Density functional theory for a simple model of dendrimers is proposed. The theory is based on fundamental measure theory, which accounts for the hard-sphere repulsion of the segments and on the Wertheim first-order perturbation theory for the correlations due to connectivity. Set of the recurrence formulas for the ideal chain contribution involving simple integrals is derived. By using perturbation theory dispersion forces can be easily included.

We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultrawide band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultrawide-band source of radio waves.

A density oscillator is a well-known system, which exhibits relaxation oscillation. It alternately exhibits up and down flows through a pipe that connects two containers filled with fluids that have different densities. Although the up-flow, down-flow, and flow-reversal processes have been studied separately, the entire oscillatory dynamics has not been modeled quantitatively. In this study, we derive a model of a density oscillator by considering all the above mentioned processes. The model thus obtained describes the oscillatory behavior in a unified manner, and its viscosity and pipe-length dependence is well described. Moreover, for the demonstration of this model, we have extended it to describe the dynamical behaviors observed in coupled density oscillators. Thus, this model provides a general expression for density oscillators.

We test the ability of semiclassical theory to describe quantitatively the revival of quantum wave packets—a long time phenomena—in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wave function up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times.

Phase synchronization (PS) has drawn increasing attention in recent years for its extensive applications in analyzing time series observed from coupled systems. In this paper, we examine the detection of PS in bivariate time series from the viewpoints of signal processing and circular statistics. Several definitions of instantaneous phase (IP) are first revisited and further unified into a framework, which defines IP as the argument of the signal with a specific bandpass filter applied. With this framework, the constraints for IP definition are discussed and the effect of noise in IP estimation is studied. The estimate error of IP, which is due to noise, is shown to obey a scale mixture of normal (SMN) distributions. Further, under the assumption that the SMN of IP error can be approximated by a particular normal distribution, the estimate of mean phase coherence of bivariate time series is shown to be degraded by a factor, which is determined by only the level of in-band noise. Finally, simulations are provided to support the theoretical results.

High and nearly constant evaporation rates from initially saturated porous media are sustained by capillary-driven flow from receding drying front below the evaporating surface. The spatial extent of continuous liquid pathways in homogeneous porous medium is defined by its hydraulically connected pore size distribution. We consider here evaporative losses from porous media consisting of two hydraulically coupled dissimilar domains each with own pore and particle size distributions separated by sharp vertical textural contrast. Evaporation experiments from texturally dissimilar media were monitored using neutron transmission and dye pattern imaging to quantify water distribution and drying front dynamics. Drying front invades exclusively coarse-textured domain while fine-textured domain remains saturated and its surface continuously coupled with the atmosphere. Results show that evaporation from fine-textured surface was supplied by liquid flow from adjacent coarse domain driven by capillary pressure differences between the porous media. A first characteristic length defining limiting drying front depth during which fine sand region remains saturated is deduced from difference in air-entry pressures of the two porous media. A second characteristic length defining the end of high evaporation rate includes the extent of continuous liquid films pinned in the crevices of the pore space and between particle contacts in the fine medium. We established numerically the lateral extent of evaporation-induced hydraulic coupling that is limited by viscous losses and gravity. For certain combinations of soil types the lateral extent of hydraulic coupling may exceed distances of 10 m. Results suggest that evaporative water losses from heterogeneous and coupled system are larger compared with uncoupled or homogenized equivalent systems.

We report numerical and experimental studies on a droplet moving through an array of mirofluidic ratchets. Droplets are formed at a $T$ junction and subsequently forced through microfluidic ratchets in the form of diffuser/nozzle structures. At the same flow rates of the continuous and the dispersed phases, the velocity of the droplet is determined by the viscosity of the continuous phase and the interfacial tension between the two phases. Both numerical and experimental results show that the velocity of the droplet increases with increasing capillary number. The droplet velocity is higher than the mean velocity of the fluid system and increases with increasing viscosity of the continuous phase or decreasing interfacial tension. In all experiments, the droplet moves faster in the diffuser direction than in the nozzle direction. Our findings allow the development of a measurement approach for interfacial tension. The rectification characteristics can be used for the development of micropumps for multiphase systems.

A dusty electronegative plasma containing Boltzmann electrons, Boltzmann negative ions, cold mobile positive ions, and negatively charged stationary dust has been considered. The basic features of arbitrary amplitude solitary waves (SWs) and double layers (DLs), which have been found to exist in such a dusty electronegative plasma, have been investigated by the pseudopotential method. The small amplitude limit has also been considered in order to study the small amplitude SWs and DLs analytically. It has been shown that under certain conditions, DLs do not exist, which is in good agreement with the experimental observations of Ghim and Hershkowitz [Y. Ghim (Kim) and N. Hershkowitz, Appl. Phys. Lett. 94, 151503 (2009)].

In this paper we rationalize relevant features of totally asymmetric simple-exclusion processes on topologies more complex than a single segment. We present a mean-field framework, exploiting the previously introduced notion of effective rates, which we express in terms of the average particle density on explicitly introduced junction sites. It allows us to construct the phase behavior as well as the current-density characteristic from well-known results for a linear totally asymmetric simple-exclusion-process segment in a very systematic and generic way. We validate the approach by studying a fourfold vertex in all variations in the number of entering/exiting segments and compare our predictions to simulation data. Generalizing the notion of particle–hole symmetry to take into account the topology at a junction shows that the average particle density at the junction constitutes a relevant directly observable parameter which gives detailed insight into the transport process. This is illustrated by a complete study of a simple network with figure-of-eight topology. Finally we generalize the approach to handle rate bias at a junction and discuss the surprisingly rich phenomenology of a biased figure-of-eight structure. This example highlights that the proposed framework is generic and readily extends to other topologies.

We introduce a nonlinear variant of the voter model, the $q$-voter model, in which $q$ neighbors (with possible repetition) are consulted for a voter to change opinion. If the $q$ neighbors agree, the voter takes their opinion; if they do not have a unanimous opinion, still a voter can flip its state with probability $\epsilon$. We solve the model on a fully connected network (i.e., in mean field) and compute the exit probability as well as the average time to reach consensus by employing the backward Fokker-Planck formalism and scaling arguments. We analyze the results in the perspective of a recently proposed Langevin equation aimed at describing generic phase transitions in systems with two ($Z_2$-symmetric) absorbing states. In particular, by deriving explicitly the coefficients of such a Langevin equation as a function of the microscopic flipping probabilities, we find that in mean field the $q$-voter model exhibits a disordered phase for high $\epsilon$ and an ordered one for low $\epsilon$ with three possible ways to go from one to the other: (i) a unique (generalized-voter-like) transition, (ii) a series of two consecutive transitions, one (Ising-like) in which the $Z_2$ symmetry is broken and a separate one (in the directed-percolation class) in which the system falls into an absorbing state, and (iii) a series of two transitions, including an intermediate regime in which the final state depends on initial conditions. This third (so far unexplored) scenario, in which a type of ordering dynamics emerges, is rationalized and found to be specific of mean field, i.e., fluctuations are explicitly shown to wash it out in spatially extended systems.

The alignment properties and distribution of flow speed during Poiseuille flow through a microchannel of a nematic liquid crystal in a cell with homeotropic surface alignment has been measured using a combination of conoscopy, fluorescence confocal polarizing microscopy, and time-lapse imaging. Two topologically distinct director profiles, with associated fluid velocity fields, are found to exist with the preferred state dictated by the volumetric flow rate of the liquid crystal. The results show excellent agreement with model data produced using the Ericksen-Leslie nematodynamics theory.

Oscillatory measurements of a columnar structure were performed, which was formed in an immiscible polymer blend subjected to an electric field. The formation process was observed through a confocal scanning laser microscope and the structure for the measurements was confirmed to be well defined. The storage shear modulus at low frequencies increased with increasing the electric field. A linear relation was found between the storage shear modulus and the square of the electric field. The static modulus calculated on the basis of the Maxwell stress exerted on the interface and interfacial tension was in good agreement with the experimental result.

In this paper, we investigated the spontaneous formation of aggregation structures of amyloid-forming peptide (GGVVIA) using a coarse-grained model and Monte Carlo simulations. The effects of concentration and temperature on the formation of different aggregation structures were studied. Three types of aggregation structures, single-layer $\beta$ sheet, amorphous $\beta$-sheet aggregate, and fibril-like structures, were observed in our simulations. The fibril-like structures obtained in simulations have a common cross-$\beta$ spine structure in which $\beta$ sheets twist in a left-handed fashion. The averaged twisting angle of the $\beta$ sheet in the fibril-like structures is $12°\pm 2°$. Moreover, it was found that the peptides in the same $\beta$ sheets prefer to arrange in a parallel way, which is consistent with the corresponding GGVVIA crystalline structure. On the other hand, it was found that there is a rich family of $\beta$-sheet stacking patterns in the fibril-like structures suggesting that the fibril structures are more complex than the corresponding crystalline structure and there exist many local free-energy minima rather than a distinct global minimum.

Interest rate instruments form a major component of the capital markets. The Libor market model (LMM) is the finance industry standard interest rate model for both Libor and Euribor, which are the most important interest rates. The quantum finance formulation of the Libor market model is given in this paper and leads to a key generalization: all the Libors, for different future times, are imperfectly correlated. A key difference between a forward interest rate model and the LMM lies in the fact that the LMM is calibrated directly from the observed market interest rates. The short distance Wilson expansion [Phys. Rev. 179, 1499 (1969)] of a Gaussian quantum field is shown to provide the generalization of Ito calculus; in particular, the Wilson expansion of the Gaussian quantum field $\mathcal{A}\left(t,x\right)$ driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor $\varphi \left(t,x\right)$ is defined and provides an efficient and compact representation of the quantum field theory of the Libor market model. The Lagrangian and Feynman path integrals of the Libor market model of interest rates are obtained, as well as a derivation given by its Hamiltonian. The Hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the Libor market model. The quantum finance formulation of the LMM is shown to reduce to the industry standard Bruce-Gatarek-Musiela-Jamshidian model when the forward interest rates are taken to be exactly correlated.

Roughness profiles of fracture surfaces formed as a result of the fast crack propagation through a filled rubber were analyzed by means of the height-height correlation functions. The fracture surface was found to be anisotropic in a certain domain of values of length scales; i.e., different values of roughness exponents are observed across and along the crack propagation direction. A two-dimensional analysis reveals a Family-Vicsek scaling in this domain characterized as well by two exponents. These characteristic values of the roughness exponents are found to be close to those observed for fracture surfaces of certain nonrubber materials at length scales smaller than the size of the fracture process zone. Hence, a ductile fracture process can be surmised to occur within the domain of the corresponding length scales.

An analytical approach to calculating bond percolation thresholds, sizes of $k$-cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The networks are generated using a generalization of Trapman’s [P. Trapman, Theor. Popul. Biol. 71, 160 (2007)] model of cliques embedded in treelike random graphs. The resulting networks have arbitrary degree distributions and tunable degree-dependent clustering. The effect of clustering on the bond percolation thresholds for networks of this type is examined and contrasted with some recent results in the literature. For very high levels of clustering the percolation threshold in these generalized Trapman networks is increased above the value it takes in a randomly wired (unclustered) network of the same degree distribution. In assortative scale-free networks, where the variance of the degree distribution is infinite, this clustering effect can lead to a nonzero percolation (epidemic) threshold.

Predictions of missing links of incomplete networks, such as protein-protein interaction networks or very likely but not yet existent links in evolutionary networks like friendship networks in web society, can be considered as a guideline for further experiments or valuable information for web users. In this paper, we present a local path index to estimate the likelihood of the existence of a link between two nodes. We propose a network model with controllable density and noise strength in generating links, as well as collect data of six real networks. Extensive numerical simulations on both modeled networks and real networks demonstrated the high effectiveness and efficiency of the local path index compared with two well-known and widely used indices: the common neighbors and the Katz index. Indeed, the local path index provides competitively accurate predictions as the Katz index while requires much less CPU time and memory space than the Katz index, which is therefore a strong candidate for potential practical applications in data mining of huge-size networks.

In the Axelrod’s model of cultural dissemination, we consider the mobility of cultural agents through the introduction of a density of empty sites and the possibility that agents in a dissimilar neighborhood can move to them if their mean cultural similarity with the neighborhood is below some threshold. While for low values of the density of empty sites, the mobility enhances the convergence to a global culture, for high enough values of it, the dynamics can lead to the coexistence of disconnected domains of different cultures. In this regime, the increase in initial cultural diversity paradoxically increases the convergence to a dominant culture. Further increase in diversity leads to the fragmentation of the dominant culture into domains, forever changing in shape and number, as an effect of the never ending eroding activity of cultural minorities.

We present a model describing friction due to the thermally activated formation and rupture of molecular bonds between two surfaces, with long molecules on one surface attaching to discrete or continuous binding sites on the other. The physical assumptions underlying this model are formalized using a continuum approximation resulting in a class of master-equation-like partial differential equations that is a generalization of a friction model due to Persson [Phys. Rev. B 51, 13568 (1995)] and is identical to the equations used to describe muscle contraction, first proposed by A. F. Huxley. We examine the properties of this friction model in the continuous binding site limit noting that this model is capable of producing both monotonically increasing and an increasing-decreasing force dependence on slip velocity. When monotonically increasing, the force dependence on velocity is (asymptotically) logarithmic. The model produces a transient increase in friction in response to a sudden velocity increase, whether or not the steady-state friction force is a decreasing or increasing function of steady slip velocity. The model also exhibits both stable steady slip and stick-slip-like oscillatory behavior, in the presence of compliance in the loading machine, even when the steady-state friction force is a decreasing function of steady-state slip velocity.

Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong enough, it has been shown in chaotic systems that its decay is dictated by the classical Lyapunov exponent. However, several recent studies have shown an unexpected nonuniform decay rate as a function of the perturbation strength instead of that Lyapunov decay. Here we study the systematic behavior of this regime in perturbed cat maps. We show that some perturbations produce coherent oscillations in the width of LDOS that imprint clear signals of the perturbation in LE decay. We also show that if the perturbation acts in a small region of phase space (local perturbation) the effect is magnified and the decay is given by the width of the LDOS.