Coarse Brownian Dynamics for Nematic Liquid Crystals: Bifurcation Diagrams via Stochastic Simulation

We demonstrate how time-integration of stochastic differential equations (i.e. Brownian dynamics simulations) can be combined with continuum numerical bifurcation analysis techniques to analyze the dynamics of liquid crystalline polymers (LCPs). Sidestepping the necessity of obtaining explicit closures, the approach analyzes the (unavailable in closed form) coarse macroscopic equations, estimating the necessary quantities through appropriately initialized, short bursts of Brownian dynamics simulation. Through this approach, both stable and unstable branches of the equilibrium bifurcation diagram are obtained for the Doi model of LCPs and their coarse stability is estimated. Additional macroscopic computational tasks enabled through this approach, such as coarse projective integration and coarse stabilizing controller design, are also demonstrated

Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games

We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. Our goal is to design scheduling policies that always admit a pure Nash equilibrium and guarantee a small price of anarchy for the l_k-norm social cost --- the objective balances overall quality of service and fairness. We consider policies with different amount of knowledge about jobs: non-clairvoyant, strongly-local and local. The analysis relies on the smooth argument together with adequate inequalities, called smooth inequalities. With this unified framework, we are able to prove the following results. First, we study the inefficiency in l_k-norm social costs of a strongly-local policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all deterministic, non-preemptive, strongly-local and non-waiting policies (non-waiting policies produce schedules without idle times). These results ensure that SPT is close to optimal with respect to the class of l_k-norm social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price of anarchy O(2^k). Second, we consider the makespan (l_infty-norm) social cost by making connection within the l_k-norm functions. We revisit some local policies and provide simpler, unified proofs from the framework's point of view. With the highlight of the approach, we derive a local policy Balance. This policy guarantees a price of anarchy of O(log m), which makes it the currently best known policy among the anonymous local policies that always admit a pure Nash equilibrium.Comment: 25 pages, 1 figur

High-Temperature Activated AB2 Nanopowders for Metal Hydride Hydrogen Compression

A reliable process for compressing hydrogen and for removing all contaminants is that of the metal hydride thermal compression. The use of metal hydride technology in hydrogen compression applications though, requires thorough structural characterization of the alloys and investigation of their sorption properties. The samples have been synthesized by induction - levitation melting and characterized by Rietveld analysis of the X-Ray diffraction (XRD) patterns. Volumetric PCI (Pressure-Composition Isotherm) measurements have been conducted at 20, 60 and 90 oC, in order to investigate the maximum pressure that can be reached from the selected alloys using water of 90oC. Experimental evidence shows that the maximum hydrogen uptake is low since all the alloys are consisted of Laves phases, but it is of minor importance if they have fast kinetics, given a constant volumetric hydrogen flow. Hysteresis is almost absent while all the alloys release nearly all the absorbed hydrogen during desorption. Due to hardware restrictions, the maximum hydrogen pressure for the measurements was limited at 100 bars. Practically, the maximum pressure that can be reached from the last alloy is more than 150 bars.Comment: 9 figures. arXiv admin note: text overlap with arXiv:1207.354

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201

Einstein--Maxwell--Dilaton metrics from three--dimensional Einstein--Weyl structures

A class of time dependent solutions to $(3+1)$ Einstein--Maxwell-dilaton theory with attractive electric force is found from Einstein--Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and $SU(\infty)$ Toda equations. These solutions are obtained from time--like Kaluza--Klein reductions of $(3+2)$ solitons.Comment: 12 pages, to be published in Class.Quantum Gra

A simple mechanochemical model for calcium signalling in embryonic epithelial cells

Calcium (Ca2+) signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between Ca2+ signalling and mechanical forces is critical to the healthy development of an embryo but poorly understood. Several types of embryonic cells exhibit calcium-induced contractions and many experiments indicate that Ca2+ signals and contractions are coupled via a two-way mechanochemical coupling. We present a new analysis of experimental data that supports the existence of this coupling during Apical Constriction in Neural Tube Closure. We then propose a mechanochemical model, building on early models that couple Ca2+ dynamics to cell mechanics and replace the bistable Ca2+ release with modern, experimentally validated Ca2+ dynamics. We assume that the cell is a linear viscoelastic material and model the Ca2+-induced contraction stress with a Hill function saturating at high Ca2+ levels. We also express, for the first time, the 'stretch-activation' Ca2+ flux in the early mechanochemical models as a bottom-up contribution from stretch-sensitive Ca2+ channels on the cell membrane. We reduce the model to three ordinary differential equations and analyse its bifurcation structure semi-analytically as the IP3 concentration, and the 'strength' of stretch activation, λ vary. The Ca2+ system (λ=0, no mechanics) exhibits relaxation oscillations for a certain range of IP3 values. As λ is increased the range of IP3 values decreases, the oscillation amplitude decreases and the frequency increases. Oscillations vanish for a sufficiently high value of λ. These results agree with experiments in embryonic cells that also link the loss of Ca2+ oscillations to embryo abnormalities. The work addresses a very important and understudied question on the coupling of chemical and mechanical signalling in embryogenesis

Highly damped quasinormal modes of Kerr black holes

Motivated by recent suggestions that highly damped black hole quasinormal modes (QNM's) may provide a link between classical general relativity and quantum gravity, we present an extensive computation of highly damped QNM's of Kerr black holes. We do not limit our attention to gravitational modes, thus filling some gaps in the existing literature. The frequency of gravitational modes with l=m=2 tends to \omega_R=2 \Omega, \Omega being the angular velocity of the black hole horizon. If Hod's conjecture is valid, this asymptotic behaviour is related to reversible black hole transformations. Other highly damped modes with m>0 that we computed do not show a similar behaviour. The real part of modes with l=2 and m<0 seems to asymptotically approach a constant value \omega_R\simeq -m\varpi, \varpi\simeq 0.12 being (almost) independent of a. For any perturbing field, trajectories in the complex plane of QNM's with m=0 show a spiralling behaviour, similar to the one observed for Reissner-Nordstrom (RN) black holes. Finally, for any perturbing field, the asymptotic separation in the imaginary part of consecutive modes with m>0 is given by 2\pi T_H (T_H being the black hole temperature). We conjecture that for all values of l and m>0 there is an infinity of modes tending to the critical frequency for superradiance (\omega_R=m) in the extremal limit. Finally, we study in some detail modes branching off the so--called ``algebraically special frequency'' of Schwarzschild black holes. For the first time we find numerically that QNM multiplets emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.Comment: 19 pages, 11 figures. Minor typos corrected. Updated references to take into account some recent development

Brain Bases of Reading Fluency in Typical Reading and Impaired Fluency in Dyslexia

Although the neural systems supporting single word reading are well studied, there are limited direct comparisons between typical and dyslexic readers of the neural correlates of reading fluency. Reading fluency deficits are a persistent behavioral marker of dyslexia into adulthood. The current study identified the neural correlates of fluent reading in typical and dyslexic adult readers, using sentences presented in a word-by-word format in which single words were presented sequentially at fixed rates. Sentences were presented at slow, medium, and fast rates, and participants were asked to decide whether each sentence did or did not make sense semantically. As presentation rates increased, participants became less accurate and slower at making judgments, with comprehension accuracy decreasing disproportionately for dyslexic readers. In-scanner performance on the sentence task correlated significantly with standardized clinical measures of both reading fluency and phonological awareness. Both typical readers and readers with dyslexia exhibited widespread, bilateral increases in activation that corresponded to increases in presentation rate. Typical readers exhibited significantly larger gains in activation as a function of faster presentation rates than readers with dyslexia in several areas, including left prefrontal and left superior temporal regions associated with semantic retrieval and semantic and phonological representations. Group differences were more extensive when behavioral differences between conditions were equated across groups. These findings suggest a brain basis for impaired reading fluency in dyslexia, specifically a failure of brain regions involved in semantic retrieval and semantic and phonological representations to become fully engaged for comprehension at rapid reading rates