Precise knowledge of the plasma density gradient created by an intense laser field at the surface of a solid is essential for understanding and controlling the resulting laser-plasma interaction. We present a novel experimental method for determining the scale length of such a gradient in a single shot, based on the spectral analysis of coherent wake emission by a laser-induced solid density plasma, using an analytical model of this emission process. We illustrate this approach in a pump-probe experiment, where it is used to measure the expansion velocity of a plasma into a vacuum.

We investigate the effects of the timescale of motion on the shape of energy landscapes. The distinction between the free-energy landscape and the potential of mean force is clarified. The former is related to a thermal equilibrium distribution for chosen coordinates, whereas the latter is determined by the mean force exerted on the coordinates in the equilibrium. It is found that the condition for these two energy landscapes to be the same is the constancy of the mean square velocity with respect to the position coordinate. However, even when the condition holds for the chosen coordinates, as the timescale of observation increases, the averaging effect causes a decrease in the mean square velocity nonuniformly in the configuration space, resulting in a larger distinction between the free-energy landscape and the potential of mean force. The results are expected to provide an important basis for the study of long time scale phenomena in large systems.

We investigate three force autocorrelation functions $\langle \mathbf{F}\left(0\right)·\mathbf{F}\left(t\right)\rangle$, $\langle {\mathbf{F}}^{+}\left(0\right)·{\mathbf{F}}^{+}\left(t\right)\rangle$, and $\langle {\mathbf{F}}_0\left(0\right)·{\mathbf{F}}_0\left(t\right)\rangle$ and the friction coefficient $\gamma$ for the Rayleigh model (a massive particle in an ideal gas) by analytic methods and molecular-dynamics (MD) simulations. Here, $\mathbf{F}$ and ${\mathbf{F}}^{+}$ are the total force and the Mori fluctuating force, respectively, whereas ${\mathbf{F}}_0$ is the force on the Brownian particle under the frozen dynamics, where the Brownian particle is held fixed and the solvent particles move under the external potential due to the presence of the Brownian particle. By using ensemble averaging and the ray representation approach, we obtain two expressions for $\langle {\mathbf{F}}_0\left(0\right)·{\mathbf{F}}_0\left(t\right)\rangle$ in terms of the one-particle trajectory and corresponding expressions for $\gamma$ by the time integration of these expressions. Performing MD simulations of the near-Brownian-limit (NBL) regime, we investigate the convergence of $\langle \mathbf{F}\left(0\right)·\mathbf{F}\left(t\right)\rangle$ and $\langle {\mathbf{F}}^{+}\left(0\right)·{\mathbf{F}}^{+}\left(t\right)\rangle$ and compare them with $\langle {\mathbf{F}}_0\left(0\right)·{\mathbf{F}}_0\left(t\right)\rangle$. We show that for a purely repulsive potential between the Brownian particle and a solvent particle, both expressions for $\langle {\mathbf{F}}_0\left(0\right)·{\mathbf{F}}_0\left(t\right)\rangle$ produce $\langle {\mathbf{F}}^{+}\left(0\right)·{\mathbf{F}}^{+}\left(t\right)\rangle$ in the NBL regime. On the other hand, for a potential containing an attractive component, the ray representation expression produces only the contribution of the nontrapped solvent particles. However, we show that the net contribution of the trapped particles to $\gamma$ disappears, and hence we confirm that both the ensemble-averaged expression and the ray representation expression for $\gamma$ are valid even if the potential contains an attractive component. We also obtain a closed-form expression of $\gamma$ for the square-well potential. Finally, we discuss theoretical and practical aspects for the evaluation of $\langle {\mathbf{F}}_0\left(0\right)·{\mathbf{F}}_0\left(t\right)\rangle$ and $\gamma$.

The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e., distributions of the first waiting time). Here, we consider two ensembles: the equilibrium and a typical nonequilibrium ensemble. For both ensembles, it is shown that the time-averaged mean square displacement (TAMSD) exhibits a crossover from normal to anomalous diffusion due to the spatial confinement and this crossover does not vanish even in the long measurement time limit. Moreover, for the nonequilibrium ensemble, we show that the probability density function of the diffusion constant of TAMSD follows the transient Mittag-Leffler distribution, and that scatter in the TAMSD shows a clear transition from weak ergodicity breaking (an irreproducible regime) to ordinary ergodic behavior (a reproducible regime) as the measurement time increases. This convergence to ordinary ergodicity requires a long measurement time compared to common distributions such as the exponential distribution; in other words, the weak ergodicity breaking persists for a long time. In addition, it is shown that, aside from the TAMSD, a class of observables also exhibits this slow convergence to ergodicity. We also point out that, even though the system with the equilibrium initial ensemble shows no aging, its behavior is quite similar to that for the nonequilibrium ensemble.

Many natural, technological and social systems are inherently not in equilibrium. We show, by detailed analysis of exemplar models, the emergence of equilibriumlike behavior in localized or nonlocalized domains within nonequilibrium Ising spin systems. Equilibrium domains are shown to emerge either abruptly or gradually depending on the system parameters and disappear, becoming indistinguishable from the remainder of the system for other parameter values.

We study the effects of a line of spherical interstitial particles (or intruders) placed between two adjacent uncompressed chains of larger particles in a square packing of spheres, using experiments and numerical simulations. We excite one of the chains of particles adjacent to the intruders with an impact and show how energy is transmitted across the system until equipartition is reached from the excited (or impacted) chain to the absorbing (or adjacent) chain. The coupling of the two chains, although a purely two-dimensional effect, is modeled by a simplified one-and-a-half-dimensional system in which transverse motions of the particles are neglected.

This paper deals with the experimental characterization of the collapse of wet granular columns in the pendular state, with the purpose of collecting data on triggering and jamming phenomena in wet granular media. The final deposit shape and the runout dynamics were studied for samples of glass beads, varying particle diameter, liquid surface tension, and liquid amount. We show how the runout distance decreases with increasing water amount (reaching a plateau for $w>1\%$) and increases with increasing Bond number, while the top and toe angles and the final deposit height increase with increasing water amount and decrease with decreasing Bond number. Dimensional analysis allowed to discuss possible scalings for the runout length and the top and toe angles: a satisfying scaling was found, based on the combination of Bond number and liquid amount.

We discuss the origin of coherent traveling wave patterns in a network of coupled chaotic Lorenz systems with nonlocal interaction. By systematically analyzing the dependence of the spatiotemporal network dynamics on the range and strength of the coupling, we uncover a bifurcation scenario for the transition from stationary patterns to regular traveling waves of different wave numbers. The transition is ruled by a symmetric homoclinic bifurcation and is accompanied by the appearance of periodic and chaotic breathing, as well as long chaotic transients.

We study the combined impact of a colored environmental noise and demographic noise on the extinction risk of a long-lived and well-mixed isolated stochastic population which exhibits the Allee effect. The environmental noise modulates the population birth and death rates. Assuming that the Allee effect is strong, and the environmental noise is positively correlated and Gaussian, we derive a Fokker-Planck equation for the joint probability distribution of the population sizes and environmental fluctuations. In the Wentzel-Kramers-Brillouin approximation this equation reduces to an effective two-dimensional Hamiltonian mechanics, where the most likely path to extinction and the most likely environmental fluctuation are encoded in an instanton-like trajectory in the phase space. The mean time to extinction $\tau$ is related to the mechanical action along this trajectory. We obtain new analytic results for short-correlated, long-correlated and relatively weak environmental noise. The population-size dependence of $\tau$ changes from exponential for weak environmental noise to no dependence for strong noise, implying a greatly increased extinction risk. The theory is readily extendable to population switches between different metastable states, and to stochastic population explosion, due to a combined action of demographic and environmental noise.

Using Monte Carlo simulations and free energy calculations, we study the phase behavior of hard asymmetric dumbbell particles with a constituent sphere diameter ratio of $0.5$. We find a rich phase behavior with isotropic fluid, rotator, and periodic NaCl-based and both periodic and aperiodic CrB-based crystalline phases. The rotator phases found to be stable in this study are similar to those found in systems of snowman-shaped and dumbbell particles and we investigate the behavior of these phases by comparing their stability ranges, and by looking at the orientational reorganization of particles. We also find that the NaCl-based crystalline phase can expand its range of stability by undergoing a slight modification which allows it to pack better. Finally, we see that reducing the sphere separation results in the aperiodic crystalline phases becoming destabilized as compared to the phase behavior of snowman-shaped particles.

A mode-coupling theory for the motion of a strongly forced probe particle in a dense colloidal suspension is presented. Starting point is the Smoluchowski equation for $N$ bath and a single probe particle. The probe performs Brownian motion under the influence of a strong constant and uniform external force $F_{\mathrm{ex}}$. It is immersed in a dense homogeneous bath of (different) particles also performing Brownian motion. Fluid and glass states are considered; solvent flow effects are neglected. Based on a formally exact generalized Green-Kubo relation, mode coupling approximations are performed and an integration through transients approach applied. A microscopic theory for the nonlinear velocity-force relations of the probe particle in a dense fluid and for the (de-) localized probe in a glass is obtained. It extends the mode coupling theory of the glass transition to strongly forced tracer motion and describes active microrheology experiments. A force threshold is identified which needs to be overcome to pull the probe particle free in a glass. For the model of hard sphere particles, the microscopic equations for the threshold force and the probability density of the localized probe are solved numerically. Neglecting the spatial structure of the theory, a schematic model is derived which contains two types of bifurcation, the glass transition and the force-induced delocalization, and which allows for analytical and numerical solutions. We discuss its phase diagram, forcing effects on the time-dependent correlation functions, and the friction increment. The model was successfully applied to simulations and experiments on colloidal hard sphere systems [Gazuz et al., Phys. Rev. Lett. 102, 248302 (2009)], while we provide detailed information on its derivation and general properties.

We investigate the self-assembly of crystals from reconfigurable colloidal building blocks. The building blocks possess the unique ability, inspired by recent experiments, to continuously alter their shape before, during, and after assembly. Using molecular simulations, we report the assembly of a reconfigurable degenerate crystal containing a fractionally filled kagome sublattice. We show that this degenerate crystal differs from, and assembles more easily than, its counterpart known for rigid dimers. We further report that the reconfigurable crystal has unique mechanical properties under shear strain compared to a crystal comprised of rigid building blocks. We find that even a small amount of reconfigurability in an assembly of otherwise rigid building blocks can greatly affect mechanical properties.

Proteins appear to be the most dramatic natural example of self-organized criticality (SOC), a concept that explains many otherwise apparently unlikely phenomena. Protein conformational functionality is often dominated by long-range hydrophobic or hydrophilic interactions which both drive protein compaction and mediate protein-protein interactions. Superfamily transmembrane G-protein-coupled receptors (GPCRs) are the largest family of proteins in the human genome; their amino acid sequences form the largest database for protein-membrane interactions. While there are now structural data on the heptad transmembrane structures of representatives of several heptad families, here we show how fresh insights into global and some local chemical trends in GPCR properties can be obtained accurately from sequences alone, especially by algebraically separating the extracellular and cytoplasmic loops from transmembrane segments. The global mediation of long-range water-protein interactions occurs in conjunction with modulation of these interactions by roughened interfaces. Hydropathic roughening profiles are defined here solely in terms of amino acid sequences, and knowledge of protein coordinates is not required. Roughening profiles both for GPCR and some simpler protein families display accurate and transparent connections to protein functionality, and identify natural length scales for protein functionality.

We study the effect of intrinsic heterogeneity on the activity of a population of leaky integrate-and-fire neurons. By rescaling the dynamical equation, we derive mathematical relations between multiple neuronal parameters and a fluctuating input noise. To this end, common input to heterogeneous neurons is conceived as an identical noise with neuron-specific mean and variance. As a consequence, the neuronal output rates can differ considerably, and their relative spike timing becomes desynchronized. This theory can quantitatively explain several recent experimental findings.

Reaction-diffusion systems with cross-diffusion terms that depend linearly on density are studied via linear stability analysis and weakly nonlinear analysis. We obtain and analyze the conditions for the Turing instability and derive a universal form of these conditions. We discuss the features of the pattern-forming regions in parameter space for a cross activator-inhibitor system, the Brusselator model, and for a pure activator-inhibitor system, the two-variable Oregonator model. The supercritical or subcritical character of the Turing bifurcation for the Brusselator is determined by deriving an amplitude equation for patterns near the instability threshold.

We present a theoretical analysis of the capillary driven transport of liquid in porous media that undergoes a sudden expansion. The use of appropriate coordinates allows for exactly and analytically solving different cases in two and three dimensions. The time dependence of liquid front motion in an expanding porous media is shown to be different from the one-dimensional Lucas-Washburn [Lucas, Kolloid Z. 23, 15 (1918); Washburn, Phys. Rev. 17, 273 (1921)] results as well as from the solution for two- and three-dimensional circular expansions obtained by Hyväluoma et al. [Phys. Rev. E 73, 036705 (2006)] and Xiao et al. [Langmuir 28, 4208 (2012)]. These cases appear as asymptotic limits of our solutions. We also observe that capillary flow in expanding three-dimensional porous materials exhibits a steady state solution for the bulk flow rate at the entrance of the expansion.

Natural convection that results from the dissolution of a diffusive species into a fluid saturated porous layer in the presence of a capillary transition zone is an important phenomenon in geological flows. The prediction of the onset of convection has remained elusive under the theory of gravitationally unstable multiphase flow in porous media. The present study offers a paradigm for the stability of two-phase buoyancy-driven flow in the presence of the capillary transition zone in a saturated porous medium, which allows for a quantitative description of the onset of natural convection. The analysis, which is based on the quasi-steady-state approximation, stresses the critical role of the capillary transition zone and the upward crossflow between the diffusive boundary layer and the capillary transition zone in the stability of the system, as well as in the transient growth of perturbations. We show that the instability problem can be characterized by capillary-dominant and buoyancy-dominant regimes with a transition in between. In the capillary-dominant regime, capillarity has a strong role in destabilizing the diffusive boundary layer. While in the buoyancy-dominant regime, the capillary transition zone is small enough that it can be ignored and the buoyancy force is the sole cause of the instability. Furthermore, our analysis shows that the capillary transition zone can potentially accelerate the evolution of the natural convection over 6 times faster than the buoyancy-dominant regime. Finally, the nonlinear dynamics of the system is studied using direct numerical simulations. The nonlinear simulations confirm the predictions from the linear stability analysis.

A weak wave turbulence theory is developed for two-dimensional (2D) magnetohydrodynamics. We derive and analyze the kinetic equation describing the three-wave interactions of pseudo-Alfvén waves. Our analysis is greatly helped by the fortunate fact that in 2D the wave kinetic equation is integrable. In contrast with the three-dimensional case, in 2D the wave interactions are nonlocal. Another distinct feature is that strong derivatives of spectra tend to appear in the region of small parallel (i.e., along the uniform magnetic field direction) wave numbers leading to a breakdown of the weak-turbulence description in this region. We develop a qualitative theory beyond weak turbulence describing subsequent evolution and formation of a steady state.

Out-of-equilibrium quasistationary states (QSSs) are one of the signatures of a broken ergodicity in long-range interacting systems. For the widely studied Hamiltonian mean-field model, the lifetime of some QSSs has been shown to diverge with the number $N$ of degrees of freedom with a puzzling $N^{1.7}$ scaling law, contradicting the otherwise widespread $N$ scaling law. It is shown here that this peculiar scaling arises from the locality properties of the dynamics captured through the computation of the diffusion coefficient in terms of the action variable. The use of a mean first passage time approach proves to be successful in explaining the nontrivial scaling at stake here and sheds some light on another case, where lifetimes diverging as $e^N$ above some critical energy have been reported.

The population growth of a Staphylococcus aureus culture, an active colloidal system of spherical cells, was followed by rheological measurements, under steady-state and oscillatory shear flows. We observed a rich viscoelastic behavior as a consequence of the bacteria activity, namely, of their multiplication and density-dependent aggregation properties. In the early stages of growth (lag and exponential phases), the viscosity increases by about a factor of 20, presenting several drops and full recoveries. This allows us to evoke the existence of a percolation phenomenon. Remarkably, as the bacteria reach their late phase of development, in which the population stabilizes, the viscosity returns close to its initial value. Most probably, this is caused by a change in the bacteria physiological activity and in particular, by the decrease of their adhesion properties. The viscous and elastic moduli exhibit power-law behaviors compatible with the “soft glassy materials” model, whose exponents are dependent on the bacteria growth stage.