The effect of charge on the dynamics of a gas bubble undergoing forced oscillations in a liquid due to incidence of an ultrasonic wave is theoretically investigated. The limiting values of the possible charge a bubble may physically carry are obtained. The presence of charge influences the regime in which the bubble's radial oscillations fall. The extremal compressive and expansive dimensions of the bubble are also studied as a function of the amplitude of the driving pressure. It is shown that the limiting value of the bubble charge is dictated both by the minimal value reachable of the bubble radius as well as the amplitude of the driving ultrasound pressure wave. A non-dimensional ratio ζ is defined that is a comparative measure of the extremal values the bubble can expand or contract to and find the existence of an unstable regime for ζ as a function of the driving pressure amplitude, Ps. This unstable regime is gradually suppressed with increasing bubble size. The Blake and the upper transient pressure thresholds for the system are then discussed.

can show highly irregular oscillations which are chaotic and of unpredictable amplitude. For applications where damage caused on surfaces due to bubble cavitation can be disastrous, such as in medicine, it is desirous to operate the sonic device in a "safe" regime, and / or to be able to have control over the bubble's motion. Often in biological systems, it is known that bubbles in fluids can be electrostatically charged. Studies of the dynamics governing the oscillations, growth and collapse of charged bubbles are therefore of immense relevance because of their prevalence in diverse applications and situations. Experimental and theoretical work on the presence of charge on gas bubbles in fluids goes back to, for example, the work of McTaggart, Alty and Akulichev [9, 10, 16, 17], and more recently the work of Shiran and Watmough and Atchley [11, 12, 18]. None of the work, though, has addressed the issue of dynamics of a charged bubble under ultrasonic forcing. It is interesting to know what effect the presence of electric charge on the bubble would have and see if the motion of such a charged bubble forced by ultrasound would vary significantly from that of an electrically neutral bubble in a fluid. This especially becomes of practical significance when we are looking at cavitation phenomena in fluids in real-life, be it in the context of cavitation in mechanical systems or in the case of bubbles in fluids in living tissue in a medical context. Apart from the work in [15], we are not aware of any other studies in the literature of the dynamics of acoustically forced charged bubbles suspended in a fluid. Their work however used the value 4/3 for the polytropic constant which entailed cancellation of all the charged terms; thus their work does not really address the issue of charge which it sets out to do. The extremely nonlinear nature

For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature and the time. We recover the known solution of Fick's law of diffusion in the flat space limit. In the biological context, this result would be useful in understanding the variations in the diffusion rates of integral proteins and other molecules on membranes. *

Periodic outbreaks of the larch budmoth Zeiraphera diniana population (and the massive forest defoliation they engender) have been recorded in the Alps over the centuries and are known for their remarkable regularity. But these have been conspicuously absent since 1981. On the other hand, budmoth outbreaks have been historically unknown in the larches of the Carpathian Tatra mountains. To resolve this puzzle, we propose here a model which includes the influence of climate and explains both the 8–9 year periodicity in the budmoth cycle and the variations from this, as well as the absence of cycles. We successfully capture the observed trend of relative frequencies of outbreaks, reproducing the dominant periodicities seen. We contend that the apparent collapse of the cycle in 1981 is due to changing climatic conditions following a tipping point and propose the recurrence of the cycle with a changed periodicity of 40 years – the next outbreak could occur in 2021. Our model also predicts longer cycles.

For a system of type-I neurons bidirectionally coupled through a nonlinear feedback mechanism, we discuss the issue of noise-induced complete synchronization (CS). For the inputs to the neurons, we point out that the rate of change of instantaneous frequency with the instantaneous phase of the stochastic inputs to each neuron matches exactly with that for the other in the event of CS of their outputs. Our observation can be exploited in practical situations to produce completely synchronized outputs in artificial devices. For excitatory-excitatory synaptic coupling, a functional dependence for the synchronization error on coupling and noise strengths is obtained. Finally we report an observation of noise-induced CS between non-identical neurons coupled bidirectionally through random non-zero couplings in an allto-all way in a large neuronal ensemble.