We present a first-principles theory for the slow dynamics of a fluid of entangling rigid crosses of zero excluded volume based on a generalization of the dynamic mean-field approach of Szamel for infinitely thin nonrotating rods. The latter theory exactly includes topological constraints at the two-body collision level and self-consistently renormalizes an effective diffusion tensor to account for many-body effects. Remarkably, it predicts scaling laws consistent with the phenomenological reptation-tube predictions of Doi and Edwards for the long-time diffusion and the localization length in the heavily entangled limit. We generalize this approach to a different macromolecular architecture, infinitely thin three-dimensional crosses, and also extend the range of densities over which a dynamic localization length can be calculated for rods. Ideal gases of nonrotating crosses have recently received attention in computer simulations and are relevant as a simple model of both a strong-glass former and entangling star-branched polymers. Comparisons of our theory with these simulations reveal reasonable agreement for the magnitude and reduced density dependence of the localization length and also the self-diffusion constant if the consequences of local density fluctuations are taken into account.

Thermodynamic parameters such as free energies and heat capacities are important quantities for understanding processes involving structural transitions in complex molecules such as proteins. Computational investigations provide simulated data that can be used for calculating thermodynamic parameters. However, calculations give accurate results only if the simulations sample all of configuration space with the appropriate temperature-dependent Boltzmann equilibrium probabilities. For many systems, truly comprehensive sampling of configuration space is not computationally feasible. We present an approximation technique for the calculations that will give accurate values for thermodynamic parameters when the data is incomplete. Our work is applicable to systems in which there are two distinct, important regions of configuration space that must be sampled. Importantly, the results are also valid when the system is more complex than two-state systems. Transition pathways that involve intermediate configurations between two stable regions are allowed in this treatment, and therefore the results are valid for multistate systems.

In nanofluidic devices, nonuniform confinement induces an entropic force that automatically drives biopolymers toward less-confined regions to gain entropy. To understand this phenomenon, we first analyze the diffusion of an entropy-driven particle system. The derived Fokker-Planck equation reveals an effective driving force as the negative gradient of the free energy. The derivation also shows that both the diffusion constant and drag coefficient are location dependent on an arbitrary free-energy landscape. As an application, DNA motion and deformation in nonuniform channels are investigated. Typical solutions reveal large gradients of stress on the polymer where the channel width changes rapidly. Migration of DNA in several nonuniform channels is discussed.

We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic—it is caused by the viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation supplemented with a kinematic criterion captures quantitatively the flow diagram. Surprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure the rheological properties of dilute polymer solutions that are difficult to assess otherwise.

We examine driven nonlinear dynamical systems that are known to be in a state of generalized synchronization with an external drive. The chaotic time series of the response system are subject to empirical mode decomposition analysis. The instantaneous intrinsic mode frequencies (and their variance) present in these signals provide suitable order parameters for detecting the transition between the regimes of strong and weak generalized synchrony. Application is made to a variety of chaotically driven flows as well as maps.

We study analytically and numerically a delay differential model of a passively mode-locked semiconductor laser subjected to a single-frequency coherent injection. The width of the locking cone is calculated asymptotically in the limit of small injection and zero line-width enhancement factors and compared to that obtained by direct numerical integration of the model equations. The dependence of the locking cone on the laser parameters is discussed.

Electro-osmotic effect in a porous medium arises from the electrically charged double layer at the fluid-solid interface, whereby an externally applied electric field can give rise to fluid flow. The electro-osmotic pump (EOP) is potentially useful for a variety of engineering and biorelated applications, but its generally low efficiency is a negative factor in this regard. A study to determine the optimal efficiency of the EOP and the condition(s) under which it can be realized is therefore of scientific interest and practical importance. We present the results of a theoretical and experimental study on the maximum efficiency optimization of the electrokinetic effect in artificially fabricated porous media with controlled pore diameters. It is shown that whereas the EOP efficiency increases with decreasing channel diameter, from 4.5 to 2.5 μm for samples fabricated on oxidized silicon wafers as expected for the interfacial nature of the electro-osmotic effect, the opposite trend was observed for samples with much smaller channel diameters fabricated on anodized aluminum oxide films, with the pore surface coated with silica. These results are in agreement with the theoretical prediction, based on the competition between interfacial area and the no-slip flow boundary condition, that an optimal efficiency of ∼$1\%$ is attained at a microchannel diameter that is five times the Debye length, with a zeta potential of ∼100 mV.

We present an analytic method to generate solutions for the optical fiber soliton system that reveals self-steepening effects on solitons coupled to a continuous wave. Exact soliton solutions are obtained by adopting a universal Lax pair technique that solves simultaneously the nonlinear Schrödinger (NLS) equation and the derivative NLS equation. We find that, in the presence of a self-steepening term, the bright type NLS equation with abnormal group velocity dispersion is related to the dark type NLS equation with normal group velocity dispersion and, accordingly, exact soliton solutions of the bright type NLS equation describe both bright and dark solitons depending on the strength of the continuous wave. The self-steepening effect on solitons and possible applications of a continuous wave for the control of solitons are explained.

The value of the internal energy per spin is independent of the strip width for a certain class of spin systems on two-dimensional infinite strips. It is verified that the Ising model on the kagome lattice belongs to this class through an exact transfer-matrix calculation of the internal energy for the two smallest widths. More generally, one can suggest an upper bound for the critical coupling strength $K_c(q)$ for the $q$-state Potts model from exact calculations of the internal energy for the two smallest strip widths. Combining this with the corresponding calculation for the dual lattice and using an exact duality relation enables us to conjecture the critical coupling strengths for the three- and four-state Potts models on the kagome lattice. The values are $K_c(q=3)=1.0565094269290$ and $K_c(q=4)=1.1493605872292$, and the values can, in principle, be obtained to an arbitrary precision. We discuss the fact that these values are in the middle of earlier approximate results and furthermore differ from earlier conjectures for the exact values.

In this work, we present the results of a systematic exploration of the effect caused by the introduction of nonmagnetic impurities (or defects) on the stabilization of the interface between two magnetic domains of opposite magnetic orientation. Those defects are simulated as spin vacancies along the center of confined two-dimensional Ising films, which have competing magnetic fields acting on the confinement walls. The calculations are performed for different $L\times M$ film sizes and by using the standard Metropolis dynamics. In the absence of defects, the film is characterized by an interface running along the $M$ direction, which is induced by the competing surface fields. That interface undergoes a localization-delocalization transition that is the precursor of a true wetting transition taking place in the thermodynamic limit. When the density of defects is relatively low, our results show that the wetting phase transition is of second order, as in the absence of defects. On the other hand, when the density of nonmagnetic impurities is relatively high, a pinning effect of the interface gives rise to a first-order wetting phase transition. The observed transitions are characterized by measuring relevant properties, such as magnetization profiles, cumulants, magnetization fluctuations, etc., as a function of the density of defects. So, our main finding is that the presence of nonmagnetic impurities introduces a rich physical scenery, such as a line of second-order wetting transitions (observed for low density of defects) that merges into a first-order one just at a tricritical point. Precisely, these two latter findings are the major contributions of our study.

We consider the unidirectional particle transport in a suspension of colloidal particles which interact with each other via a pair potential having a hard-core repulsion plus an attractive tail. The colloids are confined within a long narrow channel and are driven along by a dc or an ac external potential. In addition, the walls of the channel interact with the particles via a ratchetlike periodic potential. We use dynamical density functional theory to compute the average particle current. In the case of dc drive, we show that as the attraction strength between the colloids is increased beyond a critical value, the stationary density distribution of the particles loses its stability leading to depinning and a time-dependent density profile. Attraction induced symmetry breaking gives rise to the coexistence of stable stationary density profiles with different spatial periods and time-periodic density profiles, each characterized by different values for the particle current.

We use time-resolved rheology to elucidate the slow dynamics and aging in highly concentrated suspensions of multiarm star polymers. The linear and nonlinear rheological properties exhibit a terminal regime corresponding to a well-defined maximal relaxation time. Terminal relaxation is driven by arm relaxation which speeds up the escape of stars from their cages. The fact that the system fully relaxes and flows at long times has important consequences. The yield stress only exists in the limited range of frequencies or shear rates where solid-like behavior is observed. Aging is controlled by the total time elapsed after flow cessation and not by the time elapsed from flow cessation to the beginning of the measurement as in other glassy materials. Our results, which demonstrate the importance of particle architecture with respect to glassy dynamics, should be generic for long hairy particles.

Many cellular functions are based on the rhythmic organization of biological processes into self-repeating cascades of events. Some of these periodic processes, such as the cell cycles of several species, exhibit conspicuous irregularities in the form of period skippings, which lead to polymodal distributions of cycle lengths. A recently proposed mechanism that accounts for this quantized behavior is the stabilization of a Hopf-unstable state by molecular noise. Here we investigate the effect of varying noise in a model system, namely an excitable activator-repressor genetic circuit, that displays this noise-induced stabilization effect. Our results show that an optimal noise level enhances the regularity (coherence) of the cycles, in a form of coherence resonance. Similar noise levels also optimize the multimodal nature of the cycle lengths. Together, these results illustrate how molecular noise within a minimal gene regulatory motif confers robust generation of polymodal patterns of periodicity.

Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that we explore a method for fitting power laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation.

An optimization procedure for the estimation of Kramers-Moyal coefficients from stationary, one-dimensional, Markovian time series data is presented. The method takes advantage of a recently reported approach that allows one to calculate exact finite sampling interval effects by solving the adjoint Fokker-Planck equation. Therefore, it is well suited for the analysis of sparsely sampled time series. The optimization can be performed either by making a parametric ansatz for drift and diffusion functions or parameter free. We demonstrate the power of the method in several numerical examples with synthetic time series.

The evolution of a cluster of three identical nontouching spheres settling in a vertical plane due to gravity in Stokes flow has been evaluated numerically for a two-parameter family of initial configurations, with the sphere centers close to each other and located on a horizontal line. A condition has been specified which relates the cluster lifetime to its geometry. The cluster lifetime and the label of the sphere left behind are very sensitive to initial conditions, as within the point-particle approximation of Jánosi et al. [Phys. Rev. E 56, 2858 (1997)]. The finding is that an increase of the sphere radii always reduces the range of initial conditions leading to chaotic scattering. The hydrodynamic interactions between close spheres stabilize the cluster.

Complex combinatorial optimization can be used to design network systems having desired dynamics and that are robust against structural perturbations. Here genetic networks exhibiting limit-cycle oscillations with prescribed periods and, furthermore, that are robust against the deletion of links and nodes or the application of noise are constructed. Large ensembles of robust genetic clocks with different periods could thus be obtained, and some of their statistical properties have been investigated. Similar methods can be used to design robust network oscillators of various origins.

An Ising model with quenched random magnetic fields is examined for single-Gaussian, bimodal, and double-Gaussian random-field distributions by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. Random-field distribution shape dependencies of the phase diagrams and magnetization curves are investigated for simple cubic, body-centered-cubic, and face-centered-cubic lattices. The conditions for the occurrence of reentrant behavior and tricritical points on the system are also discussed in detail.

We develop an analytical approach that provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two strongly different behaviors depending on the type—compact or non compact—of the random walk. In the case of non compact exploration, we show that the MFPT scales linearly with the inverse connectivity of the target and is largely independent of the starting point. On the contrary, in the compact case, the MFPT is controlled by the source-target distance, and we find that unexpectedly the target connectivity becomes irrelevant for remote targets.