We have studied oscillation of a pendulum in water using spherical bobs. By measuring the loss in potential energy, we estimate the drag coefficient on the sphere and compare to data from liquid-helium experiments. The drag coefficients compare very favorably illustrating the true scaling behavior of this phenomenon. We also studied the decay of amplitude of the pendulum over time. As observed previously, at small amplitudes, the drag on the bob is given by the linear Stokes drag and the decay is exponential. For larger amplitudes, the pendulum bob sheds vortex rings as it reverses direction. The momentum imparted to these vortex rings results in an additional discrete drag on the bob. We present experiments and a theoretical estimate of this vortex-ring-induced drag. We analytically derive an estimate for a critical amplitude beyond which vortex ring shedding will occur as well as an estimate of the radius of the ring as a function of amplitude.

We report a numerical study on heat conduction in one-dimensional homogeneous lattices in both the linear and the nonlinear response regime, with a comparison among three prototypical nonlinear lattice models. In the nonlinear response regime, negative differential thermal resistance (NDTR) can occur in both the Frenkel-Kontorova model and the ${\varphi }^4$ model. In the Fermi-Pasta-Ulam-$\beta$ model, however, only positive differential thermal resistance can be observed, as shown by a monotonous power-law dependence of the heat flux on the applied temperature difference. In general, it was found that NDTR can occur if there is nonlinearity in the onsite potential of the lattice model. It was also found that the regime of NDTR becomes smaller as the system size increases, and eventually vanishes in the thermodynamic limit. For the ${\varphi }^4$ model, a phenomenological description of the size-induced crossover from the existence to the nonexistence of a NDTR regime is provided.

Colloids coated with complementary single-stranded DNA “sticky ends” associate and dissociate upon heating. Recently, microscopy experiments have been carried out where this association-dissociation transition has been investigated for different types of DNA and different DNA coverages [R. Dreyfus, M. E. Leunissen, R. Sha, A. V. Tkachenko, N. C. Seeman, D. J. Pine, and P. M. Chaikin, Phys. Rev. Lett. 102, 048301 (2009)]. It has been shown that this transition can be described by a simple quantitative model which takes into account the features of the tethered DNA on the particles and unravels the importance of an entropy cost due to DNA confinement between the surfaces. In this paper, we first present an extensive description of the experiments that were carried out. A step-by-step model is then developed starting from the level of statistical mechanics of tethered DNA to that of colloidal aggregates. This model is shown to describe the experiments with excellent agreement for the temperature and width of the transition, which are both essential properties for complex self-assembly processes.

The effect of random or uniform magnetic fields on spin glasses on some $d=3$ hierarchical lattices has been studied, using renormalization-group theory, by Salmon and Nobre. In this work, the recursion relation for the local magnetic field is incorrect. It erroneously weakens the amplitude of the renormalization contribution to the magnetic field by a factor of $1/q_{\mu }$, where $q_{\mu }$ is the site coordination number.

We study a pair of endogenously bursting neurons with fast nondelayed inhibitory connections. We show that fast reciprocal inhibition, known to facilitate antiphase bursting, can stably synchronize bursting neurons. This contrasts with the classical view that reciprocal inhibition has to be slow or time delayed to establish in-phase synchronization. Through stability analysis, we reveal the emergent mechanism of in-phase synchronization and discuss its implications for various types of bursting neurons and networks.

Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network. We demonstrate the effectiveness of our approximation schemes using both real and artificial networks, showing in particular that we can accurately obtain the spectral ranking of small subgraphs. We also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links. Our results may not only contribute to our theoretical understanding of dynamical processes on networks, but also lead to practical applications in ranking subgraphs of real complex networks.

A fundamental question in nonlinear science and evolutionary biology is how epidemic spreading may affect coexistence. We address this question in the framework of mobile species under cyclic competitions by investigating the roles of both intra- and interspecies spreading. A surprising finding is that intraspecies infection can strongly promote coexistence while interspecies spreading cannot. These results are quantified and a theoretical paradigm based on nonlinear partial differential equations is derived to explain the numerical results.

We consider the dynamical system described by the area-preserving standard mapping. It is known for this system that $P\left(t\right)$, the normalized number of recurrences staying in some given domain of the phase space at time $t$ (so-called “survival probability”) has the power-law asymptotics, $P\left(t\right)\sim t^{-\nu }$. We present new semiphenomenological arguments which enable us to map the dynamical system near the chaos border onto the effective “ultrametric diffusion” on the boundary of a treelike space with hierarchically organized transition rates. In the framework of our approach we have estimated the exponent $\nu$ as $\nu =\text{ln}2/\text{ln}\left(1+r_g\right)\approx 1.44$, where $r_g=\left(\sqrt{5}-1\right)/2$ is the critical rotation number.

It has been shown recently [A. Siria, A. Drezet, F. Marchi, F. Comin, S. Huant, and J. Chevrier, Phys. Rev. Lett. 102, 254503 (2009)] that in the plane-plane configuration, a mechanical resonator vibrating close to a rigid wall in a simple fluid can be overdamped to a frozen regime. Here, by solving analytically the Navier-Stokes equations with partial slip boundary conditions at the solid-fluid interface, we develop a theoretical approach justifying and extending these earlier findings. We show in particular that in the perfect-slip regime, the abovementioned results are, in the plane-plane configuration, very general and robust with respect to lever geometry considerations. We compare the results to those obtained previously for the sphere moving perpendicularly and close to a plane in a simple fluid and discuss in more details the differences concerning the dependence of the friction forces with the gap distance separating the moving object (i.e., plane or sphere) from the fixed plane. We show that the plane-plane geometry is more sensitive than the sphere-plane geometry for the measurement of slippage coefficients. Finally, we show that the submicron fluidic effect reported in the reference above, and discussed further in the present work, can have dramatic implications in the design of nanoelectromechanical systems.

In this paper, the modified nonlinear Schrödinger equation is investigated, which describes the femtosecond optical pulse propagation in a monomodal optical fiber. Based on the Wadati-Konno-Ichikawa system, another type of Lax pair and infinitely many conservation laws are derived. Dark and antidark soliton solutions in the normal dispersion regime are obtained by means of the Hirota method. Parametric regions for the existence of the dark and antidark soliton solutions are given. Asymptotic analysis of the two-soliton solution shows that collisions between two solitons (two antidark solitons, two dark solitons, and dark and antidark solitons) are elastic. In addition, collision between dark and antidark solitons reveals that dark and antidark solitons can co-exist on the same background in the normal dispersion regime.

We study the stability of classical structures in chaotic systems when a dissipative quantum evolution takes place. We consider a paradigmatic model, the quantum baker map in contact with a heat bath at finite temperature. We analyze the behavior of the purity, fidelity and Husimi distributions corresponding to initial states localized on short periodic orbits (scar functions) and map eigenstates. Scar functions, that have a fundamental role in the semiclassical description of chaotic systems, emerge as robust relative to other states (which are localized on classical structures) against environmental perturbations. Also, purity and fidelity show a complementary behavior as decoherence measures.

Near-critical binary mixtures containing ionic solutes near a charged wall preferentially adsorbing one component of the solvent are studied. Within the Landau-Ginzburg approach extended to include electrostatic interactions and the chemical preference of ions for one component of the solvent, we obtain a simple form for the leading-order correction to the Debye-Hückel theory result for the charge density profile. Our result shows that critical adsorption influences significantly distribution of ions near the wall. This effect may have important implications for the screening of electrostatic interactions between charged surfaces immersed in binary near-critical solvents.

We propose an interpolation expression using the difference moment (Kolmogorov transient structural function) of the second order as the average characteristic of displacements for identifying the anomalous diffusion in complex processes when the stochastic (the term “stochastic” in this paper refers to random variability in the signals of complex systems characterized by nonlinear interactions, dissipation, and inertia) dynamics of the system under study reaches a steady state (large time intervals). Our procedure based on this expression for identifying anomalous diffusion and calculating its parameters in complex processes is applied to the analysis of the dynamics of blinking fluorescence of quantum dots, x-ray emission from accreting objects, fluid velocity in Rayleigh-Bénard convection, and geoelectrical signal for a seismic area. For all four examples, the proposed interpolation is able to adequately describe the stochastic part of the experimental difference moment, which implies that anomalous diffusion manifests itself in these complex processes. The results of this study make it possible to broaden the range of complex natural processes in which anomalous diffusion can be identified.

We study the diffusion of tagged hard-core interacting Brownian point particles under the influence of an external force field in one dimension. Using the Jepsen line we map this many-particle problem onto a single particle one. We obtain general equations for the distribution and the mean-square displacement $⟨{\left(x_T\right)}^2⟩$ of the tagged center particle valid for rather general external force fields and initial conditions. The case of symmetric distribution of initial conditions around the initial position of the tagged particle on $x=0$ and symmetric potential fields $V\left(x\right)=V\left(-x\right)$ yields zero drift $⟨x_T⟩=0$ and is investigated in detail. We find $⟨{\left(x_T\right)}^2⟩=\mathcal{R}\left(1-\mathcal{R}\right)/2N{r}^2$ where $2N$ is the (large) number of particles in the system. $\mathcal{R}$ is a single particle reflection coefficient, i.e., the probability that a particle free of collisions starts on $x_0>0$ and remains in $x>0$ while $r$ is the probability density of noninteracting particles on the origin. We show that this equation is related to the mathematical theory of order statistics and it can be used to find $⟨{\left(x_T\right)}^2⟩$ even when the motion between collision events is not Brownian (e.g., it might be ballistic or anomalous diffusion). As an example we derive the Percus relation for non-Gaussian diffusion. A wide range of physical behaviors emerge which are very different than the classical single file subdiffusion $⟨{\left(x_T\right)}^2⟩\sim t^{1/2}$ found for uniformly distributed particles in an infinite space and in the absence of force fields.

We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem that apply to driven dissipative systems, in which time-reversal symmetry or local detailed balance is broken. Uniformly sheared granular systems and driven inelastic Lorentz-gas model are considered as examples. It is discussed how statistical mechanical theory dealing with nonequilibrium steady-state properties can be constructed for such systems for which equilibrium state does not exist.

The temperature dependence of characteristic length scales associated to the glass transition such as the cooperativity length scale introduced by Adam and Gibbs [cooperative rearranging region (CRR)] or the dynamic heterogeneity as estimated from the four point correlation function ${\chi }_4$, is at the center of large interests. Broadband dielectric spectroscopy and temperature modulated differential scanning calorimetry allow to study the CRR size temperature dependence in the temperature range of ergodicity loss for glass-forming liquids, starting from the onset of cooperativity in the crossover region down to the glass transition temperature. Furthermore, the correlation between these two techniques allows to explore a large frequency range (from 1 mHz to 10 MHz). The goal of this work is to follow the cooperativity evolution along the Arrhenius plot for two different polymeric systems: poly(ethylene 1,4-cyclohexylenedimethylene terephthalate glycol) and poly(bisphenol A carbonate).

Here we present a systematic study of supercoil formation in DNA minicircles under varying linking number by using molecular-dynamics simulations of a two-bead coarse-grained model. Our model is designed with the purpose of simulating long chains without sacrificing the characteristic structural properties of the DNA molecule, such as its helicity, backbone directionality, and the presence of major and minor grooves. The model parameters are extracted directly from full-atomistic simulations of DNA oligomers via Boltzmann inversion; therefore, our results can be interpreted as an extrapolation of those simulations to presently inaccessible chain lengths and simulation times. Using this model, we measure the twist/writhe partitioning in DNA minicircles, in particular its dependence on the chain length and excess linking number. We observe an asymmetric supercoiling transition consistent with experiments. Our results suggest that the fraction of the linking number absorbed as twist and writhe is nontrivially dependent on chain length and excess linking number. Beyond the supercoiling transition, chains of the order of one persistence length carry equal amounts of twist and writhe. For longer chains, an increasing fraction of the linking number is absorbed by the writhe.

This paper studies the transfer behavior of electronic excitations on the circular and elliptically deformed B850 rings theoretically. It shows that degree of delocalization of the electronic excitation is dependent on the kinds of measured electronically excited states and the kinds of studied structures. It finds that if initial excitation is a coherent exciton, then the elliptical deformation of the B850 ring will work against energy transfer. It depicts wavelike energy transfer persisting for several hundred femtoseconds on the circular and elliptically deformed B850 rings at cryogenic temperature and finds that under the deformation, inducing localized excitation at the site near the elliptical major axis will be in favor of energy transfer, whereas at the minor axis will work against energy transfer both visibly in wavelike region.

In this Brief Report we show how the low-temperature thermodynamics of the dissipative motion of an electron in a magnetic field is sensitive to the nature of the spectral density function, $J\left(\omega \right)$, of the quantum heat bath. In all cases of couplings considered here the free energy and the entropy of the cyclotron motion of the electron fall off to zero as power law in conformity with the third law of thermodynamics. The power of the power law however depends on the nature of $J\left(\omega \right)$. We also separately discuss the influence of confinement.

We present a simple model of the emergence of the division of labor and the development of a system of resource subsidy from an agent-based model of directed resource production with variable degrees of trust between the agents. The model has three distinct phases corresponding to different forms of societal organization: disconnected (independent agents), homogeneous cooperative (collective state), and inhomogeneous cooperative (collective state with a leader). Our results indicate that such levels of organization arise generically as a collective effect from interacting agent dynamics and may have applications in a variety of systems including social insects and microbial communities.