Interplay between an Absorbing Phase Transition and Synchronization in a Driven Granular System.

Absorbing phase transitions (APTs) are widespread in nonequilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state in which the system becomes entrapped, along with a transition, either continuous or discontinuous, to an active state. Understanding which physical mechanisms determine the order of these transitions represents a challenging open problem in nonequilibrium statistical mechanics. Here, by numerical simulations and mean-field analysis, we show that a quasi-2D vibrofluidized granular system exhibits a novel form of APT. The absorbing phase is observed in the horizontal dynamics below a critical packing fraction, and can be continuous or discontinuous based on the emergent degree of synchronization in the vertical motion. Our results provide a direct representation of a feasible experimental scenario, showcasing a surprising interplay between dynamic phase transition and synchronization.

Blast Dynamics in a Dissipative Gas.

The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution is a prototypical example of self-similarity driven by conservation laws. In dissipative media, however, energy conservation is violated, yet a distinctive self-similar solution appears. It hinges on the decoupling of random and coherent motion permitted by a broad class of dissipative mechanisms. This enforces a peculiar layered structure in the shock, for which we derive the full hydrodynamic solution, validated by a microscopic approach based on molecular dynamics simulations. We predict and evidence a succession of temporal regimes, as well as a long-time corrugation instability, also self-similar, which disrupts the blast boundary. These generic results may apply from astrophysical systems to granular gases, and invite further cross-fertilization between microscopic and hydrodynamic approaches of shock waves.

Kovacs-like memory effect in driven granular gases.

While memory effects have been reported for dense enough disordered systems such as glasses, we show here by a combination of analytical and simulation techniques that they are also intrinsic to the dynamics of dilute granular gases. By means of a certain driving protocol, we prepare the gas in a state where the granular temperature T coincides with its long time limit. However, T does not subsequently remain constant but exhibits a nonmonotonic evolution before reaching its nonequilibrium steady value. The corresponding so-called Kovacs hump displays a normal behavior for weak dissipation (as observed in molecular systems) but is reversed under strong dissipation, where it, thus, becomes anomalous.

Nonequilibrium solutions of the Boltzmann equation under the action of an external force.

We construct a novel class of exact solutions to the Boltzmann equation, in both its classical and quantum formulation, for arbitrary collision laws. When the system is subjected to a specific external forcing, the precise form of which is worked out, nonequilibrium dampingless solutions are admissible. They do not contradict the H theorem, but are constructed from its requirements. Interestingly, these solutions hold for time-dependent confinement. We exploit them, in a reverse-engineering perspective, to work out a protocol that shortcuts any adiabatic transformation between two equilibrium states in an arbitrarily short time span, for an interacting system. Particle simulations of the direct Monte Carlo type fully corroborate the analytical predictions.

Generalized Onsager theory for strongly anisometric patchy colloids.

The implications of soft "patchy" interactions on the orientational disorder-order transition of strongly elongated colloidal rods and flat disks is studied within a simple Onsager-van der Waals density functional theory. The theory provides a generic framework for studying the liquid crystal phase behaviour of highly anisometric cylindrical colloids which carry a distinct geometrical pattern of repulsive or attractive soft interactions localized on the particle surface. In this paper, we apply our theory to the case of charged rods and disks for which the local electrostatic interactions can be described by a screened-Coulomb potential. We consider infinitely thin rod like cylinders with a uniform line charge and infinitely thin discotic cylinders with several distinctly different surface charge patterns. Irrespective of the backbone shape the isotropic-nematic phase diagrams of charged colloids feature a generic destabilization of nematic order at low ionic strength, a dramatic narrowing of the biphasic density region, and a reentrant phenomenon upon reducing the electrostatic screening. The low screening regime is characterized by a complete suppression of nematic order in favor of positionally ordered liquid crystal phases.

Confinement effects on the kinetics and thermodynamics of protein dimerization.

In the cell, protein complexes form by relying on specific interactions between their monomers. Excluded volume effects due to molecular crowding would lead to correlations between molecules even without specific interactions. What is the interplay of these effects in the crowded cellular environment? We study dimerization of a model homodimer when the mondimers are free and when they are tethered to each other. We consider a structured environment: Two monomers first diffuse into a cavity of size L and then fold and bind within the cavity. The folding and binding are simulated by using molecular dynamics based on a simplified topology based model. The confinement in the cell is described by an effective molecular concentration C approximately L(-3). A two-state coupled folding and binding behavior is found. We show the maximal rate of dimerization occurred at an effective molecular concentration C(op) approximately = 1 mM, which is a relevant cellular concentration. In contrast, for tethered chains the rate keeps at a plateau when C < C(op) but then decreases sharply when C > C(op). For both the free and tethered cases, the simulated variation of the rate of dimerization and thermodynamic stability with effective molecular concentration agrees well with experimental observations. In addition, a theoretical argument for the effects of confinement on dimerization is also made.

Counter-ions at charged walls: two-dimensional systems.

We study equilibrium statistical mechanics of classical point counter-ions, formulated on 2D Euclidean space with logarithmic Coulomb interactions (infinite number of particles) or on the cylinder surface (finite particle numbers), in the vicinity of a single uniformly charged line (one single double layer), or between two such lines (interacting double layers). The weak-coupling Poisson-Boltzmann theory, which applies when the coupling constant [Formula: see text] is small, is briefly recapitulated (the coupling constant is defined as [Formula: see text] [Formula: see text] [Formula: see text] e (2) , where [Formula: see text] is the inverse temperature, and e the counter-ion charge). The opposite limit ( [Formula: see text] [Formula: see text] ∞ is treated by using a recent method based on an exact expansion around the ground-state Wigner crystal of counter-ions. These two limiting results are compared at intermediary values of the coupling constant [Formula: see text] = 2[Formula: see text] ([Formula: see text] = 1, 2, 3) , to exact results derived within a 1D lattice representation of 2D Coulomb systems in terms of anti-commuting field variables. The models (density profile, pressure) are solved exactly for any particles numbers N at [Formula: see text] = 2 and up to relatively large finite N at [Formula: see text] = 4 and 6. For the one-line geometry, the decay of the density profile at asymptotic distance from the line undergoes a fundamental change with respect to the mean-field behavior at [Formula: see text] = 6 . The like-charge attraction regime, possible for large [Formula: see text] but precluded at mean-field level, survives for [Formula: see text] = 4 and 6, but disappears at [Formula: see text] = 2 .

Condensation transition in polydisperse hard rods.

We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume v, with the constraint of a fixed total volume V= sum(i=1) (N)v(i), N being the total number of particles. The particles, referred to as p-spheres, have a linear size that behaves as v(i) (1/p) and our model thus represents a gas of polydisperse hard rods with variable diameters v(i) (1/p). We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard-rod system, under the constraints of fixed N and V. Complementary approaches (explicit construction of the steady state distribution on the one hand; density functional theory on the other hand) completely and consistently specify the behavior of the system. A real space condensation transition is shown to take place for p>1; beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles.

On the effective charge of hydrophobic polyelectrolytes.

In this paper, we analyze the behavior of hydrophobic polyelectrolytes. It has been proposed that this system adopts a pearl necklace structure reminiscent of the Rayleigh instability of a charged droplet. Using a Poisson-Boltzmann approach, we calculate the counterion distribution around a given pearl, assuming the latter to be penetrable for the counterions. This allows us to calculate the effective electric charge of the pearl as a function of the chemical charge. Our predictions are in good agreement with the recent experimental measurements of the effective charge by Essafi et al. (Essafi, W.; Lafuma, F.; Baigl, D.; Williams, C. E. Europhys. Lett. 2005, 71, 938.). Our results allow us to understand the large deviation from the Manning law observed in these experiments.

Optimal work in a harmonic trap with bounded stiffness.

We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness κ. We work out the optimal time dependence κ(t) by minimizing the work performed on the particle under the nonholonomic constraint 0≤κ≤κ_{max}, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analyzed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time t_{f} and the desired compression ratio κ_{f}/κ_{i}, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimization of heat engines.

Planar screening by charge polydisperse counterions.

We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane (plate), when the counterions are characterised by a distribution of charges (or valence), [Formula: see text]. We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions [Formula: see text], for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous [Formula: see text] behaviour are already featured by discrete mixtures with a relatively small number of constituents.

Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction.

Combining analytical and numerical methods, we study within the framework of the homogeneous nonlinear Boltzmann equation a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism: namely, a deterministic nonlinear friction force. We derive analytically the high-energy tail of the velocity distribution and compare the theoretical predictions with high-precision numerical simulations. Stretched exponential forms are obtained when the nonequilibrium steady state is stable. We derive subleading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple Bhatnagar-Gross-Krook models, driven by similar heating devices, to test the robustness of our predictions.

Macroion virial contribution to the osmotic pressure in charge-stabilized colloidal suspensions.

Our interest goes to the different virial contributions to the equation of state of charged colloidal suspensions. Neglect of surface effects in the computation of the colloidal virial term leads to spurious and paradoxical results. This pitfall is one of the several facets of the danger of a naive implementation of the so called one component model, where the microionic degrees of freedom are integrated out to only keep in the description the mesoscopic (colloidal) degrees of freedom. On the other hand, due incorporation of wall induced forces dissolves the paradox brought forth in the naive approach, provides a consistent description, and confirms that for salt-free systems, the colloidal contribution to the pressure is dominated by the microionic one. Much emphasis is put on the no salt case but the situation with added electrolyte is also discussed.

Reply to "Comment on 'Long-range electrostatic interactions between like-charged colloids: steric and confinement effects' ".

In his Comment to [Phys. Rev. E 60, 6530 (1999)], Mateescu shows that while the effective interactions remain repulsive when the specific size of the microions is taken into account via a Modified Poisson-Boltzmann equation, a similar conclusion cannot be reached for the situation of complete lateral confinement. This point is correct but has already been considered in a more general study [Phys. Rev. E 62, R1465 (2000), where repulsion is generically obtained]; moreover, we argue that it illustrates the irrelevancy of the notion of pair potential in completely confined configurations, as shown in a simple example.

Randomly driven granular fluids: collisional statistics and short scale structure.

We present a molecular-dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short-distance correlations in the nonequilibrium steady state, in order to analyze in a quantitative manner the breakdown of molecular chaos, i.e., factorization of the two-particle distribution function, f((2))(x(1),x(2)) approximately chif((1))(x(1))f((1))(x(2)) in a product of single-particle ones, where x(i)=[r(i),v(i)] with i=1,2 and chi represents the position correlation. We have found that molecular chaos is only violated in a small region of the two-particle phase space [x(1),x(2)], where there is a predominance of grazing collisions. The size of this singular region grows with increasing inelasticity. The existence of particle- and noise-induced recollisions magnifies the departure from mean-field behavior. The implications of this breakdown in several physical quantities are explored.

Memory effect in uniformly heated granular gases.

We evidence a Kovacs-like memory effect in a uniformly driven granular gas. A system of inelastic hard particles, in the low density limit, can reach a nonequilibrium steady state when properly forced. By following a certain protocol for the drive time dependence, we prepare the gas in a state where the granular temperature coincides with its long time value. The temperature subsequently does not remain constant but exhibits a nonmonotonic evolution with either a maximum or a minimum, depending on the dissipation and on the protocol. We present a theoretical analysis of this memory effect at Boltzmann-Fokker-Planck equation level and show that when dissipation exceeds a threshold, the response can be called anomalous. We find excellent agreement between the analytical predictions and direct Monte Carlo simulations.

Effective interactions between like-charged macromolecules

We investigate, within a local density functional theory formalism, the interactions between like-charged polyions immersed in a confined electrolyte. We obtain a simple condition for a repulsive effective pair potential, which can be related to the thermodynamic stability criterion of the uncharged counterpart of microscopic species constituting the electrolyte. Under the same condition, the phenomenon of charge inversion (over-charging), where the polyion bare charge is over-screened by its electric double layer, is shown to be impossible. These results hold beyond standard mean-field theories (such as Poisson-Boltzmann or modified Poisson-Boltzmann approaches).

Random inelasticity and velocity fluctuations in a driven granular gas.

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the "stochastic thermostat" model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high-velocity stretched-exponential behavior with an exponent 3/2. The experimental observations lead to refine a recently proposed random restitution coefficient model. Very good agreement is then found with experimental velocity distributions within this framework, which appears self-consistent and further provides relevant probes to investigate the universality of the velocity statistics.

The interplay between screening properties and colloid anisotropy: towards a reliable pair potential for disc-like charged particles.

The electrostatic potential of a highly charged disc (clay platelet) in an electrolyte is investigated in detail. The corresponding non-linear Poisson-Boltzmann (PB) equation is solved numerically, and we show that the far-field behaviour (relevant for colloidal interactions in dilute suspensions) is exactly that obtained within linearized PB theory, with the surface boundary condition of a uniform potential. The latter linear problem is solved by a new semi-analytical procedure and both the potential amplitude (quantified by an effective charge) and potential anisotropy coincide closely within PB and linearized PB, provided the disc bare charge is high enough. This anisotropy remains at all scales; it is encoded in a function that may vary over several orders of magnitude depending on the azimuthal angle under which the disc is seen. The results allow to construct a pair potential for discs interaction, that is strongly orientation dependent.