We study the interaction of both dense and sparse multiarmed spirals in bistable media modeled by equations of the FitzHugh-Nagumo type. A dense one-armed spiral is characterized by its fixed tip. For dense multiarmed spirals, when the initial distance between tips is less than a critical value, the arms collide, connect, and disconnect continuously as the spirals rotate. The continuous reconstruction between the front and the back drives the tips to corotate along a rough circle and to meander zigzaggedly. The rotation frequency of tip, the frequency of zigzagged displacement, the frequency of spiral, the oscillation frequency of media, and the number of arms satisfy certain relations as long as the control parameters of the model are fixed. When the initial distance between tips is larger than the critical value, the behaviors of individual arms within either dense or sparse multiarmed spirals are identical to that of corresponding one-armed spirals.

Conventional studies of the centrifugally driven fingering instability are performed in rotating Hele-Shaw cells presenting perfectly parallel plates. In this setup, the fluid-fluid interface can become unstable due to the density difference between the fluids, forming a variety of complex patterns. We study a modified, tapered version of this rotating flow problem where the cell plates are not exactly parallel, but present a constant gap gradient in the radial direction. Our analytical results indicate that the stability of the interface is significantly sensitive to the presence of the depth gradient. This allows a proper monitoring of pattern-forming features just by slightly changing the cell's taper angle. In this context, we have verified that by manipulating the sign and magnitude of the gap gradient one can favor, restrain, or even suppress the development of centrifugally driven instabilities. A taper-induced mechanism for the selection of the number of emerging fingers is also discussed.

We present an analytical method for the calculation of shapes of Stark-broadened spectral lines in plasmas, applicable to hydrogen and hydrogenlike transitions (including Rydberg ones) with $\Delta n>1$. The method is based on the recently suggested quasicontiguous approximation of the static Stark line shapes, while the dynamical effects are accounted for using the frequency-fluctuation-model approach. Comparisons with accurate computer simulations show excellent agreement.

A lattice Boltzmann model for thermal gas mixtures is derived. The kinetic model is designed in a way that combines properties of two previous literature models, namely, (a) a single-component thermal model and (b) a multicomponent isothermal model. A comprehensive platform for the study of various practical systems involving multicomponent mixture flows with large temperature differences is constructed. The governing thermohydrodynamic equations include the mass, momentum, energy conservation equations, and the multicomponent diffusion equation. The present model is able to simulate mixtures with adjustable Prandtl and Schmidt numbers. Validation in several flow configurations with temperature and species concentration ratios up to nine is presented.

We study the properties of heat conduction induced by non-Gaussian noises from athermal environments. We find that new terms should be added to the conventional Fourier law and the fluctuation theorem for the heat current, where its average and fluctuation are determined not only by the noise intensities but also by the non-Gaussian nature of the noises. Our results explicitly show the absence of the zeroth law of thermodynamics in athermal systems.

This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “$1/f$ noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and $1/f$ noises.

We analyze the transport of heat along a chain of particles interacting through anharmonic potentials consisting of quartic terms in addition to harmonic quadratic terms and subject to heat reservoirs at its ends. Each particle is also subject to an impulsive shot noise with exponentially distributed waiting times whose effect is to change the sign of its velocity, thus conserving the energy of the chain. We show that the introduction of this energy-conserving stochastic noise leads to Fourier's law. The behavior of the heat conductivity for small intensities of the shot noise and large system sizes is found to obey a finite-size scaling relation. We also show that the heat conductivity is not constant but is an increasing monotonic function of temperature.

Spherical catalytic micromotors fabricated as described in Wheat et al. [Langmuir 26, 13052 (2010)] show fuel concentration dependent translational and rotational velocity. The motors possess short-time and long-time diffusivities that scale with the translational and rotational velocity with respect to fuel concentration. The short-time diffusivities are two to three orders of magnitude larger than the diffusivity of a Brownian sphere of the same size, increase linearly with concentration, and scale as $v^2/2\omega$. The measured long-time diffusivities are five times lower than the short-time diffusivities, scale as $v^2/\left\{2D_r\left[1+{(\omega /D_r)}^2\right]\right\}$, and exhibit a maximum as a function of concentration. Maximums of effective diffusivity can be achieved when the rotational velocity has a higher order of dependence on the controlling parameter(s), for example fuel concentration, than the translational velocity. A maximum in diffusivity suggests that motors can be separated or concentrated using gradients in fuel concentration. The decrease of diffusivity with time suggests that motors will have a high collision probability in confined spaces and over short times; but will not disperse over relatively long distances and times. The combination of concentration dependent diffusive time scales and nonmonotonic diffusivity of circle-swimming motors suggests that we can expect complex particle responses in confined geometries and in spatially dependent fuel concentration gradients.

The nonlinear dynamics of a thin axisymmetric liquid film on a horizontal cylindrical substrate subjected to an axial double-frequency forcing that consists of two components of different amplitudes and frequencies and a possible phase shift is considered in this paper. A nonlinear evolution equation governing the spatiotemporal dynamics of the film interface has been derived in the long-wave limit. Similar to the case of a single-frequency forcing considered in our earlier work, there exists a critical forcing amplitude below which the film undergoes a long-time capillary rupture typical for a static cylinder, whereas above it the film remains continuous. We find that it is possible to arrest the rupture even if the forcing parameters of each of the two components correspond separately to the domain where rupture takes place. It is shown that the critical forcing amplitude is easily determined via a single-frequency case when the two forcing frequencies are equal. In the case of different forcing amplitudes and frequencies, the variation of the critical forcing amplitude as a function of the frequency ratio exhibits a unique behavior displaying the emergence of spikes. A related case of an amplitude-modulated single-frequency forcing is also addressed here. For a sufficiently small frequency of the amplitude modulation, a significant increase of the pattern amplitude is observed. In the case of commensurate forcing frequencies, the flow is found to be quasiperiodic.

The pair-distance distribution function (PDDF) contains all structural information probed in an elastic scattering experiment of macromolecular solutions. However, in small-angle x-ray scattering (SAXS) or small-angle neutron scattering (SANS) experiments only their Fourier transform is measured over a restricted range of scattering angles. We therefore developed a mathematically simple and computationally efficient method to calculate the PDDFs as well as accurate scattering intensities from molecular dynamics simulations. The calculated solution scattering intensities are in excellent agreement with SAXS and wide-angle x-ray scattering (WAXS) experiments for a series of proteins. The corresponding PDDFs are remarkably rich in features reporting on the detailed protein structure. Using an inverse Fourier transform method, most of these features can be recovered if scattering intensities are measured up to a momentum transfer of $q\approx 2$–$3{\AA }^{-1}$. Our results establish that high-precision solution scattering experiments utilizing x-ray free-electron lasers and third generation synchrotron sources can resolve subnanometer structural detail, well beyond size, shape, and fold.

The mean square displacement is a central tool in the analysis of single-particle tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time averages on single-particle trajectories followed by ensemble averaging. This procedure, however, suffers from two systematic errors when applied to particles that perform anomalous diffusion. The first is significant at short-time lags and is induced by measurement errors. The second arises from the natural heterogeneity in biophysical systems. We show how to estimate and correct these two errors and improve the estimation of the anomalous parameters for the whole particle distribution. As a consequence, we manage to characterize ensembles of heterogeneous particles even for rather short and noisy measurements where regular time-averaged mean square displacement analysis fails. We apply this method to both simulations and in vivo measurements of telomere diffusion in 3T3 mouse embryonic fibroblast cells. The motion of telomeres is found to be subdiffusive with an average exponent constant in time. Individual telomere exponents are normally distributed around the average exponent. The proposed methodology has the potential to improve experimental accuracy while maintaining lower experimental costs and complexity.

We study the static and dynamic properties of networks of crumpled creases formed in hand crushed sheets of paper. The fractal dimensionalities of crumpling networks in the unfolded (flat) and folded configurations are determined. Some other noteworthy features of crumpling networks are established. The physical implications of these findings are discussed. Specifically, we state that self-avoiding interactions introduce a characteristic length scale of sheet crumpling. A framework to model the crumpling phenomena is suggested. Mechanics of sheet crushing under external confinement is developed. The effect of compaction geometry on the crushing mechanics is revealed.

The random 3-satisfiability (3-SAT) problem is in the unsatisfiable (UNSAT) phase when the clause density $\alpha$ exceeds a critical value ${\alpha }_s\approx 4.267$. Rigorously proving the unsatisfiability of a given large 3-SAT instance is, however, extremely difficult. In this paper we apply the mean-field theory of statistical physics to the unsatisfiability problem, and show that a reduction to 3-XORSAT, which permits the construction of a specific type of UNSAT witnesses (Feige-Kim-Ofek witnesses), is possible when the clause density $\alpha >19$. We then construct Feige-Kim-Ofek witnesses for single 3-SAT instances through a simple random sampling algorithm and a focused local search algorithm. The random sampling algorithm works only when $\alpha$ scales at least linearly with the variable number $N$, but the focused local search algorithm works for clause density $\alpha >c{N}^b$ with $b\approx 0.59$ and prefactor $c\approx 8$. The exponent $b$ can be further decreased by enlarging the single parameter $S$ of the focused local search algorithm.

In this paper we examine the anisotropic slip theory for gas flows based on tangential accommodation coefficients and compare it with molecular dynamics (MD) results. A special gas-wall boundary condition is employed within MD simulations to mimic the anisotropic gas-wall collision mechanism. Results from MD simulations with different surface orientations show good agreement with the slip quantification proposed in this work.

To probe the effects of hydrogel particle additives on the water-accessible pore structure of sandy soils, we introduce a custom pressure plate method in which the volume of water expelled from a wet granular packing is measured as a function of applied pressure. Using a capillary bundle model, we show that the differential change in retained water per pressure increment is directly related to the cumulative cross-sectional area distribution $f\left(r\right)$ of the water-accessible pores with radii less than $r$. This is validated by measurements of water expelled from a model sandy soil composed of 2-mm-diameter glass beads. In particular, it is found that the expelled water is dramatically dependent on sample height and that analysis using the capillary bundle model gives the same pore size distribution for all samples. The distribution is found to be approximately log normal, and the total cross-sectional area fraction of the accessible pore space is found to be $f_0=0.34$. We then report on how the pore distribution and total water-accessible area fraction are affected by superabsorbent hydrogel particle additives, uniformly mixed into a fixed-height sample at varying concentrations. Under both fixed volume and free swelling conditions, the total area fraction of water-accessible pore space in a packing decreases exponentially as the gel concentration increases. The size distribution of the pores is significantly modified by the swollen hydrogel particles, such that large pores are clogged while small pores are formed.

The understanding of the competition between different substances while condensing on a cold surface is of high interest in situations in which it is desirable to control their condensation rates and the formed morphologies. We do the experiments for mixtures of water and hexamethyldisiloxane vapors at several concentrations. The dropwise condensation of the vapors forms breath figures on a substrate that is repellant to both substances. We report the average radius of the drops for each specie as a function of time. Also, we pay attention to the evolution of the corresponding morphologies and the appearance of hybrid clusters.

Exact solutions are reported for a stream of asymmetric bubbles steadily moving in a Hele-Shaw channel. From the periodicity along the streamwise direction, the flow region is reduced to a rectangular unit cell containing one bubble, which is conformally mapped to an annulus in an auxiliary complex plane. Analytic expressions for the bubble shape as well as for the velocity field are obtained in terms of the generalized Schwarz-Christoffel formula for doubly connected domains.

The local density of states or its Fourier transform, usually called fidelity amplitude, are important measures of quantum irreversibility due to imperfect evolution. In this Rapid Communication we study both quantities in a paradigmatic many body system, the Dicke Hamiltonian, where a single-mode bosonic field interacts with an ensemble of $N$ two-level atoms. This model exhibits a quantum phase transition in the thermodynamic limit, while for finite instances the system undergoes a transition from quasi-integrability to quantum chaotic. We show that the width of the local density of states clearly points out the imprints of the transition from integrability to chaos but no trace remains of the quantum phase transition. The connection with the decay of the fidelity amplitude is also established.

We investigate the three-dimensional evolution of shock impact on a membraneless gas bubble. When a shock wave impacts a gas interface, gas layer is generally perturbed via the Richtmyer-Meshkov instability. We show the vortex structure evolves from the merging process of the extending spikes on the compressed D-shaped surface via the Richtmyer-Meshkov instability. The spikes are found to have a linear growth before 11 $\mu$s (of 1.4 mm). A ripple-typed fluctuating ring structure is observed and discussed with the scaling relation. We also notice that a thin layer exists in the intersection of the counterpropagating shock shells. The superposition of the rarefaction waves from both sides of the intersection is suspected to be responsible for the density change.

We report fully relativistic molecular-dynamics simulations that verify the appearance of thermal equilibrium of a classical gas inside a uniformly accelerated container. The numerical experiments confirm that the local momentum distribution in this system is very well approximated by the Jüttner function—originally derived for a flat spacetime—via the Tolman-Ehrenfest effect. Moreover, it is shown that when the acceleration or the container size is large enough, the global momentum distribution can be described by the so-called modified Jüttner function, which was initially proposed as an alternative to the Jüttner function.