Resolution requirements for numerical simulations of transition

The resolution requirements for direct numerical simulations of transition to turbulence are investigated. A reliable resolution criterion is determined from the results of several detailed simulations of channel and boundary-layer transition

Thermal counterflow in a periodic channel with solid boundaries

We perform numerical simulations of finite temperature quantum turbulence produced through thermal counterflow in superfluid 4He, using the vortex filament model. We investigate the effects of solid boundaries along one of the Cartesian directions, assuming a laminar normal fluid with a Poiseuille velocity profile, whilst varying the temperature and the normal fluid velocity. We analyze the distribution of the quantized vortices, reconnection rates, and quantized vorticity production as a function of the wall-normal direction. We find that the quantized vortex lines tend to concentrate close to the solid boundaries with their position depending only on temperature and not on the counterflow velocity. We offer an explanation of this phenomenon by considering the balance of two competing effects, namely the rate of turbulent diffusion of an isotropic tangle near the boundaries and the rate of quantized vorticity production at the center. Moreover, this yields the observed scaling of the position of the peak vortex line density with the mutual friction parameter. Finally, we provide evidence that upon the transition from laminar to turbulent normal fluid flow, there is a dramatic increase in the homogeneity of the tangle, which could be used as an indirect measure of the transition to turbulence in the normal fluid component for experiments

Interaction Between Convection and Pulsation

This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages, 14 figure

The Temporal Winner-Take-All Readout

How can the central nervous system make accurate decisions about external stimuli at short times on the basis of the noisy responses of nerve cell populations? It has been suggested that spike time latency is the source of fast decisions. Here, we propose a simple and fast readout mechanism, the temporal Winner-Take-All (tWTA), and undertake a study of its accuracy. The tWTA is studied in the framework of a statistical model for the dynamic response of a nerve cell population to an external stimulus. Each cell is characterized by a preferred stimulus, a unique value of the external stimulus for which it responds fastest. The tWTA estimate for the stimulus is the preferred stimulus of the cell that fired the first spike in the entire population. We then pose the questions: How accurate is the tWTA readout? What are the parameters that govern this accuracy? What are the effects of noise correlations and baseline firing? We find that tWTA sensitivity to the stimulus grows algebraically fast with the number of cells in the population, N, in contrast to the logarithmic slow scaling of the conventional rate-WTA sensitivity with N. Noise correlations in first-spike times of different cells can limit the accuracy of the tWTA readout, even in the limit of large N, similar to the effect that has been observed in population coding theory. We show that baseline firing also has a detrimental effect on tWTA accuracy. We suggest a generalization of the tWTA, the n-tWTA, which estimates the stimulus by the identity of the group of cells firing the first n spikes and show how this simple generalization can overcome the detrimental effect of baseline firing. Thus, the tWTA can provide fast and accurate responses discriminating between a small number of alternatives. High accuracy in estimation of a continuous stimulus can be obtained using the n-tWTA

Predicting climate change using response theory: global averages and spatial patterns

The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(105105) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is non-autonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting—at any lead time and in an ensemble sense—the change in climate properties resulting from increase in the concentration of CO22 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change