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Diffusion-limited reactions (DLR) are usually described within the Smoluchowski theory, which neglects interactions between the diffusing components. We propose a first extension of such frame- work that incorporates excluded-volume effects, considering hard diffusing agents in the presence of an absorbing sink. For large values of the absorber-to-diffuser size ratio Rs, the encounter rate obtained from the simulations is in very good agreement with a simple generalization of the Smolu- chowski equation at high densities. Reducing Rs, the rate gets substantially depressed at interme- diate packing and become even non-monotonic for Rs << 1. Concurrently with the saturation of the rate, stationary density waves set in close to the absorbing center. A mean-field, effective-potential analysis of the Smoluchowski equation under crowding sheds light on the subtle link between such ordering and the slowing down of the encounter dynamics. Finally, we show how an infinitesimal amount of non-reacting impurities can equally slow down dramatically the reaction., Comment: 4 pages, 5 figures, to appear on Phys. Rev. Lett

On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbours whereas its average escape time, the structural relaxation time $\tau_\alpha$, increases from a few picoseconds up to thousands of seconds. A thorough study of the correlation between $\tau_\alpha$ and the rattling amplitude, expressed by the Debye-Waller factor (DW), was carried out. Molecular-dynamics (MD) simulations of both a model polymer system and a binary mixture were performed by varying the temperature, the density $\rho$, the potential and the polymer length to consider the structural relaxation as well as both the rotational and the translation diffusion. The simulations evidence the scaling between the $\tau_\alpha$ and the Debye-Waller factor. An analytic model of the master curve is developed in terms of two characteristic length scales pertaining to the distance to be covered by the kinetic unit to reach a transition state. The model does not imply $\tau_\alpha$ divergences. The comparison with the experiments supports the numerical evidence over a range of relaxation times as wide as about eighteen orders of magnitude. A comparison with other scaling and correlation procedures is presented. The study suggests that the equilibrium and the moderately supercooled states of the glassformers possess key information on the huge slowing-down of their relaxation close to the glass transition. The latter, according to the present simulations, exhibits features consistent with the Lindemann melting criterion and the free-volume model., Comment: 8 pages, 11 figures

The correlation between the fast cage dynamics and structural relaxation is investigated in a model polymer system. It is shown that the cage vibration amplitude, as expressed by the Debye-Waller factor, and the relaxation time $\tau_\alpha$ collapse on a single universal curve with a simple analytic form when the temperature, the density, the chain length and the monomer-monomer interaction potential are changed. For the physical states with the same $\tau_\alpha$ coincidence of the mean-square displacement, the intermediate scattering function and the non-Gaussian parameter is observed in a wide time window spanning from the ballistic regime to the onset of the Rouse dynamics driven by the chain connectivity. The role of the non-Gaussian effects is discussed., Comment: 8 pages, 5 figures

Hard spheres interacting through a square-well potential were simulated using two different methods: Brownian Cluster Dynamics (BCD) and Event Driven Brownian Dynamics (EDBD). The structure of the equilibrium states obtained by both methods were compared and found to be almost the identical. Self diffusion coefficients ($D$) were determined as a function of the interaction strength. The same values were found using BCD or EDBD. Contrary the EDBD, BCD allows one to study the effect of bond rigidity and hydrodynamic interaction within the clusters. When the bonds are flexible the effect of attraction on $D$ is relatively weak compared to systems with rigid bonds. $D$ increases first with increasing attraction strength, and then decreases for stronger interaction. Introducing intra-cluster hydrodynamic interaction weakly increases $D$ for a given interaction strength. Introducing bond rigidity causes a strong decrease of $D$ which no longer shows a maximum as function of the attraction strength.

We study the dynamics of monodisperse hard ellipsoids via a new event-driven molecular dynamics algorithm as a function of volume fraction $\phi$ and aspect ratio $X_0$. We evaluate the translational $D_{trans}$ and the rotational $D_{rot}$ diffusion coefficient and the associated isodiffusivity lines in the $\phi-X_0$ plane. We observe a decoupling of the translational and rotational dynamics which generates an almost perpendicular crossing of the $D_{trans}$ and $D_{rot}$ isodiffusivity lines. While the self intermediate scattering function exhibits stretched relaxation, i.e. glassy dynamics, only for large $\phi$ and $X_0 \approx 1$, the second order orientational correlator $C_2(t)$ shows stretching only for large and small $X_0$ values. We discuss these findings in the context of a possible pre-nematic order driven glass transition., Comment: accepted by Phys. Rev. Lett

We show that the universal properties of the rainfall phenomenon are the scaling properties of the probability density function of inter-drop intervals during quiescent periods, time intervals of sparse precipitation, and the universal shape of the probability density function of drop diameters during non-quiescent periods, time intervals of active precipitation. Our results indicate that the continuous flux-like vision of rainfall based on quantities such as the rain duration, rain intensity and drought duration is ineffective in detecting the universality of the phenomenon. A comprehensive understanding of rainfall behavior must rest on the acknowledgment of its discrete drop-like nature., Comment: 5 pages, 5 figures

We report Brownian dynamics simulation of the out-of-equilibrium dynamics (aging) in a colloidal suspension composed of rigid charged disks, one possible model for Laponite, a synthetic clay deeply investigated in the last few years by means of various experimental techniques. At variance with previous numerical investigations, mainly focusing on static structure and equilibrium dynamics, we explore the out-of-equilibrium aging dynamics. We analyze the wave-vector and waiting time dependence of the dynamics, focusing on the single-particle and collective density fluctuations (intermediate scattering functions), the mean squared displacement and the rotational dynamics. Our findings confirm the complexity of the out-of-equilibrium dynamical behavior of this class of colloidal suspensions and suggest that an arrested disordered state driven by a repulsive Yukawa potential, i.e., a Wigner glass can be observed in this model.

Brownian dynamics algorithms integrate numerically Langevin equations and allow to probe long time scales in simulations. A common requirement for such algorithms is that interactions in the system should vary little during an integration time step: therefore, computational efficiency worsens as the interactions become steeper. In the extreme case of hard-body interactions, standard numerical integrators become ill defined. Several approximate schemes have been invented to handle such cases with little emphasis on testing the correctness of the integration scheme. Starting from the two-body Smoluchowsky equation, we discuss a general method for the overdamped Brownian dynamics of hard-spheres, recently developed by one of us. We test the accuracy of the algorithm with the exact solution of the Smoluchowsky equation in the case of twobody collisions and in the low-density limit.

We report extensive Monte Carlo and event-driven molecular dynamics simulations of the fluid and liquid phase of a primitive model for silica recently introduced by Ford, Auerbach and Monson [J. Chem. Phys. 17, 8415 (2004)]. We evaluate the iso-diffusivity lines in the temperature-density plane to provide an indication of the shape of the glass transition line. Except for large densities, arrest is driven by the onset of the tetrahedral bonding pattern and the resulting dynamics is strong in the Angell's classification scheme. We compare structural and dynamic properties with corresponding results of two recently studied primitive models of network forming liquids -- a primitive model for water and a angular-constraint free model of four-coordinated particles -- to pin down the role of the geometric constraints associated to the bonding. Eventually we discuss the similarities between "glass" formation in network forming liquids and "gel" formation in colloidal dispersions of patchy particles., Comment: 9 pages, 10 figures

We numerically investigate the competition between phase separation and dynamical arrest in a colloidal system interacting via a short ranged attractive potential. Equilibrium fluid configurations are quenched at two different temperatures below the critical temperature and followed during their time evolution. At the lowest studied $T$, the phase separation process is interrupted by the formation of an attractive glass in the dense phase. At the higher $T$, no arrest is observed and the phase separation process proceeds endless in the simulated time window. The final structure of the glass retains memory of the interrupted phase separation process in the form of a frozen spinodal decomposition peak, whose location and amplitude is controlled by the average packing fraction. We also discuss the time evolution of the non ergodicity parameter, providing evidence of a progressively decreasing localization length on increasing the packing fraction. Finally, we confirm that the reported results are independent on the microscopic dynamics., Comment: 19 pages, 14 figures (figures 4, 5, 10 and 11 are not included for space restriction on preprint servers, for any queries please contact the corresponding author). To be published on J.Chem.Phys

We numerically study the dependence of the dynamics on the range of interaction $\Delta$ for the short-range square well potential. We find that, for small $\Delta$, dynamics scale exactly in the same way as thermodynamics, both for Newtonian and Brownian microscopic dynamics. For interaction ranges from a few percent down to the Baxter limit, the relative location of the attractive glass line and the liquid-gas line does not depend on $\Delta$. This proves that in this class of potentials, disordered arrested states (gels) can be generated only as a result of a kinetically arrested phase separation., Comment: 4 pages, 4 figures

We report a numerical study of saddles properties of the potential energy landscape for soft spheres with different softness, i.e. different power n of the interparticle repulsive potential. We find that saddle-based quantities rescale into master curves once energies and temperatures are scaled by mode-coupling temperature T_MCT, confirming and generalizing previous findings obtained for Lennard-Jones like models., Comment: 2 pages, 2 figures

The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic fragility proposed in the last years and discuss their interrelations. At the same time we analyze some recently introduced models for the statistical properties of the potential energy landscape. Building on the Adam-Gibbs relation, which connects structural relaxation times to configurational entropy, we analyze the relation between statistical properties of the landscape and fragility. We call attention to the fact that the knowledge of number, energy depth and shape of the basins of the potential energy landscape may not be sufficient for predicting fragility. Finally, we discuss two different possibilities for generating strong behavior., Comment: 17 pages, 10 figures; accepted version, minor corrections