To investigate the link between discrete small-scale and continuous large scale mechanical properties of a foam, we observe its two-dimensional flow in a channel, around an elliptical obstacle. We measure the drag, lift, and torque acting on the ellipse versus the angle between its major axis and the flow direction. The drag increases with the spanwise dimension, in marked contrast with a square obstacle. The lift passes through a smooth extremum at an angle close to, but smaller than 45°. The torque peaks at a significantly smaller angle 26°. No existing model can reproduce the observed viscous, elastic, plastic behavior. We propose a microscopic visco-elasto-plastic model which agrees qualitatively with the data.

The thermodynamics of the small SH3 protein domain is studied by means of a simplified model where each beadlike amino acid interacts with the others through a contact potential controlled by a $20\times 20$ random matrix. Good folding sequences, characterized by a low native energy, display three main thermodynamical ensembles, namely, a coil-like ensemble, an unfolded globule, and a folded ensemble (plus two other states, frozen and random coils, populated only at extreme temperatures). Interestingly, the unfolded globule has some regions already structured. Poorly designed sequences, on the other hand, display a wide transition from the random coil to a frozen state. The comparison with the analytic theory of heteropolymers is discussed.

We discuss a class of models for the evolution of tree networks in which new nodes are recruited into the network at random times, and nodes already in the network may die at random times. Stochastic mechanisms for growth and death of the network that are either sensitive or insensitive to the coordination number or degree of nodes are studied using simulations and mean-field approximations. Critical behavior is observed in the long-time coordination number distribution of the system; associated exponents are universal in one part of parameter space, but depend on the ratio of birth and death parameters elsewhere.

The percolation threshold of the network model by Barabási and Albert [Science 286, 509 (1999)] (BA) has thus far only been “guessed” based on simulations and comparison with other models. Due to the still uncertain influence of correlations, the reference to other models cannot be justified. In this paper, we explicitly derive the well-known values for the BA model. To underline the importance of a null model like that of Barabási and Albert, we close with two basic remarks. First, we establish a connection between the abundance of scale-free networks in nature and the fact that power-law tails in the degree distribution result only from (at least asymptotically) linear preferential attachment: Only in the case of linear preferential attachment does a minimum of topological knowledge about the network suffice for the attachment process. Second, we propose a very simple and realistic extension of the BA model that accounts for clustering. We discuss the influence of clustering on the percolation properties.

The motion of oscillatorylike nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly driven system, based on a specific Poincaré map, is proposed and justified. Physical manifestations of these regions of stability are coherent clusters. We illustrate the method and demonstrate the appearance of coherent clusters with two models motivated by the problems of waveguide sound propagation and Lagrangian mixing of passive scalars in the ocean. We find bunches of sound rays propagating coherently in an underwater waveguide through a randomly fluctuating ocean at long distances. We find clusters of passive particles to be advected coherently for a comparatively long time by a random two-dimensional flow modeling mixing around a fixed vortex.

The effects of a spatially periodic forcing on an oscillating chemical reaction as described by the Lengyel-Epstein model are investigated. We find a surprising competition between two oscillating patterns, where one is harmonic and the other subharmonic with respect to the spatially periodic forcing. The occurrence of a subharmonic pattern is remarkable as well as its preference up to rather large values of the modulation amplitude. For small modulation amplitudes we derive from the model system a generic equation for the envelope of the oscillating reaction that includes an additional forcing contribution, compared to the amplitude equations known from previous studies in other systems. The analysis of this amplitude equation allows the derivation of analytical expressions even for the forcing corrections to the threshold and to the oscillation frequency, which are in a wide range of parameters in good agreement with the numerical analysis of the complete reaction equations. In the nonlinear regime beyond threshold, the subharmonic solutions exist in a finite range of the control parameter that has been determined by solving the reaction equations numerically for various sets of parameters.

The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development forth and back under the influence of two slightly different Hamiltonians. It was shown by Prosen and Žnidarič in the linear-response approximation that the decay of the fidelity is frozen if the Hamiltonian of the perturbation contains off-diagonal elements only. In the present work the results of Prosen and Žnidarič are extended by a supersymmetry calculation to arbitrary strengths of the perturbation for the case of an unperturbed Hamiltonian taken from the Gaussian orthogonal ensemble and a purely imaginary antisymmetric perturbation. It is found that for the exact calculation the freeze of fidelity is only slightly reduced as compared to the linear-response approximation. This may have important consequences for the design of quantum computers.

We focus on an estimate of the decay exponent $\left(m\right)$ in the initial period of decay of homogeneous isotropic turbulence at low Taylor microscale Reynolds number $R_{\lambda }$ $(\simeq 20–50)$. Lattice Boltzmann simulations in a periodic box of ${256}^3$ points are performed and compared with measurements in grid turbulence at similar $R_{\lambda }$. Good agreement is found between measured and calculated energy spectra. The exponent $m$ is estimated in three different ways: from the decay of the turbulent kinetic energy, the decay of the mean energy dissipation rate, and the rate of growth of the Taylor microscale. Although all estimates are close, as prescribed by theory, that from the Taylor microscale has the largest variability. It is then suggested that the virtual origin for the decay rate be determined from the Taylor microscale, but the actual value of $m$ be estimated from the decay rate of the kinetic energy. The dependence of $m$ on $R_{\lambda }\left(0\right)$ (the value of $R_{\lambda }$ at the beginning of the simulation) is also analyzed, using the present data as well as data from the literature. The results confirmed that $m$ approaches 1, as $R_{\lambda }\left(0\right)$ increases.

We demonstrate the stability of a stationary vortex breather with vorticity $S=2$ in the two-dimensional discrete nonlinear Schrödinger model for a square lattice and also discuss the effects of exciting internal sites in a vortex ring. We also point out the fundamental difficulties of observing these solutions with current experimental techniques. Instead, we argue that relevant initial conditions will lead to the formation of quasiperiodic vortex breathers.

In this paper, the scattering matrix of sphere with dielectric biaxial anisotropy is obtained exactly within the framework of the extended Mie theory. By incorporating the scattering matrix into the multiple scattering method, we study theoretically the photonic band structure of three dimensional photonic crystals consisting of biaxial dielectric spheres. Our results demonstrate that complete photonic bandgaps can be found in both fcc and sc lattice structures, which are absent in photonic crystals composed of isotropic dielectric spheres. Moreover we have compared our results with those coming from the photonic crystals consisting of the uniaxially birefringent dielectric spheres. It is found that because of the enhancement of the anisotropy, the degeneracy is lifted further, resulting in two neighboring photonic bandgaps, the lower one is complete while the upper one is partial existing only in some special regions of the first Brillouin zone.

The work by Barbi, Bologna, and Grigolini [Phys. Rev. Lett. 95, 220601 (2005)] discusses a response to alternating external field of a non-Markovian two-state system, where the waiting time between the two attempted changes of state follows a power law. It introduced a new instrument for description of such situations based on a stochastic master equation with reset. In the present Brief Report we provide an alternative description of the situation within the framework of a generalized master equation. The results of our analytical approach are corroborated by direct numerical simulations of the system.

It is argued that the method used by Cleve et al. [Phys. Rev. E 69, 066316 (2004)], to determine the intermittency exponent $\mu$ is biased at moderate Reynolds numbers $R_{\lambda }$. Thus, the claimed dependence of $\mu$ upon $\left(R_{\lambda }\right)$ is questionable. Other determinations give a constant value for $\mu$.

In reply to Castaing’s comment on Cleve et al. [Phys. Rev. E 69, 066316 (2004)], we note that the discrepancy that exists between the air data and jet data in helium occurs at high Reynolds numbers. The helium data at high Reynolds numbers do not adequately resolve the small scales and so the dissipation statistics deduced from them should be used with caution.

The translational Brownian motion of a particle in a tilted washboard potential is considered. The dynamic structure factor and longest relaxation time are evaluated from the solution of the governing Langevin equation by using the matrix continued fraction method. The longest relaxation time is compared with the Kramers theory of the escape rate of a Brownian particle from a potential well as extended to the Kramers turnover region by Mel’nikov [Physics Reports 209, 1 (1991)]. It is shown that in the low temperature limit, the universal Mel’nikov expression for the escape rate provides a good estimate of the longest relaxation time for all values of dissipation including the very low damping (VLD), very high damping (VHD), and turnover regimes. For low barriers (where the Mel’nikov method is not applicable) and zero tilt, analytic equations for the relaxation times in the VLD and VHD limits are derived.

We study the equilibrium sediment of a multicomponent system of charged colloids using primitive model Monte Carlo simulations, which include counterions explicitly. We find separation of the different colloidal components into almost pure layers, where colloids with large charge-to-mass ratio sediment higher in the sample. This effect appears due to a competition between ionic entropy, gravitational energy, and electrostatic energy. Our simulations provide a direct confirmation of recent theoretical predictions on the sedimentation of multicomponent mixtures of charged colloids in regimes with relatively low total densities and low colloidal charges. To explore the limitations of the theory we perform simulations at higher total densities for monodisperse and multicomponent systems and at stronger electrostatic couplings by increasing the colloidal charge for monodisperse suspensions. We find good agreement between theory and simulation when the colloidal charge is increased in the monodisperse case. However, we find deviations between simulations and theory upon increasing the total densities in the monodisperse and multicomponent systems. The density profiles obtained from simulations are more homogeneous than those predicted by theory. The spontaneous formation of layered structures predicted by the theory and found by simulation can serve as a useful tool to separate different components from a mixture of charged colloids.

The dynamics of silica displays an Arrhenius temperature dependence, classifying silica as a strong glass-former. Using recently developed concepts to analyze the potential energy landscape, one can get a far-reaching understanding of the long-range transport of silica. It can be expressed in terms of properties of the thermodynamics as well as local relaxation processes, thereby extending the phenomenological standard picture of a strong glass-former. The local relaxation processes are characterized by complex correlated sequences of bond breaking and reformation processes.

Using collision driven discrete molecular dynamics, we investigate the thermodynamics and dynamics of systems of 500 dumbbell molecules interacting by a purely repulsive ramplike discretized potential, consisting of $n$ steps of equal size. We compare the behavior of the two systems, with $n=18$ and $n=144$ steps. Each system exhibits both thermodynamic and dynamic anomalies, a density maximum and the translational and rotational mobilities show anomalous behavior. Starting with very dense systems and decreasing the density, both mobilities first increase, reach a maximum, then decrease, reach a minimum, and finally increase; this behavior is similar to the behavior of SPC/E (Simple Point Charge-Extended) water. The regions in the pressure-temperature plane of translational and rotational mobility anomalies depend strongly on $n$. The product of the translational diffusion coefficient and the orientational correlation time increases with temperature, in contrast with the behavior of most liquids.

The dielectric response of surface stabilized ferroelectric liquid crystals with chevron layer structure is studied within low and intermediate frequency ranges, characteristic for collective molecular excitations. By analytically solving the dynamic equation for collective molecular fluctuations under a weak alternating electric field, it is demonstrated that chevron cells stabilized by both nonpolar and polar surface interactions undergo at medium frequencies two Debye relaxation processes, connected with two chevron slabs, on opposite sides of the interface plane. This result is confirmed, experimentally, making use of the electro-optic technique. Based on qualitative arguments supported by microscopic observations of zigzag defects at different frequencies and amplitudes of the external electric field, it is shown that, at low frequencies, the electro-optic response of chevron samples is determined by three kinds of motions of zigzag walls. The first two dynamic categories are related to collective relaxation processes at weak fields, within smectic A layers forming zigzag walls, and drift or creep motions of thick walls occurring at stronger field amplitudes. Dynamic processes of the third kind correspond to sliding of zigzag walls, which appear at yet stronger field amplitudes, but below the switching threshold.

Cellular aggregates may be considered as collections of membrane enclosed units with a pressure difference between the internal and external liquid phases. Cells are kept together by membrane adhesion and/or confined space compression. Pattern formation and, in particular, intercellular spacing have important roles in controlling solvent diffusion within such aggregates. A physical approach is used to study generic aspects of cellular packings in a confined space. Average material properties are derived from the free energy. The appearance of penetrating intercellular void channels is found to be critically governed by the cell wall adhesion mechanisms during the formation of dense aggregates. A fully relaxed aggregate efficiently hinders solvent diffusion at high hydrostatic pressures, while a small fraction $(\sim 0.1)$ of adhesion related packing frustration is sufficient for breaking such a blockage even at high a pressure.

Large-scale computer simulations with more than four million particles have been performed to study the melting transition in a two-dimensional hard disk fluid. The van der Waals loop previously observed in the pressure-density relationship of smaller simulations is shown to disappear systematically with increase in sample size, but even with these large system sizes, the freezing transition still exhibits what appears to be weakly first-order behavior, though the scaling of the bond orientation order is consistent with the Halperin-Nelson-Young picture. Above this freezing transition region, scaling analysis of the translational order yields a lower bound for the melting density that is much higher than previously thought and provides compelling evidence that the solid phase first melts into a hexatic phase via a continuous transition, before it goes into the isotropic phase.