Swimmers in thin films: from swarming to hydrodynamic instabilities

We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses (force dipoles or quadrupoles) on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to the collective behaviour. In contrast, for quadrupolar swimmers, our analysis shows that detailed features of the internal dynamics play an important role in determining the bulk behaviour. In the broken symmetry phases, we investigate fluctuations of hydrodynamic variables of the system and find that these destabilize order. Interestingly, this instability is not generic and depends on length-scale.Comment: 4 pages, 2 figures, references added, typos corrected, new introductio

Turbocharged Solid Oxide Fuel Cell System: Design and Emulation

This paper presents a design model of a turbocharged solid oxide fuel cell system fueled by biogas. The aim of this plant layout is the development of a low-cost solution considering the coupling of the solid oxide fuel cell (SOFC) with a low-cost machine such as a turbocharger (instead of a microturbine). The whole system model calculates the operational conditions and realizes the coupling between the turbocharger, the recuperator and the solid oxide fuel cell system (comprising SOFC, air preheater, fuel compressor and pre-heater, reformer, off-gas burner and anodic ejector). This model also supports the design of an emulator test rig in which a burner, located inside a thermal insulated vessel, replaces the solid oxide fuel cell system. The emulator test rig will be useful to study the matching between the turbocharger and the fuel cell to validate simulation models, design innovative solutions and test the control system of the whole plant

Polynomial growth of volume of balls for zero-entropy geodesic systems

The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{pol}$} and the {\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and we show that for the flat torus this inequality becomes an equality. We then study the explicit example of the torus of revolution for which we can give an exact asymptotic equivalent of the growth rate of volume of balls, which we relate to the weak polynomial entropy.Comment: 22 page

Migraine and cluster headache show impaired neurosteroids patterns

Background: Perturbation of neuronal excitability contributes to migraine. Neurosteroids modulate the activity of γ-aminobutyric acid A and N-methyl-d-aspartate receptors, and might be involved in the pathogenesis of migraine. Here, we measured plasma levels of four neurosteroids, i.e., allopregnanolone, epiallopregnanolone, dehydroepiandrosterone and deydroepiandrosterone sulfate, in patients affected by episodic migraine, chronic migraine, or cluster headache. Methods: Nineteen female patients affected by episodic migraine, 51 female patients affected by chronic migraine, and 18 male patients affected by cluster headache were recruited to the study. Sex- and age-matched healthy control subjects (31 females and 16 males) were also recruited. Patients were clinically characterized by using validated questionnaires. Plasma neurosteroid levels were measured by liquid chromatography-tandem mass spectrometry. Results: We found disease-specific changes in neurosteroid levels in our study groups. For example, allopregnanolone levels were significantly increased in episodic migraine and chronic migraine patients than in control subjects, whereas they were reduced in patients affected by cluster headache. Dehydroepiandrosterone and dehydroepiandrosterone sulfate levels were reduced in patients affected by chronic migraine, but did not change in patients affected by cluster headache. Conclusion: We have shown for the first time that large and disease-specific changes in circulating neurosteroid levels are associated with chronic headache disorders, raising the interesting possibility that fluctuations of neurosteroids at their site of action might shape the natural course of migraine and cluster headache. Whether the observed changes in neurosteroids are genetically determined or rather result from exposure to environmental or intrinsic stressors is unknown. This might also be matter for further investigation because stress is a known triggering factor for headache attacks in both migraineurs and cluster headache patients

On the terminal velocity of sedimenting particles in a flowing fluid

The influence of an underlying carrier flow on the terminal velocity of sedimenting particles is investigated both analytically and numerically. Our theoretical framework works for a general class of (laminar or turbulent) velocity fields and, by means of an ordinary perturbation expansion at small Stokes number, leads to closed partial differential equations (PDE) whose solutions contain all relevant information on the sedimentation process. The set of PDE's are solved by means of direct numerical simulations for a class of 2D cellular flows (static and time dependent) and the resulting phenomenology is analysed and discussed.Comment: 13 pages, 2 figures, submitted to JP

Simulations of viscous shape relaxation in shuffled foam clusters

We simulate the shape relaxation of foam clusters and compare them with the time exponential expected for Newtonian fluid. Using two-dimensional Potts Model simulations, we artificially create holes in a foam cluster and shuffle it by applying shear strain cycles. We reproduce the experimentally observed time exponential relaxation of cavity shapes in the foam as a function of the number of strain steps. The cavity rounding up results from local rearrangement of bubbles, due to the conjunction of both a large applied strain and local bubble wall fluctuations

Virtually Abelian Quantum Walks

We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus on the easiest case of virtually Abelian groups, and introduce a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system having larger dimension. We apply the technique in the case of two quantum walks on virtually Abelian groups with planar Cayley graphs, finding the exact solution.Comment: 10 pages, 3 figure