Thermal fluctuations in the lattice Boltzmann method for nonideal fluids

We introduce thermal fluctuations in the lattice Boltzmann method for nonideal fluids. A fluctuation-dissipation theorem is derived within the Langevin framework and applied to a specific lattice Boltzmann model that approximates the linearized fluctuating Navier-Stokes equations for fluids based on square-gradient free-energy functionals. The obtained thermal noise is shown to ensure equilibration of all degrees of freedom in a simulation to high accuracy. Furthermore, we demonstrate that satisfactory results for most practical applications of fluctuating hydrodynamics can already be achieved using thermal noise derived in the long-wavelength limit.

Endogenous quasicycles and stochastic coherence in a closed endemic model

We study the role of demographic fluctuations in typical endemics as exemplified by the stochastic SIRS model. The birth-death master equation of the model is simulated using exact numerics and analyzed within the linear noise approximation. The endemic fixed point is unstable to internal demographic noise, and leads to sustained oscillations. This is ensured when the eigenvalues (λ) of the linearized drift matrix are complex, which in turn, is possible only if detailed balance is violated. In the oscillatory state, the phases decorrelate asymptotically, distinguishing such oscillations from those produced by external periodic forcing. These so-called quasicycles are of sufficient strength to be detected reliably only when the ratio |Im(λ)/Re(λ)| is of order unity. The coherence or regularity of these oscillations show a maximum as a function of population size, an effect known variously as stochastic coherence or coherence resonance. We find that stochastic coherence can be simply understood as resulting from a nonmonotonic variation of |Im(λ)/Re(λ)| with population size. Thus, within the linear noise approximation, stochastic coherence can be predicted from a purely deterministic analysis. The non-normality of the linearized drift matrix, associated with the violation of detailed balance, leads to enhanced fluctuations in the population amplitudes.

Run-and-tumble particles with hydrodynamics: sedimentation, trapping, and upstream swimming

We simulate by lattice Boltzmann the nonequilibrium steady states of run-and-tumble particles (inspired by a minimal model of bacteria), interacting by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic interactions barely perturb the steady state found without them, but for particles in a harmonic trap such a state is quite changed if the run length is larger than the confinement length: a self-assembled pump is formed. Particles likewise confined in a narrow channel show a generic upstream flux in Poiseuille flow: chiral swimming is not required.

Biaxiality at the isotropic-nematic interface with planar anchoring

We revisit the classic problem of the structure of the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory, refining previous analytic treatments of biaxiality at the interface. We compare our analysis with numerical results obtained through a highly accurate spectral collocation scheme for the solution of the Landau-Ginzburg-de Gennes equations. In comparison to earlier work, we obtain improved agreement with numerics for both the uniaxial and biaxial profiles, accurate asymptotic results for the decay of biaxial order on both nematic and isotropic sides of the interface, and accurate fits to data from density-functional approaches to this problem.

Entropic evidence for linguistic structure in the Indus script

The script of the ancient Indus civilization remains undeciphered. The hypothesis that the script encodes language has recently been questioned. Here, we present evidence for the linguistic hypothesis by showing that the script's conditional entropy is closer to those of natural languages than various types of nonlinguistic systems.

All-sky LIGO search for periodic gravitational waves in the early fifth-science-run data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

All-sky LIGO search for periodic gravitational waves in the early fifth-science-run data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

All-sky LIGO search for periodic gravitational waves in the early fifth-science-run data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

All-sky LIGO search for periodic gravitational waves in the early fifth-science-run data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1100 Hz and with the frequency's time derivative in the range -5 x 10{-9}-0 Hz s{-1}. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semicoherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 10{-24} are obtained over a 200-Hz band, and the sensitivity improvement over previous searches increases the spatial volume sampled by an average factor of about 100 over the entire search band. For a neutron star with nominal equatorial ellipticity of 10{-6}, the search is sensitive to distances as great as 500 pc.

The eigenspectra of Indian musical drums

In a family of drums used in the Indian subcontinent, the circular drum head is made of material of nonuniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the nonuniform membrane are harmonic. In this work the drum head is modeled as a nonuniform membrane whose density varies smoothly between two prescribed values. The eigenmodes and eigenvalues of the drum head are obtained using a high-resolution numerical method. The mathematical model and the numerical method are able to handle both concentric and eccentric nonuniformities, which correspond, respectively, to the dayan and the bayan drums. For a suitable choice of parameters, which are found by optimizing the harmonicity of the drum, the eigenspectra obtained from the model are in excellent agreement with experiment. The model and the numerical method should find application in numerical sound synthesis.

Duality in matrix lattice Boltzmann models

The notion of duality between the hydrodynamic and kinetic (ghost) variables of lattice kinetic formulations of the Boltzmann equation is introduced. It is suggested that this notion can serve as a guideline in the design of matrix versions of the lattice Boltzmann equation in a physically transparent and computationally efficient way.

Search for gravitational-wave bursts from soft gamma repeaters

We present a LIGO search for short-duration gravitational waves (GWs) associated with soft gamma ray repeater (SGR) bursts. This is the first search sensitive to neutron star f modes, usually considered the most efficient GW emitting modes. We find no evidence of GWs associated with any SGR burst in a sample consisting of the 27 Dec. 2004 giant flare from SGR 1806-20 and 190 lesser events from SGR 1806-20 and SGR 1900+14. The unprecedented sensitivity of the detectors allows us to set the most stringent limits on transient GW amplitudes published to date. We find upper limit estimates on the model-dependent isotropic GW emission energies (at a nominal distance of 10 kpc) between 3x10;{45} and 9x10;{52} erg depending on waveform type, detector antenna factors and noise characteristics at the time of the burst. These upper limits are within the theoretically predicted range of some SGR models.

Numerical method of lines for the relaxational dynamics of nematic liquid crystals

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase, and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic-nematic interface, illustrate the anisotropic character of droplets in the nucleation regime, and validate dynamical scaling in the coarsening regime.

Arrest of fluid demixing by nanoparticles: a computer simulation study

We use lattice Boltzmann simulations to investigate the formation of arrested structures upon demixing of a binary solvent containing neutrally wetting colloidal particles. Previous simulations for symmetric fluid quenches pointed to the formation of "bijels": bicontinuous interfacially jammed emulsion gels. These should be created when a glassy monolayer of particles forms at the fluid-fluid interface, arresting further demixing and rigidifying the structure. Experimental work has broadly confirmed this scenario, but it shows that bijels can also be formed in volumetrically asymmetric quenches. Here, we present new simulation results for such quenches, compare these to the symmetric case, and find a crossover to an arrested droplet phase at strong asymmetry. We then make extensive new analyses of the postarrest dynamics in our simulated bijel and droplet structures, on time scales comparable to the Brownian time for colloid motion. Our results suggest that, on these intermediate time scales, the effective activation barrier to ejection of particles from the fluid-fluid interface is smaller by at least 2 orders of magnitude than the corresponding barrier for an isolated particle on a flat interface.

Singular forces and pointlike colloids in lattice Boltzmann hydrodynamics

We present an accurate method to include arbitrary singular distributions of forces in the lattice Boltzmann formulation of hydrodynamics. We validate our method with several examples involving Stokeslet, stresslet, and rotlet singularities, finding excellent agreement with analytical results. A minimal model for sedimenting particles is presented using the method. In the dilute limit, this model has accuracy comparable to, but computational efficiency much greater than, algorithms that explicitly resolve the size of the particles.

Nonequilibrium steady states in sheared binary fluids

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths L(x,y) in the directions (x,y) of velocity and velocity gradient. Apparent scaling exponents are estimated as Lx approximately gamma (-2/3) and Ly approximately gamma(-3/4). We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.