Recently, we presented a generalization of the Jarzynski nonequilibrium work theorem for phase space mappings. The formalism shows that one can determine free energy differences from approximate trajectories obtained from molecular dynamics simulations in which very large time steps are used. In this work we test the method by simulating the force-induced unfolding of a deca-alanine helix in vacuum. The excellent agreement between results obtained with a small, conservative time step of $0.5\mathrm{fs}$ and results obtained with a time step of $3.2\mathrm{fs}$ (i.e., close to the stability limit) indicates that the large-time-step approach is practical for such complex biomolecules. We further adapt the method of Hummer and Szabo for the simulation of single molecule force spectroscopy experiments to the large-time-step method. While trajectories generated with large steps are approximate and may be unphysical—in the simulations presented here we observe a violation of the equipartition theorem—the computed free energies are exact in principle. In terms of efficiency, the optimum time step for the unfolding simulations lies in the range $1–3\mathrm{fs}$.

This paper describes the concentration dependence of the interaction between water droplets coated by a surfactant monolayer using the contrast variation small-angle neutron scattering technique. In the first part, we explain the idea of how to extract a relatively model free structure factor from the scattering data, which is called the relative form factor method. In the second part, the experimental results for the shape of the droplets (form factor) are described. In the third part the relatively model free structure factor is shown, and finally the concentration dependence of the interaction potential between droplets is discussed. The result indicates the validity of the relative form factor method, and the importance of the estimation of the model free structure factor to discuss the nature of structure formation in microemulsion systems.

It has been established that the strongly interacting dipoles form orientationally ordered liquid phases. However, most of the computer simulations adapt the point dipole model. In this paper, we report molecular dynamics simulations of orientationally order phases formed by extended dipoles, where the potential energy consists of the site-site Lennard-Jones potential and electrostatic contribution of partial charges. The calculations were performed for a range of densities along an isotherm and for different temperatures at the same reduced densities. It is found that orientationally ordered phases are present in the wide density regime, the extended dipole tends to form chains at low density, and the isotropic liquid phase is not seen in the density regime studied for a specific temperature.

We investigate the density fluctuations in crystalline polymers under uniaxial stretch in the order of submicrons to microns with two-dimensional ultrasmall-angle x-ray scattering. Before uniaxial stretch, we found isotropic density fluctuations obeying the mass fractal with the fractal dimension 2.6. After uniaxial stretch, the isotropic scattering pattern was transformed into the butterfly pattern. The butterfly pattern is caused by the stress-induced density fluctuations and the heterogeneous deformation associating with the spatial heterogeneity of stress field due to the distribution of crystalline and amorphous regions.

We report on strong nonuniformities in target heating with intense, laser-produced proton beams. The observed inhomogeneity in energy deposition can strongly perturb equation of state (EOS) measurements with laser-accelerated ions which are planned in several laboratories. Interferometric measurements of the target expansion show different expansion velocities on the front and rear surfaces, indicating a strong difference in local temperature. The nonuniformity indicates at an additional heating mechanism, which seems to originate from electrons in the keV range.

We study, both experimentally and numerically, a system of two coupled semiconductor lasers in an asymmetric configuration. A laser subject to optical feedback is bidirectionally coupled to a free running laser. While maintaining the coupling strength, we change the feedback rate and observe a transition from highly correlated low-frequency fluctuations to episodic synchronization between dropouts and jump-ups. Our results resemble those obtained recently in a unidirectionally coupled system [Buldú et al., Phys. Rev. Lett. 96, 024102 (2006)].

Measurements of the temperature distribution were performed in the upper (cold) boundary layer of a rectangular Rayleigh-Bénard cell with aspect ratios ${\Gamma }_x=5$ and ${\Gamma }_y=1$ using air with Prandtl number $\mathrm{Pr}=0.71$ as the working fluid. The range of investigated Rayleigh numbers was from $\mathrm{Ra}\approx 6\times {10}^7$ to $\mathrm{Ra}\approx 6\times {10}^8$, and the measurements were taken at two different positions with the purpose of understanding the variation of the properties of the thermal boundary layer along the cell. We present profiles of the mean temperature, rms temperature fluctuations, skewness, and kurtosis as a function of the distance from the cooling plate from which we extract scaling exponents and boundary layer thicknesses. Whereas most of these quantities are found to depend monotonically on the Rayleigh number for the peripheral measurement position, their values at the central measurement position exhibit a high degree of variability. These observations indicate that the properties of the thermal boundary layer in large-aspect-ratio convection can have strong spatial variations.

The Fisher-Kolmogorov-Petrovskii-Piskunov equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity: this allows a one-dimensional model to predict the biomass, productivity, and extinction transitions. All results are illustrated with a simple growth and stirring model.

A luminescence pulse is observed from laser-created bubbles in pressurized liquid nitrogen and argon, occurring at the first collapse point of the bubble motion. The duration of the light pulse depends linearly on the bubble size, ranging from $200\mathrm{ns}\text{to}1\mu \mathrm{s}$ for bubbles with maximum diameters between 0.2 and $1\mathrm{mm}$. The spectrum of the light consists entirely of atomic lines, which surprisingly turns out to contain strong emission lines from excited states of the neutral chromium atom. It is likely that this results from small microflakes of stainless steel knocked off the walls of the sample cell by the shock waves generated from the laser pulse. The small metallic flakes are preferentially ionized by the laser, resulting in bubbles containing chromium and other metal atoms in their interior. An analysis of the relative intensities of the triplet chromium lines shows that the compression in the bubble collapse is heating the chromium to temperatures of order $4500\mathrm{K}$.

We demonstrate that a two-dimensional complete photonic band-gap (PBG) can be realized in a layered periodic structure with a double-layer unit cell containing an anisotropic left-handed metamaterial layer. A set of criteria is derived for the geometric and material parameters to realize a two-dimensional complete PBG in such systems, and a detailed phase diagram is given. We discuss the underlying physics of the mechanism and illustrate the complete band-gap effects with several concrete examples.

Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue of generating random numbers in a parallel, distributed environment. In this contribution we demonstrate that multiple linear recurrences in finite fields are an ideal method to produce high quality pseudorandom numbers in sequential and parallel algorithms. Their known weakness (failure of sampling points in high dimensions) can be overcome by an appropriate delinearization that preserves all desirable properties of the underlying linear sequence.

In this paper, synchronization based parameter identification of dynamical systems from time series is carefully revisited. It is shown, based on rigorous theoretical analysis and concrete counterexamples, that some recent research reports on this issue are incomplete or even incorrect. A linear independence condition is pointed out, which is sufficient for such parameter identification of general dynamical systems.

The damage spreading (DS) method provided a useful tool to obtain analytical results of the thermodynamics and stability of the two-dimensional (2D) Ising model—amongst many others—but it suffered both from ambiguities in its results and from large computational costs. In this paper we propose an alternative method, the so-called self-overlap method, based on the study of correlation functions measured at subsequent time steps as the system evolves towards its equilibrium. Applying Markovian and mean-field approximations to a 2D Ising system we obtain both analytical and numerical results on the thermodynamics that agree with the expected behavior. We also provide some analytical results on the stability of the system. Since only a single replica of the system needs to be studied, this method would seem to be free from the ambiguities that afflicted the DS method. It also seems to be numerically more efficient and analytically simpler.

We use an exact renormalization-group transformation to study the Ising model on a complex network composed of tightly knit communities nested hierarchically with the fractal scaling recently discovered in a variety of real-world networks. Varying the ratio $K∕J$ of intercommunity to intracommunity couplings, we obtain an unusual phase diagram: at high temperatures or small $K∕J$ we have a disordered phase with a Griffiths singularity in the free energy, due to the presence of rare large clusters, which we analyze through the Yang-Lee zeros in the complex magnetic field plane. As the temperature is lowered, true long-range order is not seen, but there is a transition to algebraic order, where pair correlations have power-law decay with distance, reminiscent of the $XY$ model. The transition is infinite order at small $K∕J$ and becomes second order above a threshold value $(K∕J{)}_m$. The existence of such slowly decaying correlations is unexpected in a fat-tailed scale-free network, where correlations longer than nearest neighbor are typically suppressed.

The rational function approximation method, density functional theory, and $NVT$ Monte Carlo simulation are used to obtain the density profiles of multicomponent hard-sphere mixtures near a planar hard wall. Binary mixtures with a size ratio 1:3 in which both components occupy a similar volume are specifically examined. The results indicate that the present version of density functional theory yields an excellent overall performance. A reasonably accurate behavior of the rational function approximation method is also observed, except in the vicinity of the first minimum, where it may even predict unphysical negative values.

Equations to calculate the optical properties of a flat but rough interface are given. This interface is supposed to be much thinner than the wavelength of the light, and made of $N-1$ layers of refractive indices $n_m$ (for layer $m$) between two media of refractive indices $n_0$ and $n_N$. The interfaces separating two layers are rough. The roughness is supposed to have weak slopes $(\mid \mathbf{\nabla }Z\mid \left(z\right)⪡1)$. These equations can be solved very simply for any $N$ values. The explicit solution for $N=2$ (one rough layer) is given for the incidence angle equal to the Brewster angle in order to apply the result to ellipsometric measurements, specially on liquid interfaces whose roughness originates from thermal fluctuations and is depending on a small number of parameters.

Cells often measure their local environment via the interaction of diffusible chemical signals with cell surface receptors. At the level of a single receptor, this process is inherently stochastic, but cells can contain many such receptors which can reduce the variability in the detected signal by suitable averaging. Here, we use explicit Monte Carlo simulations and analytical calculations to characterize the noise level as a function of the number of receptors. We show that the residual level approaches zero and that the correlation time, i.e., the waiting time needed to obtain statistically independent data, diverges, both for large receptor numbers. This result has important implications for such processes as eukaryotic chemotaxis.

The transient deformation of liquid capsules enclosed by elastic membranes with bending rigidity in shear flow has been studied numerically, using an improved immersed boundary-lattice Boltzmann method. The purpose of the present study is to investigate the effect of interfacial bending stiffness on the deformation of such capsules. Bending moments, accompanied by transverse shear tensions, usually develop due to a preferred membrane configuration or its nonzero thickness. The present model can simulate flow induced deformation of capsules with arbitrary resting shapes (concerning the in-plane tension) and arbitrary configurations at which the bending energy has a global minimum (minimum bending-energy configurations). The deformation of capsules with initially circular, elliptical, and biconcave resting shapes was studied; the capsules’ minimum bending-energy configurations were considered as either uniform-curvature shapes (like circle or flat plate) or their initially resting shapes. The results show that for capsules with minimum bending-energy configurations having uniform curvature (circle or flat plate), the membrane carries out tank-treading motion, and the steady deformed shapes become more rounded if the bending stiffness is increased. For elliptical and biconcave capsules with resting shapes as minimum bending-energy configurations, it is quite interesting to find that with the bending stiffness increasing, the capsules’ motion changes from tank-treading mode to flipping mode, and resembles Jeffery’s flipping mode at large bending stiffness.

Boundary effects are investigated for fluids with internal orientational degrees of freedom such as molecular liquids, thermotropic and lyotropic liquid crystals, and polymeric fluids. The orientational degrees of freedom are described by the second rank alignment tensor which is related to the birefringence. We use a standard model to describe the orientational dynamics in the presence of flow, the momentum balance equations, and a constitutive law for the pressure tensor to describe our system. In the spirit of irreversible thermodynamics, boundary conditions are formulated for the mechanical slip velocity and the flux of the alignment. They are set up such that the entropy production at the wall inferred from the entropy flux is positive definite. Even in the absence of a true mechanical slip, the coupling between orientation and flow leads to flow profiles with an apparent slip. This has consequences for the macroscopically measurable effective velocity. In analytical investigations, we consider the simplified case of an isotropic fluid in the Newtonian and stationary flow regime. For special geometries such as plane and cylindrical Couette flow, plane Poiseuille flow, and a flow down an inclined plane, we demonstrate explicitly how the boundary conditions lead to an apparent slip. Furthermore, we discuss the dependence of the effective viscosity and of the effective slip length on the model parameters.

It is known that the transmission spectrum of the so-called locally resonant phononic crystal can exhibit absolute sharp dips in the sonic frequency range due to the resonance scattering of elastic waves. In this paper, we study theoretically, using a finite difference time domain method, the propagation of acoustic waves through a two-dimensional locally resonant crystal in which the matrix is a fluid (such as water) instead of being a solid as in most of the previous papers. The transmission is shown to be dependent upon the fluid or solid nature of the matrix as well as upon the nature of the coating material in contact with the matrix. The other main purpose of this paper is to consider inclusions constituted by coaxial cylindrical multilayers consisting of several alternate shells of a soft material (such as a soft rubber) and a hard material (such as steel). With respect to the usual case of a hard core coated with a soft rubber, the transmission spectrum can exhibit in the same frequency range several peaks instead of one. If two or more phononic crystals are associated together, we find that the structure displays all the zeros of transmission resulting from each individual crystal. Moreover, we show that it is possible to overlap the dips by an appropriate combination of phononic crystals and create a larger acoustic stop band.