From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

New horizons for black holes and branes

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes

Oscillations, phase-of-firing coding, and spike timing-dependent plasticity: an efficient learning scheme

Recent experiments have established that information can be encoded in the spike times of neurons relative to the phase of a background oscillation in the local field potential—a phenomenon referred to as “phase-of-firing coding” (PoFC). These firing phase preferences could result from combining an oscillation in the input current with a stimulus-dependent static component that would produce the variations in preferred phase, but it remains unclear whether these phases are an epiphenomenon or really affect neuronal interactions—only then could they have a functional role. Here we show that PoFC has a major impact on downstream learning and decoding with the now well established spike timing-dependent plasticity (STDP). To be precise, we demonstrate with simulations how a single neuron equipped with STDP robustly detects a pattern of input currents automatically encoded in the phases of a subset of its afferents, and repeating at random intervals. Remarkably, learning is possible even when only a small fraction of the afferents (~10%) exhibits PoFC. The ability of STDP to detect repeating patterns had been noted before in continuous activity, but it turns out that oscillations greatly facilitate learning. A benchmark with more conventional rate-based codes demonstrates the superiority of oscillations and PoFC for both STDP-based learning and the speed of decoding: the oscillation partially formats the input spike times, so that they mainly depend on the current input currents, and can be efficiently learned by STDP and then recognized in just one oscillation cycle. This suggests a major functional role for oscillatory brain activity that has been widely reported experimentally.

Holographic optical tweezers combined with back-focal-plane displacement detection

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.

The effect of virtual reality on visual vertigo symptoms in patients with peripheral vestibular dysfunction: a pilot study.

Individuals with vestibular dysfunction may experience visual vertigo (VV), in which symptoms are provoked or exacerbated by excessive or disorientating visual stimuli (e.g. supermarkets). VV can significantly improve when customized vestibular rehabilitation exercises are combined with exposure to optokinetic stimuli. Virtual reality (VR), which immerses patients in realistic, visually challenging environments, has also been suggested as an adjunct to VR to improve VV symptoms. This pilot study compared the responses of sixteen patients with unilateral peripheral vestibular disorder randomly allocated to a VR regime incorporating exposure to a static (Group S) or dynamic (Group D) VR environment. Participants practiced vestibular exercises, twice weekly for four weeks, inside a static (Group S) or dynamic (Group D) virtual crowded square environment, presented in an immersive projection theatre (IPT), and received a vestibular exercise program to practice on days not attending clinic. A third Group D1 completed both the static and dynamic VR training. Treatment response was assessed with the Dynamic Gait Index and questionnaires concerning symptom triggers and psychological state. At final assessment, significant betweengroup differences were noted between Groups D (p = 0.001) and D1 (p = 0.03) compared to Group S for VV symptoms with the former two showing a significant 59.2% and 25.8% improvement respectively compared to 1.6% for the latter. Depression scores improved only for Group S (p = 0.01) while a trend towards significance was noted for Group D regarding anxiety scores (p = 0.07). Conclusion: Exposure to dynamic VR environments should be considered as a useful adjunct to vestibular rehabilitation programs for patients with peripheral vestibular disorders and VV symptoms.