We perform a detailed analysis of the contact force network in a dense confined packing of pentagonal particles simulated by means of the contact dynamics method. The effect of particle shape is evidenced by comparing the data from pentagon packing and from a packing with identical characteristics, except for the circular shape of the particles. A counterintuitive finding of this work is that, under steady shearing, the pentagon packing develops a lower structural anisotropy than the disk packing. We show that this weakness is compensated by a higher force anisotropy, leading to enhanced shear strength of the pentagon packing. We revisit “strong” and “weak” force networks in the pentagon packing, but our simulation data also provide evidence for a large class of “very weak” forces carried mainly by vertex-to-edge contacts. The strong force chains are mostly composed of edge-to-edge contacts with a marked zigzag aspect and a decreasing exponential probability distribution as in a disk packing.

Theoretical studies of self-assembly processes and condensed phases in colloidal systems are often based on effective interparticle potentials. Here we show that developing an effective potential for particles interacting with a limited number of “lock-and-key” selective bonds (due to the specificity of biomolecular interactions) requires—in addition to the nonsphericity of the potential—a (many body) constraint that prevents multiple bonding on the same site. We show the importance of retaining both valence and bond selectivity by developing, as a case study, a simple effective potential describing the interaction between colloidal particles coated by four single-strand DNA chains.

We study the influence of fluctuations in molecular shape on the stability of the biaxial nematic phase by generalizing the mean-field model of Mulder and Ruijgrok [Physica A 113, 145 (1982)]. We limit ourselves to the case when the molecular shape anisotropy, represented by the alignment tensor, is a random variable of an annealed type. A prototype of such behavior can be found in lyotropic systems—a mixture of potassium laurate, 1-decanol, and ${\mathrm{D}}_2\mathrm{O}$, where distribution of the micellar shape adjusts to actual equilibrium conditions. Further examples of materials with the biaxial nematic phase, where molecular shape is subject to fluctuations, are thermotropic materials composed of flexible trimericlike or tetrapodlike molecular units. Our calculations show that the Gaussian equilibrium distribution of the variables describing molecular shape (dispersion force) anisotropy gives rise to new classes of the phase diagrams, absent in the original model. Depending on properties of the shape fluctuations, the stability of the biaxial nematic phase can be either enhanced or depressed, relative to the uniaxial nematic phases. In the former case the splitting of the Landau point into two triple points with a direct phase transition line from isotropic to biaxial phase is observed.

Using x-ray and optical methods we have probed the structural organization of an antiferroelectric twist grain boundary phase $\left(\mathrm{TGB}{C}_a\right)$ lying between the regular antiferroelectric smectic-$C$ $\left(\mathrm{Sm}{C}_a^{*}\right)$ and the smectic-$Q$ (Sm$Q$) or isotropic phase. We find that the twist axis is everywhere perpendicular to the local smectic layer normal and that the helical superstructure is incommensurate with the smectic layer structure. The twist grain boundaries consist of a periodic lattice of alternating $+1∕2$ and $-1∕2$ dispirations, i.e., unit screw dislocations in combination with half unit disclinations. The molecular tilt plane is alternatingly parallel and perpendicular to the twist axis. We find that the optically measured tilt angle in the $\mathrm{Sm}{C}_a^{*}$ phase is smaller than that measured by x rays, which is the opposite to what is found in the $\mathrm{Sm}{C}^{*}$ phase. This means that the core part tilts less than the end chains in the $\mathrm{Sm}{C}_a^{*}$ phase, while it tilts more in the $\mathrm{Sm}{C}^{*}$ phase. On entering the TGB phase a clear decrease is measured in the tilt angle. This is explained by the elastic influence from the disclinations, which appear in this phase.

Quantum resonance (QR) is defined in the free-falling frame of the quantum kicked particle subjected to gravity. The general QR conditions are derived. They imply the rationality of the gravity parameter $\eta$, the kicking-period parameter $\tau ∕\left(2\pi \right)$, and the quasimomentum $\beta$. Exact results are obtained concerning wave-packet evolution for arbitrary periodic kicking potentials in the case of integer $\tau ∕\left(2\pi \right)$ (the main QRs). It is shown that a quantum ratchet generally arises in this case for resonant $\beta$. The noninertial nature of the free-falling frame affects the ratchet by effectively changing the kicking potential to one depending on $(\beta ,\eta )$. For a simple class of initial wave packets, it is explicitly shown that the ratchet characteristics are determined to a large extent by symmetry properties and by number-theoretical features of $\eta$.

The rapid accumulation of knowledge and the recent emergence of new dynamic and practically unmoderated information repositories have rendered the classical concept of the hierarchal knowledge structure irrelevant and impossible to impose manually. This led to modern methods of data location, such as browsing or searching, which conceal the underlying information structure. We here propose methods designed to automatically construct a hierarchy from a network of related terms. We apply these methods to Wikipedia and compare the hierarchy obtained from the article network to the complementary acyclic category layer of the Wikipedia and show an excellent fit. We verify our methods in two networks with no a priori hierarchy (the E. Coli genetic regulatory network and the C. Elegans neural network) and a network of function libraries of modern computer operating systems that are intrinsically hierarchical and reproduce a known functional order.

We propose a procedure to distinguish quasiperiodic from chaotic orbits in short-time series, which is based on the recurrence properties in phase space. The histogram of the return times in a recurrence plot is introduced to disclose the recurrence property consisting of only three peaks imposed by Slater’s theorem. Noise effects on the statistics are studied. Our approach is demonstrated to be efficient in recognizing regular and chaotic trajectories of a Hamiltonian system with mixed phase space.

How to improve the transmission efficiency of Internet-like packet switching networks is one of the most important problems in complex networks as well as for the Internet research community. In this paper we propose a convenient method to enhance the transmission efficiency of scale-free networks dramatically by kicking out the edges linking to nodes with large betweenness, which we called the “black sheep.” The advantages of our method are of facility and practical importance. Since the black sheep edges are very costly due to their large bandwidth, our method could decrease the cost as well as gain higher throughput of networks. Moreover, we analyze the curve of the largest betweenness on deleting more and more black sheep edges and find that there is a sharp transition at the critical point where the average degree of the nodes $⟨k⟩\to 2$.

We report on the observation of a white-eye pattern in an air dielectric barrier discharge. The patterned discharges undergo a development as follows: random spots–quasihexagonal pattern–hexagonal pattern (type I)–hexagonal pattern (type II)–white-eye pattern–chaos, as the voltage is increased. The spatiotemporal characteristics of the patterned discharges are investigated by using an optical method. Results show that the two discharge modes, uniform mode and filamentary mode, are actually two different spatial presentations of the same origin: the microdischarge. From the viewpoint of pattern dynamics, the white-eye pattern results from a three-wave resonance interaction.

We report numerical simulations of one-dimensional cellular solutions of the stabilized Kuramoto-Sivashinsky equation. This equation offers a range of generic behavior in pattern-forming instabilities of moving interfaces, such as a host of secondary instabilities or transition toward disorder. We compare some of these collective behaviors to those observed in experiments. In particular, destabilization scenarios of bifurcated states are studied in a spatially semi-extended situation, which is common in realistic patterns, but has been barely explored so far.

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k\text{th}$ order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

We investigate asymptotical behavior of numbers of long Hamiltonian walks (HWs), i.e., self-avoiding random walks that visit every site of a lattice, on various fractal lattices. By applying an exact recursive technique we obtain scaling forms for open HWs on three-simplex lattice, Sierpinski gasket, and their generalizations: Given-Mandelbrot (GM), modified Sierpinski gasket (MSG), and $n$-simplex fractal families. For GM, MSG and $n$-simplex lattices with odd values of $n$, the number of open HWs $Z_N$, for the lattice with $N⪢1$ sites, varies as ${\omega }^N{N}^{\gamma }$. We explicitly calculate the exponent $\gamma$ for several members of GM and MSG families, as well as for $n$-simplices with $n=3$, 5, and 7. For $n$-simplex fractals with even $n$ we find different scaling form: $Z_N\sim {\omega }^N{\mu }^{N^{1∕d_f}}$, where $d_f$ is the fractal dimension of the lattice, which also differs from the formula expected for homogeneous lattices. We discuss possible implications of our results on studies of real compact polymers.

Small-angle x-ray scattering (SAXS) was used to measure the microstructure of isotopic mixtures of ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ adsorbed into silica aerogels as a function of temperature and ${}^3\mathrm{He}$ concentration. The SAXS measurements could be well described by the formation of a nearly pure film of ${}^4\mathrm{He}$ which separates from the bulk mixture onto the aerogel strands and which thickens with decreasing temperature. Previous observations of a superfluid ${}^3\mathrm{He}$-rich phase are consistent with superfluidity existing within this film phase. Observed differences between different density aerogels are explained in terms of the depletion of ${}^4\mathrm{He}$ from the bulk mixture due to film formation.

We present theoretical arguments and numerical results to demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers, which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion $u\left(s\right)\approx s∕\rho R^3\left(s\right)\approx c_e∕\sqrt{s}$ when connecting two segments together where $s$ denotes the curvilinear length of a segment, $R\left(s\right)$ its typical size, $c_e\approx 1∕\rho b_e^3$ the “swelling coefficient,” $b_e$ the effective bond length, and $\rho$ the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to $u\left(s\right)$. The analysis of different moments of this distribution allows for a precise determination of the effective bond length $b_e$ and the swelling coefficient $c_e$ of asymptotically long chains. At striking variance to the short-range decay suggested by Flory’s ideality hypothesis the bond-bond correlation function of two bonds separated by $s$ monomers along the chain is found to decay algebraically as $1∕s^{3∕2}$. Effects of finite chain length are briefly considered.

The quantum state diffusion equation is applied to the problem of energy transfer in proteins. Lindblad operators, capable of coupling the full quantum Davydov-Scott monomer to a thermal bath, are derived. Numerical simulations with the QSD equation show that the Lindblad operators derived do recreate the exact equilibrium ensemble for the Davydov-Scott monomer. Comparison of the results obtained with the full quantum and with the semiclassical systems shows that, at biological temperatures, the latter provides a good approximation of the former.

We present hysteresis phenomena of the intelligent driver model for traffic flow in a circular one-lane roadway. We show that the microscopic structure of traffic flow is dependent on its initial state by plotting the fraction of congested vehicles over the density, which shows a typical hysteresis loop, and by investigating the trajectories of vehicles on the velocity-over-headway plane. We find that the trajectories of vehicles on the velocity-over-headway plane, which usually show a hysteresis loop, include multiple loops. We also point out the relations between these hysteresis loops and the congested jams or high-density clusters in traffic flow.

Under laminar, microscale flow conditions, rapid mixing can be difficult to achieve. In these low Reynolds number flows, mixing rates are governed by molecular diffusion, and in the absence of enhanced mixing techniques, mixing lengths and residence times can be much longer than most applications will allow. A number of active mixing techniques have been developed to improve mixing; however, they can be complex to implement and expensive to fabricate. In this paper, we describe a passive mixing method that utilizes a series of ultrahydrophobic surfaces. Our previous experiments have demonstrated that a shear-free air-water interface supported between hydrophobic microridges results in large slip velocities along these ultrahydrophobic surfaces, and significant drag reduction. By aligning the microridges and therefore the air-water interface at an oblique angle to the flow direction, a secondary flow is generated, which is shown to efficiently stretch and fold the fluid elements and reduce the mixing length by more than an order of magnitude compared to that of a smooth microchannel. The designs of the ultrahydrophobic surfaces were optimized through experiments and numerical simulations. A Y-shaped channel was used to bring two streams of water together, one tagged with a fluorescent dye. A confocal microscope was used to measure fluorescence intensity and dye concentration. Quantitative agreement between the experiments and the numerical simulations was achieved for both the flow patterns and degree of mixing. Increasing the angle of the microridges was found to reduce the mixing length up to a critical angle of about 60°, beyond which the mixing length was found to increase with further increases to the angle of the microridge. The mixing enhancement was found to be much less sensitive to changes in microridge width or separation.

The interaction of laser light with a metal surface yields a complex configuration of point defects, e.g., droplets and holes and vortex microfilaments. When a single filament interacts with a defect it “winds” around the defect and can form loops, and rings. Interaction of a single filament with a single defect gives rise to arc deformation bending, formation of loops and rings, while its interaction with a two-dimensional (2D) random lattice of defects gives rise to the vortex filament splitting and breaking which occur at nodal points of the Voronoi lattice. Interaction of one-dimensional (1D) vortex filament lattice with 2D lattice of defects results in the formation of knotted structures such as the Hopf links as well as 1D and 2D Hopf link crystals, knotted along the sides of the Voronoi lattice. We observed that configurations of vortex filaments are organized at three hierarchical levels of growing complexity. Every level is comprised of the elements of the lower complexity one, indicating the presence of a supercomplexity.

Reflection-refraction properties of photonic barriers, formed by dielectric gradient nanofilms, for inclined incidence of both $S$- and $P$-polarized electromagnetic waves are examined by means of exactly solvable models. We present generalized Fresnel formulas, describing the influence of the nonlocal dispersion on the reflectance and transmittance of single- and double-layer gradient photonic barriers for $S$ and $P$ waves and arbitrary angles of incidence. The nonlocal dispersion of such layers, arising due to a concave spatial profile of dielectric susceptibility across the plane film, is shown to result in a peculiar heterogeneity-induced optical anisotropy, providing the propagation of $S$ $\left(P\right)$ waves in tunneling (traveling) regimes. The results obtained indicate the possibility of narrow-band nonattenuated tunneling (complete transmittance) of oblique $S$ waves through such heterogeneous barriers, and the existence of spectral areas characterized by the strong reflection of $P$ waves and profound contrast between transmitted $S$ and $P$ waves. The scalability of obtained exact analytical solutions of Maxwell equations into the different spectral ranges is discussed and the application potential of these phenomena for miniaturized polarizers and filters is demonstrated.

We show that time-dependent couplings may lead to nontrivial scaling properties of the surface fluctuations of the asymptotic regime in nonequilibrium kinetic roughening models. Three typical situations are studied. In the case of a crossover between two different rough regimes, the time-dependent coupling may result in anomalous scaling for scales above the crossover length. In a different setting, for a crossover from a rough to either a flat or damping regime, the time-dependent crossover length may conspire to produce a rough surface, although the most relevant term tends to flatten the surface. In addition, our analysis sheds light into an existing debate in the problem of spontaneous imbibition, where time-dependent couplings naturally arise in theoretical models and experiments.