands for experiments among such waves.To accomplish these subjects, present paper investigates the characteristics of directional distribution by carrying out numerical generation of directional spectrum waves and its analysis for the case of without and with side-wall reflection. This calculation is based on the superposition of ring waves generated by the periodic line source distributions representing each wave maker unit. Mirror images are also introduced for considering reflections of side-wall including the ratio of reflection (reflection coefficient) because directional waves will not be reflected perfectly from real side-wall. In addition to this, directivity (Dd) and tapering effect for the distribution of source strength will be evaluated to generate more accurate directional spectrum waves. Especially, influence of spurious waves generated by the combined effect of finite width of segmented wave maker, wave length and main wave propagating direction will be investigated.To analyze directional spectrum waves, we use MLM (Maximum Likelihood Method) from calculated time series of wave elevation and two component wave slopes at the arbitrary spatial point. This corresponds to the Laser Beam Type Surface Wave Probe developed in Y. N. U, and reliability of this method was examined already.

Simulations of Collisions between Two Gas‐rich Galaxy Disks with Heating and Cooling

Particle hydrodynamics (SPH) simulations are presented of direct collisions between two model galaxies, most consisting of a rigid halo and a gas disk. Local self-gravity is also computed in the gas. The companion galaxy in these simulations is about one-third of the mass of the primary, and its disk is half the size. An adiabatic equation of state is combined with simple approximations for the effects of radiative cooling and local heating due to young star activity, which allows a continuous range of thermal phases to develop. These terms and multiple phases have not generally been included in galaxy collision simulations to date. Their effects are assessed in part by repeating runs with an isothermal equation of state and comparing the results. One model with a star plus gas disk is also included for comparison. These models are most relevant to interactions involving low surface brightness, or other late-type galaxies with extensive gas disks, including the precursors to well-known ring galaxies like the Cartwheel and VII Zw 466. In the simulations, the companion impact is slightly off center in the target disk, as is probably the case in these systems. In all cases, clear ring waves develop in the primary despite the disruption of parts of the disk by impact shocks. The gas density in the disk of the primary is initialized to values slightly below the gravitational instability threshold throughout, and the ring waves induce star formation in all the heating and cooling models. The structure of the waves and other interaction morphologies are found to be quite similar on large scales in both isothermal and heating/cooling cases, despite the fact that at certain stages large quantities of gas are heated above the initial temperature in the latter. On a finer scale, there are clear differences, including the fact that star formation heating in ring waves increases the vertical scale height of the primary gas disk and delays spoke development. The companion disk is largely disrupted in most of these simulations, and a substantial mass of gas is splashed out into a bridge connecting the two potential centers. The companion disk reforms by accreting gas out of the bridge, though generally in a different plane than its initial one. There is also a good deal of infall back onto the primary disk. Although heated by impact, the gas in the bridge cools rapidly. However, kinematic expansion prevents it from reaching threshold density, and there is no star formation heating there. A comparison run with a diskless companion produced no significant bridge, so in this type of collision the bridge is primarily a hydrodynamic phenomenon. The amount of material pushed out into the splash bridge and how much of it comes from each galaxy depends on the relative orientation of the disks at impact. This orientation also affects how much bridge material accretes onto each galaxy. The onset of accretion is initially delayed but then accelerates to a peak and declines thereafter in both galaxies. The infall is spatially asymmetric and is primarily located in well-defined streams. Most of the accreted gas ends up in the central regions of the model galaxies, but only after spiraling around the center and passing through one or more shocks. Accretion heating is substantial, and is shown to inhibit or delay global star formation enhancements. The thermal effects of the impact between galaxies are short-lived, but the models predict that accretion and young star heating effect the global thermal phase balance for a much longer period. The magnitude and duration of these effects also depend on the relative orientation of the disks at impact. Thus, the postcollision Hubble type of the companion is a sensitive function of initial orientation.

Ring wave solutions of a n+1-dimensional Sine-Gordon model.

The dynamical properties of the ring wave solutions of the model psi(tt)- nabla (n) (2)psi+sin psi+ varepsilon sin (psi/2)+alphapsi(t)=0 (0</= varepsilon <<1,0</=alpha<<1) are studied analytically and numerically for spatial dimension (n=2,3). The model is obtained as a continuum approximation of a multidimensional Frenkel-Kontorowa lattice. We will show that in the case varepsilon >0, alpha=0 (or alpha>0) the return effect of the ring wave does not occur only for well defined values of varepsilon. It will be shown numerically that the dissipative perturbation alphapsi(t) (alpha>0) stabilizes both the velocity and the wave profile of the ring wave when the return effect does not occur. (c) 1997 American Institute of Physics.

Surface Brightness Gradients Produced by the Ring Waves of Star Formation

We compute surface brightness profiles of galactic disks for outwardly propagating waves of star formation with a view to investigate the stellar populations in ring galaxies. We consider two mechanisms which can create outwardly propagating star forming rings in a purely gaseous disk --- a self-induced wave and a density wave. We show that the surface brightness profiles produced by both scenarios of ring formation are similar and are strongly sensitive to the velocity of the wave. The results of our computations are compared with the observational quantities sensitive to the young and old stellar populations in the ring galaxies A0035-335 (the Cartwheel galaxy) and VIIZw466. The best fit to the observed radial H_alpha surface brightness distribution in the Cartwheel galaxy is obtained for a wave velocity of about 90 km/s. The red continuum brightness of the ring can be fully explained by the evolving stars present in the trailing part of the wave. However the red continuum brightness in regions internal to the ring indicates that the wave of star formation propagates in a pre-existing stellar disk in the Cartwheel. The H_alpha and K-band surface brightness profiles in VIIZw466 match the values expected from stellar populations produced by a wave of star formation propagating in a purely gaseous disk very well. We conclude that VIIZw466 is probably experiencing the first event of star formation in the disk.

Resonant excitation of density waves in Saturn's rings: the effect of spatial inhomogeneity

The investigation of the first papers of the present series (Griv, Planet. Space Sci. 44, 579–589, 1996; Griv and Yuan, Planet. Space Sci. 44, 1185–1190, 1996) is extended to include the effect of spatial inhomogeneity, i.e. the surface density gradient of Saturn's ring disk of mutual-gravitating identical particles. The model of an infinitely thin inhomogeneous disk with rare physical (inelastic) collisions between particles is considered. Similar to the investigation of the first papers, the well-elaborated mathematical methods of plasma linear kinetic theory are utilized. The influence of disk inhomogeneity on the oscillation spectrum of different small-amplitude oscillations in the Saturnian ring system is studied. Estimates are made for the frequencies and the growth rate of the oscillations. It is shown that, as a rule, in Saturn's A ring the spatial inhomogeneity reinforces the growth rate of the oscillating instability (or the resonant self-excitation of density waves), and weakens the growth rate both in the C ring and in the inner portions of the B ring. In addition, the investigation of waves and their instabilities in the plane of Saturn's rings is extended by taking into account the density wave excitation/absorption at Lindblad's resonances and the weak effect of the finite but not large ring disk thickness.

Analysis of Cell Movement and Signalling during Ring Formation in an Activated Gα1 Mutant ofDictyostelium discoideumThat Is Defective in Prestalk Zone Formation

Mound formation in the cellular slime mouldDictyosteliumresults from the chemotactic aggregation of competent cells. Periodic cAMP signals propagate as multiarmed spiral waves and coordinate the movement of the cells. In the late aggregate stage the cells differentiate into prespore and several prestalk cell types. Prestalk cells sort out chemotactically to form the tip, which then controls all further development. The tip organises cell movement via a scroll wave that converts to planar waves in the prespore zone leading to rotational cell movement in the tip and periodic forward movement in the prespore zone. Expression of an activated Gα1 protein under its own promoter leads to a severely altered morphogenesis from the mound stage onwards. Instead of forming a tipped mound, the cells form a ring-shaped structure without tip. Wave propagation pattern and dynamics during aggregation and mound formation in the mutant are indistinguishable from the parental strain AX3. However, at the time of tip formation the spiral waves that organise the late aggregate do not evolve in a scroll-organising centre in the tip but transform into a circularly closed (twisted) scroll ring wave. This leads to the formation of a doughnut-shaped aggregate. During further development, the doughnut increases in diameter and the twisted scroll wave converts into a train of planar waves, resulting in periodic rotational cell movement. Although biochemical consequences resulting from this mutation are still unclear, it must affect prestalk cell differentiation. The mutant produces the normal proportion of prespore cells but is unable to form functional prestalk cells, i.e., prestalk cells with an ability to sort out from the prespore cells and form a prestalk zone. Failure of sorting leads to an altered signal geometry, ring-shaped scroll waves, that then directs ring formation. This mutant demonstrates the importance of prestalk cell sorting for the stabilisation of the scroll wave that organises the tip.

Resonant excitation of density waves in Saturn's rings: the effect of interparticle collisions

Kinetic theory with the phenomenological Bhatnagar-Gross-Krook binary collision integral is used to study the small amplitude oscillations and their stability of a collisional planetary ring system of identical particles. A differentially rotating, spatially homogeneous disk is considered, with the property that both the epicyclic frequency and the angular velocity of differential rotation exceeds the frequency of inelastic (physical) collisions between particles, that is, a disk with rare collisions is considered. The stabilizing influence of collisions on the growth rate of the oscillating resonant type instability, studied in the first paper of the series, is shown. Also it is shown that in low optical depth regions of Saturn's rings rare collisions cannot suppress the resonant excitation of spiral density waves investigated by Griv ( Planet. Space Sci. 44, 579–587, 1996) in the first paper of the present series.

The Head-on Collision between Two Gas-rich Galaxies: Neutral Hydrogen Debris from the Centrally Smooth Ring Galaxy VII ZW 466

We present VLA observations of the distribution and kinematics of the HI gas in the classical ring galaxy VIIZw466 and its immediate surroundings. The HI gas corresponding to the bright optical star forming ring exhibits the typical profile of a rotating-expanding ring. The systemic velocity of the galaxy is found to be 14,468km/s. A formal fit to the HI kinematics in the ring is consistent with both ring rotation and expansion (expansion velocity 32 km/s). However, H\,I in the northeast quadrant of the ring is severely disturbed, showing evidence of tidal interaction. We also detect a hydrogen plume from the southern edge-on companion galaxy (G2) pointing towards the ring galaxy. This, and other peculiarities associated with G2 suggest that it is the intruder galaxy which recently collided with VIIZw466 and formed the ring. Numerical hydrodynamic models are presented which show that most of the observed features can be accounted for as a result of the impact splash between two gas disks. The resultant debris is stretched by ring wave motion in the bridge and later forms accretion streams onto the two galaxies.Finally, we detect HI emission from two previously unknown dwarf galaxies located northeast and southeast of VIIZw466 respectively. This brings the total number of members of the VIIZw466 group to five. Using the projected mass method, the upper limit of the dynamical mass of the group was estimated to be Mo =3.5x10^{12} M_sun, which implies that the mass to light ratio of the group is (M/L)_{group} \approx$ 70. This rather low value of M/L, as compared with other loose groups, suggests the group may be in a state of collapse at the present time. Plunging orbits would naturally lead to an enhanced probability of head-on collisions and ring galaxy formation.

Resonant excitation of density waves in Saturn's rings

The dynamics of regions in the Saturnian ring system with rare collisions between particles, that is, Ω 2⪢ν c 2 , where Ω is the orbital angular frequency and ν c the collision frequency, is considered. According to observations, such low optical depth regions can be found in the C ring, the inner portions of the B ring and the A ring. Kinetic theory with the Vlasov and Poisson equations is used to obtain the eigen-frequencies of oscillations propagating in the plane of the system. In the considered case of rare collisions the resulting kinetic equation for the perturbed distribution function can be solved by successive approximations, neglecting the effect of binary particle collisions in the zeroth-order approximation. An oscillating instability of the kinetic type is discussed. This instability of a particulate disk is similar to the magneto-drift instability first discovered by Krall and Rosenbluth ( Physics Fluids 6, 254–265, 1963) in a nonuniform magnetic plasma, and belongs to the class of microinstabilities of an inhomogeneous plasma. The cause of the oscillating instability in Saturn's rings is a resonant interaction of drifting particles with nonaxisymmetric Jeans-stable waves at the corotation. The waves that may be produced by the corotation-resonance interaction represent non-radial normal modes of the gravitationally stable disk modified by a particle drift. It is shown that density waves are effectively excited at this resonance: the growth rate of the mode of maximum instability is large, Im ω∗∼Ω. The resonant excitation of density waves investigated in the present paper may be proposed as the cause of the irregular, small-scale ∼ 100 m structure in regions of low optical depth in Saturn's rings. It is suggested that Cassini spacecraft high-resolution images of low optical depth regions will show this kind of structure.

Uniform excitation of a cylindrical plasma column by a microwave ring resonator

To overcome the problem of insufficient absorption of microwave power by a plasma column a new concept for the microwave excitation of cylindrical gas discharges on the basis of a microwave ring resonator is presented. A theoretical description of this resonator loaded by a gas discharge is developed using the S parameters of its elements by which is determined the dependence of the two ring waves on the tuning of the resonator. It is predicted from theory and confirmed by measurements that one ring wave can be suppressed to a high degree by a proper tuning of the resonator. With the ring resonator a high power absorption at a frequency of 2.45 GHz is achieved over a wide pressure range. A uniform cylindrical plasma column with a length of more than 30 cm suitable for laser operation can be realized.