Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective-medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rods connected by flexible cross-links to an elastic continuum. This effective medium is treated in a linear elastic limit as well as in a more general framework, in which the medium self-consistently represents the nonlinear network behavior. This model predicts that the nonlinear elastic response sets in at strains proportional to cross-linker length and inversely proportional to filament length. Furthermore, we find that the differential modulus scales linearly with the stress in the stiffening regime. These results are in excellent agreement with bulk rheology data.

We have investigated the rate of substitution of advantageous mutations in populations of haploid organisms where the rate of recombination can be controlled. We have verified that in all the situations recombination speeds up adaptation through recombination of beneficial mutations from distinct lineages in a single individual, and so reducing the intensity of clonal interference. The advantage of sex for adaptation is even stronger when deleterious mutations occur since now recombination can also restore genetic background free of deleterious mutations. However, our simulation results demonstrate that evidence of clonal interference, as increased mean selective effect of fixed mutations and reduced likelihood of fixation of small-effect mutations, are also present in sexual populations. What we see is that this evidence is delayed when compared to asexual populations.

Networks—collections of interacting elements or nodes—abound in the natural and manmade worlds. For many networks, complex spatiotemporal dynamics stem from patterns of physical interactions unknown to us. To infer these interactions, it is common to include edges between those nodes whose time series exhibit sufficient functional connectivity, typically defined as a measure of coupling exceeding a predetermined threshold. However, when uncertainty exists in the original network measurements, uncertainty in the inferred network is likely, and hence a statistical propagation of error is needed. In this manuscript, we describe a principled and systematic procedure for the inference of functional connectivity networks from multivariate time series data. Our procedure yields as output both the inferred network and a quantification of uncertainty of the most fundamental interest: uncertainty in the number of edges. To illustrate this approach, we apply a measure of linear coupling to simulated data and electrocorticogram data recorded from a human subject during an epileptic seizure. We demonstrate that the procedure is accurate and robust in both the determination of edges and the reporting of uncertainty associated with that determination.

We studied the dynamics of synchronization in asymmetrically coupled neural oscillators with time delay. Stability analysis revealed that symmetric excitatory coupling results in synchrony at multiple phase relations. Asymmetry yields two saddle-node bifurcations of the stable states when coupling is asymmetric. By contrast, with inhibitory coupling only in phase or antiphase is stable as long as coupling is symmetric. Otherwise, these stable states shift or even vanish. The reduced bistability range suggests the beneficial role of asymmetric coupling for reliable neural information transfer.

We demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. More generally, this relationship (including the case of dispersive and negative-index materials) offers a perspective on the phenomena of backward waves and left-handed media. As an application of this relationship, we demonstrate and explain an irrecoverable failure of perfectly matched layer absorbing boundaries in computer simulations for constant cross-section waveguides with backward-wave modes and suggest an alternative in the form of adiabatic isotropic absorbers.

The quantum Zakharov system in three spatial dimensions and an associated Lagrangian description, as well as its basic conservation laws, are derived. In the adiabatic and semiclassical cases, the quantum Zakharov system reduces to a quantum modified vector nonlinear Schrödinger (NLS) equation for the envelope electric field. The Lagrangian structure for the resulting vector NLS equation is used to investigate the time dependence of the Gaussian-shaped localized solutions, via the Rayleigh-Ritz variational method. The formal classical limit is considered in detail. The quantum corrections are shown to prevent the collapse of localized Langmuir envelope fields, in both two and three spatial dimensions. Moreover, the quantum terms can produce an oscillatory behavior of the width of the approximate Gaussian solutions. The variational method is shown to preserve the essential conservation laws of the quantum modified vector NLS equation. The possibility of laboratory tests in the next generation intense laser-solid plasma compression experiment is discussed.

Numerical simulations of flows of fluids with granular materials using the Eulerian-Lagrangian approach involve the problem of modeling of collisions: both between the particles and particles with walls. One of the most popular techniques is the hard-sphere model. This model, however, has a major drawback in that it does not take into account cohesive or adhesive forces. In this paper we develop an extension to a well-known hard-sphere model for modeling particle-wall interactions, making it possible to account for adhesion. The model is able to account for virtually any physical interaction, such as van der Waals forces or liquid bridging. In this paper we focus on the derivation of the new model and we show some computational results.

The structure and dynamics of the two-dimensional linear shear flow of inelastic disks at high area fractions are analyzed. The event-driven simulation technique is used in the hard-particle limit, where the particles interact through instantaneous collisions. The structure (relative arrangement of particles) is analyzed using the bond-orientational order parameter. It is found that the shear flow reduces the order in the system, and the order parameter in a shear flow is lower than that in a collection of elastic hard disks at equilibrium. The distribution of relative velocities between colliding particles is analyzed. The relative velocity distribution undergoes a transition from a Gaussian distribution for nearly elastic particles, to an exponential distribution at low coefficients of restitution. However, the single-particle distribution function is close to a Gaussian in the dense limit, indicating that correlations between colliding particles have a strong influence on the relative velocity distribution. This results in a much lower dissipation rate than that predicted using the molecular chaos assumption, where the velocities of colliding particles are considered to be uncorrelated.

We show that the statistical properties of a vibrated granular bead chain are similar to standard models of polymers in equilibrium. Granular chains of length up to $N=1024$ beads were confined within a circular vibrating bed, and their configurations were imaged. To differentiate the effects of persistence and confinement on the chain, we compared with simulations of both persistent random-walk (RW) and self-avoiding walk (SAW) models. Static properties, such as the radius of gyration and structure factor, are governed for short chains $\left(N\le 128\right)$ by persistence and can be matched by those of RWs. Self-avoidance and confinement effects are both important for longer chains and the results are well described by equilibrated SAWs. We also find that the collective dynamics of the granular chain is similar to the Rouse model of polymers. In particular, as long as confinement is negligible, the center of mass of the chain diffuses with a diffusion coefficient that scales as $1/N$, and the dynamic structure factor decays exponentially in time.

The author presents a kinetic model describing the formation of new metastases by cancer stem cells in premetastatic stem-cell niches induced by the factors produced by a primary tumor and already formed metastases. The corresponding kinetics is analyzed by employing mean-field kinetic equations and Monte Carlo simulations. In agreement with observations, the model predicts a long latent period with low rate of the metastase growth followed by explosive increase in the number of metastases. The duration of the latent period is found to depend on a multitude of rate constants characterizing various processes.

During the process of adding links, we find that the synchronizability of the classical Barabási-Albert (BA) scale-free or Watts-Strogatz (WS) small-world networks can be statistically quantified by three essentially structural quantities of these networks, i.e., the eccentricity, variance of the degree distribution, and clustering coefficients. The results indicate that both the eccentricity and clustering coefficient are positively linearly correlated with synchronizability, while the variance is negatively linearly correlated. Moreover, the efficiency of some particular strategies of adding links to change the synchronizability is also investigated. This information can be used to guide us to design corresponding strategies of structure-evolving processes to manipulate the synchronizability of a given network.

Binary mixtures of larger and smaller colloids having charges of equal sign display unusual response to low-frequency electric fields. We show here that the previously reported negative torque acting on rodlike particles when in presence of a sea of smaller particles is accompanied by a field-induced clearing of the suspension. Measurements of transmitted intensity performed on mixtures of large (dilute) and small (semidilute) spherical particles indicate that such a clearing effect is universal and due to an anisotropic $E^2$-dependent redistribution of the small spheres around the large ones. We interpret this behavior as resulting from $O\left(E^2\right)$ electro-osmotic flows whose magnitude is greatly enhanced by the presence of the small particles.

When a fluid at a constant density $\rho$ in between the densities of coexisting vapor $\left({\rho }_{\text{v}}\right)$ and liquid $\left({\rho }_{\ell }\right)$ at temperatures below criticality is studied in a (cubic) box of finite linear dimension $L$, phase separation occurs in this finite volume, provided $L$ is large enough. For a range of densities, one can observe a liquid droplet (at density ${\rho }_{\ell }^{\prime }$ slightly exceeding ${\rho }_{\ell }$) coexisting in stable thermal equilibrium with surrounding vapor (with density ${\rho }_{\text{v}}^{\prime }>{\rho }_{\text{v}}$, so in the thermodynamic limit such a vapor would be supersaturated). We show, via Monte Carlo simulations of a Lennard-Jones model of a fluid and based on a phenomenological thermodynamic analysis, that via recording the chemical potential $\mu$ as function of $\rho$, one can obtain precise estimates of the droplet surface free energy for a wide range of droplet radii. We also show that the deviations of this surface free energy from the prediction based on the “capillarity approximation” of classical nucleation theory (i.e., using the interfacial free energy of a flat liquid-vapor interface for the surface free energy of a droplet irrespective of its radius) are rather small. We also study carefully the limitation of the present method due to the “droplet evaporation/condensation transition” occurring for small volumes and demonstrate that very good equilibrium is achieved in our study, by showing that the radial profile of the local chemical potential from the droplet center to the outside is perfectly flat.

The evaluation of the specific heat of an open damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath alone. For the free damped particle it has been shown, however, that the ensuing specific heat may become negative for appropriately chosen environments. Being an open system this quantity then naturally must be interpreted as the change in the specific heat obtained as the difference between the specific heat of the heat bath coupled to the system degrees of freedom and the specific heat of the bath alone. While this difference may become negative, the involved specific heats themselves are always positive; thus, the known thermodynamic stability criteria are perfectly guaranteed. For a damped quantum harmonic oscillator, instead of negative values, under appropriate conditions one can observe a dip in the difference of specific heats as a function of temperature. Stylized minimal models containing a single oscillator heat bath are employed to elucidate the occurrence of the anomalous temperature dependence of the corresponding specific heat values. Moreover, we comment on the consequences for the interpretation of the density of states based on the thermal partition function.

In the bulk state, the Ising face-centered-cubic (fcc) antiferromagnet is fully frustrated and is known to have a very strong first-order transition. In this paper, we study the nature of this phase transition in the case of a thin film as a function of the film thickness. Using Monte Carlo simulations, we show that the transition remains first order down to a thickness of four fcc cells (eight atomic layers). It becomes clearly second order at a thickness of two fcc cells, i.e., four atomic layers. It is also interesting to note that the presence of the surface reduces the ground-state degeneracy found in the bulk. For the two-cell thickness, the surface magnetization is larger than the interior one. It undergoes a second-order phase transition at a temperature $T_C$ while interior spins become disordered at a lower temperature $T_D$. This loss of order is characterized by a peak of the interior spins susceptibility and a peak of the specific heat which do not depend on the lattice size suggesting that either it is not a real transition or it is a Kosterlitz-Thouless nature. The surface transition, on the other hand, is shown to be of second order with critical exponents deviated from those of pure two-dimensional Ising universality class. We also show results obtained from the Green’s function method. A discussion is given.

A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its equations, such as the previous ones, reflect the interplay between confinement-induced relaxation phenomena and glassy dynamics through the presence of two contributions in the slow part of the memory kernel, which are linear and quadratic in the density correlation functions, respectively. From numerical solutions for two simple models with pure hard-core interactions, it is shown that two different scenarios result for the diffusion-localization transition depending on the strength of the confinement. For weak confinement, this transition is discontinuous and coincides with the ideal glass transition, such as in one-component bulk systems, while, for strong confinement, it is continuous and occurs before the collective dynamics gets nonergodic. In the latter case, the glass transition manifests itself as a secondary transition, which can be either continuous or discontinuous, in the already arrested single-particle dynamics. The main features of the anomalous dynamics found in the vicinity of all these transitions are reviewed and illustrated with detailed computations.

In the present work, we show that the autocorrelation function of the capillary-wave displacement is expressed by the sum of the ordinary oscillator and the bulk shear-mode terms. The former is expressed by a simple damped oscillator form or a sum of exponentially damping functions depending on the extent of damping. The latter is also written by superposition of exponentially damping modes, and an analytically exact formulation is obtained. We performed surface dynamic light-scattering experiment for the surface of an ionic liquid, 1-butyl- 3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide, and compared the experimental autocorrelation function with the theoretical one. We observed for the first time the bulk shear-mode contribution, and confirmed that the experimental data is well explained by the theoretical autocorrelation function.

Physical and mathematical considerations are presented in support of the suggestion that social hornets and bees, which construct brood combs with large arrays of cells in a honeycomb structure, exploit ultrasonic acoustic resonances in those cells in order to achieve the great accuracy of the hexagonal symmetry exhibited by these honeycomb-structured arrays. We present a numerical calculation of those resonances for the case of a perfect-hexagon duct utilizing a Bloch-Floquet-type theorem. We calculate the rate of energy dissipation in those resonances and use that, along with other considerations, to identify the resonance that is best suited for the suggested use by bees and hornets. Previously recorded ultrasonic data on social hornets and honeybees are cited which agree with some of our predictions and thus provide support for the above-mentioned suggestion.

Information encoding in a globally coupled network is studied. When the network is in an oscillatory state, the network activities are dominated by the intrinsic oscillatory current and the stimulus is poorly encoded. However, when the amplitude of the input signal is large, the input can still be well read from the population rate and the temporal correlation between spike trains. The underlying reason is that there exists a competition between the intrinsic correlation caused by the oscillatory current and the external correlation caused by the input signal. With small input signal, the rate code performs better than the temporal correlation code. Our results provide insights into the effects of network dynamics on neuronal computations.