We conduct a lattice Boltzmann simulation of gas slip flow in microchannels incorporating rough surface effects as characterized by fractal geometry with a focus on gas-solid interaction. The gas slip flow in rough microchannels, which is characterized by Poiseuille number and mass flow rate, is evaluated and compared with smooth microchannels. The effects of roughness height, surface fractal dimension, and Knudsen number on slip behavior of gas flow in microchannels are all investigated and discussed. The results indicate that the presence of surface roughness reduces boundary slip for gas flow in microchannels with respect to a smooth surface. The gas flows at the valleys of rough walls are no-slip while velocity slips are observed over the top of rough walls. We find that the gas flow behavior in rough microchannels is insensitive to the surface topography irregularity (unlike the liquid flow in rough microchannels) but is influenced by the statistical height of rough surface and rarefaction effects. In particular, decrease in roughness height or increase in Knudsen number can lead to large wall slip for gas flow in microchannels.

Single-bubble sonoluminescence (SBSL) was explored under a variety of multifrequency excitations. In particular, biharmonic excitation was used to produce SBSL for unprecedented low dissolved noble gas concentrations in a sulfuric acid solution. Reducing the amount of dissolved noble gas makes it possible to reach higher acoustic pressures on the SL bubble, which otherwise are not attainable because of the Bjerknes instability. By using biharmonic excitation, we were able to experimentally trap and to spatially stabilize SL bubbles for xenon pressure overhead as low as $1\mathrm{mbar}$. As a result, we have access to regions in phase space where the plasma temperatures are higher than the ones reached before for bubbles driven at $\approx 30\mathrm{kHz}$.

We use the spherical coordinate system in the momentum space and an appropriate discretization procedure to derive a hierarchy of lattice Boltzmann $\left(\mathrm{LB}\right)$ models with variable temperature. The separation of the integrals in the momentum space into angular and radial parts allows us to compute the moments of the equilibrium distribution function by means of Gauss-Legendre and Gauss-Laguerre quadratures, as well as to find the elements of the discrete momentum set for each $\mathrm{LB}$ model in the hierarchy. The capability of the high-order models in this hierarchy to capture specific effects in microfluidics is investigated through a computer simulation of Couette flow by using the Shakhov collision term to get the right value of the Prandtl number.

In this work we study the problem of targeting signals in networks using entropy information measurements to quantify the cost of targeting. We introduce a penalization rule that imposes a restriction on the long paths and therefore focuses the signal to the target. By this scheme we go continuously from fully random walkers to walkers biased to the target. We found that the optimal degree of penalization is mainly determined by the topology of the network. By analyzing several examples, we have found that a small amount of penalization reduces considerably the typical walk length, and from this we conclude that a network can be efficiently navigated with restricted information.

We study a contact process (CP) with two species that interact in a symbiotic manner. In our model, each site of a lattice may be vacant or host individuals of species A and/or B; multiple occupancy by the same species is prohibited. Symbiosis is represented by a reduced death rate $\mu <1$ for individuals at sites with both species present. Otherwise, the dynamics is that of the basic CP, with creation (at vacant neighbor sites) at rate $\lambda$ and death of (isolated) individuals at a rate of unity. Mean-field theory and Monte Carlo simulation show that the critical creation rate ${\lambda }_c\left(\mu \right)$ is a decreasing function of $\mu$, even though a single-species population must go extinct for $\lambda <{\lambda }_c\left(1\right)$, the critical point of the basic CP. Extensive simulations yield results for critical behavior that are compatible with the directed percolation (DP) universality class, but with unusually strong corrections to scaling. A field-theoretic argument supports the conclusion of DP critical behavior. We obtain similar results for a CP with creation at second-neighbor sites and enhanced survival at first neighbors in the form of an annihilation rate that decreases with the number of occupied first neighbors.

The quantum dynamics of a particle coupled to the dissipative degrees of freedom of a generalized spin bath in the presence of an external force field is presented. Based on Holstein-Primakoff transformation, which sets up a mapping between boson and spin operators, we show that the spin-$\frac{1}{2}$ bath and the harmonic bath can be realized as two special limits of the generalized bath. In the large spin limit, the Hamiltonian reduces to well-known Zwanzig Hamiltonian. Making use of spin coherent states and canonical thermal distributions of the associated $c$ numbers, we derive and explore the quantum Langevin equation and the properties of the spin and harmonic baths in the context of quantum dissipation of the system.

Using kinetic Monte Carlo simulation, we model gas-liquid spinodal decomposition in a size-polydisperse square well fluid, representing a “near-monodisperse” colloidal dispersion. We find that fractionation (demixing) of particle sizes between the phases begins asserting itself shortly after the onset of phase ordering. Strikingly, the direction of size fractionation can be reversed by a seemingly trivial choice between two interparticle potentials which, in the monodisperse case, are identical—we rationalize this in terms of a perturbative, equilibrium theory of polydispersity. Furthermore, our quantitative results show that kinetic Monte Carlo simulation can provide detailed insight into the role of fractionation in real colloidal systems.

Although DNA conformation plays an integral role in all genetic processes from transcription to chromosome segregation, there is as yet no tractable method for capturing the in vivo conformation of a chromosome at high resolution. Labeling and fluorescently imaging thousands of loci along the chromosome would readily yield a conformation if each locus could be uniquely distinguished in the image, but this would unrealistically require thousands of distinguishable labels and a tedious experimental process. Here we present a computational method for extracting conformations when the total number of labels far exceeds the number of distinguishable labels. We evaluate our technique using simulated conformations with lengths ranging from 10 to 100 kilobases, and discuss the prospects for an experiment.

Spatially resolved trace rare gases optical emission spectroscopy was used to analyze the electron energy-distribution function (EEDF) in low-pressure argon plasma columns sustained by surface waves. At frequencies >1 GHz, in the microwave-sustained region, the EEDF departs from a Maxwellian, characterized by a depletion of low-energy electrons and a high-energy tail, whereas in the field-free zone, the EEDF is Maxwellian. Abnormal behavior of the EEDF results from the acceleration of low-energy electrons due to the conversion of surface waves into volume plasmons at the resonance point where the plasma frequency equals the wave frequency and their absorption by either collisional or Landau damping.

We study the statistics of the number of records $R_{n,N}$ for $N$ identical and independent symmetric discrete-time random walks of $n$ steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance ${\sigma }^2$ of the jump distribution is finite and (II) when ${\sigma }^2$ is divergent as in the case of Lévy flights with index $0<\mu <2$. In both cases we find that the mean record number $\langle R_{n,N}\rangle$ grows universally as $\sim$${\alpha }_N\sqrt{n}$ for large $n$, but with a very different behavior of the amplitude ${\alpha }_N$ for $N>1$ in the two cases. We find that for large $N$, ${\alpha }_N\approx 2\sqrt{\ln N}$ independently of ${\sigma }^2$ in case I. In contrast, in case II, the amplitude approaches to an $N$-independent constant for large $N$, ${\alpha }_N\approx 4/\sqrt{\pi }$, independently of $0<\mu <2$. For finite ${\sigma }^2$ we argue—and this is confirmed by our numerical simulations—that the full distribution of $(R_{n,N}/\sqrt{n}-2\sqrt{\ln N})\sqrt{\ln N}$ converges to a Gumbel law as $n\to \infty$ and $N\to \infty$. In case II, our numerical simulations indicate that the distribution of $R_{n,N}/\sqrt{n}$ converges, for $n\to \infty$ and $N\to \infty$, to a universal nontrivial distribution independently of $\mu$. We discuss the applications of our results to the study of the record statistics of 366 daily stock prices from the Standard & Poor's 500 index.

The scaling properties of the continuous flowing layer in a quasi-2D circular tumbler half filled with a granular material are studied experimentally in the presence of three different interstitial fluids (air, water, and glycerine). In the dry case, the dimensionless flowing layer thickness ${\delta }_0/d$ scales with the dimensionless flow rate $Q_{\mathrm{dry}}^{*}=Q/\left(d\sqrt{gd}\right)$, where $Q$ is the flow rate, $d$ is the particle diameter, and $g$ is the acceleration due to gravity, in agreement with previous studies. However, unlike previous studies, we show that the exponent for the power-law relation between the two depends on the range of $Q_{\mathrm{dry}}^{*}$. Meanwhile, the angle of repose increases linearly with $Q_{\mathrm{dry}}^{*}$. In the immersed case, the interstitial fluid changes the relevant time scales, which can be accommodated by considering the fluid properties. The result is that there are two different expressions for the dimensionless flow rate in the immersed flow; one corresponding to a free fall regime for a large Stokes number, and one corresponding to a viscous regime at small Stokes number. On this basis, a single dimensionless flow rate that incorporates both buoyancy and viscous friction is proposed. The effect of side walls is also investigated. For dry flows and those immersed in water, the thickness of the flowing layer decreases while the slope of the free surface increases as the gap separating the walls becomes smaller. For immersed granular flows with glycerine as the interstitial fluid, however, the ratio of the thickness of the flowing layer to the bead diameter is independent of the distance the between the side walls because viscous effects dominate.

We study the spectral properties of thermal fluctuations on simple liquid surfaces, sometimes called ripplons. Analytical properties of the spectral function are investigated and are shown to be composed of regions with simple analytic behavior with respect to the frequency or the wave number. The derived expressions are compared to spectral measurements performed orders of magnitude below shot-noise levels, which is achieved using a novel noise reduction method. The agreement between the theory of thermal surface fluctuations and the experiment is found to be excellent, elucidating the spectral properties of the surface fluctuations. The measurement method requires relatively only a small sample both spatially (few $\mu$m) and temporally ($\sim 20$ s). The method also requires relatively weak light power ($\sim 0.5$mW) so that it has a broad range of applicability, including local measurements, investigations of time-dependent phenomena, and noninvasive measurements.

Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are grown on real surfaces; eventually, surface imperfections are on the same scale as the lattice constant. Here, we gain insights into this general problem by studying two-dimensional smectic order on substrates with highly localized intrinsic curvature, constructed from cones and their intersections with planes. In doing so we take advantage of fully tractable “paper and tape” constructions, allowing us to understand, in detail, the induced cusps and singularities.

Active targeting by Brownian particles in a fluid-filled porous environment is investigated by computer simulation. The random motion of the particles is enhanced by diffusiophoresis with respect to concentration gradients of chemical signals released by the particles in the proximity of a target. The mathematical model, based on a combination of the Brownian dynamics method and a diffusion problem is formulated in terms of key parameters that include the particle diffusiophoretic mobility and the signaling threshold (the distance from the target at which the particles release their chemical signals). The results demonstrate that even a relatively simple chemical signaling scheme can lead to a complex collective behavior of the particles and can be a very efficient way of guiding a swarm of Brownian particles towards a target, similarly to the way colonies of living cells communicate via secondary messengers.

This study reports on a solution to Poisson's equation describing an electric potential and field generated by a dipolar current source positioned inside a set of concentric spherical shells characterized by a homogeneous anisotropic conductivity inside each shell. Formulas giving a unique continuation of potentials and fields between the shells are derived. The formulas are applied to a spherical model of the human head to show that (i) real human skulls comprising isotropic compact and cancellous bone layers can be closely approximated by a single shell with radial-tangential conductivity anisotropy $\sim 1:2$ and radial conductivity equal to 1/30 of the brain/scalp conductivity; (ii) errors due to the spherical approximation of the head shape are of the same magnitude as errors due to poorly known electrical properties of the modeled head tissues; (iii) commonly used electroencephalography (EEG) average reference contributes 15$\%$ of the signal (on the average) and, therefore, makes EEG measurements significantly nonlocal; and (iv) the surface Laplacian of EEG measurements closely approximates electric currents at the skull-scalp interface, providing a parameter-free (up to a constant factor) deblurring and dereferencing of EEG data. These results can be useful for localization of sources underlying electric activity of the brain.

We consider the Dicke model in the ultrastrong-coupling limit to investigate thermal phase transitions and their precursors at finite particle numbers $N$ for bosonic and fermionic systems. We derive partition functions with degeneracy factors that account for the number of configurations and derive explicit expressions for the Landau free energy. This allows us to discuss the difference between the original Dicke (fermionic) and the bosonic case. We find a crossover between these two cases that shows up, for example, in the specific heat.

We propose a method to identify the direction of interactions between the components of a coupled system from observed data. This method tries to identify the direction of coupling for various severe conditions including for nonlinear dynamics, small sample size, weak coupling strength, noisy and multiscale data, and multistructure systems. Thus, it appears to be a promising method for real-world problems encountered in a variety of disciplines, such as physics, economics, and biology.

A recent macroscopic mixture theory for two-phase immiscible displacement in porous media has introduced percolating and nonpercolating phases. Quasi-analytic solutions are computed and compared to the traditional theory. The solutions illustrate physical insights and effects due to spatiotemporal changes of nonpercolating phases, and they highlight the differences from traditional theory. Two initial and boundary value problems are solved in one spatial dimension. In the first problem a fluid is displaced by another fluid in a horizontal homogeneous porous medium. The displacing fluid is injected with a flow rate that keeps the saturation constant at the injection point. In the second problem a horizontal homogeneous porous medium is considered which is divided into two subdomains with different but constant initial saturations. Capillary forces lead to a redistribution of the fluids. Errors in the literature are reported and corrected.

It is well known that the Poisson-Nernst-Planck (PNP) theory and the classical Gouy-Chapman theory are inconsistent at a high applied voltage. For solving this problem, we propose an ion-conserving Poisson-Boltzmann theory, which shows remarkable agreement with the numerical PNP solutions, even at a high applied voltage. In other words, we have found the exact analytical solutions for steady PNP equations; we believe that this finding greatly contributes to understanding surface science between solids and liquids.

We provide a detailed analysis of structural transitions leading to rapid changes in the dimensionality of small Yukawa clusters. These transformations are induced by variations in the shape of confinement as well as the screening strength. We show that even in the most primitive systems composed of only a few strongly interacting particles, the order parameter exhibits a power-law behavior in the vicinity of the critical point of the continuous transition. The critical exponent $\gamma =1/2$ is found to be universal in all studied cases, which is consistent with the general theory of continuous phase transitions.