We present a small and compact two-color cross-correlation light-scattering setup designed to study the structure and dynamics of colloidal suspensions in the regime of considerable turbidity. Using a homemade concentric four-arm goniometer, combined with fiber-optical illumination and detection devices, allows an easy and long time stable alignment—even under a temperature variation of ∼5 °C. Tests with a nearly multiple scattering free suspension of small Rayleigh scatterers show intercepts in cross correlation near 0.4 over a wide range of scattering angles from 20° to 150°. Measuring slightly turbid samples in cross-correlation mode multiple scattering is sufficiently suppressed allowing the determination of multiple scattering free dynamic structure factors as well as particle form factors.

We present a method for designing an appropriate coupling scheme for two dynamical systems in order to realize extreme multistability. We achieve the coexistence of infinitely many attractors for a given set of parameters by using the concept of partial synchronization based on Lyapunov function stability. We show that the method is very general and allows a great flexibility in choosing the coupling. Furthermore, we demonstrate its applicability in different models, such as the Rössler system and a chemical oscillator. Finally we show that extreme multistability is robust with respect to parameter mismatch and, hence, a very general phenomenon in coupled systems.

Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading paths in real-world networks. One is the practical difficulty of observing a dynamic process on a network, and the other is the typical constraint of only partially observing a network. Using static, structurally realistic social networks as platforms for simulations, we juxtapose three distinct paths: (1) the stochastic path taken by a simulated spreading process from source to target; (2) the topologically shortest path in the fully observed network, and hence the single most likely stochastic path, between the two nodes; and (3) the topologically shortest path in a partially observed network. In a sampled network, how closely does the partially observed shortest path (3) emulate the unobserved spreading path (1)? Although partial observation inflates the length of the shortest path, the stochastic nature of the spreading process also frequently derails the dynamic path from the shortest path. We find that the partially observed shortest path does not necessarily give an inflated estimate of the length of the process path; in fact, partial observation may, counterintuitively, make the path seem shorter than it actually is.

Jarzynski's equality (JE) allows us to compute free-energy differences from distributions of work. In molecular dynamics simulations, the traditional way of constructing work distributions is to perform as many pulling simulations as possible. But reliable work distributions are not always produced in a finite number of simulations. The computational cost of using JE is not less than other commonly used methods such as thermodynamic integration and umbrella sampling methods. Here we first show a different proof of JE based on the idea of stepwise pulling procedures that is efficient in computing free energies by using JE. The key point in our proof is that the processes of turning on or off a harmonic potential to perform work are described by double Heaviside functions of time. We then show that the distributions of work performed by the potential can be easily generated from the distributions of a reaction coordinate along a pathway. Based on the proof, we propose sequential and parallel stepwise pulling protocols for generating work distributions that require suitable relaxation time at each pulling step. The criterion for reliable work distributions is that there must be sufficient mutual overlaps between the adjacent distributions of the reaction coordinate along the pathway. We arrive at an alternative formula (besides JE) to compute free-energy differences from the averaged values of the reaction coordinate. The combination of JE and the alternative formula provides a viable way to determine the accuracy of computed free-energy differences. For the stretching of a deca-alanine molecule, our approach requires 21 parallel simulations and relaxation time as small as 0.4 ns for each simulation to estimate free-energy differences with an uncertainty of about 13$\%$.

A class of compact second-order finite difference algorithms is proposed for solving steady-state laminar natural convection in a square cavity using the stream-function–velocity ($\psi -u$) form of Navier-Stokes equations. The stream-function–velocity equation and the energy equation are all solved as a coupled system of equations for the four field variables consisting of stream function, two velocities, and temperature. Two strategies are considered for the discretizaton of the temperature equation, which are a second-order five-point compact scheme and a fourth-order nine-point compact scheme, respectively. The numerical capability of the presented algorithm is demonstrated by the application to natural convection in a square enclosure for a wide range of Rayleigh numbers (from ${10}^3$ to ${10}^8$) and compared with some of the accurate results available in the literature. The presented schemes not only show second-order accurate, but also prove effective. For larger Rayleigh numbers, the algorithm combining the second-order compact scheme for the stream-function–velocity equation with the fourth-order compact scheme for the temperature equation performs more stably and effectively.

We introduce a generalized loop move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's low-energy states consist of an extensive number of degenerate or near-degenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and near-degenerate sets of configurations are favored at low temperatures. The GLM update's potential to be straightforwardly extended to different lattices and spin interactions allows it to be readily adopted on many other frustrated Ising models of physical relevance.

We study the smectic-$A$–smectic-$C$ phase transition in biaxial disordered environments, e.g., fully anisotropic aerogel. We find that both the $A$ and $C$ phases belong to the universality class of the “$XY$ Bragg glass,” and therefore have quasi-long-ranged translational smectic order. The phase transition itself belongs to a new universality class, which we study using an $\epsilon =7/2-d$ expansion. We find a stable fixed point, which implies a continuous transition, the critical exponents of which we calculate.

We present an analysis of the price impact associated with single trades effected by different financial firms. Using data from the Spanish Stock Market, we find a high degree of heterogeneity across different market members, both in the instantaneous impact functions and in the time-dependent market response to trades by individual members. This heterogeneity is statistically incompatible with the existence of market-wide universal impact dynamics that apply uniformly to all trades and suggest that, rather, market dynamics emerge from the complex interaction of different behaviors of market participants. Several possible reasons for this are discussed, along with potential extensions one may consider to increase the range of applicability of existing models of market impact.

For a class of integrate-and-fire, pulse-coupled networks with complex topology, we study the dependence of the pulse rate on the underlying architectural connectivity statistics. We derive the distribution of the pulse rate from this dependence and determine when the underlying scale-free architectural connectivity gives rise to a scale-free pulse-rate distribution. We identify the scaling of the pairwise coupling between the dynamical units in this network class that keeps their pulse rates bounded in the infinite-network limit. In the process, we determine the connectivity statistics for a specific scale-free network grown by preferential attachment.

The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports results regarding the properties of accessibility, including its relationship with the average minimal time to visit all nodes reachable after $h$ steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the exploration time), conjecture that the maximum accessibility implies the minimal exploration time, and confirm the relationship between the accessibility values and the number of nodes visited after a basic time unit. The latter relationship is investigated with respect to three types of dynamics: traditional random walks, self-avoiding random walks, and preferential random walks.

Kicked atoms under a constant Stark or gravity field are investigated for experimental setups with cold and ultracold atoms. The parametric stability of the quantum dynamics is studied using the fidelity. In the case of a quantum resonance, it is shown that the behavior of the fidelity depends on arithmetic properties of the gravity parameter. Close to a quantum resonance, the long-time asymptotics of the fidelity is studied by means of a pseudoclassical approximation introduced by Fishman et al. [J. Stat. Phys. 110, 911 (2003)]. The long-time decay of fidelity arises from the tunneling out of pseudoclassical stable islands, and a simple ansatz is proposed which satisfactorily reproduces the main features observed in numerical simulations.

We consider an unusual shear layer occuring between two parallel Couette flows. Contrary to the classical free shear layer, the width of the shear zone does not vary in the streamwise direction but rather exhibits a lateral variation. Based on some simplifying assumptions, an analytic solution is derived for this shear layer. These assumptions are justified by a comparison with numerical solutions of the full Navier-Stokes equations, which accord with the analytical solution to better than $1\%$ in the entire domain. An explicit formula is found for the width of the shear zone as a function of the wall-normal coordinate. This width is independent of the wall velocities in the laminar regime. Preliminary results for a cocurrent laminar-turbulent shear layer in the same geometry are also presented. Shear-layer instabilities are then developed and result in an unsteady mixing zone at the interface between the two cocurrent streams.

Nonlinear cubic Euler-Lagrange equations of motion in the traveling variable are usually derived from Ginzburg-Landau free energy functionals frequently encountered in several fields of physics. Many authors considered in the past damped versions of such equations, with the damping term added by hand simulating the friction due to the environment. It is known that even in this damped case kink solutions can exist. By means of a factorization method, we provide analytic formulas for several possible kink solutions of such equations of motion in the undriven and constant field driven cases, including the recently introduced Riccati parameter kinks, which were not considered previously in such a context. The latter parameter controls the delay of the switching stage of the kinks. The delay is caused by antikink components that are introduced in the structure of the solution through this parameter.

The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small correlation lengths in frustrated Ising systems, we develop a method for obtaining first approximations to the energetic properties of frustrated two-dimensional Ising systems using small networks of less than 30 spins. These small networks allow much faster numerical simulations, and more importantly, analytical evaluations of their properties are numerically tractable. We choose Ising systems on the triangular lattice, the kagome lattice, and the triangular kagome lattice as prototype systems and find small systems that can serve as good approximations to these prototype systems. Through comparisons between the properties of extended models and small systems, we develop a set of criteria for constructing small networks to approximate general infinite two-dimensional frustrated Ising systems. This method of using small networks provides a different and efficient way to obtain a first approximation to the properties of frustrated spin systems.

Relaxation of the thermal Casimir or van der Waals force (the high temperature limit of the Casimir force) for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit, the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out-of-equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. For the interaction between dielectric slabs, it is found that the spatial dependence of the out-of-equilibrium force is the same as the equilibrium one, but it has a time dependent amplitude, or Hamaker coefficient, which increases in time to its equilibrium value. The final relaxation of the force to its equilibrium value is exponential in systems with a single or finite number of polarization field relaxation times. However, in systems, such as those described by the Havriliak-Negami dielectric constant with a broad distribution of relaxation times, we observe a much slower power law decay to the equilibrium value.

We examine energy transport in an ensemble of closed quantum systems driven by stochastic perturbations. One can show that the probability and energy fluxes can be described in terms of quantum advection modes (QAMs) associated with the off-diagonal elements of the density matrix. These QAMs play the role of Landauer channels in a system with discrete energy spectrum and the eigenfunctions that cannot be described as plane waves. In order to determine the type of correlations that exist between the direction and magnitudes of each QAM and the average direction of energy and probability fluxes we have numerically solved the time-dependent Schrödinger equation describing a single particle trapped in a parabolic potential well which is perturbed by stochastic ripples. The ripples serve as a localized energy source and are offset to one side of the potential well. As the result a nonzero net energy flux flows from one part of the potential well to another across the symmetry center of the potential. We find that some modes exhibit positive correlation with the direction of the energy flow. Other modes, that carry a smaller energy per unit of the probability flux, anticorrelate with the energy flow and thus provide a backflow of the probability. The overall picture of energy transport that emerges from our results is very different from the conventional one based on a system with continuous energy spectrum.

I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.

A continuous phase transition occurs in the topography of toppling surfaces of stochastic and rotational sandpile models when they are flooded with liquid, say water. The toppling surfaces are extracted from the sandpile avalanches that appear due to sudden burst of toppling activity in the steady state of these sandpile models. Though a wide distribution of critical flooding heights exists, a critical point is defined by merging the flooding thresholds of all the toppling surfaces. The criticality of the transition is characterized by power-law distribution of island area in the critical regime. A finite size scaling theory is developed and verified by calculating several new critical exponents. The flooding transition is found to be an interesting phase transition and does not belong to the percolation universality class. The universality class of this transition is found to depend on the degree of self-affinity of the toppling surfaces characterized by the Hurst exponent $H$ and the fractal dimension $D_f$ of critical spanning islands. The toppling surfaces of different stochastic sandpile models are found to have a single Hurst exponent, whereas those of different rotational sandpile models have another Hurst exponent. As a consequence, the universality class of different sandpile models remains preserved within the same symmetry of the models.

We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field $\mathcal{E}$ and collides, elastically or inelastically, with a bath of particles at temperature $T$. We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production $\Delta s_{\mathrm{tot}}$. One is the entropy production of the medium $\Delta s_m$, which is equal to the energy exchanged with the scatterers, divided by a parameter $\theta$, coinciding with the particle temperature at $\mathcal{E}=0$. The other is the work $W$ done by the external field, again rescaled by $\theta$. At small $\mathcal{E}$, a good collapse of the two distributions is found: in this case, the two quantities also verify the fluctuation relation (FR), indicating that both are good approximations of $\Delta s_{\mathrm{tot}}$. Differently, for large values of $\mathcal{E}$, the fluctuations of $W$ violate the FR, while $\Delta s_m$ still verifies it.