When a coffee drop dries on a solid surface, it leaves a ringlike deposit along the edge and this is known as the “coffee-ring effect.” We find a different motion of particles repelling the coffee-ring effect in drying droplets; the motion of particles that is initially toward the edge by the coffee-ring effect is reversed toward the center by a capillary force. The reversal takes place when the capillary force prevails over the outward coffee-ring flow. We discuss the geometric constraints for the capillary force and the reverse motion. Our findings of reversal phenomena would be important in many scenarios of drying colloidal fluids.

Numerical integrations of the derivative nonlinear Schrödinger equation for Alfvén waves, supplemented by a weak dissipative term (originating from diffusion or Landau damping), with initial conditions in the form of a bright soliton with nonvanishing conditions at infinity (oblique soliton), reveal an interesting phenomenon of “quasicollapse”: as the dissipation parameter is reduced, larger amplitudes are reached and smaller scales are created, but on an increasing time scale. This process involves an early bifurcation of the initial soliton toward a breather that is analyzed by means of a numerical inverse scattering technique. This evolution leads to the formation of persistent dark solitons that are only weakly affected when crossed by the decaying breather which has the form of either a localized structure or an extended wave packet.

In this paper we report on the radiography of a shock-compressed target using laser produced proton beams. A low-density carbon foam target was shock compressed by long pulse high-energy laser beams. The shock front was transversally probed with a proton beam produced in the interaction of a high intensity laser beam with a gold foil. We show that from radiography data, the density profile in the shocked target can be deduced using Monte Carlo simulations. By changing the delay between long and short pulse beams, we could probe different plasma conditions and structures, demonstrating that the details of the steep density gradient can be resolved. This technique is validated as a diagnostic for the investigation of warm dense plasmas, allowing an in situ characterization of high-density contrasted plasmas.

A generalized version of the nonequilibrium linear Glauber model with $q$ states in $d$ dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the $q$ states. Exact expressions for the two-time autocorrelation and response functions on a $d$-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

A reciprocating quantum refrigerator is studied with the purpose of determining the limitations of cooling to absolute zero. The cycle is based on demagnetization and magnetization of a working medium. We find that if the energy spectrum of the working medium possesses an uncontrollable gap, and in addition there is noise on the controls, then there is a minimum achievable temperature above zero. The reason is that even a negligible amount of noise prevents adiabatic following during the demagnetization stage. This results with a minimum temperature, $T_c\left(\text{min}\right)>0$, which scales with the energy gap. The refrigerator is based on an Otto cycle where the working medium is an interacting spin system with an energy gap. For this system the external control Hamiltonian does not commute with the internal interaction. As a result during the demagnetization and magnetization segments of the operating cycle the system cannot follow adiabatically the temporal change in the energy levels. We connect the nonadiabatic dynamics to quantum friction. An adiabatic measure is defined characterizing the rate of change of the Hamiltonian. Closed-form solutions are found for a constant adiabatic measure for all the cycle segments. We have identified a family of quantized frictionless cycles with increasing cycle times. These cycles minimize the entropy production. Such frictionless cycles are able to cool to $T_c=0$. External noise on the controls eliminates these frictionless cycles. The influence of phase and amplitude noise on the demagnetization and magnetization segments is explicitly derived. An extensive numerical study of optimal cooling cycles was carried out which showed that at sufficiently low temperature the noise always dominated restricting the minimum temperature.

This is the first of two papers investigating the mechanical response of cemented granular materials by means of contact dynamics simulations. In this paper, a two-dimensional polydisperse sample with high-void ratio is constructed and then sheared in a simple shear numerical device at different confinement levels. We study the macroscopic response of the material in terms of mean and deviatoric stresses and strains. We show that the introduction of a local force scale, i.e., the tensile strength of the cemented bonds, causes the material to behave in a rigid-plastic fashion, so that a yield surface can be easily determined. This yield surface has a concave-down shape in the mean:deviatoric stress plane and it approaches a straight line, i.e., a Coulomb strength envelope, in the limit of a very dense granular material. Beyond yielding, the cemented structure gradually degrades until the material eventually behaves as a cohesionless granular material. Strain localization is also investigated, showing that the strains concentrate in a shear band whose thickness increases with the confining stress. The void ratio inside the shear band at the steady state is shown to be a material property that depends only on contact parameters.

This is the second of two papers investigating the mechanical response of cemented granular materials by means of contact dynamics simulations. In this paper, a two-dimensional polydisperse sample with high void ratio is sheared in a load-controlled simple shear numerical device until the stress state of the sample reaches the yield stress. We first study the stress transmission properties of the granular material in terms of the fabric of different subsets of contacts characterized by the magnitude of their normal forces. This analysis highlights the existence of a peculiar force carrying structure in the cemented material, which is reminiscent of the bimodal stress transmission reported for cohesionless granular media. Then, the evolution of contact forces and torques is investigated trying to identify the micromechanical conditions that trigger macroscopic yielding. It is shown that global failure can be associated to the apparition of a group of particles whose contacts fulfill at least one of the local rupture conditions. In particular, these particles form a large region that percolates through the sample at the moment of failure, evidencing the relationship between macroscopic yielding and the emergence of large-scale correlations in the system.

Aqueous foams present an anomalous macroscopic viscoelastic response at high frequency, previously shown to arise from collective relaxations in the disordered bubble packing. We demonstrate experimentally how these mesoscopic dynamics are in turn tuned by physico-chemical processes on the scale of the gas-liquid interfaces. Two specific local dissipation processes are identified, and we show how the rigidity of the interfaces selects the dominant one, depending on the choice of the surfactant.

Dielectric spectroscopy is used to investigate fundamental length scales describing the structure of hyaluronic acid sodium salt (Na-HA) semidilute aqueous solutions. In salt-free regime, the length scale of the relaxation mode detected in MHz range scales with HA concentration as $c_{\text{HA}}^{-0.5}$ and corresponds to the de Gennes-Pfeuty-Dobrynin correlation length of polyelectrolytes in semidilute solution. The same scaling was observed for the case of long, genomic DNA. Conversely, the length scale of the mode detected in kilohertz range also varies with HA concentration as $c_{\text{HA}}^{-0.5}$ which differs from the case of DNA $\left(c_{\text{DNA}}^{-0.25}\right)$. The observed behavior suggests that the relaxation in the kilohertz range reveals the de Gennes-Dobrynin renormalized Debye screening length, and not the average size of the chain, as the pertinent length scale. Similarly, with increasing added salt the electrostatic contribution to the HA persistence length is observed to scale as the Debye length, contrary to scaling pertinent to the Odijk-Skolnick-Fixman electrostatic persistence length observed in the case of DNA. We argue that the observed features of the kilohertz range relaxation are due to much weaker electrostatic interactions that lead to the absence of Manning condensation as well as a rather high flexibility of HA as compared to DNA.

The transport of organelles and other cargoes in living cells has been described by a kinetic tug-of-war model advanced by Müller, Klumpp, and Lipowsky, in which, as a function of time, $t$, a team of $n_{+}\left(t\right)=0,1,\cdots ,N_{+}$ molecular motors may attach a cargo to a filamentous track and pull it towards the plus end in competition with $n_{-}\left(t\right)=0,1,\cdots ,N_{-}$ motors that pull towards the opposite end. In recent work [Y. Zhang, Phys. Rev. E 79, 061918 (2009)] this model was analyzed for $N_{+},N_{-}⪢1$, establishing the existence, depending on the motor parameters and the ratio $\nu =N_{+}/N_{-}$, of system states with either one, two, or three distinct stable stationary modes of motion. Here, adopting a theoretical perspective, we study the parametric and $\nu$ dependence of the transitions between these mono-, bi-, or tristable system states and examine their associated trajectories and domains of attraction in the flow space, $\left(n_{+},n_{-}\right)$, of the attached motor numbers. Various sequences of winning, losing, and “stalemate” or close-to-motionless modes are uncovered. When, as realistic, $N_{+}$ and $N_{-}$ are of order 2 to 10, fluctuations will move the system from one of two or three modes of motion to another mode. An analysis of the associated probability fluxes demonstrates that the mean time between mode-to-mode transitions increases exponentially with $N_{+}$ and $N_{-}$. The overall stall force, i.e., the externally imposed load under which the mean cargo velocity vanishes, is similarly elucidated and shown to vary strongly but sublinearly with $N_{+}$ and $N_{-}$, as well as depending in a less than transparent manner on other model parameters beyond the stall forces of the individual $+$ and $-$ motors.

The folding of the triangular lattice embedded in two dimensions (discrete planar folding) is investigated numerically. As the bending rigidity $K$ varies, the planar folding exhibits a series of crumpling transitions at $K\approx -0.3$ and $K\approx 0.1$. By means of the transfer-matrix method for the system sizes $L\le 14$, we analyze the singularity of the transition at $K\approx -0.3$. As a result, we estimate the transition point and the latent heat as $K=-0.270\left(2\right)$ and $Q=0.043\left(10\right)$, respectively. This result suggests that the singularity belongs to a weak-first-order transition.

A class of artificial microswimmers with combined translational and rotational self-propulsion is studied experimentally. The chemically fueled microswimmers are made of doublets of Janus colloidal beads with catalytic patches that are positioned at a fixed angle relative to one another. The mean-square displacement and the mean-square angular displacement of the active doublets are analyzed in the context of a simple Langevin description, using which the physical characteristics of the microswimmers such as the spontaneous translational and rotational velocities are extracted. Our work suggests strategies for designing microswimmers that could follow prescribed cycloidal trajectories.

Empirical studies show that real world networks often exhibit multiple scales of topological descriptions. However, it is still an open problem how to identify the intrinsic multiple scales of networks. In this paper, we consider detecting the multiscale community structure of network from the perspective of dimension reduction. According to this perspective, a covariance matrix of network is defined to uncover the multiscale community structure through the translation and rotation transformations. It is proved that the covariance matrix is the unbiased version of the well-known modularity matrix. We then point out that the translation and rotation transformations fail to deal with the heterogeneous network, which is very common in nature and society. To address this problem, a correlation matrix is proposed through introducing the rescaling transformation into the covariance matrix. Extensive tests on real world and artificial networks demonstrate that the correlation matrix significantly outperforms the covariance matrix, identically the modularity matrix, as regards identifying the multiscale community structure of network. This work provides a novel perspective to the identification of community structure and thus various dimension reduction methods might be used for the identification of community structure. Through introducing the correlation matrix, we further conclude that the rescaling transformation is crucial to identify the multiscale community structure of network, as well as the translation and rotation transformations.

Modularity is a fundamental feature of real networks, being intimately bounded to their functionality, i.e., to their capability of performing parallel tasks in a coordinated way. Although the modular structure of real graphs has been intensively studied, very little is known on the interactions between functional modules of a graph. Here, we present a general method based on synchronization of networking oscillators, that is able to detect overlapping structures in multimodular environments. We furthermore report the full analytical and theoretical description on the relationship between the overlapping dynamics and the underlying network topology. The method is illustrated by means of a series of applications.

We discuss a modification to random matrix theory eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian; instead it requires only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard random matrix theory and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations, and show that significant improvement in accuracy is obtained for simple chaotic systems where comparison can be made with brute-force diagonalization. The accuracy of the method persists even when the short-time dynamics of the system or ensemble is known only in a classical approximation. Further improvement in the rate of convergence is obtained when the method is combined with the correlation function bootstrapping approach introduced previously.

Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is “statistics of statistics” with two largely separated time scales, offers a consistent theoretical framework for such a description. Here, a theory is developed for log-normal superstatistics based on the fluctuation theorem for entropy changes as well as the maximum entropy method. This gives novel physical insight into log-normal statistics, other than the traditional multiplicative random processes. A comment is made on a possible application of the theory to the fluctuating energy dissipation rate in turbulence.

The diffusion equation is related to the Schrödinger equation by analytic continuation. The formula $E^2=p^2{c}^2+m^2{c}^4$ leads to a relativistic Schrödinger equation, and analytic continuation yields a relativistic diffusion equation that involves fractional calculus. This paper develops stochastic models for relativistic diffusion and equivalent differential equations with no fractional derivatives. Connections to anomalous diffusion are also discussed, along with alternative models.

Camera-based single-particle tracking enables quantitative determination of transport properties and provides nanoscale information about material characteristics such as viscosity and elasticity. However, static localization noise and the blurring of a particle’s position over camera integration times introduce artifacts into measurement results even for a particle executing simple diffusion. Common data analysis methods based on the mean-square displacement do not properly account for these effects. In this paper, we analyze the statistics of tracking data for freely diffusing particles in realistic experimental scenarios. We derive a convenient and asymptotically optimal maximum likelihood estimator for the diffusion coefficient and for the magnitude of localization noise together with the corresponding Fisher information, which bounds the performance of all unbiased estimators. We find that the effect of varying the illumination profile during the camera integration time is quantified by a motion blur coefficient, $R$. We also find that a double-pulse illumination sequence maximizes the information content in some common experimental scenarios. Our results provide a rigorous theoretical framework and practical experimental recipe for achieving optimal performance in camera-based single-particle tracking.

Starting with stochastic rate equations for the fundamental interactions between microbes and their viruses, we derive a mean-field theory for the population dynamics of microbe-virus systems, including the effects of lysogeny. In the absence of lysogeny, our model is a generalization of that proposed phenomenologically by Weitz and Dushoff. In the presence of lysogeny, we analyze the possible states of the system, identifying a limit cycle, which we interpret physically. To test the robustness of our mean-field calculations to demographic fluctuations, we have compared our results with stochastic simulations using the Gillespie algorithm. Finally, we estimate the range of parameters that delineate the various steady states of our model.