Abstract. One of the most spectacular phenomena in physics in terms of dynamical range is the glass transition and the associated slowing down of flow and relaxation with decreasing temperature. That it occurs in many different liquids seems to call for a "universal" theory. In this article, we review one such theoretical approach which is based on the concept of "frustration". Frustration in this context describes an incompatibility between extension of the locally preferred order in a liquid and tiling of the whole space. We provide a critical assessment of what has been achieved within this approach and we discuss the relation with other theories of the glass transition.

The adsorption or adhesion of large particles (proteins, colloids, cells, . . . ) at the liquid-solid interface plays an important role in many diverse applications. Despite the apparent complexity of the process, two features are particularly important: 1) the adsorption is often irreversible on experimental time scales and 2) the adsorption rate is limited by geometric blockage from previously adsorbed particles. A coarse-grained description that encompasses these two properties is provided by sequential adsorption models whose simplest example is the random sequential adsorption (RSA) process. In this article, we review the theoretical formalism and tools that allow the systematic study of kinetic and structural aspects of these sequential adsorption models. We also show how the reference RSA model may be generalized to account for a variety of experimental features including particle anisotropy, polydispersity, bulk diffusive transport, gravitational effects, surface-induced conformational and orientational change, desorption, and multilayer formation. In all cases, the significant theoretical results are presented and their accuracy (compared to computer simulation) and applicability (compared to experiment) are discussed.

We study the random sequential adsorption (RSA) of unoriented anisotropic objects onto a flat uniform surface, for various shapes (spherocylinders, ellipses, rectangles, and needles) and elongations. The asymptotic approach to the jamming limit is shown to follow the expected algebraic behavior, 0(03)-0(t)-t-1'3, where 8 is the surface coverage; this result is valid for all shapes and elongations, provided the objects have a nonzero proper area. In the limit of very small elongations, the long-time behavior consists of two successive critical regimes: The first is characterized by Feder's law, t-l", and the second by the t-1'3 law; the crossover occurs at a time that scales as E-"2 when e-+0, where E is a parameter of anisotropy. The influence of shape and elongation on the saturation coverage 0(03) is also discussed. Finally, for very elongated objects, we derive from scaling arguments that when the aspect ratio a of the objects becomes infinite, e(00) goes to zero according to a power law a-4 where p= l/(1+2fl). The fractal dimension of the system of adsorbed needles is also discussed.

We investigate the influence of space curvature, and of the associated "frustration", on the dynamics of a model glassformer: a monatomic liquid on the hyperbolic plane. We find that the system's fragility, i.e. the sensitivity of the relaxation time to temperature changes, increases as one decreases the frustration. As a result, curving space provides a way to tune fragility and make it as large as wanted. We also show that the nature of the emerging "dynamic heterogeneities", another distinctive feature of slowly relaxing systems, is directly connected to the presence of frustration-induced topological defects.Among the many anomalous properties associated with glass formation, "fragility" is one that has attracted much attention [1,2,3,4,5,6,7]. Large fragility, i.e. large deviation of the temperature dependence of the viscosity and of the structural relaxation time from an Arrhenius behavior, is usually taken as the signature of a collective phenomenon that grows as temperature decreases. This is certainly one incentive for the continuing search for a theory of the glass transition [2,4,5,6,7]. Yet, the absence of a simple glassforming liquid model in which one can control the degree of fragility, hence the extent to which collective behavior develops, has hindered progress on developing and testing candidate theories.Since the early work of Frank[8], a promising line of research on supercooled liquids and the glass transition has relied on the concept of "geometric frustration" [7,9,10]. Frustration in this context can be defined as an incompatibility between extension of the local order preferred in a liquid and tiling of the whole space. The paradigm is the icosahedral order in metallic liquids and glasses, which although locally favored cannot tile space due to topological reasons [8]. Frustration of the icosahedral order, however, can be suppressed by leaving the Euclidean world and curving space [9,10]. In a series of insightful articles [10,11,12], Nelson and collaborators have proposed a simpler two-dimensional (2D) analog: by placing a liquid of disks on a 2D manifold of constant negative curvature (the hyperbolic plane), the local hexagonal order that can tile the ordinary Euclidean plane is now frustrated in a way which mimics by many aspects the frustration of icosahedral order in 3D Euclidean space. The model of a monatomic liquid on the hyperbolic plane therefore offers the opportunity to investigate, at a microscopic level, the influence of the degree of frustration, here controlled by the curvature, on the slowing down of the relaxation associated with glass formation.We present the results of the first computer simulation of the dynamics of a liquid in curved hyperbolic space. The hyperbolic plane H 2 , also called pseudosphere or Bolyai-Lobatchevski plane, is a Riemannian surface of constant negative curvature [13,14]. Contrary to a sphere, which is a surface of constant positive curvature, H 2 is infinite: this allows one to envisage the thermodynamic limit at constant curvature. However, ...

Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons that can ultimately improve classification performance. In this study, we propose a more realistic spike train generation model. It incorporates both a description of "nontrivial" (i.e., non-Poisson) neuronal discharge statistics and a description of spike waveform dynamics (e.g., the events amplitude decays for short interspike intervals). We show that this spike train generation model is analogous to a one-dimensional Potts spin-glass model. We can therefore tailor to our particular case the computational methods that have been developed in fields where Potts models are extensively used, including statistical physics and image restoration. These methods are based on the construction of a Markov chain in the space of model parameters and spike train configurations, where a configuration is defined by specifying a neuron of origin for each spike. This Markov chain is built such that its unique stationary density is the posterior density of model parameters and configurations given the observed data. A Monte Carlo simulation of the Markov chain is then used to estimate the posterior density. We illustrate the way to build the transition matrix of the Markov chain with a simple, but realistic, model for data generation. We use simulated data to illustrate the performance of the method and to show that this approach can easily cope with neurons firing doublets of spikes and/or generating spikes with highly dynamic waveforms. The method cannot automatically find the "correct" number of neurons in the data. User input is required for this important problem and we illustrate how this can be done. We finally discuss further developments of the method.

Within the framework of a Boltzmann-Lorentz equation, we analyze the dynamics of a granular rotor immersed in a bath of thermalized particles in the presence of a frictional torque on the axis. In numerical simulations of the equation, we observe two scaling regimes at low and high bath temperatures. In the large friction limit, we obtain the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation. In the limit of large rotor mass and small friction, we derive a Fokker-Planck equation for which the exact solution is also obtained. 45.70.Vn,05.10.Gg Recently, Eshuis et al.[1], inspired by Smoluchowski's gedankenexperiment, constructed a macroscopic rotational motor consisting of four vanes immersed in a granular gas. When a soft coating was applied to one side of each vane, a ratchet effect was observed above a critical granular temperature. While this was the first experimental realization of a granular motor, similar Brownian ratchets exist in many diverse applications, e.g., photovoltaic devices and biological motors; See [2]. All of these motors share the common features of non-equilibrium conditions and spatial symmetry breaking. Several recent theoretical studies of idealized models of granular motors, which use a Boltzmann-Lorentz description [3][4][5][6][7][8], show that the motor effect is particularly pronounced when the device is constructed from two different materials, as was the case in the recent experiment [1]. The existing theories, however, predict a motor effect for any temperature of the granular gas while in the experiment the phenomenon is only observed if the bath temperature is sufficiently large. The presence of friction is at the origin of this difference and it is therefore highly desirable to incorporate it in the theoretical schemes.Several studies have considered the effect of friction on Brownian motion. The pioneering work of de Gennes [9] was motivated by the motion of a coin on a horizontally vibrating plate[10] and a liquid droplet on non-wettable surfaces subjected to an asymmetric lateral vibration; he obtained the stationary velocity distribution, as well as the velocity correlation function. A notable result, obtained independently by Hayakawa [11], is that the Einstein relation no longer holds in the presence of dry friction. More recently, Touchette and coworkers [12-14] obtained a solution of a model with dry friction and viscous damping.In this Letter, we investigate the kinetic properties of a heterogeneous granular rotor in the presence of dry (Coulomb) friction and we provide exact solutions in the limit of large motor mass (Brownian limit) and also in the limit of strong friction for arbitrary mass .We consider a two-dimensional system where a heterogeneous chiral rotor with moment of inertia I, mass M and the length L immersed in a granular gas at density ρ with a velocity distribution φ(v) characterized by a granular temperature T . The motor is composed of two materials with coefficients of restitution α + and α − . Coll...

We present a theoretical study of the phase diagram of a frustrated Ising model with nearest-neighbor ferromagnetic interactions and long-range (Coulombic) antiferromagnetic interactions. For nonzero frustration, long-range ferromagnetic order is forbidden, and the ground state of the system consists of phases characterized by periodically modulated structures. At finite temperatures, the phase diagram is calculated within the mean-field approximation. Below the transition line that separates the disordered and the ordered phases, the frustration-temperature phase diagram displays an infinite number of "flowers," each flower being made by an infinite number of modulated phases generated by structure combination branching processes. The specificities introduced by the long-range nature of the frustrating interaction and the limitation of the mean-field approach are finally discussed.

We study the kinetics of random sequential adsorption (RSA) of anisotropic bodies (rectangles, ellipses, spherocylinders or, more precisely, discorectangles, and needles) at lowto-intermediate coverages. In this regime, the adsorption probability can be expressed as a power series in the coverage. We calculate numerically the second-and third-order coefficients of the series and compare the results to simulation data. The results for the low-coverage kinetics are then combined with the asymptotic results of Paper I [J. Chem. Phys. 97, 5212 (1992)] to construct approximate equations for the adsorption probability over the entire coverage range. While the equations provide a reasonably good description of the RSA kinetics, they produce unsatisfactory estimates of the saturation coverages. The effect of particle shape on the adsorption kinetics and surface structure is discussed. Finally, the available surface function is compared with that corresponding to equilibrium configurations of the adsorbed particles.