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In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts that increase coverage are accepted. The process continues indefinitely on an infinite substrate, and we analyze the dynamics of random sequential covering of $\mathbb{Z}$ using $k$-mers. We introduce a method that provides a comprehensive solution to the dynamics of this process. We derive explicit solutions for trimers, tetramers, and pentamers; we study numerically random sequential covering by longer polymers ($k>5$)., Comment: 19 pages 4 figures

The adoption of agroecological practices will be crucial to address the challenges of climate change and biodiversity loss. Such practices favor the cultivation of plants in complex mixtures with layouts differing from the monoculture approach of conventional agriculture. Inspired by random sequential adsorption processes, we propose a one-dimensional model in which the plants are represented as line segments that start as points and grow at a constant rate until they reach length $\sigma$ after a time interval $\tau$. The planting positions and times are randomly chosen with the constraint that plant overlap is forbidden. We apply an exact, event-driven simulation to investigate the resulting spatiotemporal patterns and yields in both mono- and duocultures. After a transient period, with oscillations in the density and coverage, the field reaches a steady state in which the mean age of plants is one half of the time to maturity. The structure of the active plants is characterized by correlation functions between the fluctuation of the age of a plant and its $k$th neighbour. Nearest neighbours are negatively correlated, while next nearest neighbours tend to have similar ages. The steady state yield increases with the planting rate and approaches a maximum value of 4/3 plants per unit length per unit time. For two species with the same size at maturity but different growth rates, the more slowly growing species is enriched in the harvest compared to the seed mix composition. If two species have the same time to maturity but different sizes, the smaller one is enriched in the harvest and, at a sufficiently high planting rate, the larger species may be completely absent. For two species with the same ratio of $\sigma/\tau$ the selectivity is insensitive to the planting rate. The model may be extended to higher dimensions, more species and other planting strategies., Comment: 14 pages, 13 figures

We study the stochastic dynamics of a two-dimensional particle assuming that the components of its position are two coupled random-acceleration processes evolving in a confining parabolic potential and are the subjects of independent Gaussian white noises with different amplitudes (temperatures). We determine the standard characteristic properties, i.e., the moments of position's components and their velocities, mixed moments and two-time correlations, as well as the position-velocity probability density function (pdf). We show that if the amplitudes of the noises are not equal, then the particle experiences a non-zero (on average) torque, such that the angular momentum L and the angular velocity W have non-zero mean values. Both are (irregularly) oscillating with time t, such that the characteristics of a rotational motion are changing their signs. We also evaluate the pdf-s of L and W and show that the former has exponential tails for any fixed t, and hence, all moments. In addition, in the large-time limit this pdf converges to a uniform distribution with a diverging variance. The pdf of W possesses heavy power-law tails such that the mean W is the only existing moment. This pdf converges to a limiting form which, surprisingly, is completely independent of the amplitudes of noises., Comment: 33 pages, 5 Figures

The Brownian gyrator (BG) is a minimal model of a nano-engine performing a rotational motion, judging solely upon the fact that in non-equilibrium conditions its torque, angular momentum ${\cal L}$ and angular velocity $\cal W$ have non-zero mean values. For a time-discretized model, we calculate the previously unknown probability density functions (PDFs) of ${\cal L}$ and $\cal W$. We find that when the time-step $\delta t \to 0$, both PDFs converge to uniform distributions with diverging variances. For finite $\delta t$, the PDF of ${\cal L}$ has exponential tails and all moments, but its noise-to-signal ratio is generically much bigger than $1$. The PDF of ${\cal W}$ exhibits heavy power-law tails and its mean ${\cal W}$ is the only existing moment. The BG is therefore not an engine in common sense: it does not exhibit regular rotations on each run and its fluctuations are not only a minor nuisance. Our theoretical predictions are confirmed by numerical simulations and experimental data. We discuss some improvements of the model which may result in a more systematic behavior., Comment: 5 pages +SM 11 pages

We present a theoretical analysis of a non-equilibrium dynamics in a model system consisting of two particles which move randomly on a plane. The two particles interact via a harmonic potential, experience their own (independent from each other) noises characterized by two different temperatures $T_1$ and $T_2$, and each particle is being held by its own optical tweezer. Such a system with two particle coupled by hydrodynamic interactions was previously realised experimentally in B\'erut et al. [EPL {\bf 107}, 60004 (2014)], and the difference between two temperatures has been achieved by exerting an additional noise on either of the tweezers. Framing the dynamics in terms of two coupled over-damped Langevin equations, we show that the system reaches a non-equilibrium steady-state with non-zero (for $T_1 \neq T_2$) probability currents that possess non-zero curls. As a consequence, in this system the particles are continuously spinning around their centers of mass in a completely synchronised way - the curls of currents at the instantaneous positions of two particles have the same magnitude and sign. Moreover, we demonstrate that the components of currents of two particles are strongly correlated and undergo a rotational motion along closed elliptic orbits., Comment: 17 pages, 4 figures

We study the two-dimensional Langevin dynamics of a two-component system, whose components are in contact with heat baths kept at different temperatures. Dynamics is constrained by an optical trap and the \text{dissimilar} species interact via a quadratic potential. We realize that the system evolves towards a peculiar non-equilibrium steady-state with a non-zero probability current possessing a non-zero curl, such that the randomly moving particles are spinning around themselves, like "spinning top" toys. Our analysis shows that the spinning motion is correlated and also reveals an emerging cooperative behavior of the spatial components of the probability currents of dissimilar species., Comment: 24 pages, 7 Figures

When a physical system evolves in a thermal bath at a constant temperature, it arrives eventually to an equilibrium state whose properties are independent of the kinetic parameters and of the precise evolution scenario. This is generically not the case for a system driven out of equilibrium which, on the contrary, reaches a steady-state with properties that depend on the full details of the dynamics such as the driving noise and the energy dissipation. How the steady state depends on such parameters is in general a non-trivial question. Here, we approach this broad problem using a minimal model of a two-dimensional nano-machine, the Brownian gyrator, that consists of a trapped particle driven by fractional Gaussian noises -- a family of noises with long-ranged correlations in time and characterized by an anomalous diffusion exponent $\alpha$. When the noise is different in the different spatial directions, our fractional Brownian gyrator persistently rotates. Even if the noise is non-trivial, with long-ranged time correlations, thanks to its Gaussian nature we are able to characterize analytically the resulting nonequilibrium steady state by computing the probability density function, the probability current, its curl and the angular velocity and complement our study by numerical results., Comment: 28 pages, 7 figures

Motivated by the physical properties of Vesignieite BaCu$_3$V$_2$O$_8$(OH)$_2$, we study the $J_1-J_3$ Heisenberg model on the kagom\'e lattice, that is proposed to describe this compound for $J_1<0$ and $J_3\gg|J_1|$. The nature of the classical ground state and the possible phase transitions are investigated through analytical calculations and parallel tempering Monte Carlo simulations. For $J_1<0$ and $J_3>\frac{1+\sqrt{5}}4|J_1|$, the ground states are not all related by an Hamiltonian symmetry. Order appears at low temperature via the order by disorder mechanism, favoring colinear configurations and leading to an emergent $q=4$ Potts parameter. This gives rise to a finite temperature phase transition. Effect of quantum fluctuations are studied through linear spin wave approximation and high temperature expansions of the $S=1/2$ model. For $J_3$ between $\frac14|J_1|$ and $\frac{1+\sqrt{5}}4|J_1|$, the ground state goes through a succession of semi-spiral states, possibly giving rise to multiple phase transitions at low temperatures.

In two dimensions, a system of self-gravitating particles collapses and forms a singularity in finite time below a critical temperature $T_c$. We investigate experimentally a quasi two-dimensional cloud of cold neutral atoms in interaction with two pairs of perpendicular counter-propagating quasi-resonant laser beams, in order to look for a signature of this ideal phase transition: indeed, the radiation pressure forces exerted by the laser beams can be viewed as an anisotropic, and non-potential, generalization of two-dimensional self-gravity. We first show that our experiment operates in a parameter range which should be suitable to observe the collapse transition. However, the experiment unveils only a moderate compression instead of a phase transition between the two phases. A three-dimensional numerical simulation shows that both the finite small thickness of the cloud, which induces a competition between the effective gravity force and the repulsive force due to multiple scattering, and the atomic losses due to heating in the third dimension, contribute to smearing the transition., Comment: 11 pages, 8 figures, accepted in Physical Review A

We model a particulate flow of constant velocity through confined geometries, ranging from a single channel to a bundle of $N_c$ identical coupled channels, under conditions of reversible blockage. Quantities of interest include the exiting particle flux (or throughput) and the probability that the bundle is open. For a constant entering flux, the bundle evolves through a transient regime to a steady state. We present analytic solutions for the stationary properties of a single channel with capacity $N\le 3$ and for a bundle of channels each of capacity $N = 1$. For larger values of $N$ and $N_c$, the system's steady state behavior is explored by numerical simulation. Depending on the deblocking time, the exiting flux either increases monotonically with intensity or displays a maximum at a finite intensity. For large $N$ we observe an abrupt change from a state with few blockages to one in which the bundle is permanently blocked and the exiting flux is due entirely to the release of blocked particles. We also compare the relative efficiency of coupled and uncoupled bundles. For $N=1$ the coupled system is always more efficient, but for $N>1$ the behavior is more complex., Comment: 14 pages, 15 figures

Networks of channels conveying particles are often subject to blockages due to the limited carrying capacity of the individual channels. If the channels are coupled, blockage of one causes an increase in the flux entering the remaining open channels leading to a cascade of failures. Once all channels are blocked no additional particle can enter the system. If the blockages are of finite duration, however, the system reaches a steady state with an exiting flux that is reduced compared to the incoming one. We propose a stochastic model consisting of $N_c$ channels each with a blocking threshold of $N$ particles. Particles enter the system according to a Poisson process with the entering flux of intensity $\Lambda$ equally distributed over the open channels. Any particle in an open channel exits at a rate $\mu$ and a blocked channel unblocks at a rate $\mu^*$. We present a method to obtain the exiting flux in the steady state, and other properties, for arbitrary $N_c$ and $N$ and we present explicit solutions for $N_c=2,3$. We apply these results to compare the efficiency of conveying a particulate stream of intensity $\Lambda$ using different channel configurations. We compare a single "robust" channel with a large capacity with multiple "fragile" channels with a proportionately reduced capacity. The "robust" channel is more efficient at low intensity, while multiple, "fragile" channels have a higher throughput at large intensity. We also compare $N_c$ coupled channels with $N_c$ independent channels, both with threshold $N=2$. For $N_c=2$ if $\mu^*/\mu>1/4$, the coupled channels are always more efficient. Otherwise the independent channels are more efficient for sufficiently large $\Lambda$., Comment: 13 pages submitted to J. Phys. Cond. Matter

This paper focuses on solving coupled problems of lumped parameter models. Such problems are of interest for the simulation of severe accidents in nuclear reactors~: these coarse-grained models allow for fast calculations for statistical analysis used for risk assessment and solutions of large problems when considering the whole severe accident scenario. However, this modeling approach has several numerical flaws. Besides, in this industrial context, computational efficiency is of great importance leading to various numerical constraints. The objective of this research is to analyze the applicability of explicit coupling strategies to solve such coupled problems and to design implicit coupling schemes allowing stable and accurate computations. The proposed schemes are theoretically analyzed and tested within CEA's procor platform on a problem of heat conduction solved with coupled lumped parameter models and coupled 1D models. Numerical results are discussed and allow us to emphasize the benefits of using the designed coupling schemes instead of the usual explicit coupling schemes.

Filtration, flow in narrow channels and traffic flow are examples of processes subject to blocking when the channel conveying the particles becomes too crowded. If the blockage is temporary, which means that after a finite time the channel is flushed and reopened, one expects to observe a maximum throughput for a finite intensity of entering particles. We investigate this phenomenon by introducing a queueing theory inspired, circular Markov model. Particles enter a channel with intensity $\lambda$ and exit at a rate $\mu$. If $N$ particles are present at the same time in the channel, the system becomes blocked and no more particles can enter until the blockage is cleared after an exponentially distributed time with rate $\mu^*$. We obtain an exact expression for the steady state throughput (including the exiting blocked particles) for all values of $N$. For $N=2$ we show that the throughput assumes a maximum value for finite $\lambda$ if $\mu^*/\mu < 1/4$. The time-dependent throughput either monotonically approaches the steady state value, or reaches a maximum value at finite time. We demonstrate that, in the steady state, this model can be mapped to a previously introduced non-Markovian model with fixed transit and blockage times. We also examine an irreversible, non-Markovian blockage process with constant transit time exposed to an entering flux of fixed intensity for a finite time and we show that the first and second moments of the number of exiting particles are maximized for a finite intensity., Comment: 20 pages, 13 figures

We study by Molecular Dynamics simulation a dense one-component system of particles confined on a spherical substrate. We more specifically investigate the evolution of the structural and dynamical properties of the system when changing the control parameters, the temperature and the curvature of the substrate. We find that the dynamics becomes glassy at low temperature, with a strong slowdown of the relaxation and the emergence of dynamical heterogeneity. The prevalent local $6$-fold order is frustrated by curvature and we analyze in detail the role of the topological defects in the statics and the dynamics of the particle assembly., Comment: 15 pages, 18 Figures

We consider the two dimensional motion of a particle into a confining potential, subjected to Brownian forces, associated with two different temperatures on the orthogonal directions. Exact solutions are obtained for an asymmetric harmonic potential in the overdamped and underdamped regimes, whereas perturbative approaches are used for more general potentials. The resulting non equilibrium stationary state is characterized with a nonzero orthoradial mean current, corresponding to a global rotation of the particle around the center. The rotation is due to two symmetry breaking: two different temperatures and a mismatch between the principal axes of the confining asymmetric potential and the temperature axes. We confirm our predictions by performing Brownian dynamics simulation. Finally, we propose to observe this effect on a laser cooled atomic system., Comment: 11 pages, 9 Figures, submitted to PRE

Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle number. We show here that, by applying a suitable perturbation operator for a finite time interval, we obtain, in a family of long-range systems, non-equilibrium states which appear to be strictly stationary. They exist even in the case of a harmonic potential, and are characterised by an ordered microscopic phase space structure. We give some simple heuristic arguments which predict reasonably well some properties of these states., Comment: 5 pages, 5 figures, 1 supplemental material 2 simulation movies

For many years, lunar laser ranging (LLR) observations using a green wavelength have suffered an inhomogeneity problem both temporally and spatially. This paper reports on the implementation of a new infrared detection at the Grasse LLR station and describes how infrared telemetry improves this situation. Our first results show that infrared detection permits us to densify the observations and allows measurements during the new and the full Moon periods. The link budget improvement leads to homogeneous telemetric measurements on each lunar retro-reflector. Finally, a surprising result is obtained on the Lunokhod 2 array which attains the same efficiency as Lunokhod 1 with an infrared laser link, although those two targets exhibit a differential efficiency of six with a green laser link.

Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSS we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique non-equilibrium stationary state, completely different to its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g. spatial density or velocity distribution) of the system itself., Comment: 16 pages, 12 figures

We study the dynamics of a one-component liquid constrained on a spherical substrate, a 2-sphere, and investigate how the mode-coupling theory (MCT) can describe the new features brought by the presence of curvature. To this end we have derived the MCT equations in a spherical geometry. We find that, as seen from the MCT, the slow dynamics of liquids in curved space at low temperature does not qualitatively differ from that of glass-forming liquids in Euclidean space. The MCT predicts the right trend for the evolution of the relaxation slowdown with curvature but is dramatically off at a quantitative level., Comment: 10 pages, 7 figures

We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value $N$, a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the $n$ particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particle and their time correlation. We generalize previous results for $N=2$ to an arbitrary distribution of entry times and obtain new, exact solutions for $N=3$ for a Poisson distribution and partial results for $N\ge 4$., Comment: 13 pages, 9 figures

We investigate by Molecular Dynamics simulation a system of $N$ particles moving on the surface of a two-dimensional sphere and interacting by a Lennard-Jones potential. We detail the way to account for the changes brought by a nonzero curvature, both at a methodological and at a physical level. When compared to a two-dimensional Lennard-Jones liquid on the Euclidean plane, where a phase transition to an ordered hexagonal phase takes place, we find that the presence of excess defects imposed by the topology of the sphere frustrates the hexagonal order. We observe at high density a rapid increase of the relaxation time when the temperature is decreased, whereas in the same range of temperature the pair correlation function of the system evolves only moderately., Comment: 10 oages, 5 figures

Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such systems in the presence of dissipation. Using an appropriate mean-field kinetic description, we show that models with dissipation due to a viscous damping or due to inelastic collisions admit "scaling quasi-stationary states", i.e., states which are quasi-stationary in rescaled variables. A numerical study of one dimensional self-gravitating systems confirms both the relevance of these solutions, and gives indications of their regime of validity in line with theoretical predictions. We underline that the velocity distributions never show any tendency to evolve towards a Maxwell-Boltzmann form., Comment: 5 pages, 3 figures, to appear in Phys. Rev. Lett

We investigate models in which blocking can interrupt a particulate flow process at any time. Filtration, and flow in micro/nano-channels and traffic flow are examples of such processes. We first consider concurrent flow models where particles enter a channel randomly. If at any time two particles are simultaneously present in the channel, failure occurs. The key quantities are the survival probability and the distribution of the number of particles that pass before failure. We then consider a counterflow model with two opposing Poisson streams. There is no restriction on the number of particles passing in the same direction, but blockage occurs if, at any time, two opposing particles are simultaneously present in the passage., Comment: 5 pages, 5 figures, to appear in Phys. Rev. Letters

We investigate the influence of dry friction on an asymmetric, granular piston of mass $M$ composed of two materials undergoing inelastic collisions with bath particles of mass $m$. Numerical simulations of the Boltzmann-Lorentz equation reveal the existence of two scaling regimes depending on the strength of friction. In the large friction limit, we introduce an exact model giving the asymptotic behavior of the Boltzmann-Lorentz equation. For small friction and for large mass ratio $M/m$, we derive a Fokker-Planck equation for which the exact solution is also obtained. Static friction attenuates the motor effect and results in a discontinuous velocity distribution., Comment: 10 pages, 8 Figures

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., Comment: 4 pages, 4 Figures, To be published in Phys. Rev. Lett

We study the properties of a heterogeneous, chiral granular rotor that is capable of performing useful work when immersed in a bath of thermalized particles. The dynamics can be obtained in general from a numerical solution of the Boltzmann-Lorentz equation. We show that a mechanical approach gives the exact mean angular velocity in the limit of an infinitely massive rotor. We examine the dependence of the mean angular velocity on the coefficients of restitution of the two materials composing the motor. We compute the power and efficiency and compare with numerical simulations. We also perform a realistic numerical simulation of a granular rotor which shows that the presence of non uniformity of the bath density within the region where the motor rotates, and that the ratchet effect is slightly weakened, but qualitatively sustained. Finally we discuss the results in connection with recent experiments., Comment: 19 pages, 12 figures

In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero curvature and on the influence of the latter on the phase behavior, thermodynamics and structure of simple liquids. Reference will also be made to existing work on three-dimensional curved space and two-dimensional manifolds with varying curvature., Comment: 66 pages, 15 Figures. Submitted to Adv. Chem. Phys

The explicit solution of the discrete time filtering problems with exponential criteria for a general Gaussian signal is obtained through an approach based on a conditional Cameron-Martin type formula. This key formula is derived for conditional expectations of exponentials of some quadratic forms of Gaussian sequences. The formula involves conditional expectations and conditional covariances in some auxiliary optimal risk-neutral filtering problem which is used in the proof. Closed form recursions of Volterra type for these ingredients are provided. Particular cases for which the results can be further elaborated are investigated., Comment: 34 pages

We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk thermodynamic pressure to the pair correlation function and we develop the appropriate setting for extending the integral-equation approach of liquid-state theory in order to describe the fluid structure. We apply the formalism and study the influence of negative space curvature on two types of systems that have been recently considered: Coulombic systems, such as the one- and two-component plasma models, and fluids interacting through short-range pair potentials, such as the hard-disk and the Lennard-Jones models., Comment: 25 pages, 10 Figures

Filtering problems with general exponential quadratic criteria are investigated for Gauss-Markov processes. In this setting, the Linear Exponential Gaussian and Risk-Sensitive filtering problems are solved and it is shown that they may have different solutions.

We study the thermostatistical fluctuations of a single Delrin monomer on a granular lattice of dimer particles using both experiment and simulation. The goal is to examine the collision frequency, energy injection, and sidewall effects on a single second-layer particle in a bi-layer granular gas experiment. Non-Gaussian velocity statistics are observed for the single particle of the top layer and result from the presence of defects in the first layer. These deviations are not directly due to the presence of the boundary wall, since the form of velocity distributions is quite spatially homogeneous, but are the consequence of the presence of a few mobile defects in the first layer., Comment: 12 pages, 5 figures, accepted for publication in Phys. Rev. E

We investigate the velocity-correlation distributions after $n$ collisions of a tagged particle undergoing binary collisions. Analytical expressions are obtained in any dimension for the velocity-correlation distribution after the first-collision as well as for the velocity-correlation function after an infinite number of collisions, in the limit of Gaussian velocity distributions. It appears that the decay of the first-collision velocity-correlation distribution for negative argument is exponential in any dimension with a coefficient that depends on the mass and on the coefficient of restitution. We also obtained the velocity-correlation distribution when the velocity distributions are not Gaussian: by inserting Sonine corrections of the velocity distributions, we derive the corrections to the velocity-correlation distribution which agree perfectly with a DSMC (Direct Simulation Monte Carlo) simulation. We emphasize that these new quantities can be easily obtained in simulations and likely in experiments: they could be an efficient probe of the local environment and of the degree of inelasticity of the collisions., Comment: 11 pages, 7 figures

We introduce a minimal model describing the physics of classical two-dimensional (2D) frustrated Heisenberg systems, where spins order in a non-planar way at T=0. This model, consisting of coupled trihedra (or Ising-$\mathbb{R}P^3$ model), encompasses Ising (chiral) degrees of freedom, spin-wave excitations and $\Z_2$ vortices. Extensive Monte Carlo simulations show that the T=0 chiral order disappears at finite temperature in a continuous phase transition in the 2D Ising universality class, despite misleading intermediate-size effects observed at the transition. The analysis of configurations reveals that short-range spin fluctuations and $\Z_2$ vortices proliferate near the chiral domain walls explaining the strong renormalization of the transition temperature. Chiral domain walls can themselves carry an unlocalized $\Z_2$ topological charge, and vortices are then preferentially paired with charged walls. Further, we conjecture that the anomalous size-effects suggest the proximity of the present model to a tricritical point. A body of results is presented, that all support this claim: (i) First-order transitions obtained by Monte Carlo simulations on several related models (ii) Approximate mapping between the Ising-$\mathbb{R}P^3$ model and a dilute Ising model (exhibiting a tricritical point) and, finally, (iii) Mean-field results obtained for Ising-multispin Hamiltonians, derived from the high-temperature expansion for the vector spins of the Ising-$\mathbb{R}P^3$ model., Comment: 15 pages, 12 figures, 1 table

We examine the reversible adsorption of spherical solutes on a random site surface in which the adsorption sites are uniformly and randomly distributed on a substrate. Each site can be occupied by one solute provided that the nearest occupied site is at least one diameter away. The model is characterized by the site density and the bulk phase activity of the adsorbate. We develop a general statistical mechanical description of the model and we obtain exact expressions for the adsorption isotherms in limiting cases of large and small activity and site density, particularly for the one dimensional version of the model. We also propose approximate isotherms that interpolate between the exact results. These theories are in good agreement with numerical simulations of the model in two dimensions., Comment: 10 Pages, 11 Figures

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., Comment: 4 pages, 3 figures

A new methodology is proposed to estimate 3D displacement fields from pairs of images obtained from X-Ray Computed Micro Tomography (XCMT). Contrary to local approaches, a global approach is followed herein that evaluates {\em continuous} displacement fields. Although any displacement basis could be considered, the procedure is specialized to finite element shape functions. The method is illustrated with the analysis of a compression test on a polypropylene solid foam (independently studied in a companion paper). A good stability of the measured displacement field is obtained for cubic element sizes ranging from 16 voxels to 6 voxels., Comment: nombre de pages = 34