We study the problem of pattern selection in an array of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems, using an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [Phys. Rev. E 73, 016214 (2006)]. We describe the transitions between standing-wave patterns of different wave numbers as the drive amplitude is varied either quasistatically, abruptly, or as a linear ramp in time. We find interesting hysteretic effects, which are confirmed by numerical integration of the original equations of motion of the interacting nonlinear resonators.

Fully developed homogeneous isotropic turbulent fields, computed by direct numerical simulation, are compared to divergence-free random fields having the same energy spectrum and either the same helicity spectrum as that of the turbulent data, or vanishing helicity. We show that the scale-dependent velocity flatness quantifies the spatial variability of the energy spectrum. The flatness exhibits a substantial increase at small scales for the turbulent field, but remains constant for the random fields. A diagnostic, the scale-dependent helicity, is proposed to quantify the geometrical statistics of the flow, which shows that only the turbulent flow is intermittent. Finally, statistical scale-dependent analyses of both Eulerian and Lagrangian accelerations confirm the inherently different dynamics of turbulent and random flows.

The effect of helicity (velocity-vorticity correlations) is studied in direct numerical simulations of rotating turbulence down to Rossby numbers of 0.02. The results suggest that the presence of net helicity plays an important role in the dynamics of the flow. In particular, at small Rossby number, the energy cascades to large scales, as expected, but helicity then can dominate the cascade to small scales. A phenomenological interpretation in terms of a direct cascade of helicity slowed down by wave-eddy interactions leads to the prediction of non-Kolmogorovian inertial indices for the small-scale energy and helicity spectra.

Nonequilibrium molecular dynamics simulation is applied to investigate the effect of periodic wall roughness on the flow of liquid argon through krypton nanochannels. The effect of the length of a rectangular protrusion on the flow is investigated and compared to the case of nanochannels with flat walls. The results show a clear trapping of fluid atoms inside the rectangular cavities that are formed between successive protrusions. The size of the cavities affects the potential energy map and, consequently, fluid atom localization. This localization results in a reduction of velocity values inside the cavities, as well as a reduction of the slip length near the rough wall.

We report an interesting and important observation of the velocity fields from immersed boundary lattice Boltzmann methods (IB-LBM). The computed velocity profiles can deviate from theoretical predictions greatly even for very simple flow situations, both in the immersed boundary layer and the bulk region. A rigorous analysis of the IB-LBM simulated velocity for a symmetric shear flow is carried out, and the analytical solutions indicate a strong dependence of velocity on the relaxation parameter (kinetic viscosity). Also our simulations demonstrate that simply increasing the immersed boundary layer thickness is not an efficient approach to reduce such velocity discrepancy. We hope this work will bring the awareness of this essential issue to people using IB-LBM for various flow situations.

Cumulants of a fluctuating current can be obtained from a free-energy-like generating function, which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the density-matrix renormalization group for stochastic systems. We calculate the variance of the current in the different phases, and at the phase transitions, of the totally asymmetric exclusion process. Our results can be described in the terms of a scaling ansatz that involves the dynamical exponent $z$. We also calculate the generating function of the dynamical activity (total number of configuration changes) near the absorbing-state transition of the contact process. Its scaling properties can be expressed in terms of known critical exponents.

Extensive nonequilibrium molecular dynamics (NEMD) simulations have been carried out in order to estimate the Newtonian shear viscosity of a fluid composed of short chains (up to 16 segments) of jointed spheres [Lennard-Jones chain (LJC)] over a large range of thermodynamic conditions. Using the NEMD results, it is shown that the zero-density contribution decreases with the chain length for a given temperature and is simply proportional to $N^{-1∕2}$, where $N$ is the number of spheres composing the chain. In addition, it has been noticed that the residual shear viscosity is proportional to the chain length. Then, using these results, a relation is proposed to correlate the shear viscosity of the LJC fluid using the LJ fluid (the monomer) as a reference. It is shown that this correlation is able to provide an excellent estimation of the LJC fluid viscosity compared to NEMD results for $N⩽16$ over the domain $0⩽{\rho }^{*}⩽1.1$ and $0.7⩽T^{*}⩽6$. Finally, it is shown that the LJC model is unambiguously more efficient than a simple LJ approximation when applied to estimate the shear viscosity of $n$-butane, if only the sphere or segment diameter is used as an adjustable parameter in both models.

Nanosecond pulsed laser heating was used to control the assembly of spatially correlated nanoparticles from lithographically patterned pseudo-one-dimensional nickel lines. The evolution of the nickel line instabilities and nanoparticle formation with a correlated size and spacing was observed after a series of laser pulses. To understand the instabilities that direct the nanoparticle assembly, we have carried out nonlinear time-dependent simulations and linear stability analysis based on a simple hydrodynamic model. We find that the simulated time scales and length scales agree well with the experimental results. Interestingly, in both experiments and simulations, the instabilities associated with the line edge, and with the surface perturbation-driven mechanism, are found to result in similar particle sizes and spacings.

Laser-induced fluorescence (LIF) processes through the Stark and electric-quadrupole moment (QDP) transitions of $\mathrm{He}\mathrm{I}$ $(2{}^{1}S\to n{}^{1}D\to 2{}^{1}P,n=3,4)$ have been investigated for reliable electric-field measurements in plasmas. A linear-polarization model is formulated for various configurations of electric fields, magnetic fields, and laser polarization. To extend the model to higher-particle-density plasmas we develop a rate-equation model involving a collisional disalignment term. Disalignment rates of $n{}^{1}D$ states, $R_{\mathrm{da}}$, due to a collision with He gas were measured. Spatial distributions in intensity and polarization of LIF were observed in a discharge plasma. For $n=3$ with small $R_{\mathrm{da}}$, the same electric-field distribution in the sheath was obtained from either of the intensity ratios of the Stark to QDP component and the polarization, and the sheath potential agreed well with that by an electric probe. For $n=4$ with large $R_{\mathrm{da}}$, the distribution was also correctly obtained from partially depolarized LIF wave forms by using the extended model. These results show that our extended model provides an accurate measurement of the electric field. The minimum detectable field strength was $80\mathrm{V}∕\mathrm{cm}$ for $n=4$. Application and limitations of the methods are discussed.

In our previous paper, we developed an optical measurement for absolute densities of fast (tens of keV) H ions in an abnormal hollow cathode discharge of hydrogen in the units to tens of mTorr pressure range. We apply this method to a cylindrically symmetric inertial electrostatic confinement (IEC) discharge of hydrogen using the Doppler spectrum of ${\mathrm{H}}_{\alpha }$. We predict neutron production rates for an equivalent discharge of deuterium and compare these with experimental values under the separate conditions of constant deuterium gas pressure $(\sim 6\mathrm{mTorr})$ and voltage $\left(30\mathrm{kV}\right)$. Our predictions capture the variation of production rates with dc current $(10–50\mathrm{mA})$ and agree with experiment to within an order of magnitude. The applicability of this diagnostic to the cylindrical IEC discharge is thus demonstrated, with our results supporting the theory that the discharge is dominated by energetic neutrals emerging from the cathode apertures.

We analyze the modulational instability of the zone boundary mode (ZBM) and the band edge modes (BEMs) in a one-dimensional nonlinear diatomic lattice and obtain rigorous results. Some numerical calculations of modulational instability in these modes are presented. These results indicate that the modulational instability of the BEMs leads to excitation of the discrete breathers (DBs) in the band gap, while that of the ZBM leads to excitation of the DBs above the phonon band.

Brownian dynamics simulations with hydrodynamic interaction (HI) are performed to study the effect of chain length on the diffusion of a polymer chain adsorbed onto flat surfaces. Bead-rod as well as bead-spring chains, with Hookean and finitely extensible nonlinear elastic (FENE) springs, are used to model the polymer chain, and the no-slip boundary condition for the solvent is incorporated exactly. Simulations for short chains $(N⩽100)$ predict that the translational diffusivity in the planar direction $D_{\parallel }\sim N^{-\nu }$, where $N$ is the chain length, with $\nu \approx 0.75$ for bead-rod chains and bead-spring chains connected by stiff FENE springs and $\nu \approx 1$ for bead-spring chains connected by flexible FENE and Hookean springs. We find that near chemically homogeneous surfaces, the scaling exponent $\nu$ depends upon three factors: chain flexibility, strength of HI, and solvent quality. The $\nu$ value changes from 0.75 to 1 with either an increase in chain flexibility, a decrease in the strength of HI, or a decrease in solvent quality. However, near a chemically heterogeneous surface, $\nu$ is always 1.

The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high-resolution three-dimensional (3D) imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D microarchitecture of trabecular bone. We introduce an approach based on spatial geometrical properties and define structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organization and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high-resolution microcomputed tomography $\left(\mu \mathrm{CT}\right)$ from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analyzed geometrical features of trabecular bone and loss of bone density, but also indicate that the measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the $\mu \mathrm{CT}$ data sets.

Recently, crust cooling times have been measured for neutron stars after extended outbursts. These observations are very sensitive to the thermal conductivity $\kappa$ of the crust and strongly suggest that $\kappa$ is large. We perform molecular dynamics simulations of the structure of the crust of an accreting neutron star using a complex composition that includes many impurities. The composition comes from simulations of rapid proton capture nucleosynthesis followed by electron captures. We find that the thermal conductivity is reduced by impurity scattering. In addition, we find phase separation. Some impurities with low atomic number $Z$ are concentrated in a subregion of the simulation volume. For our composition, the solid crust must separate into regions of different compositions. This could lead to an asymmetric star with a quadrupole deformation. Observations of crust cooling can constrain impurity concentrations.

The existence of coefficients for diffusion, viscosity, and thermal conductivity is examined for two-dimensional (2D) liquids. Equilibrium molecular dynamics simulations are performed using a Yukawa potential and the long-time behavior of autocorrelation functions is tested. Advances reported here as compared to previous 2D Yukawa liquid simulations include an assessment of the thermal conductivity, using a larger system size to allow meaningful examination of longer times, and development of improved analysis methods. We find that the transport coefficient exists for diffusion at high temperature and viscosity at low temperature, but not in the opposite limits. The thermal conductivity coefficient does not appear to exist at high temperature. Further advances in computing power could improve these assessments by allowing even larger system sizes and longer time series.

Depending on the parameters of a particle and of a host medium, a particle in a rotating electric field can rotate either in the direction of rotation of electric field or in the opposite direction. There exists a range of parameters where both regimes of rotation can be realized simultaneously. In this study we investigate stability of rotation regimes in the whole range of parameters. We determine the range of parameters where different modes of particle rotation are stable, the range of parameters where only one regime of rotation is stable and the range of parameters where both regimes of rotation are unstable. It is shown that if the mode of rotation is realized outside the domain of the existence of two regimes of rotation, then this rotation mode is stable. Consequently, unstable regimes can be realized only in the range of parameters where both modes of rotation can exist simultaneously. We suggest a simple algorithm for determining the range of stability through the parameters of the system which does not require calculating frequencies of particle rotation in each of the possible rotation regimes.

A comprehensive study of the static and dynamical properties of a representative stochastic model of Brownian ratchet effects for molecular motors is reported. The model describes Brownian motions on two periodic potentials under static and time-dependent forces, where there are two distinct locations of chemical reactions coupling the levels with reversible rates within a period. Complete stationary properties have been obtained analytically for arbitrary potentials under external force. Dynamical relaxation properties near nonequilibrium stationary states were examined by considering the response function of velocity upon time-dependent external force, expressed in terms of the conditional probability density of the model. The latter is fully calculated using a systematic numerical method using matrix diagonalization, which is easily generalized to more complicated models for studying both static and dynamical properties. The behavior of the time-dependent response examined for model potentials suggests that the characteristic relaxation time near stationary states generally decreases linearly with respect to increasing velocity as one goes away from equilibrium via an increase in chemical potential of fuel species, a prediction testable in single molecule experiments.

We consider the problem of finding the densest closed packing of hard disks with proposed different radii in a circular environment, such that the radius of the circumcircle is minimal. With our approach, we are able to find denser packings for various problem instances than known from the literature. Both for the dynamics of the simulation and for the optimum values of the radii of the circumcircles, we find various scaling laws.

We report the formation of a crater at the free surface of an immersed granular bed, locally crossed by an ascending gas flow. In two dimensions, the crater consists of two piles which develop around the location of the gas emission. We observe that the typical size of the crater increases logarithmically with time, independently of the gas emission dynamics. We describe the related granular flows and give an account of the influence of the experimental parameters, especially of the grain size and of the gas flow.