Fluctuations in granular gases

A driven granular material, e.g. a vibrated box full of sand, is a stationary system which may be very far from equilibrium. The standard equilibrium statistical mechanics is therefore inadequate to describe fluctuations in such a system. Here we present numerical and analytical results concerning energy and injected power fluctuations. In the first part we explain how the study of the probability density function (pdf) of the fluctuations of total energy is related to the characterization of velocity correlations. Two different regimes are addressed: the gas driven at the boundaries and the homogeneously driven gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of homogeneity in hydrodynamics profiles, even in the absence of velocity correlations, the fluctuations of total energy are non-trivial and may lead to erroneous conclusions about the role of correlations. In the second part of the chapter we take into consideration the fluctuations of injected power in driven granular gas models. Recently, real and numerical experiments have been interpreted as evidence that the fluctuations of power injection seem to satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an alternative interpretation of such results which invalidates the Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and using techniques from large deviation theory, the general validity of a Fluctuation Relation for power injection in driven granular gases is questioned. Finally a functional is defined using the Lebowitz-Spohn approach for Markov processes applied to the linear inelastic Boltzmann equation relevant to describe the motion of a tracer particle. Such a functional results to be different from injected power and to satisfy a Fluctuation Relation.Comment: 40 pages, 18 figure

Molecular dynamics simulations of oscillatory Couette flows with slip boundary conditions

The effect of interfacial slip on steady-state and time-periodic flows of monatomic liquids is investigated using non-equilibrium molecular dynamics simulations. The fluid phase is confined between atomically smooth rigid walls, and the fluid flows are induced by moving one of the walls. In steady shear flows, the slip length increases almost linearly with shear rate. We found that the velocity profiles in oscillatory flows are well described by the Stokes flow solution with the slip length that depends on the local shear rate. Interestingly, the rate dependence of the slip length obtained in steady shear flows is recovered when the slip length in oscillatory flows is plotted as a function of the local shear rate magnitude. For both types of flows, the friction coefficient at the liquid-solid interface correlates well with the structure of the first fluid layer near the solid wall.Comment: 31 pages, 11 figure

Structural efficiency of percolation landscapes in flow networks

Complex networks characterized by global transport processes rely on the presence of directed paths from input to output nodes and edges, which organize in characteristic linked components. The analysis of such network-spanning structures in the framework of percolation theory, and in particular the key role of edge interfaces bridging the communication between core and periphery, allow us to shed light on the structural properties of real and theoretical flow networks, and to define criteria and quantities to characterize their efficiency at the interplay between structure and functionality. In particular, it is possible to assess that an optimal flow network should look like a "hairy ball", so to minimize bottleneck effects and the sensitivity to failures. Moreover, the thorough analysis of two real networks, the Internet customer-provider set of relationships at the autonomous system level and the nervous system of the worm Caenorhabditis elegans --that have been shaped by very different dynamics and in very different time-scales--, reveals that whereas biological evolution has selected a structure close to the optimal layout, market competition does not necessarily tend toward the most customer efficient architecture.Comment: 8 pages, 5 figure

Simulations of extensional flow in microrheometric devices

We present a detailed numerical study of the flow of a Newtonian fluid through microrheometric devices featuring a sudden contraction–expansion. This flow configuration is typically used to generate extensional deformations and high strain rates. The excess pressure drop resulting from the converging and diverging flow is an important dynamic measure to quantify if the device is intended to be used as a microfluidic extensional rheometer. To explore this idea, we examine the effect of the contraction length, aspect ratio and Reynolds number on the flow kinematics and resulting pressure field. Analysis of the computed velocity and pressure fields show that, for typical experimental conditions used in microfluidic devices, the steady flow is highly three-dimensional with open spiraling vortical structures in the stagnant corner regions. The numerical simulations of the local kinematics and global pressure drop are in good agreement with experimental results. The device aspect ratio is shown to have a strong impact on the flow and consequently on the excess pressure drop, which is quantified in terms of the dimensionless Couette and Bagley correction factors. We suggest an approach for calculating the Bagley correction which may be especially appropriate for planar microchannels

Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group

The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a self-consistent formulation which includes both the original sharp cut-off procedure and the smooth cut-off implementation, which has been recently investigated. The critical properties of HRT are summarized, together with the behavior of the theory at first order phase transitions. However, the emphasis of this presentation is on the close relationship between HRT and non perturbative renormalization group methods, as well as on recent generalizations of HRT to microscopic models of interest in soft matter and quantum many body physics.Comment: 17 pages, 5 figures. Review paper to appear in Molecular Physic

Lattice Boltzmann simulations in microfluidics: probing the no-slip boundary condition in hydrophobic, rough, and surface nanobubble laden microchannels

In this contribution we review recent efforts on investigations of the effect of (apparent) boundary slip by utilizing lattice Boltzmann simulations. We demonstrate the applicability of the method to treat fundamental questions in microfluidics by investigating fluid flow in hydrophobic and rough microchannels as well as over surfaces covered by nano- or microscale gas bubbles.Comment: 11 pages, 6 figure

Investigating a training supporting shared decision making (IT'S SDM 2011): study protocol for a randomized controlled trial

<p/> <p>Background</p> <p>Shared Decision Making (SDM) is regarded as the best practice model for the communicative challenge of decision making about treatment or diagnostic options. However, randomized controlled trials focusing the effectiveness of SDM trainings are rare and existing measures of SDM are increasingly challenged by the latest research findings. This study will 1) evaluate a new physicians' communication training regarding patient involvement in terms of SDM, 2) validate SDM_MASS, a new compound measure of SDM, and 3) evaluate the effects of SDM on the perceived quality of the decision process and on the elaboration of the decision.</p> <p>Methods</p> <p>In a multi-center randomized controlled trial with a waiting control group, 40 physicians from 7 medical fields are enrolled. Each physician contributes a sequence of four medical consultations including a diagnostic or treatment decision.</p> <p>The intervention consists of two condensed video-based individual coaching sessions (15min.) supported by a manual and a DVD. The interventions alternate with three measurement points plus follow up (6 months).</p> <p>Realized patient involvement is measured using the coefficient SDM_MASSdrawn from the Multifocal Approach to the Sharing in SDM (MAPPIN'SDM) which includes objective involvement, involvement as perceived by the patient, and the doctor-patient concordance regarding their judges of the involvement. For validation purposes, all three components of SDM_MASSare supplemented by similar measures, the OPTION observer scale, the Shared Decision Making Questionnaire (SDM-Q) and the dyadic application of the Decisional Conflict Scale (DCS). Training effects are analyzed using t-tests. Spearman correlation coefficients are used to determine convergent validities, the influence of involvement (SDM_MASS) on the perceived decision quality (DCS) and on the elaboration of the decision. The latter is operationalised by the ELAB coefficient from the UP24 (Uncertainty Profile, 24 items version).</p> <p>Discussion</p> <p>Due to the rigorous blinded randomized controlled design, the current trial promises valid and reliable results. On the one hand, we expect this condensed time-saving training to be adopted in clinical routine more likely than previous trainings. On the other hand, the exhaustivity of the MAPPIN'SDM measurement system qualifies it as a reference measure for simpler instruments and to deepen understanding of decision-making processes.</p> <p>Trial registration</p> <p>Current Controlled Trials <a href="http://www.controlled-trials.com/ISRCTN78716079">ISRCTN78716079</a></p

Turing patterns on networks

Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical simulations, using a prey-predator model on a scale-free random network, demonstrate that the final, asymptotically reached Turing patterns can be largely different from the critical modes at the onset of instability, and multistability and hysteresis are typically observed. An approximate mean-field theory of nonlinear Turing patterns on the networks is constructed.Comment: 4 pages, 4 figure

Pulsating White Dwarf Stars and Precision Asteroseismology

Galactic history is written in the white dwarf stars. Their surface properties hint at interiors composed of matter under extreme conditions. In the forty years since their discovery, pulsating white dwarf stars have moved from side-show curiosities to center stage as important tools for unraveling the deep mysteries of the Universe. Innovative observational techniques and theoretical modeling tools have breathed life into precision asteroseismology. We are just learning to use this powerful tool, confronting theoretical models with observed frequencies and their time rate-of-change. With this tool, we calibrate white dwarf cosmochronology; we explore equations of state; we measure stellar masses, rotation rates, and nuclear reaction rates; we explore the physics of interior crystallization; we study the structure of the progenitors of Type Ia supernovae, and we test models of dark matter. The white dwarf pulsations are at once the heartbeat of galactic history and a window into unexplored and exotic physics.Comment: 70 pages, 11 figures, to be published in Annual Review of Astronomy and Astrophysics 200