The linear 1-alcohols $n{\text{-C}}_{16}{\text{H}}_{33}\text{OH}$, $n{\text{-C}}_{17}{\text{H}}_{35}\text{OH}$, $n{\text{-C}}_{19}{\text{H}}_{39}\text{OH}$ have been imbibed and solidified in lined up, tubular mesopores of silicon with 10 and 15 nm mean diameters, respectively. X-ray diffraction measurements reveal a set of six discrete orientation states (“domains”) characterized by a perpendicular alignment of the molecules with respect to the long axis of the pores and by a fourfold symmetry about this direction, which coincides with the crystalline symmetry of the Si host. A Bragg peak series characteristic of the formation of bilayers indicates a lamellar structure of the spatially confined alcohol crystals in 15 nm pores. By contrast, no layering reflections could be detected for 10 nm pores. The growth mechanism responsible for the peculiar orientation states is attributed to a nanoscale version of the Bridgman technique of single-crystal growth, where the dominant growth direction is aligned parallel to the long pore axes. Our observations are analogous to the growth phenomenology encountered for medium length $n$-alkanes confined in mesoporous silicon [A. Henschel, T. Hofmann, P. Huber, and K. Knorr, Phys. Rev. E 75, 021607 (2007)] and may further elucidate why porous silicon matrices act as an effective nucleation-inducing material for protein solution crystallization.

Periodically forced oscillatory reaction-diffusion systems may show complex spatiotemporal patterns. At high-frequency resonant forcing, multiple-phase patterns can be found. In the present work, the dynamics of turbulent CO oxidation on Pt(110), forced with the fourth harmonic of the system’s natural frequency, is investigated. Experiments result in subharmonic entrainment, where the system locks to a quarter of the forcing frequency. Cluster patterns are observed, where different parts of the pattern show a defined phase difference. The experimental results are compared with numerical simulations using the realistic Krischer-Eiswirth-Ertl model for catalytic CO oxidation. Using the fourth harmonic of an uncoupled surface element’s natural frequency, we find 3:1 entrainment with three-phase cluster patterns in a wide parameter range of forcing amplitudes and frequency detuning. Numerical analysis of the spatially extended, turbulent system reveals a remarkable upshift of the mean oscillation frequency compared to homogeneous oscillations. Using the fourth harmonic of the most prominent frequency found in the turbulent system results in four-phase patterns with partial or full 4:1 entrainment, depending on the forcing parameters chosen.

In recent years we have constructed closely packed spheres using the Lubachevsky-Stillinger algorithm to generate morphological models of heterogeneous solid propellants. Improvements to the algorithm now allow us to create large polydisperse packs on a laptop computer, and to create monodisperse packs with packing fractions greater than 70% which display significant crystal order. The use of these models in the physical context motivates efforts to examine in some detail the nature of the packs, including certain statistical properties. We compare packing fractions for binary packs with long-known experimental data. Also, we discuss the near-neighbor number and the radial distribution function (RDF) for monodisperse packs and make comparisons with experimental data. We also briefly discuss the RDF for bidisperse packs. We also consider bounded monodisperse packs, and pay particular attention to the near-wall structure where we identify significant order.

A simple model of language evolution proposed by Komarova, Niyogi, and Nowak is characterized by a payoff in communicative function and by an error in learning that measure the accuracy in language acquisition. The time scale for language change is generational, and the model’s equations in the mean-field approximation are a particular case of the replicator-mutator equations of evolutionary dynamics. In well-mixed populations, this model exhibits a critical coherence threshold; i.e., a minimal accuracy in the learning process is required to maintain linguistic coherence. In this work, we analyze in detail the effects of different fitness-based dynamics driving linguistic coherence and of the network of interactions on the nature of the coherence threshold by performing numerical simulations and theoretical analyses of three different models of language change in finite populations with two types of structure: fully connected networks and regular random graphs. We find that although the threshold of the original replicator-mutator evolutionary model is robust with respect to the structure of the network of contacts, the coherence threshold of related fitness-driven models may be strongly affected by this feature.

We introduce a family of area-preserving maps representing a (nontrivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations, providing analytical and numerical estimates. We study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments. Finally, the dynamical effects of a stochastic perturbation are considered.

When soluble metal salts are placed in a silicate solution, chemical gardens grow. These gardens are treelike structures formed of long, thin, hollow tubes. Here we study one particular case: a calcium nitrate pellet in a solution of sodium trisilicate. We observe that tube growth results from a relaxation oscillation. The average period and the average growth rate are approximately constant for most of the structures growth. The period does fluctuate from cycle to cycle, with the oscillation amplitude proportional to the period. Based on our observations, we develop a model of the relaxation oscillations which calculates the average oscillation period and the average tube radius in terms of fundamental membrane parameters. We also propose a model for the average tube growth rate. Predictions are made for future experiments.

Normal-incidence transmission and dispersion properties of optical multilayers and one-dimensional stepwise potential barriers in the nontunneling regime are analytically investigated. The optical paths of every constituent layer in a multilayer structure, as well as the parameters of every step of the stepwise potential barrier, are constrained by a generalized quarter-wave condition. No other restrictions on the structure geometry are imposed, i.e., the layers are arranged arbitrarily. We show that the density of states (DOS) spectra of the multilayer or barrier in question are subject to integral conservation rules similar to the Barnett-Loudon sum rule but occurring within a finite frequency or energy interval. In the optical case, these frequency intervals are regular. For the potential barriers, only nonperiodic energy intervals can be present in the spectrum of any given structure, and only if the parameters of constituent potential steps are properly chosen. The integral conservation relations derived analytically have also been verified numerically. The relations can be used in dispersion-engineered multilayer-based devices, e.g., ultrashort pulse compressors or ultracompact optical delay lines, as well as to design multiple-quantum-well electronic heterostructures with engineered DOS.

We compute exact asymptotic results for the probability of the occurrence of large deviations of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary, and symplectic ensembles. In particular, we show that the probability that all the eigenvalues of an $\left(N\times N\right)$ random matrix are positive (negative) decreases for large $N$ as $\sim \text{exp}\left[-\beta \theta \left(0\right)N^2\right]$ where the Dyson index $\beta$ characterizes the ensemble and the exponent $\theta \left(0\right)=\left(\text{ln}3\right)/4=0.274653\dots$ is universal. We compute the probability that the eigenvalues lie in the interval $\left[{\zeta }_1,{\zeta }_2\right]$ which allows us to calculate the joint probability distribution of the minimum and the maximum eigenvalue. As a by-product, we also obtain exactly the average density of states in Gaussian ensembles whose eigenvalues are restricted to lie in the interval $\left[{\zeta }_1,{\zeta }_2\right]$, thus generalizing the celebrated Wigner semi-circle law to these restricted ensembles. It is found that the density of states generically exhibits an inverse square-root singularity at the location of the barriers. These results are confirmed by numerical simulations. Some of the results presented in detail here were announced in a previous paper [D. S. Dean and S. N. Majumdar, Phys. Rev. Lett. 97, 160201 (2006)].

Compressing or cooling a fluid typically enhances its static interparticle correlations. However, there are notable exceptions. Isothermal compression can reduce the translational order of fluids that exhibit anomalous waterlike trends in their thermodynamic and transport properties, while isochoric cooling (or strengthening of attractive interactions) can have a similar effect on fluids of particles with short-range attractions. Recent simulation studies by Yan et al. [Phys. Rev. E 76, 051201 (2007)] on the former type of system and Krekelberg et al. [J. Chem. Phys. 127, 044502 (2007)] on the latter provide examples where such structural anomalies can be related to specific changes in second and more distant coordination shells of the radial distribution function. Here, we confirm the generality of this microscopic picture through analysis, via molecular simulation and integral equation theory, of coordination shell contributions to the two-body excess entropy for several related model fluids which incorporate different levels of molecular resolution. The results suggest that integral equation theory can be an effective and computationally inexpensive tool for assessing, based on the pair potential alone, whether new model systems are good candidates for exhibiting structural (and hence thermodynamic and transport) anomalies.

Motivated by rolling adhesion of white blood cells in the vasculature, we study how cells move in linear shear flow above a wall to which they can adhere via specific receptor-ligand bonds. Our computer simulations are based on a Langevin equation accounting for hydrodynamic interactions, thermal fluctuations, and adhesive interactions. In contrast to earlier approaches, our model not only includes stochastic rules for the formation and rupture of bonds, but also fully resolves both receptor and ligand positions. We identify five different dynamic states of motion in regard to the translational and angular velocities of the cell. The transitions between the different states are mapped out in a dynamic state diagram as a function of the rates for bond formation and rupture. For example, as the cell starts to adhere under the action of bonds, its translational and angular velocities become synchronized and the dynamic state changes from slipping to rolling. We also investigate the effect of nonmolecular parameters. In particular, we find that an increase in viscosity of the medium leads to a characteristic expansion of the region of stable rolling to the expense of the region of firm adhesion, but not to the expense of the regions of free or transient motion. Our results can be used in an inverse approach to determine single bond parameters from flow chamber data on rolling adhesion.

This Brief Report studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating genomes, whose only source of genetic variation is due to copying errors during replication. We consider a time-dependent, single-fitness-peak landscape where the master sequence changes by a single point mutation at every time $\tau$. We are able to analytically solve for the evolutionary dynamics of the population in the point-mutation limit. In particular, our model provides an analytical expression for the fraction of mutators in the dynamic fitness landscape that agrees well with results from stochastic simulations.

We report on transcritical bifurcations of periodic orbits in nonintegrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties using a recent mathematical description of transcritical bifurcations in families of symplectic maps. We then present numerical examples of transcritical bifurcations in a class of generalized Hénon-Heiles Hamiltonians and illustrate their stabilities and unfoldings under various perturbations of the Hamiltonians. We demonstrate that for Hamiltonians containing straight-line librating orbits, the transcritical bifurcation of these orbits is the typical case which occurs also in the absence of any discrete symmetries, while their isochronous pitchfork bifurcation is an exception. We determine the normal forms of both types of bifurcations and derive the uniform approximation required to include transcritically bifurcating orbits in the semiclassical trace formula for the density of states of the quantum Hamiltonian. We compute the coarse-grained density of states in a specific example both semiclassically and quantum mechanically and find excellent agreement of the results.

A recently developed method is used for the analysis of structures of planar disordered granular assemblies. Within this method, the assemblies are partitioned into volume elements associated either with grains or with more basic elements called quadrons. Our first aim is to compare the relative usefulness of description by quadrons or by grains for entropic characterization. The second aim is to use the method to gain better understanding of the different roles of friction and grain shape and size distributions in determining the disordered structure. Our third aim is to quantify the statistics of basic volumes used for the entropic analysis. We report the following results. (1) Quadrons are more useful than grains as basic ‘‘quasiparticles’’ for the entropic formalism. (2) Both grain and quadron volume distributions show nontrivial peaks and shoulders. These can be understood only in the context of the quadrons in terms of particular conditional distributions. (3) Increasing friction increases the mean cell size, as expected, but does not affect the conditional distributions, which is explained on a fundamental level. We conclude that grain size and shape distributions determine the conditional distributions, while their relative weights are dominated by friction and by the pack formation process. This separates sharply the different roles that friction and grain shape distributions play. (4) The analysis of the quadron volumes shows that $\Gamma$ distributions, which are accepted to describe foamlike structures well, are too simplistic for general granular systems. (5) A range of quantitative results is obtained for the ‘‘density of states’’ of quadron and grain volumes and calculations of expectation values of structural properties are demonstrated. The structural characteristics of granular systems are compared with numerically generated foamlike Dirichlet-Voronoi constructions.

The mean flow and the linear stability characteristics of a two-dimensional particulate suspension, driven horizontally via harmonic oscillation, are analyzed. A constitutive model based on the kinetic theory of granular materials, which takes into account the dissipative collisional interactions among particles as well as their interactions with the interstitial fluid, is used; the effects of the interstitial fluid are incorporated in the balance equations for the particle phase. Assuming that the suspension is thin along the vertical direction, the effects of driving are incorporated into the governing equations in a mean-field manner. Using Floquet theory, a linear stability analysis of the time-periodic mean flow indicates that the oscillatory suspension supports stationary- and traveling-wave instabilities which correspond to particle banding patterns that are aligned parallel or orthogonal or at an oblique angle to the driving direction. The effects of external driving parameters and various system control parameters on the phase diagram of instabilities are studied. The fluid-particle interaction is shown to be responsible for the emergence of traveling instabilities in this flow.

Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at frequency ${\omega }_1$) states; periodic forcing produces forced-entrained $\left({\omega }_F\right)$ states. As a result of the interaction of mutual and forced entrainment, resonant cluster states occur with equal spacing of frequencies that have discretized frequencies following a resonance rule ${\omega }_n\cong n{\omega }_1-\left(n-1\right){\omega }_F$. Resonance clustering requires an optimal, intermediate global coupling strength; at weak coupling the clusters have smaller sizes and do not strictly follow the resonance rule, while at strong coupling the population behaves similar to a single, giant oscillator.

In this experimental and theoretical study a single drop impact onto a liquid layer of finite thickness is investigated. It is focused on the formation, expansion, receding, and merging of a cavity generated by the impact. The shape of the cavity is observed and the evolution of its diameter is measured at various times after impact. The drop velocity, the initial film thickness, and the liquid properties are varied in the experiments. The propagation of the crater diameter in the liquid layer is described theoretically using the kinematic discontinuity approach. The mass and momentum balance equations of the liquid layer account for the inertial effects, surface tension, and gravity. A remote asymptotic solution for the temporal evolution of the crater diameter is obtained. The theoretical predictions agree well with the experimental data.

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of four phases, for this system: (i) classical nonpersistence, (ii) classical persistence, (iii) log-periodic nonpersistence, and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however, log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.

At time $t$ after an initial quench, an aging system responds to a perturbation turned on at time $t_{\text{w}}<t$ in a way mainly depending on the number of intermittent energy fluctuations, so-called quakes, which fall within the observation interval $\left(t_{\text{w}},t\right]$ [P. Sibani, G. F. Rodriguez, and G. G. Kenning, Phys. Rev. B 74, 224407 (2006); P. Sibani, Eur. J. Phys. B 58, 483 (2007)]. The temporal distribution of the quakes implies a functional dependence of the average response on the ratio $t/t_{\text{w}}$. Further insight is obtained imposing small temperature steps, so-called $T$ shifts. The average response as a function of $t/t_{\text{w},\text{eff}}$, where $t_{\text{w},\text{eff}}$ is the effective age, is similar to the response of a system aged isothermally at the final temperature. Using an Ising model with plaquette interactions, the applicability of analytic formulas for the average isothermal magnetization is confirmed. The $T$-shifted aging behavior of the model is approximately described using effective ages. Large positive shifts nearly reset the effective age. Negative $T$ shifts offer a more detailed probe of the dynamics. Assuming the marginal stability of the “current” attractor against thermal noise fluctuations, the scaling form $t_{\text{w},\text{eff}}=t_{\text{w}}^x$ and the dependence of the exponent $x$ on the aging temperatures before and after the shift are theoretically available. The predicted form of $x$ has no adjustable parameters. Both the algebraic scaling of the effective age and the form of the exponent reasonably agree with the data. The present simulations thus confirm the crucial role of marginal stability in glassy relaxation.

We investigate the diffusion of a colloidal particle in a tilted periodic potential created by means of ten rotating optical tweezers arranged on a circle. Because of the viscous drag, the trap rotation leads to the onset of a tilting force in the corotating reference frame, so that in that frame the system can be described as an overdamped Brownian particle in a tilted periodic potential. The excellent agreement of the velocity and diffusion coefficient as a function of rotating frequency with theoretical predictions allowed us to extract the main parameters characterizing the system—the coefficient of free thermal diffusion and the potential corrugation depth—from the experimental results.

The response to a localized force provides a sensitive test for models of stress transmission in granular solids. Elasto-plastic models, traditionally used by engineers, have been challenged by theories and experiments that suggest a wavelike (hyperbolic) propagation of the stress, as opposed to the elliptic equations of static elasticity. Simulations of two-dimensional granular systems subject to a localized external force have been employed to examine the nature of stress transmission in these systems as a function of the magnitude of this force, the frictional parameters, and degree of disorder. The results indicate that in large systems (as considered by engineers) the response is close to that predicted by isotropic elasticity, whereas for small systems (or strongly forced ones) it is strongly anisotropic. In the latter case the applied force induces changes in the contact network accompanied by frictional sliding and gives rise to hyperboliclike stress propagation. The larger the static friction, the more extended the range of forces for which the response is elastic, and the smaller the anisotropy. Increase in the degree of polydispersity (in the studied range, up to 25%) decreases the range of elastic response. This paper is an extension of a previously published Letter [C. Goldenberg and I. Goldhirsch, Nature (London) 435, 188 (2005)].