The coevolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of a gene regulatory network. We find that a critical state emerges spontaneously resulting from the interplay between topology and dynamics during the evolution. The final evolved state is shown to be independent of initial conditions. The network appears to be driven to a random Boolean network with uniform in-degree of 2 in the large-network limit. However, for biologically realized network sizes, significant finite-size effects are observed including a broad in-degree distribution and an average in-degree connections between 2 and 3. These results may be important for explaining the properties of gene regulatory networks.

We present a method to investigate the dynamics of a single semiflexible polymer, subject to anisotropic friction in a viscous fluid. In contrast to previous approaches, we do not rely on a discrete bead-rod model, but introduce a suitable normal mode decomposition of a continuous space curve. By means of a perturbation expansion for stiff filaments, we derive a closed set of coupled Langevin equations in mode space for the nonlinear dynamics in two dimensions, taking into account exactly the local constraint of inextensibility. The stochastic differential equations obtained this way are solved numerically, with parameters adjusted to describe the motion of actin filaments. As an example, we show results for the tumbling motion in shear flow.

We obtain a formal solution for a large class of diffusion equations with a spatial kernel dependence in the diffusive term. The presence of this kernel represents a nonlocal dependence of the diffusive process and, by a suitable choice, it has the spatial fractional diffusion equations as a particular case. We also consider the presence of a linear external force and source terms. In addition, we show that a rich class of anomalous diffusion, e.g., the Lévy superdiffusion, can be obtained by an appropriated choice of kernel.

We observe Fresnel edge diffraction of the x-ray beam generated by the relativistic interaction of a high-intensity laser pulse with He gas. The observed diffraction at center energy $4.5\mathrm{keV}$ agrees with Gaussian incoherent source profile of full-width-half-maximum $\left(\mathrm{FWHM}\right)<8\mu \mathrm{m}$. Analysis indicates this corresponds to an upper limit on the transverse profile of laser-accelerated electrons within the plasma in agreement with three-dimensional, particle-in-cell results $(\mathrm{FWHM}=4\mu \mathrm{m})$.

An approach leading to the development of spiral turbulence is reported here in an oscillatory reaction-diffusion medium, which is through the spontaneous formation of targetlike waves near the core of a spiral wave. The newly formed target wave emerges with its own characteristic frequency and propagates on top of the original spiral wave, which eventually leads to the breakup of the spiral at a location far from the spiral center. The radius of the surviving spiral segment decreases rapidly with the bifurcation control parameter. Calculation of power spectra suggests that the meandering of the spiral tip is responsible for the onset of the superimposed target and the phase desynchronization of the superimposed target waves.

The propagation of acoustic waves in a phononic crystal slab consisting of piezoelectric inclusions placed periodically in an isotropic host material is analyzed. Numerical examples are obtained for a square lattice of quartz cylinders embedded in an epoxy matrix. It is found that several complete band gaps with a variable bandwidth exist for elastic waves of any polarization and incidence. In addition to the filling fraction, it is found that a key parameter for the existence and the width of these complete band gaps is the ratio of the slab thickness, $d$, to the lattice period, $a$. Especially, we have explored how these absolute band gaps close up as the parameter $d∕a$ increases. Significantly, it is observed that the band gaps of a phononic crystal slab are distinct from those of bulk acoustic waves propagating in the plane of an infinite two-dimensional phononic crystal with the same composition. The band gaps of the slab are strongly affected by the presence of cutoff frequency modes that cannot be excited in infinite media.

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton’s method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

Score-dependent and agent-dependent payoffs of the strategies are introduced into the standard minority game. The intrinsic periodicity is consequently removed, and the stylized facts arise, such as long-range volatility correlations and “fat tails” in the distribution of the returns. The agent dependence of the payoffs is essential in producing the long-range volatility correlations. The new payoffs lead to a better performance in the dynamic behavior nonlocal in time, and can coexist with the inactive strategy. We also observe that the standard deviation ${\sigma }^2∕N$ is significantly reduced, thus the efficiency of the system is distinctly improved. Based on this observation, we give a qualitative explanation for the long-range volatility correlations.

We introduce a general class of stochastic processes forced by instantaneous random fires (i.e., jumps) that reset the state variable $x$ to a given value. Since in many physical systems the fire activity is often dependent on the actual value of the state variable, as in the case of natural fires in ecosystems and firing dynamics in neuronal activity, the frequency of fire occurrence is assumed to be state dependent. Such dynamics leads to independent interfire statistics—i.e., to renewal point processes. Various functions relating the frequency of fire occurrence to $x\left(t\right)$ are analyzed and compared. The relation between the probabilistic dynamics of $x\left(t\right)$ and the interfire statistics is derived and some exact probability distribution of both $x\left(t\right)$ and the interfire times are obtained for systems with different degrees of complexity. After studying processes in which the fire activity is coupled only to a deterministic drift, we also analyze processes forced by either additive or multiplicative Gaussian white noise.

Polymer self-consistent field theory numerical tools are applied to a two-dimensional hard-rod colloidal system. Rods are represented through an interaction site model density functional theory that is derived and expressed from a self-consistent field theory perspective. A weighted density approximation is used within the density functional theory, and the phase space is sampled without bias for any particular morphology. A completely ordered crystal phase is found as well as a liquid crystal state.

We investigate the limiting mechanical tension (negative pressure) that liquid water can sustain before cavitation occurs. The temperature dependence of this quantity is of special interest for water, where it can be used as a probe of a postulated anomaly of its equation of state. After a brief review of previous experiments on cavitation, we describe our method which consists in focusing a high amplitude sound wave in the bulk liquid, away from any walls. We obtain highly reproducible results, allowing us to study in detail the statistics of cavitation, and to give an accurate definition of the cavitation threshold. Two independent pressure calibrations are performed. The cavitation pressure is found to increase monotonically from $-26\mathrm{MPa}$ at $0°\mathrm{C}$ to $-17\mathrm{MPa}$ at $80°\mathrm{C}$. While these values lie among the most negative pressures reported in water, they are still far away from the cavitation pressure expected theoretically and reached in the experiment by Angell and his group [Zheng et al., Science 254, 829 (1991)] (around $-120\mathrm{MPa}$ at $40°\mathrm{C}$). Possible reasons for this discrepancy are considered.

We have observed strong phase-matched (PM) quadrupole optical second-harmonic generation (SHG) from nematic liquid crystals that possess inversion symmetry. PM conditions were achieved for two configurations by voltage control of the molecular orientation and thus of the refractive indices. Quadrupole SHG was separated from electric-field-induced dipole-type SHG with the help of time-gated measurements in a pulsed electric field.

We show how an extended object’s strain field is redistributed when the material ruptures under by thermal activation. Through analytical calculations and molecular dynamics simulations, we show that in a polymer chain the distribution is exponentially localized around the point of rupture. The length scale of localization is determined by the strain and microscopic parameters of the interaction potential. We also derive an analytic expression for the rate of bond rupture by consistently treating the collective modes of the chain and the effect of dissipation on those modes. Our theoretical estimates are of the same order of magnitude as those obtained by simulations, as compared to earlier theories which had overestimated the rate of rupture by approximately two orders of magnitude. It is also noteworthy that the correction comes about through the effective attempt frequency rather than the effective barrier height.

The interaction of laser-generated single inertial bubbles (collapse $\text{time}=121\mu \mathrm{s}$) near a silicon rubber membrane with a shock wave ($55\mathrm{MPa}$ in peak pressure and $1.7\mu \mathrm{s}$ in compressive pulse duration) is investigated. The interaction leads to directional, forced asymmetric collapse of the bubble with microjet formation toward the surface. Maximum jet penetration into the membrane is produced during the bubble collapse phase with optimal shock wave arrival time and stand-off distance. Such interaction may provide a unique acoustic means for in vivo microinjection, applicable to targeted delivery of macromolecules and gene vectors to biological tissues.

The rise and fall time behavior of a pulsed microwave oscillator is a problem of academic interest. It is also of importance to radar and other applications because it can lead to phase and frequency jitters or even lock the entire pulse into an undesired mode. Here we present a study of the rise and fall time behavior in the gyrotron backward-wave oscillator (gyro-BWO). Single-mode simulations reveal that, during the rise and fall portions of the electron beam pulse, oscillation frequencies of the axial modes vary in such a way that their transit angles remain at the respective optimum values. Thus, axial mode competition and mode switching can readily take place in these transient stages. Time-dependent simulations demonstrate that, under both the gradual and instant turn-on conditions, the axial modes compete in a pattern governed by the characteristic asymmetry of the mode profiles. Other aspects of physics interest include the analysis and explanation of a resultant hysteresis effect between the rise and fall portions of the beam pulse. These understandings are expected to provide the basis for achieving a stable gyro-BWO operating at a single mode throughout the entire beam pulse.

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Spreight [Nonlinearity 12, 1373 (1999)] and Barashenkov et al. [Phys. Rev. E 72, 035602(R) (2005)], such that they support not only kinks but a one-parameter set of exact static solutions. These solutions can be obtained iteratively from a two-point nonlinear map whose role is played by the discretized first integral of the static Klein-Gordon field, as suggested by Dmitriev et al. [J. Phys. A 38, 7617 (2005)]. We then discuss some discrete ${\varphi }^4$ models free of the Peierls-Nabarro barrier and identify for them the full space of available static solutions, including those derived recently by Cooper et al. [Phys. Rev. E 72, 036605 (2005)] but not limited to them. These findings are also relevant to standing wave solutions of discrete nonlinear Schrödinger models. We also study stability of the obtained solutions. As an interesting aside, we derive the list of solutions to the continuum ${\varphi }^4$ equation that fill the entire two-dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models.

We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group technique, we compute the distribution of pinning forces in the quasistatic limit. This distribution is universal up to two parameters, the average critical force and its width. We discuss possible definitions for threshold forces in finite-size samples. We show how our results compare to the distribution of the latter computed recently within a numerical simulation of the so-called critical configuration.

Towards the prediction of thermodynamic properties for complex systems and the design of self-assembly techniques for the production of nanocomposite materials, we employ Monte Carlo simulations to calculate the effective interactions between colloidal brushes dissolved in nonadsorbing polymer solutions. For simplicity, all interactions are reduced to excluded-volume potentials. Our results indicate that (1) due to excluded-volume effects and the absence of attractive van der Waals forces in our calculations, the effective interactions between colloidal brushes in a continuum medium are always repulsive; and (2) that the short-ranged repulsion between the colloidal brushes may be coupled to a midrange attraction when nonadsorbing polymers are in solution. We prove that a depletion mechanism is responsible for the midranged attraction and we observe that the strength of the induced attraction is weaker compared to the depletion attraction computed for hard-sphere colloids in nonadsorbing polymer solutions. More interestingly, however, our results indicate that, even for the simple interaction potentials employed here, it is not possible to superimpose depletion attraction and steric repulsion to predict the correct pair potential between colloidal brushes in nonadsorbing polymer solutions.

We consider the influence of quenched noise upon interface dynamics in two-dimensional (2D) and 3D capillary rise with rough walls by using a phase-field approach, where the local conservation of mass in the bulk is explicitly included. In the 2D case, the disorder is assumed to be in the effective mobility coefficient, while in the 3D case we explicitly consider the influence of locally fluctuating geometry along a solid wall using a generalized curvilinear coordinate transformation. To obtain the equations of motion for meniscus and contact lines, we develop a systematic projection formalism that allows inclusion of disorder. Using this formalism, we derive linearized equations of motion for the meniscus and contact line variables, which become local in the Fourier space representation. These dispersion relations contain effective noise that is linearly proportional to the velocity. The deterministic parts of our dispersion relations agree with results obtained from other similar studies in the proper limits. However, the forms of the noise terms derived here are quantitatively different from the other studies.

During the filling of a one-dimensional lattice by $k$-site-long hard particles, we find that after initial “jamming” a power-law-like decay of the density of interparticle gaps occurs, described by a much larger exponent than that expected from mean-field theory. We show that this effect dominates post-jamming filling for large $k$ and should be observable, e.g., during the binding of proteins along a long, stretched DNA molecule.