Crossover from weak to strong chaos in high-dimensional Hamiltonian systems at the strong stochasticity threshold (SST) was anticipated to indicate a global transition in the geometric structure of phase space. Our recent study of Fermi-Pasta-Ulam models showed that corresponding to this transition the energy density dependence of all Lyapunov exponents is identical apart from a scaling factor. The current investigation of the dynamic $XY$ model discovers an alternative scenario for the energy dependence of the system dynamics at SSTs. Though similar in tendency, the Lyapunov exponents now show individually different energy dependencies except in the near-harmonic regime. Such a finding restricts the use of indices such as the largest Lyapunov exponent and the Ricci curvatures to characterize the global transition in the dynamics of high-dimensional Hamiltonian systems. These observations are consistent with our conjecture that the quasi-isotropy assumption works well only when parametric resonances are the dominant sources of dynamical instabilities. Moreover, numerical simulations demonstrate the existence of hydrodynamical Lyapunov modes (HLMs) in the dynamic $XY$ model and show that corresponding to the crossover in the Lyapunov exponents there is also a smooth transition in the energy density dependence of significance measures of HLMs. In particular, our numerical results confirm that strong chaos is essential for the appearance of HLMs.

The larger magnetic particles in ferrofluids are known to form chains, causing the fluid to display non-Newtonian behavior. In this paper, a generalization of the familiar ferrofluid dynamics by Shliomis is shown capable of realistically accounting for these fluids. The modification consists of identifying the relaxing magnetization as that of the chain-forming particles, while accounting for the free magnetic particles by dissipative terms in the Maxwell equations.

The interrelation between data channels of multivariate data sets may lead to cluster formation. Revealing the cluster structure can give important information about the underlying systems’ properties. Here we investigate the features of a recent genuinely multivariate cluster detection algorithm that is suitable for time-resolved and unsupervised application to nonstationary and noisy time series. Using numerical test systems it is discussed under which conditions intra- and inter-cluster relations can be disentangled and quantified. In addition different types of errors occurring when channels are automatically attributed to clusters are investigated quantitatively. Finally, the algorithm is applied to nonstationary model time series and its time-dependent performance is compared to other cluster detection algorithms.

The use of memory kernels stemming from a Mori-Zwanzig approach to time series analysis is discussed. We show that despite its success in determining properties from an analytical model, the kernel itself is not easily interpreted. We consider a recently introduced discretization of the kernel and show that its properties can be quite different from its continuous counterpart. We provide a rigorous analysis of the discrete case and show for several analytically calculated memory kernels of simple time series processes that their features are not readily detectable in the kernel. We show furthermore that practical relevant Mori-Zwanzig models with a finite kernel form a true subclass of the autoregressive moving average (ARMA) models. The fact that this approach already veils the properties of these simple time series gives rise to severe doubts about its applicability in more complex situations.

By using a correlated projection operator, the time-convolutionless (TCL) method to derive a quantum master equation can be utilized to investigate the transport behavior of quantum systems as well. Here, we analyze a three-dimensional anisotropic quantum model system according to this technique. The system consists of Heisenberg coupled two-level systems in one direction and weak random interactions in all other ones. Depending on the partition chosen, we obtain ballistic behavior along the chains and normal transport in the perpendicular direction. These results are perfectly confirmed by the numerical solution of the full time-dependent Schrödinger equation.

In this work, we investigate the interplay between surface anchoring and finite-size effects on the smectic-isotropic transition in free-standing smectic films. Using an extended McMillan model, we study how a homeotropic anchoring stabilizes the smectic order above the bulk transition temperature. In particular, we determine how the transition temperature depends on the surface ordering and film thickness. We identify a characteristic anchoring for which the transition temperature does not depend on the film thickness. For strong surface ordering, we found that the thickness dependence of the transition temperature can be well represented by a power-law relation. The power-law exponent exhibits a weak dependence on the range of film thicknesses, as well as on the molecular alkyl tail length. Our results reproduce the main experimental findings concerning the layer-thinning transitions in free-standing smectic films.

Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of networks with arbitrary input and output degree sequences and given 2-node degree correlations by means of statistical ensemble approach. We demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to $r$ is revealed. Numerical experiments using network randomization methods show very good agreement to our analytical estimations.

We apply the auxiliary-system approach to study paths to globally generalized synchronization in scale-free networks of identical chaotic oscillators, including Hénon maps, logistic maps, and Lorentz oscillators. As the coupling strength $\epsilon$ between nodes of the network is increased, transitions from partially to globally generalized synchronization and intermittent behaviors near the synchronization thresholds, are found. The generalized synchronization starts from the hubs of the network and then spreads throughout the whole network with the increase of $\epsilon$. Our result is useful for understanding the synchronization process in complex networks.

There exist methods for determining effective conservative interactions in coarse-grained particle-based mesoscopic simulations. The resulting models can be used to capture thermal equilibrium behavior, but the model system we study does not correctly represent transport properties. We suggest the use of force covariance to determine the full functional form of dissipative and stochastic interactions. We show that a combination of the RDF and a force covariance function can be used to determine all interactions in dissipative particle dynamics (DPD). Furthermore, we use the method to test whether the effective interactions in DPD can be adjusted to produce a force covariance consistent with the projection of a microscopic Lennard-Jones simulation. The results indicate that the DPD ansatz may not be consistent with the underlying microscopic dynamics. We discuss how this result relates to theoretical studies reported in the literature.

With the help of recursion relations derived from the self-similar structure, we obtain the solution of average path length, ${\overline{d}}_t$, for Apollonian networks. In contrast to the well-known numerical result ${\overline{d}}_t\propto {\left(\text{ln}{N}_t\right)}^{3/4}$ [J. S. Andrade, Jr. et al., Phys. Rev. Lett. 94, 018702 (2005)], our rigorous solution shows that the average path length grows logarithmically as ${\overline{d}}_t\propto \text{ln}{N}_t$ in the infinite limit of network size $N_t$. The extensive numerical calculations completely agree with our closed-form solution.

We present an entirely microscopic calculation of the Casimir force $f\left(d\right)$ between two metallic plates in the limit of large separation $d$. The models of metals consist of mobile quantum charges in thermal equilibrium with the photon field at positive temperature $T$. Fluctuations of all degrees of freedom, matter and field, are treated according to the principles of quantum electrodynamics and statistical physics without recourse to approximations or intermediate assumptions. Our main result is the correctness of the asymptotic universal formula $f\left(d\right)\sim -\frac{\zeta \left(3\right)k_{\text{B}}T}{8\pi d^3}$, $d\to \infty$. This supports the fact that, in the framework of the Lifshitz theory of electromagnetic fluctuations, transverse electric modes do not contribute in this regime. Moreover, the microscopic origin of universality is seen to rely on perfect screening sum rules that hold in great generality for conducting media.

We demonstrate that a gas of classical particles trapped in an external asymmetric potential undergoes a quasiperiodic motion, if the temperature of its initial velocity distribution $T_{\text{NE}}$ differs from the equilibrium temperature $T_{\text{eq}}$. The magnitude of the effect is determined by the value of $T_{\text{NE}}-T_{\text{eq}}$, and the direction of the motion is determined by the sign of this expression. The “loading” and “unloading” of the gas particles change directions of their motion, thereby creating a possibility of shuttle-like motion. The system works as a Carnot engine where the heat flow between kinetic and potential parts of the nonequilibrium distribution produces the useful work.

Critical wetting transitions under nonequilibrium conditions are studied numerically and analytically by means of an interface-displacement model defined by a Kardar-Parisi-Zhang equation, plus some extra terms representing a limiting, short-ranged attractive wall. Its critical behavior is characterized in detail by providing a set of exponents for both the average height and the surface order-parameter in one dimension. The emerging picture is qualitatively and quantitatively different from recently reported mean-field predictions for the same problem. Evidence is shown that the presence of the attractive wall induces an anomalous scaling of the interface local slopes.

Molecular dynamics results for the dynamic Prigogine-Defay ratio are presented for two glass-forming liquids, thus evaluating the experimentally relevant quantity for testing whether metastable-equilibrium liquid dynamics is described by a single parameter to a good approximation. For the Kob-Andersen binary Lennard-Jones mixture as well as for an asymmetric dumbbell model liquid, a single-parameter description works quite well. This is confirmed by time-domain results where it is found that energy and pressure fluctuations are strongly correlated on the $\alpha$ time scale in the constant-volume, constant-temperature ensemble; similarly, energy and volume fluctuations correlate strongly in the constant-pressure, constant-temperature ensemble.

Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion rate(s) from a uniform value does not exceed a threshold value. For larger deviations, the system exhibits a continuous phase transition into a frozen distribution of odd (or even) label species.

We investigate the adhesion of vesicles, under the influence of a contact potential, to substrates with various geometry. For axisymmetric configurations, we find that the transition from a free vesicle to a bound state depends significantly on the substrate shape. In general, the critical values of the contact potential at which these transitions take place are lower for a concave-shaped substrate than that for a flat-shaped substrate investigated in earlier studies. We observe that the transitions happen at higher critical values of the contact potential when the substrate is convex and illustrate how these critical values depend on the curvature of the substrate. In addition, we construct an approximate analytical solution that predicts the shape of the vesicle for large internal excess pressure and contact potential. The analytical solution leads to an inequality that relates the surface tension with the contact potential.

The excited-state atom densities in the negative glow of a direct-current glow discharge are derived from the spectral-line intensity of radiative atoms and the resonance-fluorescence photon flux of nonradiative atoms. The discharge is operated in a helium-argon gas mixture (molar fraction ratio 91:9; total gas pressure 5 Torr) at a dc current of 0.7–1.2 mA. The observations are made in the region of the maximum luminance in the cathode region, where high-energy electrons accelerated in the cathode fall are injected into the negative glow. The emission intensities of the He I, He II, Ar I, and Ar II spectral lines are measured with a calibrated tungsten ribbon lamp as an absolute spectral-radiance standard. Fluorescence photons scattered by helium and argon atoms in the metastable state and argon atoms in the resonance state are detected by the laser-induced fluorescence (LIF) method with the Rayleigh scattering of nitrogen molecules as an absolute standard of scattering cross section. The laser absorption method is incorporated to confirm the result of the LIF measurement. Excitation energies of the measured spectral lines range from 11.6 (Ar I) to 75.6 eV (He II), where the excitation energy is measured from the ground state of the neutral atom on the assumption that, in the plasma of this study, both the neutral and the ionic lines are excited by electron impact in a single-step process from the ground state of the corresponding neutral atoms. Experimental evidence is shown for the validity of this assumption.

The monomer-dimer model is fundamental in statistical mechanics. However, it is $\#P$-complete in computation, even for two-dimensional problems. A formulation for the partition function of the monomer-dimer system is proposed in this paper by transforming the number of all matchings of a bipartite graph into the number of perfect matchings of an extended bipartite graph, which can be given by a matrix permanent. Sequential importance sampling algorithm is applied to compute the permanents. For two-dimensional lattice with periodic condition, the monomer-dimer constant is known as $h_2=0.662798972834$. We obtain $0.6627\pm 0.0002$ for our approximation, which shows the robustness and the efficiency of the algorithm. For three-dimensional problem, our numerical result is $0.7847\pm 0.0014$, which agrees with the best known bounds.

In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to $N$, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.