We describe some solvable models which illustrate the Jarzynski theorem and related fluctuation theorems. We consider a charged particle in the presence of a magnetic field in a two-dimensional harmonic well. In the first case the center of the harmonic potential is translated with a uniform velocity, while in the other case the particle is subjected to an ac force. We show that the Jarzynski identity complements the Bohr–van Leeuwen theorem on the absence of diamagnetism in an equilibrium classical system.

We analyze the phenomenon of low-frequency signal enhancement in a bistable system excited by a sum of low-frequency and high-frequency harmonic signals. A mechanism alternate to chaotic resonance is discussed. It is shown that a high-frequency signal may generate interwell transitions of subharmonic frequency. If the frequency of the slow signal is equal or close to a subharmonic frequency of the fast signal, then the improvement of the low-frequency constituent in the output spectrum is due to sustained subharmonic resonance.

An alternative Monte Carlo estimator for the one-body density $\rho \left(\mathbf{r}\right)$ is presented. This estimator has a simple form and can be readily used in any type of Monte Carlo simulation. Comparisons with the usual regularization of the delta-function on a grid show that the statistical errors are greatly reduced. Furthermore, our expression allows accurate calculations of the density at any point in space, even in the regions never visited during the Monte Carlo simulation. The method is illustrated with the computation of accurate variational Monte Carlo electronic densities for the Helium atom (one-dimensional curve) and for the water dimer (three-dimensional grid containing up to $51\times 51\times 51=132651$ points).

In this paper we implement a Fourier method to estimate high-frequency correlation matrices from small data sets. The Fourier estimates are shown to be considerably less noisy than the standard Pearson correlation measures and thus capable of detecting subtle changes in correlation matrices with just a month of data. The evolution of correlation at different time scales is analyzed from the full correlation matrix and its minimum spanning tree representation. The analysis is performed by implementing measures from the theory of random weighted networks.

We give a theoretical explanation of the formation of the curved macropatterns in the recurrence plots of sinusoidal signals, with nonstationarity in the phase or in the frequency. We show that the large time scales observed and the curved structures are the artificial product of the discretization of the signal. Recurrence plots are highly sensitive to the phase error introduced by the sampling, and we show that this characteristic can be used to detect very small $(\sim 0.5\%)$ phase or frequency shifts of the carrier frequency.

Light emission from a dielectric cavity with a stadium shape is studied in both ray and wave models. For a passive cavity mode with low loss, a remarkable correspondence is found between the phase space representation of a quasibound wave function and its counterpart distribution in the ray model. This result provides additional and more direct evidence for good ray-wave correspondence in low-loss modes previously observed at the level of far-field emission pattern comparisons.

Recovering trajectories of quantum systems whose classical counterparts display chaotic behavior has been a subject that has received a lot of interest over the last decade. However, most of these studies have focused on driven and dissipative systems. The relevance and impact of chaoticlike phenomena to quantum systems has been highlighted in recent studies which have shown that quantum chaos is significant in some aspects of quantum computation and information processing. In this paper we study a three-body system comprising of identical particles arranged so that the system’s classical trajectories exhibit Hamiltonian chaos. Here we show that it is possible to recover very nearly classical-like, conservative, chaotic trajectories from such a system through an unravelling of the master equation. First, this is done through continuous measurement of the position of each system. Second, and perhaps somewhat surprisingly, we demonstrate that we still obtain a very good match between the classical and quantum dynamics by weakly measuring the position of only one of the oscillators.

The Winfree model consists of a population of globally coupled phase oscillators with randomly distributed natural frequencies. As the coupling strength and the spread of natural frequencies are varied, the various stable states of the model can undergo bifurcations, nearly all of which have been characterized previously. The one exception is the unlocking transition, in which the frequency-locked state disappears abruptly as the spread of natural frequencies exceeds a critical width. Viewed as a function of the coupling strength, this critical width defines a bifurcation curve in parameter space. For the special case where the frequency distribution is uniform, earlier work had uncovered a puzzling singularity in this bifurcation curve. Here we seek to understand what causes the singularity. Using the Poincaré-Lindstedt method of perturbation theory, we analyze the locked state and its associated unlocking transition, first for an arbitrary distribution of natural frequencies, and then for discrete systems of $N$ oscillators. We confirm that the bifurcation curve becomes singular for a continuum uniform distribution, yet find that it remains well behaved for any finite $N$, suggesting that the continuum limit is responsible for the singularity.

Characteristic burtsing behavior is observed in a driven, two-dimensional viscous flow, confined to a square domain and subject to no-slip boundaries. Passing a critical parameter value, an existing chaotic attractor undergoes a crisis, after which the flow initially enters a transient bursting regime. Bursting is caused by ejections from and return to a limited subdomain of the phase space, whereas the precrisis chaotic set forms the asymptotic attractor of the flow. For increasing values of the control parameter the length of the bursting regime increases progressively. Passing another critical parameter value, a second crisis leads to the appearance of a secondary type of bursting, of very large dynamical range. Within the bursting regime the flow then switches in irregular intervals from the primary to the secondary type of bursting. Peak enstrophy levels for both types of bursting are associated to the collapse of a primary vortex into a quadrupolar state.

Miscible flow displacements of a ferrofluid droplet subjected to various magnetic field configurations and confined in a time-dependent gap Hele-Shaw cell are examined through highly accurate numerical simulations. The interplay between lifting, miscibility, and applied magnetic fields resulted in complex interfacial pattern formation. By varying the symmetry properties of the applied magnetic fields and by considering the action of Korteweg stresses, a number of interesting droplet morphologies are identified and characterized. The possibility of controlling the degree of fluid mixing and the ultimate shape of the emerging patterns by appropriately adjusting the strength of the applied magnetic fields is also discussed.

We present frames from high-speed videos of the pinch-off of liquid ${}^4\mathrm{He}$ droplets. The temperature of the fluid droplets ranged from $1.33\mathrm{K}\text{to}4.8\mathrm{K}$, and the size of the drops was proportional to the temperature-dependent capillary length. We observed no qualitative difference between pinch-off in the normal and superfluid states. In both cases, the shape of the fluid in the final stages of pinch-off resembles a cone piercing a sphere, which is typical of other low-viscosity fluids. The evolution of the minimum neck radius $r_{\mathit{min}}$ can be characterized by power laws $r_{\mathit{min}}\propto {\tau }^n$, where $\tau$ is the time remaining until pinch-off occurs. In the regime near pinch-off, the data from image analysis are consistent with $n=2∕3$. The data at the beginning of the pinch process when the neck is of the order of the capillary length are also described by $n=2∕3$, but with a different proportionality factor. There is an intermediate crossover regime characterized by $n=2∕5$.

This paper deals with the application of steam to enhance the recovery from petroleum reservoirs. We formulate a mathematical and numerical model that simulates coinjection of volatile oil with steam into a porous rock in a one-dimensional setting. We utilize the mathematical theory of conservation laws to validate the numerical simulations. This combined numerical and analytical approach reveals the detailed mechanism for thermal displacement of oil mixtures discovered in laboratory experiments. We study the structure of the solution, determined by the speeds and amplitudes of the several nonlinear waves involved. Thus we show that the oil recovery depends critically on whether the boiling-point of the volatile oil is around the water boiling temperature, or much below or above it. These boiling-point ranges correspond to three types of wave structures. When the boiling point of the volatile oil is near the boiling point of water, the striking result is that the speed of the evaporation front is equal or somewhat larger than the speed of the steam condensation front. Thus the volatile oil condenses at the location where the steam condenses too, yielding virtually complete oil recovery. Conversely, if the boiling point is too high or too low, there is incomplete recovery. The condensed volatile oil stays at the steam condensation location because the steam condensation front is a physical shock.

Degenerate four-wave mixing mediated by ponderomotive-force-driven plasma gratings is demonstrated in the near-infrared regime. The quadratic dependence of the reflectivity of the probe pulse on plasma density indicates that the mixing is caused by the quasineutral plasma grating driven by the laser ponderomotive force. The experiment verifies that ponderomotive force is an effective means to produce a large-amplitude short-period plasma grating, which has many important applications in ultrahigh-intensity optics. In particular, such a grating is a crucial element for the development of plasma phase-conjugate mirrors that can be used to restore the wave-front distortion that is ubiquitous in nonlinear propagation.

The objective of this work is to investigate in which circumstances the scattering of electromagnetic waves by a thin metamaterial slab can be characterized using known effective parameters of the associated unbounded periodic bulk medium. It is proved that the classical approach or classical boundary conditions may become less accurate or incomplete if the size of inclusions is not significantly smaller than the wavelength. To circumvent this problem we demonstrate that the interaction of waves with metamaterial structures may in many cases with practical interest be conveniently described using a transverse averaged-field technique, and that this approach can be very accurate even for wide incident angles, evanescent waves, and for large and moderately large wavelengths.

We present a Monte Carlo (MC) scheme that makes it possible to perform efficient simulations of dense systems of self-avoiding polymers on a lattice. We show that the method is particularly useful to simulate dense systems of polymers with functionalized end groups. We compare the efficiency of the scheme with the configurational bias MC method and indicate the regime where the present approach is the method of choice.

We present an experimental study of the electric field distributions $E_N$ of a three-dimensional (3D) microwave chaotic rough billiard with the translational symmetry. The translational symmetry means that the cross section of the billiard is invariant under translation along the $z$ direction. The 3D electric field distributions were measured up to the level number $N=489$. In this way the experimental spatial correlation functions $C_{N,p}(\mathbf{x},\mathbf{s})\propto ⟨E_{N,p}(\mathbf{x}+\frac{1}{2}\mathbf{s})E_{N,p}^{*}(\mathbf{x}-\frac{1}{2}\mathbf{s})⟩$ were found and compared with the theoretical ones. The experimental results for higher two-dimensional level number $N_{\perp }$ appeared to be in good agreement with the theoretical predictions.

This paper contains an important message regarding the numerical modeling of left-handed media (LHM) using the finite-difference time-domain (FDTD) method which remains at the moment one of the main techniques used in studies of these exotic materials. It is shown that conventional implementation of the dispersive FDTD method leads to an inaccurate description of evanescent waves in the LHM. This defect can be corrected using spatial averaging at the interfaces. However, a number of results obtained using the conventional FDTD method have to be reconsidered. For instance, accurate simulation of subwavelength imaging by the finite-sized slabs of left-handed media does not reveal the cavity effect reported by Chen et al. [Phys. Rev. Lett. 92, 107404 (2004)]. Hence the finite transverse dimension of LHM slabs does not have significant effects on the subwavelength image quality, contrary to previous assertions.

The influence of an external magnetic field on the non-Markovian dynamics of an open two-dimensional quantum system is investigated. The fluctuations of collective coordinate and momentum and transport coefficients are studied for a charged harmonic oscillator linearly coupled to a neutral bosonic heat bath. It is shown that the dissipation of collective energy slows down with increasing strength of the external magnetic field. The role of magnetic field in the diffusion processes is illustrated by several examples.

Typical features of glass phenomenology such as the Vogel-Fulcher law, the Kauzmann paradox, and the Adam-Gibbs relationship are shown to follow from the recently discovered mapping of glasses to Ising spin glasses in a magnetic field. There seems to be sufficient universality near the glass transition temperature $T_g$ such that study of the spin-glass system can provide semiquantitative results for supercooled liquids.

Recently there has been a strong interest in the area of defect formation in ordered structures on curved surfaces. Here we explore the closely related topic of self-assembly in thin block copolymer melt films confined to the surface of a sphere. Our study is based on a self-consistent field theory (SCFT) model of block copolymers that is numerically simulated by spectral collocation with a spherical harmonic basis and an extension of the Rasmussen-Kalosakas operator splitting algorithm [J. Polym. Sci. Part B: Polym. Phys. 40, 1777 (2002)]. In this model, we assume that the composition of the thin block copolymer film varies only in longitude and colatitude and is constant in the radial direction. Using this approach we are able to study the formation of defects in the lamellar and cylindrical phases, and their dependence on sphere radius. Specifically, we compute ground-state (i.e., lowest-energy) configurations on the sphere for both the cylindrical and lamellar phases. Grain boundary scars are also observed in our simulations of the cylindrical phase when the sphere radius surpasses a threshold value $R_c\approx 5d$, where $d$ is the natural lattice spacing of the cylindrical phase, which is consistent with theoretical predictions [Bowick et al., Phys. Rev. B 62, 8738 (2000); Bausch et al., Science 299, 1716 (2003)]. A strong segregation limit approximate free energy is also presented, along with simple microdomain packing arguments, to shed light on the observed SCFT simulation results.