We propose a model for aggregation where particles are continuously growing by heterogeneous condensation in one dimension, and solve it exactly. We show that the particle size spectra exhibit a transition to dynamic scaling $c\left(x,t\right)\sim t^{-\beta }\varphi \left(x/t^z\right)$. The exponents $\beta$ and $z$ satisfy a generalized scaling relation $\beta =\left(1+q\right)z$ where the value of $q$ is fixed by a nontrivial conservation law. We show that the value of $1+q$ is always less than the value 2 for aggregation without condensation.

We study the stability of orientationally disordered crystal phases in a suspension of colloidal hard dumbbells using Monte Carlo simulations. For dumbbell bond length $L∕\sigma <0.4$ with $L$ the separation of the two spheres of the dumbbell and $\sigma$ the diameter of the spheres, we determine the difference in Helmholtz free energy of a plastic crystal with a hexagonal-close-packed (hcp) and a face-centered-cubic (fcc) structure using thermodynamic integration and the lattice-switch Monte Carlo method. We find that the plastic crystal with the hcp structure is more stable than the one with the fcc structure for a large part of the stable plastic crystal regime. In addition, we study the stability of an orientationally disordered aperiodic crystal structure in which the spheres of the dumbbells are on a random-hexagonal-close-packed lattice, and the dumbbells are formed by taking random pairs of neighboring spheres. Using free-energy calculations, we determine the fluid-aperiodic crystal and periodic-aperiodic crystal coexistence regions for $L∕\sigma >0.88$.

Helicases are molecular motors that unwind double-stranded nucleic acids (dsNA), such as DNA and RNA. Typically a helicase translocates along one of the NA single strands while unwinding and uses adenosine triphosphate (ATP) hydrolysis as an energy source. Here we model a helicase motor that can switch between two states, which could represent two different points in the ATP hydrolysis cycle. Our model is an extension of the earlier Betterton-Jülicher model of helicases to incorporate switching between two states. The main predictions of the model are the speed of unwinding of the dsNA and fluctuations around the average unwinding velocity. Motivated by a recent claim that the NS3 helicase of Hepatitis C virus follows a flashing-ratchet mechanism, we have compared the experimental results for the NS3 helicase with a special limit of our model which corresponds to the flashing-ratchet scenario. Our model accounts for one key feature of the experimental data on NS3 helicase. However, contradictory observations in experiments carried out under different conditions limit the ability to compare the model to experiments.

The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry, and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data. We propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one. This improvement is inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data.

Theoretical studies of electrical double layers typically consider the response of ionic conductors to the field of uniform charge-density distributions $\sigma$ (“$\sigma$-control”). Many such analyses predict apparent anomalies of differential capacitance, $C$, including divergences and negative values. To clarify misconceptions regarding these predictions, we critically reexamine some theoretical approaches dealing with the admissible sign of $C$. We examine the anomalies’ origin and stress its relation to the artificiality of $\sigma$-control. We show that calculations based on $\sigma$-control can illuminate the nature of instabilities and phase transitions under the physically attainable conditions of potential control, where applied voltage $\varphi$ rather than $\sigma$ is fixed. For illustration, we discuss the physical nature of the “ultimate anomaly,” negative integral capacitance predicted by some recent analyses. We also show that $\sigma$-control anomalies can explain some experimentally observed features of $C\left(\varphi \right)$.

We measure the kinematics of segregating granular mixtures in dense free-surface boundary-layer flow in a rotated drum. We find that in a segregating mixture, the different components move with roughly the same velocities, except for a relatively small segregation velocity perpendicular to the direction of flow. On the other hand, the mean variance of the velocities—often associated with a granular temperature—may differ for the two components. In the majority of the high-density boundary layer, the difference is driven by relative particle size and may be understood considering a geometrically motivated model. In the low-density region at the top of the boundary layer, the difference is driven by relative particle mass, similar to observations in more energetic systems.

We studied the effect of light-induced gliding of the easy axis of dye-doped nematic liquid crystal on an aligning polymer surface. The observed drift of the easy axis is over tens of degrees and is caused by light-induced anisotropic adsorption and/or desorption of dye molecules on or from the aligning layer in the presence of light-induced bulk torque. We present a theoretical model that explains the experimental data in terms of the light-induced changes of the adsorbed dye molecules angular distribution due to their exchange with the dye molecules from the liquid crystal bulk.

We show that colloidal superstructures could be assembled in mixtures of large and small colloidal particles dispersed in a nematic liquid crystal. Using elastic interaction of small colloidal particles with the disclination lines we succeed to demonstrate how one can decorate with small particles a topological matrix of defect rings and loops formed by an array of large colloidal particles. Our simulations show that this concept of colloidal self-assembly in nematics could be extended down to the nanoscale particles.

We study a stochastic lattice model describing the dynamics of coexistence of two interacting biological species. The model comprehends the local processes of birth, death, and diffusion of individuals of each species and is grounded on interaction of the predator-prey type. The species coexistence can be of two types: With self-sustained coupled time oscillations of population densities and without oscillations. We perform numerical simulations of the model on a square lattice and analyze the temporal behavior of each species by computing the time correlation functions as well as the spectral densities. This analysis provides an appropriate characterization of the different types of coexistence. It is also used to examine linked population cycles in nature and in experiment.

We study the influence of the driving rate in the two-dimensional Oslo rice pile model. We find that the usual power-law behavior of the avalanche size distribution still holds for small avalanches, independent of the driving rate. The signature of fast driving is, however, the increase of the incidence rate of large avalanches. For larger driving rates, this increase is more prominent and spreads to smaller avalanche sizes. As a result, the mass flow due to large avalanches is increased much more than would be expected from an increase in driving rate alone. Fast driving leads to a dramatic increase in devastating avalanches, just before the continuous flow regime is reached.

This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor $T_{\alpha \beta }\left(x,y\right)$ for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as $\psi =u+iv$. With the assumption that $u$ and $v$ are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components $T_{\alpha \beta }$. The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for $T_{\alpha \beta }\left(x,y\right)$ is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

We develop an optical measurement for densities of fast (units to tens of keV) hydrogen ions in an abnormal hollow cathode discharge in units to tens of mTorr pressure range. This method combines results from previous collisional-radiative models, comparing the intensity of Balmer ${\mathrm{H}}_{\alpha }$ due to dissociative excitation of ${\mathrm{H}}_2$ by fast electrons to Doppler-shifted emission arising from charge exchange of energetic ions. The method requires only two inputs: the current density due to fast electrons and a single ${\mathrm{H}}_{\alpha }$ spectrum of the characteristic emission channel at the anode. We model in particular the cylindrical interelectrode discharge of an inertial electrostatic confinement device. Experimentally, we find that the density of fast ions emerging from the cathode (bias $-5\mathrm{kV}$ at $20\mathrm{mTorr}$) is in the order ${10}^{14}{\mathrm{m}}^{-3}$, increasing approximately linearly with current in the $10–30\mathrm{mA}$ range. Calculated densities agree with values obtained in similar apparatus using Langmuir probes and analysis of dust particle motion.

Dilute oil dispersions of fractal carbon black particles with attractive van der Waals interactions display continuous shear thickening followed by shear thinning at high shear rates. The shear thickening transition occurs at ${\dot{\gamma }}_c\approx {10}^2-{10}^3{\mathrm{s}}^{-1}$ and is driven by hydrodynamic breakup of clusters. Pre-shearing dispersions at shear rates $\dot{\gamma }>{\dot{\gamma }}_c$ produces enhanced-modulus gels where $G^{\prime }\sim {\sigma }_{pre\text{−}shear}^{1.5-2}$ and is directly proportional to the residual stress in the gel measured at a fixed sample age. The observed data can be accounted for using a simple scaling model for the breakup of fractal clusters under shear stress.

Fermi resonance and its effect on the mean transition time and rate are studied. The necessary frequency ratio 1:2 for Fermi resonance to occur is explained by applying the deterministic averaging method to the two-dimensional conservative Pippard system, and a more frequent fluctuation of energy process due to Fermi resonance is shown by using the samples obtained from digital simulation of the stochastic Pippard system. In the case of weak coupling, the mean transition time of the reacting oscillator energy is evaluated for both nonresonance and Fermi resonance by using the standard (Stratonovich) stochastic averaging method. The theoretical results for the mean transition time in the case of Fermi resonance and nonresonance is then extended to the stochastic system with bistable potential, and the effects of frequency ratio and coupling coefficient on the mean reaction rate are analyzed. In the case of strong coupling, it is pointed out that the exciting oscillator and reacting oscillator move together like one oscillator and no Fermi resonance can occur. In this case, the mean transition rate of the system total energy is studied by using the stochastic averaging method for quasi-non-integrable Hamiltonian systems. All the theoretical results are confirmed through comparison with those from digital simulation, and the effect of Fermi resonance on the transition time and rate is discussed.

A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary in both space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can have only second-order transitions, confirming an earlier conjecture [D. L. Stein, J. Stat. Phys. 114, 1537 (2004)]. We then derive, through a combination of analytical and numerical arguments, both necessary and sufficient conditions to have a first-order vs a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier.

The validity of the Bagnold constitutive relation in gravity-driven granular flow down an inclined plane is studied by discrete element (DEM) simulations. In the limit of infinitely hard particles, the Bagnold relation is known to hold exactly. We determine deviations from this relation as a function of all parameters governing interparticle interactions. These include elastic compliance, inelastic dissipation, friction coefficient, and interparticle cohesion. We find significant deviations from Bagnold rheology in some regions of this parameter space and propose a generalized Bagnold relation to account for this effect. Moreover, we note a significant correlation between the breakdown of Bagnold rheology in the bulk and the appearance of a long-time tail in the two-particle contact time distributions.

Using a Hamilton-Jacobi equation approach, we obtain analytic equations for steady-state population distributions and mean fitness functions for Crow-Kimura and Eigen-type diploid biological evolution models with general smooth hypergeometric fitness landscapes. Our numerical solutions of diploid biological evolution models confirm the analytic equations obtained. We also study the parallel diploid model for the simple case of recombination and calculate the variance of distribution, which is consistent with numerical results.

We present evidence for the hypothesis that transitions between the low- and high-firing states of the cortical slow oscillation correspond to neuronal phase transitions. By analyzing intracellular recordings of the membrane potential during the cortical slow oscillation in rats, we quantify the temporal fluctuations in power and the frequency centroid of the power spectrum in the period of time before “down” to “up” transitions. By taking appropriate averages over such events, we present these statistics as a function of time before transition. The results demonstrate an increase in fluctuation power and time scale broadly consistent with the slowing of systems close to phase transitions. The analysis is complicated and limited by the difficulty in identifying when transitions begin, and removing dc trends in membrane potential.

We present a simple model to explain the transition from oscillatory to smooth crack propagation in brittle metallic glasses. We demonstrate that the smooth fracture propagation that is characteristic for higher temperature or higher crack opening velocities (for type 1 crack propagation) becomes unstable and oscillatory behavior is being observed. The characteristic feature size of the crack propagation may be at the nanometer scale and grows as the opening velocity decreases.

Many real networks have been found to have a rich degree of symmetry, which is a universal structural property of complex networks, yet has been rarely studied so far. One of the fascinating problems related to symmetry is exploration of the origin of symmetry in real networks. For this purpose, we summarized the statistics of local symmetric motifs that contribute to local symmetry of networks. Analysis of these statistics shows that the symmetry of complex networks is a consequence of similar linkage pattern, which means that vertices with similar degrees tend to share common neighbors. An improved version of the Barabaśi-Albert model integrating similar linkage pattern successfully reproduces the symmetry of real networks, indicating that similar linkage pattern is the underlying ingredient that is responsible for the emergence of symmetry in complex networks.