Inspired by a recent hyperbolic regularization of Burnett’s hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a simple kinetic model—a 13 moment Grad system.

Using Brownian dynamics we simulate the effect of histone modification, such as phosphorylation, acetylation, and methylation, on nucleosome structure by varying the interaction force between DNA and the histone octamer. The simulation shows that the structural stability of nucleosome is very sensitive to the interaction force, and the DNA unwrapping from the modified histone octamer usually occurs turn by turn. Furthermore, the effects of temperature and DNA break as well as the competition between modified and normal histone octamers are investigated, with the simulation results being in agreement with the experimental observation that phosphorylated nucleosomes near DNA breaks are more easily depleted. Though the simulation study may only give a coarse grained view of the DNA unwrapping process for the modified histone octamer, it may provide insight into the mechanism of DNA repair.

We investigate the effect on biomembrane mechanical properties due to the presence an external potential for a nonconductive incompressible membrane surrounded by different electrolytes. By solving the Debye-Hückel and Laplace equations for the electrostatic potential and using the relevant stress-tensor we find (1) in the small screening length limit, where the Debye screening length is smaller than the distance between the electrodes, the screening certifies that all electrostatic interactions are short range and the major effect of the applied potential is to decrease the membrane tension and increase the bending rigidity; explicit expressions for electrostatic contribution to the tension and bending rigidity are derived as a function of the applied potential, the Debye screening lengths, and the dielectric constants of the membrane and the solvents. For sufficiently large voltages the negative contribution to the tension is expected to cause a membrane stretching instability. (2) For the dielectric limit, i.e., no salt (and small wave vectors compared to the distance between the electrodes), when the dielectric constant on the two sides are different the applied potential induces an effective (unscreened) membrane charge density, whose long-range interaction is expected to lead to a membrane undulation instability.

We investigate the influence of the network’s size on the degree distribution ${\pi }_k$ in Barabási-Albert model of growing network with initial attractiveness. Our approach based on moments of ${\pi }_k$ allows us to treat analytically several variants of the model and to calculate the cutoff function, giving finite-size corrections to ${\pi }_k$. We study the effect of initial configuration as well as of addition of more than one link per time step. The results indicate that asymptotic properties of the cutoff depend only on the exponent $\gamma$ in the power-law describing the tail of the degree distribution. The method presented in this paper is very general and can be applied to other growing networks.

Certain aspects of the (linear and nonlinear) stability of sheared relativistic (slab) jets are analyzed. The linear problem has been solved for a wide range of jet models well inside the ultrarelativistic domain (flow Lorentz factors up to 20, specific internal energies $\approx 60c^2$). As a distinct feature of our work, we have combined the analytical linear approach with high-resolution relativistic hydrodynamical simulations, which has allowed us (i) to identify, in the linear regime, resonant modes specific to the relativistic shear layer, (ii) to confirm the result of the linear analysis with numerical simulations, and (iii) more interestingly, to follow the instability development through the nonlinear regime. We find that very-high-order reflection modes with dominant growth rates can modify the global, long-term stability of the relativistic flow. We discuss the dependence of these resonant modes on the jet flow Lorentz factor and specific internal energy and on the shear-layer thickness. The results could have potential applications in the field of extragalactic relativistic jets.

In this paper we develop dielectric polarization evolution equations, and the resulting frequency-domain expressions, and relationships for the resulting frequency dependent relaxation times. The model is based on a previously developed equation that was derived using statistical-mechanical theory. We extract relaxation times from dielectric data and give illustrative examples for the harmonic oscillator and derive expressions for the frequency-dependent relaxation times and a time-domain integrodifferential equation for the Cole-Davidson model.

We show how to derive a simple integrator for the Langevin equation and illustrate how it is possible to check the accuracy of the obtained distribution on the fly, using the concept of effective energy introduced in a recent paper [J. Chem. Phys. 126, 014101 (2007)]. Our integrator leads to correct sampling also in the difficult high-friction limit. We also show how these ideas can be applied in practical simulations, using a Lennard-Jones crystal as a paradigmatic case.

We present experimental data on the limiting behavior of an interreality system comprising a virtual horizontally driven pendulum coupled to its real-world counterpart, where the interaction time scale is much shorter than the time scale of the dynamical system. We present experimental evidence that, if the physical parameters of the simplified virtual system match those of the real system within a certain tolerance, there is a transition from an uncorrelated dual reality state to a mixed reality state of the system in which the motion of the two pendula is highly correlated. The region in parameter space for stable solutions has an Arnold tongue structure for both the experimental data and a numerical simulation. As virtual systems better approximate real ones, even weak coupling in other interreality systems may produce sudden changes to mixed reality states.

We develop two nonequilibrium simulation methods which are suitable for calculation of thermal conductivity with good accuracy. These methods are based on simple algorithms, and it will be very easy to extend their range of application. In particular, there are no restrictions (from, e.g., the force field) to apply them to a variety of systems. Here, they are applied to the calculation of the thermal conductivity of amorphous polyamide-6,6 systems. We treat two models of the polymer with different degrees of freedoms constrained. The results suggest that the methods are quite efficient, and that thermal conductivity strongly depends on the number of degrees of freedom in the model.

We study the scaling properties of randomly folded aluminum sheets of different thicknesses $h$ and widths $L$. We found that the fractal dimension $D=2.30\pm 0.01$ and the force scaling exponent $\delta =0.21\pm 0.02$ are independent of the sheet thickness and close to those obtained in numerical simulations with a coarse-grained model of triangulated self-avoiding surfaces with bending and stretching rigidity. So our findings suggest that finite bending rigidity and self-avoidance play the predominant roles in the scaling behavior of randomly folded plastic sheets.

We show that coupled two-level systems like qubits studied in quantum-information processing can be used as a thermodynamic machine. At least three qubits or spins are necessary and they must be arranged in a chain. The system is interfaced between two split baths and the working spin in the middle is externally driven. The machine performs Carnot-type cycles and is able to work as a heat pump or engine depending on the temperature difference of the baths, $\Delta T$, and the energy difference in the spin system, $\Delta E$. It can be shown that the efficiency is a function of $\Delta T$ and $\Delta E$.

The kinetics of a granular planar rotator with a fixed center undergoing inelastic collisions with bath particles is analyzed both numerically and analytically by means of the Boltzmann equation. The angular velocity distribution evolves from quasi-Gaussian in the Brownian limit to an algebraic decay in the limit of an infinitely light particle. In addition, we compare this model to that of a planar rotator with a free center and discuss the prospects for experimental confirmation of these results.

To describe the heterogeneous nature of stress transmission in granular materials, the concept of the “strong” network consisting of contacts with large normal forces has been proposed by Radjaï et al. [Phys. Rev. Lett. 80, 61 (1998)]. The shear stress is mainly determined by this strong network. The dual viewpoint is adopted here, by not only considering the forces at contacts, but also the deformation. It is shown that the strain increments are determined by the tangential component of the relative displacements at the contacts. A “mobile” network consisting of contacts with large tangential relative displacements is defined that primarily accounts for the strain increments. The investigation of the relation between the strong and the mobile networks shows that these networks are largely unrelated. An alternative network is defined that consists of contacts at which the contribution to the work input is large. It is found that this work input occurs primarily through the tangential forces and tangential relative displacements.

Field-induced structure formation in a ferrofluid with well-defined magnetite nanoparticles with a permanent magnetic dipole moment was studied with small-angle neutron scattering (SANS) as a function of the magnetic interactions. The interactions were tuned by adjusting the size of the well-defined, single-magnetic-domain magnetite $\left({\mathrm{Fe}}_3{\mathrm{O}}_4\right)$ particles and by applying an external magnetic field. For decreasing particle dipole moments, the data show a progressive distortion of the hexagonal symmetry, resulting from the formation of magnetic sheets. The SANS data show qualitative agreement with recent cryogenic transmission electron microscopy results obtained in 2D [Klokkenburg et al., Phys. Rev. Lett. 97, 185702 (2006)] on the same ferrofluids.

The dynamic behavior of the slip length in a fluid flow confined between atomically smooth surfaces is investigated using molecular dynamics simulations. At weak wall-fluid interactions, the slip length increases nonlinearly with the shear rate provided that the liquid/solid interface forms incommensurable structures. A gradual transition to the linear rate dependence is observed upon increasing the wall-fluid interaction. We found that the slip length can be well described by a function of a single variable that in turn depends on the in-plane structure factor, contact density, and temperature of the first fluid layer near the solid wall. Extensive simulations show that this formula is valid in a wide range of shear rates and wall-fluid interactions.

Previous results from Kundu et al. using dielectric relaxation have suggested a reentrant antiferroelectric-ferroelectric-antiferroelectric transition in the compound LN36. Our comprehensive studies of this compound using differential optical reflectivity, nonadiabatic scanning calorimetry, null transmission ellipsometry, and resonant x-ray diffraction show that in fact LN36 exhibits the usual phase sequence for chiral smectic liquid crystals: $\mathrm{Sm}{A}^{*}\text{−}\mathrm{Sm}{C}_{\alpha }^{*}\text{−}\mathrm{Sm}{C}^{*}\text{−}\mathrm{Sm}{C}_{FI1}^{*}\text{−}\mathrm{Sm}{C}_A^{*}$. Moreover, the $\mathrm{Sm}{C}_{\alpha }^{*}\text{−}\mathrm{Sm}{C}^{*}$ transition is a first-order transition, characterized by a discontinuous change in the helical pitch. At temperatures just above the $\mathrm{Sm}{C}_{\alpha }^{*}\text{−}\mathrm{Sm}{C}^{*}$ transition, two different values for the helical pitch are simultaneously observed for the first time.

We examine the time-dependent defect fluctuations and lifetimes for a bidisperse disordered assembly of Yukawa particles. At high temperatures, the noise spectrum of fluctuations is white and the coordination number lifetimes have a stretched exponential distribution. At lower temperatures, the system dynamically freezes, the defect fluctuations exhibit a $1∕f$ spectrum, and there is a power law distribution of the coordination number lifetimes. Our results indicate that topological defect fluctuations may be a useful way to characterize disordered systems.

We simulate three-dimensional flexible off-lattice ring polymers of length $L$ up to $L=4000$ for various values of the global radius of curvature $R_{grc}=0.25$, 0.48, and 1.0 and $R_{grc}=2.0$. We utilize two different ensembles: one with a $\delta$-function constraint on the radius, and the other with a $\theta$-function. For both cases the global radius of curvature provides a valid regularization of polymers with thickness $D=2R_{grc}$. The Flory-type critical exponent ${\nu }_{\mathit{SAW}}$ of self-avoiding rings at $D=2$ is found to be ${\nu }_{\mathit{SAW}}=0.5869\left(5\right)$ from the radii of gyration chain length scaling, while other $D$ values produce consistent results. For our current implementation, the numerical effort of chain thickness calculations is bounded by a number $\mathcal{O}\left(L\ln L\right)$ per single update. We also study low-temperature configurations of spatially dense Lennard-Jones homopolymers on a ring and identify some conformational building blocks.

The linear instability of Lotka-Volterra orbits in the homogenous manifold of a two-patch system is analyzed. The origin of these orbits instability in the absence of prey migration is revealed to be the dependence of the angular velocity on the azimuthal angle; in particular, the system desynchronizes at the exit from the slow part of the trajectory. Using this insight, an analogous model of a two coupled oscillator is presented and shown to yield the same type of linear instability. This enables one to incorporate the linear instability within a recently presented general framework that allows for comparison of all known stabilization mechanisms and for simple classification of observed oscillations.

We investigate convection in a fluid channel uniformly heated from below and rotating about a vertical axis. When the width of the channel is moderate, convective instabilities are characterized by two three-dimensional traveling waves having the same frequency and wave number but traveling in opposite directions with different spatial structures. This Rapid Communication demonstrates that neither the progradely nor the retrogradely traveling wave is physically realizable in the vicinity of the instability threshold. The nature of convection is marked by nonlinear interactions of the two oppositely traveling three-dimensional waves which interfere strongly, leading to either vacillating or stationary convective flows.