For autonomous quantum systems with modular structure we demonstrate that the Jarzynski relation can be reinterpreted to apply even locally: For this purpose certain contexts have to be introduced by selecting the system of interest versus its environment. The respective energy exchange is then divided into heat and work based on a generalized definition of these notions. In this way we are able to identify functional parts of the environment as either heat or work sources, respectively. We investigate different combinations of these functional parts with respect to contextual Jarzynski relations. Our analytical results are confirmed by numerical investigations on small multipartite systems.

We solve the nonlinear Poisson-Boltzmann equation for two parallel and like-charged plates both inside a symmetric electrolyte, and inside a $2:1$ asymmetric electrolyte, in terms of Weierstrass elliptic functions. From these solutions we derive the functional relation between the surface charge density, the plate separation, and the pressure between plates. For the one plate problem, we obtain exact expressions for the electrostatic potential and for the renormalized surface charge density, both in symmetric and in asymmetric electrolytes. For the two plate problems, we obtain new exact asymptotic results in various regimes.

We present an atomic force microscopy (AFM) and ellipsometry study of ultrathin smectic films on silicon substrates. By controlling the amount of the liquid-crystal material that is spin coated on the substrate, we are able to prepare films consisting of a defined small number (ranging from 1 to 4) of smectic layers. AFM measurements show that the films possess a specific surface structure with a lateral feature size of a few microns and steplike height variations of 3.3 nm. The height of the steps corresponds to the smectic layer spacing of the material used, indicating that the surface structure is the result of a partial formation of the topmost smectic layer of these films. The pattern of the surface structure either corresponds to isolated islands (regions in which the film thickness is enhanced by one smectic layer) or consists of pores (film thickness decreased by one layer). A smooth surface is only obtained if the amount of the liquid-crystal material is precisely tuned to certain values, indicating the formation of a complete smectic top layer. A well-defined relation exists between the liquid crystal concentration in the spin-coating solution and the obtained structure, enabling the controlled generation of island structures, pore structures, or smooth surfaces. The two-dimensional island or pore structure is stable on the time scale of a few days. Preliminary results concerning the thermal stability are reported. Our study highlights the usefulness of AFM measurements for the study of smectic liquid-crystal surfaces.

Non-Gaussian effects are important features in many fields of physics, and the search for non-Gaussianity motivates several new experiments. Here I show that an insidious form of non-Gaussianity can easily arise as a finite-size effect in a data analysis tool that is guaranteed to be asymptotically Gaussian. This means that experimental searches for non-Gaussianity should also include an extremely careful scrutiny of the statistical tools used to analyze data.

We investigate the temporal patterns of human communication and its influence on the spreading of information in social networks. The analysis of mobile phone calls of 20 million people in one country shows that human communication is bursty and happens in group conversations. These features have the opposite effects on the reach of the information: while bursts hinder propagation at large scales, conversations favor local rapid cascades. To explain these phenomena we define the dynamical strength of social ties, a quantity that encompasses both the topological and the temporal patterns of human communication.

Model reduction is a common goal in the study of complex systems, consisting of many components with a complex interaction structure. The quality of such reduction, however, may not be reflected correctly in the stepwise prediction error in the model since it ignores the global geometry of the dynamics. Here we introduce a general two-step framework, consisting of dimensionality reduction of the time series followed by modeling of the resulting time series, and propose the use of the shadowing distance to measure the quality of the second step. Using coupled oscillator networks as a prototypical example, we demonstrate that our approach can outperform those based on stepwise error and suggest that it sheds light on the problem of identifying and modeling low-dimensional dynamics in large-scale complex systems.

The phase-splitting behavior of coupled suprachiasmatic-nucleus neurons has been observed in many mammals, and its mechanism is still not completely understood. Based on our previous work [C. Gu, J. Wang, and Z. Liu, Phys. Rev. E 80, 030904(R) (2009)] on the free-running periods of neurons in the suprachiasmatic nucleus, we present here a modified Goodwin oscillator model to explain the mechanism of phase splitting. In contrast to the previous phase model, the modified Goodwin oscillator model contains the information on both the phase and amplitude and, thus, can show more features than the purely phase model, including all three behaviors of synchronization, phase splitting, and amplitude death and the distributed periodicity in the regions of synchronization and phase splitting, etc. An analytic phase model is extracted from the modified Goodwin oscillator model to explain the dependence of periodicity on the parameters. Moreover, both the modified Goodwin oscillator model and the analytic phase model show that the ensemble frequency can be enhanced or reduced by the time delay.

We extended the Goncharov model [V. N. Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] for nonlinear Rayleigh-Taylor instability of perfect fluids to the case of Rivlin-Ericksen viscoelastic fluids [R. S. Rivlin and J. L. Ericksen, Rat. Mech. Anal. 4, 323 (1955)], with surface tension. For Rayleigh-Taylor instability, viscosity, surface tension, and viscoelasticity decrease the exponential growth rate predicted by linear stability analysis. In particular, we find that viscosity and surface tension decrease the terminal bubble velocity, whereas viscoelasticity is found to have no effect. All three properties increase the saturation height of the bubble. In Richmyer-Meshkov instability, the decay of the asymptotic velocity depends on the balance between viscosity and surface tension, and viscoelasticity tends to slow the asymptotic velocity decay.

Recent experiments by Burton and Taborek have demonstrated a droplet-to-bubble transition in the pinchoff behavior of one inviscid fluid inside another. With $D$ the relative densities ${\rho }_{\mathcal{E}}/{\rho }_{\Im }$, they find transition from ($D=0$) droplet-to-bubble behavior at $D\approx 4$. Numerical simulations of this two-fluid system, up to and beyond the initial breakup of the inner fluid, have been carried out utilizing level set and boundary integral methods. A droplet-to-bubble transition is predicted: For $D$ sufficiently large, the volume of the satellite droplet shrinks to zero and there is no overturning of the fluid at separation. The calculated self-similar scaling exponents and the pinchoff region shapes match the known behavior at the droplet and bubble extremes ($D=0$, $D=100$). For intermediate $D$ values, the simulations presented here indicate that the transition range between droplet and bubble behavior depends upon initial drop geometry. When the neck separates two nonequal inner fluid masses the transition is mild and occurs in the range $4<D<10$, whereas in the case of equal masses an abrupt transition occurs at $D\approx 4$ in perfect agreement with the above mentioned experiments.

Population transfer in Hamiltonian systems, such as between Rydberg states of atoms and vibrational modes in diatomic molecules, has been both experimentally and theoretically demonstrated. All these systems have the property that the classical frequency of the motion changes monotonically with energy. Referred to as the twist condition, this property makes it possible to transfer population both by chirping a driving field within a ladder climbing scheme and by adiabatically chirping through a multiphoton resonance connecting two bound states. In this paper, we demonstrate that the latter method for population transfer can still be made to work in a system which violates the classical twist condition. We use classical rigid rotor as an example system where the frequency changes monotonically with energy and compare the responsible separatrix crossing mechanism in phase space to that in a system which exhibits an extremum in the frequency-energy profile. We perform both one-dimensional classical and quantum simulations and find that the quantum phase-space distribution mirrors its corresponding classical counterpart.

As an image of the many-to-one map of loop-erasing operation $\mathcal{L}$ of random walks, a self-avoiding walk (SAW) is obtained. The loop-erased random walk (LERW) model is the statistical ensemble of SAWs such that the weight of each SAW $\zeta$ is given by the total weight of all random walks $\pi$ that are inverse images of $\zeta$, $\{\pi$:$\mathcal{L}(\pi )=\zeta \}$. We regard the Brownian paths as the continuum limits of random walks and consider the statistical ensemble of loop-erased Brownian paths (LEBPs) as the continuum limits of the LERW model. Following the theory of Fomin on nonintersecting LERWs, we introduce a nonintersecting system of $N$-tuples of LEBPs in a domain $D$ in the complex plane, where the total weight of nonintersecting LEBPs is given by Fomin’s determinant of an $N\times N$ matrix whose entries are boundary Poisson kernels in $D$. We set a sequence of chambers in a planar domain and observe the first passage points at which $N$ Brownian paths $({\gamma }_1,\dots ,{\gamma }_N)$ first enter each chamber, under the condition that the loop-erased parts $[\mathcal{L}({\gamma }_1),\dots ,\mathcal{L}({\gamma }_N)]$ make a system of nonintersecting LEBPs in the domain in the sense of Fomin. We prove that the correlation functions of first passage points of the Brownian paths of the present system are generally given by determinants specified by a continuous function called the correlation kernel. The correlation kernel is of Eynard-Mehta type, which has appeared in two-matrix models and time-dependent matrix models studied in random matrix theory. Conformal covariance of correlation functions is demonstrated.

We apply a spin-coherent states formalism to study the simplest version of a central-spin model, the so-called Mermin model, in which a given (central) spin $1/2$ interacts symmetrically with a “bath” composed of $N$ spins $1/2$, characterized by a common frequency. The symmetric interaction allows one to restrict the problem to the fully symmetric sector of the Hilbert space associated with these $N$ spins and therefore to treat these as one large $N/2$ spin. In particular, we derive analytic expressions for the integrated density of states in the thermodynamic limit when the number of bath spins is taken to infinity. From the thermodynamic limit spectrum we show the phase diagram for the system can be divided into four regions, partitioned, on the one hand, into a symmetric (nondegenerate) phase or a broken symmetry (degenerate) phase, and, on the other hand, by the case of overlapping or nonoverlapping energy surfaces. The nature and position of singularities appearing in the energy surfaces change as one moves from region to region. Our spin-coherent states formalism naturally leads us to the Majorana representation, which is useful to transform the Schrödinger equation into a Ricatti-like form that can be solved in the thermodynamic limit to obtain closed-form expressions for the integrated density of states. The energy surface singularities correspond with critical points in the density of states. We then use our results to compute expectation values for the system that help to characterize the nature of the quantum phase transition between the symmetric and broken phases.

We consider the distribution $P(\varphi )$ of the Hatano-Sasa entropy, $\varphi$, in reversible and irreversible processes, finding that the Crooks relation for the ratio of the probability density functions of the forward and backward processes, $P_F(\varphi )/P_R(-\varphi )=e^{\varphi }$, is satisfied not only for reversible, but also for irreversible processes, in general, in the adiabatic limit of “slow processes.” Focusing on systems with a finite set of discrete states (and no absorbing states), we observe that two-state systems always fulfill detailed balance, and obey the Crooks relation. We also identify a wide class of systems, with more than two states, that can be “coarse grained” into two-state systems and obey the Crooks relation despite their irreversibility and violation of detailed balance. We verify these results in selected cases numerically.

We develop a microscopic theoretical framework for the time-dependent pair distribution function starting from the Liouville equation. An exact Zwanzig-Mori equation of motion for the time-dependent pair distribution function is derived based on the projection-operator formalism. It is demonstrated that, under the Markovian approximation, our equation reduces to the so-called telegraph equation that includes the potential of mean force acting between the pair particles. With the additional approximation neglecting the inertia term, our equation takes the form of Smoluchowski’s equation, which has been previously introduced with intuitive arguments and shown to satisfactorily reproduce the simulation results of the particle-pair dynamics.

We investigate the mixing of bidisperse distributions of spherical particles for slowly rotating vanes by pouring smaller beads, diameter $d_1$, onto a monodisperse bed composed of larger beads, diameter $d_0$, and monitoring the torque and lift forces. If the mixing beads are too small, $d_1/d_0<0.05$, the drag and lift are unaltered. Otherwise smaller beads displace larger beads from the shearing region, and if present in sufficient quantity both the drag and lift diminish to values of a monodisperse bed composed entirely of the smaller beads. We observe reductions in the torque up to 70%. The rate at which smaller beads leave the shearing region decreases as their size relative to the larger beads increases, and for $d_1/d_0>0.155$ the smaller beads remain inside the shearing region.

In this paper, a general equation of state (EOS) valid for fluids in the vicinity of the glass transition is derived on the basis of its isothermal precursor. This EOS is able to predict the density scaling of both isobaric and isothermal PVT data and it explicitly involves the scaling exponent ${\gamma }_{\mathrm{EOS}}$, which is most likely straightforwardly related to the exponent of the inverse power law of some effective potential valid for viscous systems. This EOS and the density scaling are very successfully tested for representatives of several material classes (van der Waals liquids, polymer melts, ionic liquids, and even strongly hydrogen-bonded systems). Additionally, if the thermodynamic scaling of primary relaxation times can be achieved with the scaling exponent $\gamma$ for a given material, then the value ${\gamma }_{\mathrm{EOS}}$ found from fitting its PVT data to the EOS enables us to evaluate the value $\gamma$, which is always considerably smaller than ${\gamma }_{\mathrm{EOS}}$.

We solve numerically the equations of nonlinear fluctuating hydrodynamics (NFH). A coarse graining of the density field is applied at each time step to avoid instabilities which otherwise plague the algorithm at long times. The equilibrium correlation of the density fluctuations at different times obtained directly from the solutions of the NFH equations are shown here to be in quantitative agreement with corresponding molecular dynamics simulation data. Low-order perturbative treatment of the these NFH equations obtains the mode coupling model. The latter has been widely studied for understanding the slow dynamics characteristic of the supercooled state. A crucial aspect of this theory is a rounded version of a possible ergodic-nonergodic transition in the supercooled liquid at a temperature $T_c$ between melting point $T_m$ and the glass transition temperature $T_g$. In the present work we demonstrate numerically the role of strongly coupled density fluctuations in giving rise to slow dynamics and how the $1/\rho$ nonlinearity in the NFH equations of motion is essential in restoring the ergodic behavior in the liquid. The relaxation data indicate that at moderate supercooling near $T_c$, the time temperature superposition holds. The relaxation gets increasingly stretched with increased supercooling. The relaxation time $\tau$ shows an initial power-law divergence approaching a transition temperature $T_c$ generally identified as the mode coupling temperature. From the direct solutions we obtain a value for $T_c$ much lower than that typically estimated from solution of low-order integral equations of mode coupling theory. This is in agreement with the trend seen in computer simulations.

Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition-state theory, we predict the rate of this plectoneme nucleation to be of order ${10}^4$ Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscous drag on the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free-energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder.

We study the nucleation dynamics of the Ising model in a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in real-world networks. By introducing a variant of a recently developed forward flux sampling method, we efficiently calculate the rate and elucidate the pathway for the nucleation process. It is found that as the network modularity worsens the nucleation undergoes a transition from a two-step to one-step process. Interestingly, the nucleation rate shows a nonmonotonic dependence on the modularity, in which a maximal nucleation rate occurs at a moderate level of modularity. A simple mean-field analysis is proposed to qualitatively illustrate the simulation results.

Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli maps, analytic results are derived for the stability of the chaotic synchronization manifold. For a single delay time, chaos synchronization is related to the spectral gap of the coupling matrix. For networks with multiple delay times, analytic results are obtained from the theory of polynomials. Finally, the analytic results are compared with networks of iterated tent maps and Lang-Kobayashi equations, which imitate the behavior of networks of semiconductor lasers.