Vertical (up-down) asymmetry is ubiquitous feature of the nonequilibrium statistical mechanics of realistic growing interfaces. Yet, the actual role of vertical asymmetry (VA) in epitaxial growth on crystal surfaces is still elusive. Is vertical asymmetry a primary or secondary factor in epitaxial growth and erosion? Can vertical asymmetry alone produce major qualitative effects on long length scale interface morphologies? To address these questions in depth, we theoretically discuss the effects of vertical growth asymmetry on far-from-equilibrium interfacial morphologies occurring in the epitaxial growth and erosion of (110) crystal surfaces. We theoretically elucidate the so-called ripple rotation transition on the Ag(110) crystal surface [F. B. de Mongeot et al.; Phys. Rev. Lett. 84, 2445 (2000), G. Constantini et al., J. Phys.: Condens. Matter 13, 5875 (2001)], as the transition between the rectangular rippled states (checker-board structures of alternating rectangular pyramids and pits). We show that the experimental surface diffraction data seen in this transition can be understood only by invoking vertical growth asymmetry. In the proximity of the transition point, we find that vertical asymmetry itself produces an interface morphology yielding a four-lobe near in-phase diffraction pattern having four peaks along the principal axes of the (110) surface, in accord with the experiments on Ag(110). Moreover, on the two sides of the ripple rotation transition, we find two exotic interface states induced by vertical asymmetry, which correspond well /to the interface morphologies seen on Ag(110). We document our results by numerical simulations and by analytic arguments. Our theoretical findings, in combination with experiments, provide the first rigorous evidence that VA plays a significant role in epitaxial growth and erosion on crystal surfaces.

A constitutive model for describing the mechanical response of an amorphous glassy polycarbonate is proposed. The model is based on an isotropic elastic phase surrounded by an SO(3) continuum of plastic phases onto which the elastic phase can collapse under strain. An approximate relaxed energy is developed for this model on the basis of physical considerations and extensive numerical testing, and it is shown that it corresponds to an ideal elastic-plastic behavior. Kinetic effects are introduced as rate-independent viscoplasticity, and a comparison with experimental data is presented, showing that the proposed model is able to capture the main features of the plastic behavior of amophous glassy polycarbonate.

Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov et al., Nature (London) 399, 461 (1999)]. This multifractal character could be manifested as the dependence of the probability density functions (PDFs) of the interbeat interval increments, which are the differences in two interbeat intervals that are separated by $n$ beats, on $n$. On the other hand, “scale invariance in the PDFs of detrended healthy human heart rate increments” was recently reported [Kiyono et al., Phys. Rev. Lett. 93, 178103 (2004)]. In this paper, we clarify that the scale invariance reported is actually exhibited by the PDFs of the increments of the “detrended” integrated healthy interbeat interval and should, therefore, be more accurately referred as the scale invariance or $n$ independence of the PDFs of the sum of $n$ detrended interbeat intervals. Indeed, we demonstrate explicitly that the PDFs of detrended healthy interbeat interval increments are scale or $n$ dependent in accord with its multifractal character. Our work also establishes that this $n$ independence of the PDFs of the sum of $n$ detrended interbeat intervals is a general feature of human heartbeat dynamics, shared by heart rate fluctuations in both healthy and pathological states.

In this paper, an enhanced local mean-field model that is suitable for simulating the electroencephalogram (EEG) in different depths of anesthesia is presented. The main building elements of the model (e.g., excitatory and inhibitory populations) are taken from Steyn-Ross et al. [M. L. Steyn-Ross et al., Phys. Rev. E 64, 011917 (2001), D. A. Steyn-Ross et al., Phys. Rev. E 64, 011918 (2001)] and Bojak and Liley [I. Bojak and D. T. Liley, Phys. Rev. E 71, 041902 (2005)] mean-field models and a new slow ionic mechanism is included in the main model. Generally, in mean-field models, some sigmoid-shape functions determine firing rates of neural populations according to their mean membrane potentials. In the enhanced model, the sigmoid function corresponding to excitatory population is redefined to be also a function of the slow ionic mechanism. This modification adapts the firing rate of neural populations to slow ionic activities of the brain. When an anesthetic drug is administered, the slow mechanism may induce neural cells to alternate between two levels of activity referred to as up and down states. Basically, the frequency of up-down switching is in the delta band $(0–4\mathrm{Hz})$ and this is the main reason behind high amplitude, low frequency fluctuations of EEG signals in anesthesia. Our analyses show that the enhanced model may have different working states driven by anesthetic drug concentration. The model is settled in the up state in the waking period, it may switch to up and down states in moderate anesthesia while in deep anesthesia it remains in the down state.

Axial ultrasound forcing applied to a vertical cylinder is shown to affect a gravity-driven flow of a thin liquid film on its outer surface. In the case of larger forcing amplitudes, we find that the film flow can be completely stopped.

The simplest null models for networks, used to distinguish significant features of a particular network from a priori expected features, are random ensembles with the degree sequence fixed by the specific network of interest. These “fixed degree sequence” (FDS) ensembles are, however, famously resistant to analytic attack. In this paper we introduce ensembles with partially-fixed degree sequences (PFDS) and compare analytic results obtained for them with Monte Carlo results for the FDS ensemble. These results include link likelihoods, subgraph likelihoods, and degree correlations. We find that local structural features in the FDS ensemble can be reasonably well estimated by simultaneously fixing only the degrees of a few nodes, in addition to the total number of nodes and links. As test cases we use two protein interaction networks (Escherichia coli, Saccharomyces cerevisiae), the internet on the autonomous system (AS) level, and the World Wide Web. Fixing just the degrees of two nodes gives the mean neighbor degree as a function of node degree, ${⟨k^{\prime }⟩}_k$, in agreement with results explicitly obtained from rewiring. For power law degree distributions, we derive the disassortativity analytically. In the PFDS ensemble the partition function can be expanded diagrammatically. We obtain an explicit expression for the link likelihood to lowest order, which reduces in the limit of large, sparse undirected networks with $L$ links and with $k_{\max }⪡L$ to the simple formula $P(k,k^{\prime })=k{k}^{\prime }∕(2L+k{k}^{\prime })$. In a similar limit, the probability for three nodes to be linked into a triangle reduces to the factorized expression $P_{\Delta }(k_1,k_2,k_3)=P(k_1,k_2)P(k_1,k_3)P(k_2,k_3)$.

Although cumulative family name distributions in many countries exhibit power-law forms, there also exist counterexamples. The origin of different family name distributions across countries is discussed analytically in the framework of a population dynamics model. Combined with empirical observations made, it is suggested that those differences in distributions are closely related to the rate of appearance of new family names.

Transport and mixing properties of passive particles advected by an array of vortices are investigated. Starting from the integrable case, it is shown that a special class of perturbations allows one to preserve separatrices which act as effective transport barriers, while triggering chaotic advection. In this setting, mixing within the two dynamical barriers is enhanced while long range transport is prevented. A numerical analysis of mixing properties depending on parameter values is performed; regions for which optimal mixing is achieved are proposed. Robustness of the targeted mixing properties regarding errors in the applied perturbation are considered, as well as slip/no-slip and/or boundary conditions for the flow.

We introduce a two-dimensional discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two types of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance $R$ from the rotation pivot, and on-axis $(R=0)$ vortex solitons (VSs), with vorticities $S=1$ and $2$. At a fixed value of rotation frequency $\Omega$, a stability interval for the FSs is found in terms of the lattice coupling constant $C$, $0<C<C_{\mathrm{cr}}\left(R\right)$, with monotonically decreasing $C_{\mathrm{cr}}\left(R\right)$. VSs with $S=1$ have a stability interval, ${\tilde{C}}_{\mathrm{cr}}^{(S=1)}\left(\Omega \right)<C<C_{\mathrm{cr}}^{(S=1)}\left(\Omega \right)$, which exists for $\Omega$ below a certain critical value, ${\Omega }_{\mathrm{cr}}^{(S=1)}$. This implies that the VSs with $S=1$ are destabilized in the weak-coupling limit by the rotation. On the contrary, VSs with $S=2$, that are known to be unstable in the standard DNLS equation, with $\Omega =0$, are stabilized by the rotation in region $0<C<C_{\mathrm{cr}}^{(S=2)}$, with $C_{\mathrm{cr}}^{(S=2)}$ growing as a function of $\Omega$. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by $\Omega \ne 0$.

In this paper we present a detailed study of the hitting set (HS) problem. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge of the hypergraph contains at least one particle. It can also be used in important practical tasks, such as the group testing procedures where one wants to detect defective items in a large group by pool testing. Using a statistical mechanics approach based on the cavity method, we study the phase diagram of the HS problem, in the case of random regular hypergraphs. Depending on the values of the variables and tests degrees different situations can occur: The HS problem can be either in a replica symmetric phase, or in a one-step replica symmetry breaking one. In these two cases, we give explicit results on the minimal density of particles, and the structure of the phase space. These problems are thus in some sense simpler than the original vertex cover problem, where the need for a full replica symmetry breaking has prevented the derivation of exact results so far. Finally, we show that decimation procedures based on the belief propagation and the survey propagation algorithms provide very efficient strategies to solve large individual instances of the hitting set problem.

The first goal of vibration-transit theory is to be able to calculate from a tractable partition function and without adjustable parameters the thermodynamic properties of the elemental monatomic liquids. The key hypothesis is that the random class of potential energy valleys dominates the statistical mechanics of the liquid at temperatures above melting $T\gtrsim T_m$ and that these valleys are macroscopically uniform in the thermodynamic limit. This allows us to use a single random valley to calculate the vibrational contribution to liquid properties, exactly in the thermodynamic limit, and as an approximation at finite number of particles $N$. This approximation is tested here for liquid Na with a physically realistic potential based on electronic structure theory. Steepest descent quenches were made from the molecular dynamics equilibrium liquid $\left(N=500\right)$ at temperatures from $0.90T_m$ to $3.31T_m$, and six potential parameters were calculated for each structure, namely, the potential energy and five principal moments of the vibrational frequency distribution. The results show temperature-independent means and small standard deviations for all potential parameters, consistent with random valley uniformity at $N\to \infty$, and with finite-$N$ broadening at $N=500$. The expected error in the single random valley approximation for Na at $N=500$ and $T\gtrsim T_m$ is 0.1% for the entropy and 0.5% for the internal energy, negligible in the current development of liquid dynamics theory. In related quench studies of recent years, the common finding of nearly temperature-independent means of structural potential energy properties at $T\gtrsim T_m$ suggests that the single random valley approximation might also apply to systems more complicated than the elemental liquids.

We report on an experimental study of single particle properties and interactions of poly(ethylene-alt-propylene)-poly(ethylene oxide) (PEP-PEO) starlike micelles. The starlike regime is achieved by an extremely asymmetric block ratio (1:20) and the number of arms (functionality) is changed by varying the composition of the solvent (the interfacial tension). Small angle neutron scattering (SANS) data in the dilute regime can be modeled by assuming a constant density profile in the micellar core (compact core) and a starlike density profile in the corona (starlike shell). The starlike morphology of the corona is confirmed by a direct comparison with SANS measurements of dilute poly butadiene star solutions. Comparison of structure factors obtained by SANS measurements in the concentrated regime shows in addition that the interactions in the two systems are equivalent. Micellar structure factors at several packing fractions can be modeled by using the ultrasoft potential recently proposed for star polymers [Likos et al., Phys. Rev. Lett. 80, 4450 (1998)]. The experimental phase diagram of PEP-PEO micelles is quantitatively compared to theoretical expectations, finding good agreement for the location of the liquid-solid boundary and excellent agreement for the critical packing fraction where the liquid-to-bcc crystal transition takes place for $f<70$. The functionality, i.e., the coronal density, strongly influences the nature of the solid phase: for $f<70$ the system crystallizes into a bcc phase, high $f>70$ formation of amorphous arrested states prevents crystallization.

Density profiles of Lennard-Jones liquid confined in slit pore with weakly attractive or hard walls are studied along the pore coexistence curve. In the large pores, the thickness $L_0$ of a drying layer increases approximately as the bulk correlation length ${\xi }_{-}$ when approaching the bulk critical temperature $T_c$. Strengthening of the fluid-wall interaction suppresses the thickness of a drying layer and yields a logarithmic growth of $L_0$ with $\tau =1-T∕T_c$. Existence of the two distinct regimes in the temperature behavior of $L_0$ may reflect a partial drying transition expected for the weak long-range fluid-wall interactions. Confinement in small pores suppresses strongly the drying layer and its thickness grows as $\sim \ln \left(\tau \right)$ upon heating with subsequent saturation. The sharpness of the interface between a liquid and a drying layer is studied in dependence on the fluid-wall interaction and pore width.

The transition from a chain-collapse process to a chain-aggregation process was studied by static light scattering on poly(methyl methacrylate) of the molecular weight $m_w=1.22\times {10}^7$ in the mixed solvent tert-butyl $\text{alcohol}+\text{water}$ $(2.5\mathrm{vol}\%)$. The concentration $c$ of the solutions ranged from $0.5\text{to}2.5\times {10}^{-4}\mathrm{g}∕{\mathrm{cm}}^3$ and the measurement was carried out at appropriate time intervals up to the time $t\left(h\right)=3250$ after the quench to $35.0°\mathrm{C}$ which was a few degrees below the phase separation temperature. The molecular weight $M_w$ and mean-square radius of gyration ${⟨s^2⟩}_z$ were estimated from each scattering curve determined at the finite concentrations. At the initial stage of $100\mathrm{h}$, ${⟨s^2⟩}_z$ decreased rapidly with the time $t$ indicating the chain collapse, while at the later stage of $3000\mathrm{h}$, ${⟨s^2⟩}_z$ increased very slowly indicating the chain aggregation. The chain-collapse process and chain-aggregation process could be analyzed separately, though the two processes overlapped appreciably at the higher concentrations. The former process depended slightly on the concentration, while the latter process showed the exponential growth of $\ln M_w\sim ct$ and $\ln {⟨s^2⟩}_z\sim ct$. In the plot of $\ln {⟨s^2⟩}_z$ versus $\ln M_w$, the chain-collapse process was depicted by different lines depending on the concentration, while the chain-aggregation process was described by a single straight line. The transition from the former to the latter process occurred distinctly near $200\mathrm{h}$ after the quench irrespective of the concentration.

Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point degree-degree correlated undirected random networks without self-edges or multiple edges among vertices. With the goal to systematically investigate the influence of two-point correlations, we furthermore develop a formalism to construct a joint degree distribution $P(j,k)$, which allows one to fix an arbitrary degree distribution $P\left(k\right)$ and an arbitrary average nearest neighbor function $k_{\mathrm{nn}}\left(k\right)$ simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks $[P\left(k\right)\propto k^{-\gamma }]$ and empirical complex networks [$P\left(k\right)$ taken from network] as examples. Finally, we generalize our algorithm to annealed networks which allows networks to be represented in a mean-field-like manner.

We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the dual role of noise in regularizing the semiclassical Wigner function and averaging over fine structures in classical phase space. The results are interpreted in the context of applying recent advances in the theory of measurement and open systems to the semiclassical quantum regime. We use these methods to show how a local semiclassical picture is stabilized and can then be approximated by a classical distribution at later times. The general results are demonstrated explicitly via high-resolution numerical simulations of the quantum master equation for a chaotic Duffing oscillator.

The peculiarities of external synchronization of a resonant limit cycle on a torus are studied in an autonomous oscillator of quasiperiodic oscillations with two basic frequencies. We show numerically and experimentally that in the resonance conditions the synchronization effect takes place only at one of the two basic frequencies of the system, while the oscillations at the second basic frequency remain unsynchronized. Our results convincingly indicate a principal difference between synchronization of the resonant limit cycle on the torus and of a typical limit cycle. This is in contrast to the well-established theory of synchronization of a limit cycle. This finding opens new strategies for controlling systems with multiple time scales.

We consider the problem of the soliton dynamics in the presence of an external noisy force for the Boussinesq type equations. A set of ordinary differential equations (ODEs) of the relevant coordinates of the system is derived. We show that for the improved Boussinesq (IBq) equation the set of ODEs has limiting cases leading to a set of ODEs which can be directly derived either from the ill-posed Boussinesq equation or from the Korteweg-de Vries (KdV) equation. The case of a soliton propagating in the presence of damping and thermal noise is considered for the IBq equation. A good agreement between theory and simulations is observed showing the strong robustness of these excitations. The results obtained here generalize previous results obtained in the frame of the KdV equation for lattice solitons in the monatomic chain of atoms.

A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The $H$ theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard—linear Fokker-Planck equation—may be also related to a family of nonlinear Fokker-Planck equations.

We study a particular return map for a class of low-dimensional chaotic models called Kolmogorov-Lorenz systems, which received an elegant general Hamiltonian description and also includes the famous Lorenz-63 case, from the viewpoint of energy and Casimir balance. In particular, a subclass of these models is considered in detail, precisely those obtained from the Lorenz-63 by a small perturbation on the standard parameters, which includes, for example, the forced Palmer-Lorenz case. The paper is divided into two parts. In the first part the extremes of the mentioned state functions are considered, which define an invariant manifold, used to construct an appropriate Poincaré surface for our return map. From the “experimental” observation of the simple orbital motion around the two unstable fixed points, together with the circumstance that these orbits are classified by their energy or Casimir maximum, we construct a conceptually simple skeletal dynamics valid within our subclass, reproducing quite well the Lorenz cusp map for the Casimir maximum. This energetic approach sheds some light on the “physical” mechanism underlying the regime transitions. The second part of the paper is devoted to an investigation of a type of maximum energy-based long-term predictions, by which knowledge of a particular maximum energy “shell” amounts to knowledge of the future (qualitative) behavior of the system. It is shown, in this respect, that a local analysis of predictability is not appropriate for a complete characterization of this behavior. A perspective on the possible extensions of this type of predictability analysis to more realistic cases in (geo)fluid dynamics is discussed at the end of the paper.