Bulk Oscillations Research Articles

Oscillations and waves in metal-ion-catalyzed bromate oscillating reactions in highly oxidized states

A mathematical model of the Belousov-Zhabotinsky (BZ) oscillating reaction is presented along with experimental data showing that the catalyst can remain almost completely oxidized during a significant part of the oscillatory cycle in the ferroin-catalyzed BZ reaction. The model semiquantitatively describes oscillations and wave propagation in both the cerium- and ferroin-catalyzed systems when the phase of catalyst oxidation occupies a significant part of the oscillatory cycle. Such modes are of special interest because they give rise to enhanced instability of the bulk oscillations, enlargement of the number of local wave sources, and decremental wave propagation. Reversibility of the catalyst oxidation by bromine dioxide radicals is crucial for the dynamics of the system under these conditions

Autonomous pacemaker of chemical waves created by spiral annihilation

A leading center of a target pattern in the Belousov-Zhabotinsky (BZ) reaction emerges after mutual annihilation of a pair of counterrotating spirals. The spiral waves propagate in an oscillatory medium which oscillates with a period much larger than that of spiral rotation. The annihilation process is induced by two methods: (1) in the light-sensitive ruthenium-catalyzed BZ reaction an inhibitory laser-spot erases the core structure of two adjacent spirals whereupon the spiral ends merge to form a continuous front; (2) in the ferroin-catalyzed BZ reaction an externally applied electric field forces the spirals to coalesce by a drift towards each other. In both cases, bulk oscillations of regular frequency follow inside the region enclosed by the newly emerging closed wave front. The phenomenon is observed and analyzed by computerized video techniques.

Electric current control of spiral wave dynamics

The control of spiral wave parameters by electric current was investigated in the Belousov-Zhabotinsky (BZ) reaction. It was found that the wavelength and the period of spiral waves increase by a factor of up to 3 with electric current (both dc and ac). Using this procedure spiral waves with a period higher than the period of medium bulk oscillations were observed. It was also found that hysteresis phenomena occur in the system considered.

Transient acoustic processes in a low-Mach-number shear flow

A systematic perturbation procedure, based on a small mean flow Mach number and large duct Reynolds number, is employed to formulate and solve an initial-boundary-value problem for acoustic processes in a shear flow contained within a rigid-walled parallel duct. The results describe the general transient evolution of acoustic waves driven by a plane source located at a given duct cross-section. Forced bulk oscillations near the source and oblique wave generation are shown to result from refraction of the basic planar axial disturbance by the shear flow. Refraction also causes the axial waves to exhibit higher-order amplitude variations in the transverse direction. As the source frequency approaches certain critical values, specific refraction-induced oblique waves evolve into amplifying purely transverse waves. As a result, the magnitude of the refraction effect increases with time, and quasi-steady solutions do not exist. The analysis is extended to the thin acoustic boundary layer adjacent to the solid walls to examine the shear-layer structure induced by the variety of acoustic waves in the core flow. Nonlinear effects and acoustic streaming are shown to be negligibly small on the scale of a few axial wavelengths.

Stable autonomous pacemakers in the enlarged Ginzburg-Landau model

We consider a three-component model of an active medium where local oscillations are coupled to a slowly propagating field. Using the Kuramoto approximation of phase dynamics, we show that this uniform medium can support steady autonomous pacemakers. These were patterns spontaneously emerge from the background of uniform bulk oscillations and are stable with respect to small perturbations.

Microtubule dynamics and microtubule caps: a time-resolved cryo-electron microscopy study.

Microtubules display the unique property of dynamic instability characterized by phase changes between growth and shrinkage, even in constant environmental conditions. The phases can be synchronized, leading to bulk oscillations of microtubules. To study the structural basis of dynamic instability we have examined growing, shrinking, and oscillating microtubules by time-resolved cryo-EM. In particular we have addressed three questions which are currently a matter of debate: (a) What is the relationship between microtubules, tubulin subunits, and tubulin oligomers in microtubule dynamics?; (b) How do microtubules shrink? By release of subunits or via oligomers?; and (c) Is there a conformational change at microtubule ends during the transitions from growth to shrinkage and vice versa? The results show that (a) oscillating microtubules coexist with a substantial fraction of oligomers, even at a maximum of microtubule assembly; (b) microtubules disassemble primarily into oligomers; and (c) the ends of growing microtubules have straight protofilaments, shrinking microtubules have protofilaments coiled inside out. This is interpreted as a transition from a tense to a relaxed conformation which could be used to perform work, as suggested by some models of poleward chromosome movement during anaphase.

Vertical oscillation of the Galactic disk

The possible oscillation modes of the local structure of the Galactic disk and their frequencies are derived for three families of one-dimensional disk models with and without external halos. Modes with horizontal as well as vertical structure are also considered. A series of simulations and interpretations based on the linearized solutions of the evolution equations is presented. The physics of oscillation modes, oscillations in models of the Galactic disk, and perturbations of the disk are examined. Linear analysis and n-body simulation demonstrated that a one-dimensional disk may have undamped oscillation modes. The higher order modes are not excited by passing satellites. In the presence of a harmonic halo, the disk undergoes a bulk oscillation; if the halo is anharmonic, this mode is still undamped. The long damping time that was found implies that ordered motion may persist for many vertical crossing times after a perturbation to the Galactic disk. The findings also suggest a general framework for studying oscillation modes. 28 refs.

Target and spiral waves in oscillatory media in the presence of obstacles

Propagation of target and spiral waves in the presence of walls and windows in a two-dimensional reaction-diffusion model is considered. The time evolution of the system is such that for a range of parameter values a supercritical Hopf bifurcation leads to bulk oscillations. It is shown that in a finite system, for sufficiently small passages, no target waves are triggered. The passage of target waves through a window induces in the next compartment spiral or target waves. In this case a new bulk frequency appears and quasi-periodic motion is observed. In presence of two windows, propagation through a large opening can inhibit the onset of waves from smaller windows.

Multipole response of metal spheres toq-dependent excitation operators

We have obtained the once and thrice energy-weighted moments of the random-phase-approximation (RPA) response to q-dependent excitation operators of type ${j}_{L}$(qr)${Y}_{L0}$ for metal spheres described within a spherical jellium model. These two moments, in conjunction with the Thomas-Fermi estimation of the RPA inverse energy-weighted moment, are used to study the response of these systems as a function of q. For small values of q, we recover the surface-mode systematics, whereas for large q's the response is mainly determined by electron-hole excitations. For intermediate q values, bulk oscillations are found and their connection with the hydrodynamical-model predictions is established. In the limit of a big sphere, we have obtained an improved bulk-plasmon pole approximation for the dispersion relation which includes in a very easy way exchange and correlation effects. We have found that these corrections are not negligible. The moments of the response corresponding to a plane wave ${e}^{i\mathrm{q}\ensuremath{\cdot}\mathrm{r}}$ are also discussed. Numerical applications to the case of Na spheres whose ground-state structure is described by models of different complexity (constant electronic density, Thomas-Fermi or Kohn-Sham) are presented.

Magnetic energy conversion in the solar transition zone

Newly emerging magnetic flux can be the energy source for the solar corona and the solar wind. Plasma bulk motions and oscillations are observed by means of UV spectroscopy at transition zone (t.z.) temperatures (∼ 20.000 K < T < 250,000 K). The particular conditions in the transition zone plasma facilitate the conversion of magnetic into kinetic energy: (1) The β-value in the transition zone can change rapidly from β⪡1 to β⪢1. (2) Radiation losses change rapidly with temperature to create instabilities. (3) The small spatial filling factor (<0.01) indicates a highly filamented plasma. Large fluctuations in density, magnetic field strength and currents may facilitate fast reconnection. The areas of strong plasma oscillations in the transition zone may be the origin of coronal heating and particle acceleration.

Solvation of thiols. An infrared and nuclear magnetic resonance study of ethanethiol

The i.r. spectra of solutions of ethanethiol in CCl4 in the S—H fundamental (v) and first overtone (2v) regions have been measured as a function of thiol concentration. A dimerisation constant of 0.038 dm3 mol–1 was estimated at 22 °C, the S—H stretching frequencies for free and mono-hydrogen-bonded thiol being at 2585 and 2570 cm–1, respectively, in the fundamental, and 5056 and 4993 cm–1 in the overtone regions. Beer's law was obeyed for the monomer in dilute solutions, giving absorbances of 9.4 and 0.53 dm2 mol–1 in the v and 2v regions. Spectra for the pure thiol in the fundamental region were analysed in terms of these two bands and a third at ca. 2559 cm–1, assigned primarily to the central molecule of linear trimers. The results show that dimers dominate at room temperature, in contrast to results for methanol, which is highly polymerised at room temperature. Also for methanol in CCl4 solutions, dimers never constitute a major component, the main equilibria being between monomeric and cyclic units. Thus the phenomenon of cooperativity in hydrogen bonding is far less for thiols than for alcohols. This reflects the reduced hydrogen-bond ‘basicity’ of sulphur and the reduced ‘acidity’ of the S—H protons. There is an inversion in the relative oscillator strengths for (SH)free and (SH)bulk oscillators on going from the fundamental (v) to the first overtone (2v). For the former, there is a marked increase as the hydrogen-bond strength in RSH-----B units increases, whereas in the 2v(SH) region, the ‘free’ band is much stronger. Both regions have been used to obtain a more complete analysis of the compositions of solutions. In basic aprotic solvents only one i.r. feature was detected, which is assigned to EtSH-----B units. We have constructed a correlation between the i.r. and the proton shift n.m.r. data, which is satisfactorily linear over the range of co-solvents from MeCN to Et2NH. There is an abrupt discontinuity for the non-basic solvents CCl4 and C6H12, for which the i.r. shifts are less than those predicted from the corresponding n.m.r. shifts. This is reflected in plots involving the solvent donor numbers. We estimate that the pure liquid at 22 °C contains ca. 49%(SH)free units. This result requires that there is an average of one hydrogen bond per thiol molecule, which accords well with the results of a recent Monte Carlo calculation for thiols.

Miniaturized Bulk and Surface Acoustic Wave Quartz Oscillators Used as Sensors

Miniaturized Bulk and Surface Acoustic Wave Quartz Oscillators Used as Sensors

Chemical waves in a two-dimensional oscillating system

The early stages of the spontaneous desynchronization of chemical oscillations of the limit cycle type in a two-dimensional medium are investigated. It is shown in the framework of a reaction-diffusion kinetics that the behavior of the system is governed by the phase dynamics. Target patterns are radiated from centers which are spontaneously emitted by the system. They have various characteristic frequencies which are always larger than the frequency of the bulk oscillations. The statistical distribution of these centers is shown to depend on the wavelength of the corresponding waves and on the parameters of the limit cycle. Rotating spiral waves which correspond to vortexlike phase fluctuations have a vanishingly small probability and have to be initiated.

Analysis of Neural Networks

1. The general form of a neural network.- 1.1 Introduction.- 1.2 The transformation of impulse frequencies into generator potentials (intercellular transmission).- 1.3 The transformation of generator potentials into impulse frequencies (intracellular transmission).- 1.4 Structures of neural networks.- 2. On the relations between several models for neural networks.- 2.1 The retinal network of Limulus polyphemus the Hartline-Ratliff equations.- 2.2 A statistical approach: activities in coupled neuron pools models of Cowan, Feldman, Wilson.- 2.3 Discrete models.- a) the logical neurons of McCulloch and Pitts.- b) discrete time and continuous states.- 3. Existence and uniqueness of time dependent solutions.- 4. Steady states of finite-dimensional networks.- 4.1 Existence problem.- 4.2 The number of steady states.- a) single neurons.- b) pairs of neurons.- c) arbitrarily many neurons.- 4.3 Input-output behavior of stationary networks.- 4.4 An example of spatial hysteresis.- 5. Local stability analysis of nets with finitely many neurons.- 5.1 Introduction.- 5.2 The linearization principle.- 5.3 Some simple general criteria for asymptotic stability.- 5.4 Single neurons.- 5.5 Pairs of neurons.- 5.6 Closed chains of neurons.- 6. Oscillations in nets with finitely many neurons.- 6.1 Introduction.- 6.2 Oscillations in closed chains of neurons.- 6.3 Oscillations in systems with delays.- 7. Homogeneous tissues with lateral excitation or lateral inhibition.- 7.1 Introduction.- 7.2 The model.- 7.3 Stationary solutions and their stability.- 7.4 Thresholds in bistable tissues.- 7.5 Traveling fronts.- 7.6 Diverging pairs of fronts (spread of excitation or depression).- 8. Homogeneous tissues with lateral excitation and self-inhibition.- 8.1 The model.- 8.2 Bulk oscillations.- 8.3 Traveling pulses (solitary waves).- 8.4 Traveling wave trains.- 9. Homogeneous tissues with lateral inhibition and self- or local excitation.- 9.1 The model.- 9.2 Periodic spatial patterns.- 9.3 Stability.- 9.4 Miscellaneous topics.- References.- List of symbols.

SAW Oscillators In UHF Transit Satellite Links

A 375-MHz surface-acoustic-wave (SAW) resonator controlled oscillator was developed for application in the Transit satellite marine navigation system. The SAW oscillator, in a 2-in/sup 3/ hybrid package, contains a heater, voltage regulator, and divider and is a direct replacement for a bulk wave oscillator and its multiplier chain. A short term stability of 2E - 10 and an aging rate of 3E - 8/day were achieved at 75°C. Comparison tests showed that the accuracy of the navigation system with the SAW oscillator was equivalent to the accuracy using the bulk oscillator.

Spectrum of bulk and surface spin oscillations in “strip” films

Experimental and theoretical investigations of the magnetic resonance of “strip” films were conducted. In magnetic fields below the saturation field, when “strip” films possess a periodic domain structure, a multimode character of the absorption spectrum was discovered. The spectrum of spin oscillation taking into account exchange and magnetic dipole interaction was computed. Comparison of the computed results with the experimental data permits the identification of the observed peaks as bulk and surface modes of a spin wave resonance.

Post-breakdown bulk oscillations in gold-doped silicon p+− i− n+ double-injection diodes

Experimental work on post-breakdown bulk oscillations in n-type gold-doped phosphorus-compensated p +− i− n + double-injection diodes is presented. An empirical relationship for the frequency of oscillation in this region is derived for the first time and discussed.

Spatial and temporal electron and ion density variations within the focal region of an intense laser beam in a tenuous plasma

The recent availability of focussed laser beams with flux densities well in excess of 1015 watts/cm2 at 1.06 μm has led to experimental investigations of direct interaction between intense electromagnetic fields and charged particles. In this paper the relevant hydrodynamic two-fluid mode equations for a singly ionized tenuous plasma eveloped by an intense spatially varying electromagnetic field at the focus of a pulsed laser beam is solved by computer simulations for a cylindrically symmetric geometry. Radial, axial and temporal variations of electron and ion densities are given for different laser intensities and particle number densities. Fluctuations in electron density are found due to the bulk oscillation of electrons relative to what is essentially a static array of massive ions. The possibility of generating intense electromagnetic fields devoid of charged particles is discussed.

Spectral broadening of light scattered from polysaccharide gels

Light scattering Rayleigh linewidth measurements have been made on 0.5% calcium alginate gels using the autocorrelation method. The degree of spectral broadening has been found to be small (∼2%) although two relaxation times (∼7 and ∼50 msec) within the broadened component have been measured. The variations in the degree of spectral broadening and the relaxation times with angle of scatter were found to be much less than predicted by any existing theory, and no systematic variation in any of the parameters with temperature was detected within the range 3° to 88°C. By scanning through the gel with the focused laser beam, however, it has been shown that long range (tenths of millimetres), long term (tens of minutes), fluctuations in alginate density occur. It is possible that the observed relaxation times represent the continual rearrangements of polymer chains which, assuming a junction zone type of structure, would be necessary for these fluctuations to take place. Oscillations were generally found to be superimposed upon the autocorrelation functions and these have been positively identified with bulk oscillations of the specimen. A theory is advanced explaining why bulk oscillations manifest themselves in the autocorrelation function and predicting the marked increase in amplitude with angle of scatter observed experimentally. Experiments are also described in which the diffusion coefficients of dextran fractions and globular proteins within 0.5% gels were measured by investigating the heterodyne beat spectrum. It was found that the movement of macromolecules with 1 D 20W less than 3 × 10 4 sec/mm 2 was virtually unimpeded by the gel. Diffusion constants fell to about one third of those in aqueous solution for values of 1 D 20W ∼ 9 × 10 4 sec/ mm 2 . Thus there are large interstitial spaces within the gel and if a junction zone type of structure is correct, each junction zone must consist of an association of some hundreds of chains. Some preliminary results are presented of experiments with agarose and bovine vitreous humour.

Spectral broadening of light scattered from alginate gels

AbstractLight scattering Rayleigh linewidth measurements have been made on calcium alginate gels using the autocorrelation method. The degree of broadening has been found to be small (∼2%) although two relaxation times (∼7 and 50 msec) within the broadened component have been measured. Oscillations were generally found to be superimposed upon the autocorrelation function and these have been positively identified with bulk oscillations of the specimen. By scanning through the gel with the focused laser beam it has been shown that there are long range (tenths of millimeters), long term (tens of minutes), fluctuations in alginate density.Experiments were also carried out in which the diffusion constants of dextran fractions and globular proteins within the gel were measured by investigating the heterodyne beat spectrum. It was found that the movement of macromolecules with hydrodynamic diameters less than 10 nm was virtually unimpeded by the gel. Diffusion constants fell to about one third of those in aqueous solution for hydrodynamic diameters of ∼30 nm.