We propose and study a model for the equilibrium statistical mechanics of a pressurized semiflexible polymer ring in two dimensions. The Hamiltonian has a term which couples to the algebraic or signed area of the ring and a term which accounts for bending (semiflexibility). The model allows for self-intersections. Using a combination of Monte Carlo simulations, Flory-type scaling theory, mean-field approximations, and lattice enumeration techniques, we obtain a phase diagram in which collapsed and inflated phases are separated by a continuous transition. The scaling properties of the averaged area as a function of the number of units of the ring are derived. For large pressures, the asymptotic behavior of the area is calculated for both continuum and lattice versions of the model. For small pressures, the area is obtained through a known mapping onto the quantum mechanical problem of an electron moving in a magnetic field. The simulation data agree well with the analytic and mean-field results.

In multicellular organisms, the initial patterns of gene expression are regulated by spatial gradients of biochemical factors, known as morphogen gradients. Because of biochemical noise in the morphogen gradients there are associated spatial errors in the positions of target gene patterns. Using a simple single morphogen and/or single target gene model, we use propagation of error analysis to derive a condition on the amount of morphogen that needs to be produced in order to have precise spatial patterning of the target. We find that there is an optimal morphogen gradient profile that requires the least amount of morphogen to be produced. Experimental results for the Bicoid-Hunchback system in early Drosophila development are consistent with the predictions of this analysis. We also discuss our results in the context of recent work that analyzed this system using mutual information as an organizing principle, and show that minimizing the amount of morphogen produced also leads to a near optimal flow of information between input and target.

As shown in earlier work [Ahlers et al., J. Fluid Mech. 569, 409 (2006)], non-Oberbeck-Boussinesq (NOB) corrections to the center temperature in turbulent Rayleigh-Bénard convection in water and also in glycerol are governed by the temperature dependences of the kinematic viscosity and the thermal diffusion coefficient. If the working fluid is ethane close to the critical point, the origin of non-Oberbeck-Boussinesq corrections is very different, as will be shown in the present paper. Namely, the main origin of NOB corrections then lies in the strong temperature dependence of the isobaric thermal expansion coefficient $\beta \left(T\right)$. More precisely, it is the nonlinear $T$ dependence of the density $\rho \left(T\right)$ in the buoyancy force that causes another type of NOB effect. We demonstrate this through a combination of experimental, numerical, and theoretical work, the last in the framework of the extended Prandtl-Blasius boundary-layer theory developed by Ahlers et al. as cited above. The theory comes to its limits if the temperature dependence of the thermal expension coefficient $\beta \left(T\right)$ is significant. The measurements reported here cover the ranges $2.1\lesssim \text{Pr}\lesssim 3.9$ and $5\times {10}^9\lesssim \text{Ra}\lesssim 2\times {10}^{12}$ and are for cylindrical samples of aspect ratios 1.0 and 0.5.

We present a version of a dynamical spectral model for large eddy simulation based on the eddy damped quasinormal Markovian approximation [S. A. Orszag, in Fluid Dynamics, edited by R. Balian, Proceedings of Les Houches Summer School, 1973 (Gordon and Breach, New York, 1977), p. 237; J. P. Chollet and M. Lesievr, J. Atmos. Sci. 38, 2747 (1981)]. Three distinct modifications are implemented and tested. On the one hand, whereas in current approaches, a Kolmogorov-like energy spectrum is usually assumed in order to evaluate the non-local transfer, in our method the energy spectrum of the subgrid scales adapts itself dynamically to the large-scale resolved spectrum; this first modification allows in particular for a better treatment of transient phases and instabilities, as shown on one specific example. Moreover, the model takes into account the phase relationships of the small scales, embodied, for example, in strongly localized structures such as vortex filaments. To that effect, phase information is implemented in the treatment of the socalled eddy noise in the closure model. Finally, we also consider the role that helical small scales may play in the evaluation of the transfer of energy and helicity, the two invariants of the primitive equations in the inviscid case; this leads as well to intrinsic variations in the development of helicity spectra. Therefore, our model allows for simulations of flows for a variety of circumstances and a priori at any given Reynolds number. Comparisons with direct numerical simulations of the three-dimensional Navier-Stokes equation are performed on fluids driven by an Arnold-Beltrami-Childress (ABC) flow which is a prototype of fully helical flows (velocity and vorticity fields are parallel). Good agreements are obtained for physical and spectral behavior of the large scales.

Bubbles are levitated in a resonator driven by an ultrasound wave. Their highly nonlinear oscillations feature a strong collapse, where fluidlike densities and temperatures of several thousand degrees Kelvin are reached, resulting in the emission of ultrashort light pulses. Previous experiments and theories explained the observed stable bubble dynamic and emission on long time scales with the requirement of a noble gas. Recent experiments reveal stable sonoluminescent emission of nitrogen bubbles in chilled water without the presence of a noble gas. Numerical calculations show that a diffusive and dissociative equilibrium can be reached when the temperature within a nitrogen bubble is limited due to the presence of water vapor. Calculated stability lines agree with published experimental results. The results show that noble-gas-free stable single bubble sonoluminescence of nitrogen bubbles is possible.

We examine the plastic deformation of a model polymeric glass under tension. Local plastic events are found at extremely small strains, well below the yielding point, in a regime where the material is traditionally described as perfectly elastic. A distinct relationship is identified between these irreversible displacements (plastic events), the amplitude of segmental motion, local structure, and local elastic moduli. By examining the motion during the deformation of individual sites, we arrive at a mechanistic explanation for how these events arise. It is shown that, upon deformation, polymer sites that exhibit relatively small but positive elastic moduli are prone to failure. Such sites are also found to exhibit a large vibration amplitude, as indicated by their respective Debye-Waller factors. Sites that fail first tend to have a higher degree of nonsphericity than the rest of the material. We also find the collective occurrence of local plastic events where percolation or concerted action leads to global failure of the material above a certain strain.

We have investigated the dynamics of water molecules in zeolites NaA and NaX by high-resolution quasielastic neutron scattering methods. Between 260 and 310 K, the local translational diffusive motion of water in the zeolites is one to two orders of magnitude slower than in bulk water. The $Q$ dependence of the scattering shows effects of confinement and the presence of both relatively mobile and immobile molecules. The speed of the diffusive motion depends strongly on hydration level. Comparison with other hydrated siliceous materials indicates that the host charge per water molecule is a major factor in determining the time scale of diffusion.

Molecular dynamics simulations are carried out for slabs of silica liquid with thicknesses between 1 and $3\mathrm{nm}$. A local analysis of the Born contribution to the elastic modulus, ${\mathrm{C}}^{\mathrm{B}}$, shows that the elasticity is not uniform throughout the slabs—${\mathrm{C}}^{\mathrm{B}}$ is identical to that of bulk silica in the slab interior, but ${\mathrm{C}}^{\mathrm{B}}$ is larger at the slab edges. The larger ${\mathrm{C}}^{\mathrm{B}}$ at the slab edges is due to a distinct atomic level structure characterized by larger density, larger concentration of more highly coordinated ions, and smaller silica rings.

We study the thermodynamic properties of spin systems with bond-disorder on small-world hypergraphs, obtained by superimposing a one-dimensional Ising chain onto a random Bethe graph with $p$-spin interactions. Using transfer-matrix techniques, we derive fixed-point equations describing the relevant order parameters and the free energy, both in the replica symmetric and one step replica symmetry breaking approximation. We determine the static and dynamic ferromagnetic transition and the spinglass transition within replica symmetry for all temperatures, and demonstrate corrections to these results when one step replica symmetry breaking is taken into account. The results obtained are in agreement with Monte-Carlo simulations.

When transport in networks follows the shortest paths, the union of all shortest path trees $G_{\cup \text{SPT}}$ can be regarded as the “transport overlay network.” Overlay networks such as peer-to-peer networks or virtual private networks can be considered as a subgraph of $G_{\cup \text{SPT}}$. The traffic through the network is examined by the betweenness $B_l$ of links in the overlay $G_{\cup \text{SPT}}$. The strength of disorder can be controlled by, e.g., tuning the extreme value index $\alpha$ of the independent and identically distributed polynomial link weights. In the strong disorder limit $\left(\alpha \to 0\right)$, all transport flows over a critical backbone, the minimum spanning tree (MST). We investigate the betweenness distributions of wide classes of trees, such as the MST of those well-known network models and of various real-world complex networks. All these trees with different degree distributions (e.g., uniform, exponential, or power law) are found to possess a power law betweenness distribution $\text{Pr}\left[B_l=j\right]\sim j^{-c}$. The exponent $c$ seems to be positively correlated with the degree variance of the tree and to be insensitive of the size $N$ of a network. In the weak disorder regime, transport in the network traverses many links. We show that a link with smaller link weight tends to carry more traffic. This negative correlation between link weight and betweenness depends on $\alpha$ and the structure of the underlying topology.

The van der Pol attractor exhibits a wide variety of behavior depending on the control parameter values: limit cycles, quasiperiodic motion on a torus, mode locking, period doubling, banded chaos, boundary crises, torus wrinkling, breakup of a torus, and toroidal chaos. The organization of these phenomena with respect to each other is well described by studying a partition of the control parameter plane of the Curry-Yorke map.

We solve a model of self-avoiding walks which allows for a site to be visited up to two times by the walk on the Husimi lattice. This model is inspired in the Domb-Joyce model and was proposed to describe the collapse transition of polymers with one-site interactions only. We consider the version in which immediate self-reversals of the walk are forbidden. The phase diagram we obtain for the grand-canonical version of the model is similar to the one found in the solution of the Bethe lattice, with two distinct polymerized phases: a tricritical point and a critical endpoint.

We analyze temperature and thermometry for simple nonequilibrium heat-conducting models. We also show in detail, for both two- and three-dimensional systems, that the ideal-gas thermometer corresponds to the concept of a local instantaneous mechanical kinetic temperature. For the ${\varphi }^4$ models investigated here the mechanical temperature closely approximates the local thermodynamic equilibrium temperature. There is a significant difference between the kinetic temperature and nonlocal configurational temperature. Neither obeys the predictions of extended irreversible thermodynamics. Overall, we find that the kinetic temperature, as modeled and imposed by the Nosé-Hoover thermostats developed in 1984, provides the simplest means for simulating, analyzing, and understanding nonequilibrium heat flows.

Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nanoscale system from one equilibrium state to another in finite time, Schmiedl and Seifert [T. Schmiedl and U. Seifert, Phys. Rev. Lett. 98, 108301 (2007)] found the Euler-Lagrange equation to be a nonlocal integrodifferential equation of correlation functions. For two linear examples, we show how this integrodifferential equation can be solved analytically. For nonlinear physical systems we show how the optimal protocol can be found numerically and demonstrate that there may exist several distinct optimal protocols simultaneously, and we present optimal protocols that have one, two, and three jumps, respectively.

We show numerically that in a binary system of Yukawa particles, a dispersity-driven disordering transition occurs. In the presence of quenched disorder this disordering transition coincides with a marked increase in the depinning threshold, known as a peak effect. We find that the addition of poorly pinned particles can increase the overall pinning in the sample by increasing the amount of topological disorder present. If the quenched disorder is strong enough to create a significant amount of topological disorder in the monodisperse system, addition of a poorly pinned species generates further disorder but does not produce a peak in the depinning force. Our results indicate that for binary mixtures, optimal pinning occurs for topological defect fraction densities from 0.2 to 0.25. For defect densities below this range, the system retains orientational order. We determine the effect of the pinning density, strength, and radius on the depinning peak and find that the peak effect is more pronounced in weakly pinning systems.

The hallmark of nonlinear complexity phenomena in magnetohydrodynamic and plasma turbulence as well as all natural sciences is the appearance of intermittent fluctuating events. We introduce here a unique procedure that is both physically explicable and quantitatively accurate in deciphering the multifractal characteristics of intermittency. The generic character of the procedure provides a natural connection between the suggested spectrum based on rank order and the idea of one-parameter scaling for monofractals. We demonstrate the utility of this method using results obtained from a large scale two-dimensional magnetohydrodynamic simulation mimicking solar wind turbulence.

We show several surprising phenomena that occur in an extremely simple system of a single frictionless, inelastic, spherical particle falling under gravity through a symmetric funnel. One might naively expect that particles would fall through funnels with steeper sides more quickly, exert a smaller total impulse on the funnel walls, and lose less energy. However, we show that there are special ranges of angles of the funnel walls for which exactly the opposite occurs. Typically, the particle will experience a sequence of collisions that is highly sensitive to the location at which it enters the funnel and nearby particle trajectories become widely dispersed. However, in the special angular ranges this is not the case and the particle can experience sequences of collisions that have a highly coherent structure. We provide a theoretical analysis that can predict and explain this surprising behavior.

In quartz crystal microbalance studies of the friction between an adsorbed monolayer film and a metallic substrate, the films are observed to slide relative to the substrate under inertial forces of order ${10}^{-14}\text{dyn}$ per film atom, a force much smaller than all existing theoretical estimates of the force that surface defects are capable of exerting on the film. We argue that defect potentials with a range comparable to an atomic spacing or more will produce a pinning force below the inertial force.

We investigate a three-component reaction-diffusion system that describes the interaction of one activator and two inhibitors where one inhibitor acts as a traveling pulse generator of the activator and the other acts as a lateral inhibition localizer. It is numerically shown that the synergistic effect of these two inhibitors on one activator induces several spatiotemporal patterns such as destabilization and nonannihilation of traveling pulses and the occurrence and splitting of traveling spots. By using singular perturbation procedures, the stability of radially symmetric equilibrium solutions is discussed. Furthermore, we discuss how such dynamics are caused under the synergistic effect of two inhibitors.