We analyze the equations governing the evolution of distributions of the work and the heat exchanged with the environment by a manipulated stochastic system, by means of a compact and general derivation. We obtain explicit solutions for these equations for the case of a dragged Brownian particle in a harmonic potential. We successfully compare the resulting predictions with the outcomes of experiments, consisting of dragging a micron-sized colloidal particle through water with a laser trap.

We consider the reversible adsorption of particles (monomers with exclusion nearest-neighbor sites) on a one-dimensional lattice, where adsorption occurs on a finite fraction of sites selected randomly. By comparing this one-dimensional system to the pure system where all sites are available for adsorption, we show that when the activity goes to infinity, there exists a mapping between this model and the pure system at the same density. By examining the susceptibilities, we demonstrate that there is no mapping at finite activity. However, when the site density is small or moderate, the mapping exists up to second order in site density. We also propose and evaluate approximate approaches that may be applied to systems where no analytic result is known.

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest descent dynamics, determining for each disorder sample the transition links appearing within a given barrier height. We find that differences between linked inherent structures are typically associated with local clusters of spins; we interpret this within a framework based on droplets in which the characteristic “length scale” grows with the barrier height. We also consider the network connectivity and the degrees of its nodes. Interestingly, for spin glasses based on random graphs, the degree distribution of the network of inherent structures exhibits a nontrivial scale-free tail.

We study real-space condensation phenomena in types of classical stochastic processes (site-particle system), such as zero-range processes and urn models. We study a stochastic process in the Ehrenfest class, i.e., particles in a site are distinguishable. In terms of the statistical mechanical analog, the Ehrenfest class obeys the Maxwell-Boltzmann statistics. We analytically clarify conditions for condensation phenomena in disordered cases in the Ehrenfest class. In addition, we discuss the preferential urn model as an example of the disordered urn model. It becomes clear that the quenched disorder property plays an important role in the occurrence of the condensation phenomenon in the preferential urn model. It is revealed that the preferential urn model shows three types of condensation depending on the disorder parameters.

We discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose-Einstein condensation. Starting from the Landsberg recursion relation for the canonic partition function, we use elementary considerations to show that in a box of size $L^3$ the sum of the cycle probabilities of length $k⪢L^2$ equals the off-diagonal long-range order parameter in the thermodynamic limit. For arbitrary systems of ideal bosons, the integer derivative of the cycle probabilities is related to the probability of condensing $k$ bosons. We use this relation to derive the precise form of the ${\pi }_k$ in the thermodynamic limit. We also determine the function ${\pi }_k$ for arbitrary systems. Furthermore, we use the cycle probabilities to compute the probability distribution of the maximum-length cycles both at $T=0$, where the ideal Bose gas reduces to the study of random permutations, and at finite temperature. We close with comments on the cycle probabilities in interacting Bose gases.

We perform molecular dynamics simulations of water using the five-site transferable interaction potential (TIP5P) model to quantify structural order in both the first shell (defined by four nearest neighbors) and second shell (defined by twelve next-nearest neighbors) of a central water molecule. We find that the anomalous decrease of orientational order upon compression occurs in both shells, but the anomalous decrease of translational order upon compression occurs mainly in the second shell. The decreases of translational order and orientational order upon compression (called the “structural anomaly”) are thus correlated only in the second shell. Our findings quantitatively confirm the qualitative idea that the thermodynamic, structural, and hence dynamic anomalies of water are related to changes upon compression in the second shell.

In this paper we investigate the influence of chiral and achiral dopants on a chiral smectic liquid crystal material, which exhibits a rich phase sequence, including the antiferroelectric phase and the three-layer intermediate smectic $\left(\mathrm{Sm}C^{*}{}_{\mathrm{FI}1}\right)$ phase. Using polarized optical microscopy, differential scanning calorimetry, and x-ray diffraction we find that small amounts of achiral dopant have the ability to significantly broaden the $\mathrm{Sm}C^{*}{}_{\mathrm{FI}1}$ phase, whereas an oppositely-handed dopant (otherwise identical to the host material) destabilizes the phase. This work clearly indicates that bulk chirality strongly influences $\mathrm{Sm}C^{*}{}_{\mathrm{FI}1}$ phase formation and that steric effects also play an important role. Interestingly, addition of the shorter achiral molecule (8CB) was observed to increase the smectic layer spacing, most likely by suppressing interdigitation of alkyl chains between adjacent smectic layers. Control of the $\mathrm{Sm}C^{*}{}_{\mathrm{FI}1}$ phase width using mixtures in this way is clearly important for effective phase characterization, and could potentially lead to commercially viable materials with a stable $\mathrm{Sm}C^{*}{}_{\mathrm{FI}1}$ phase over a large temperature range.

Proteins are known to locate their specific targets on DNA up to two orders of magnitude faster than predicted by the Smoluchowski three-dimensional diffusion rate. One of the mechanisms proposed to resolve this discrepancy is termed “intersegment transfer.” Many proteins have two DNA binding sites and can transfer from one DNA segment to another without dissociation to water. We calculate the target search rate for such proteins in a dense globular DNA, taking into account intersegment transfer working in conjunction with DNA motion and protein sliding along DNA. We show that intersegment transfer plays a very important role in cases where the protein spends most of its time adsorbed on DNA.

We develop a technique for reconstructing the phase dynamics equations for weakly coupled oscillators from data. We show how, starting from general scalar observables, one can first reconstruct the dynamics in terms of the corresponding protophases, and then, performing a transformation to the genuine, observable-independent phases, obtain an invariant description of the phase dynamics. We demonstrate that natural frequencies of oscillators can be recovered if several observations of coupled systems at different coupling strengths are available. We apply our theory to numerical examples and to a physical experiment with coupled metronomes.

The equation describing the propagation of a mode driven by external currents in an inhomogeneous dielectric is derived from the principle of the conservation of wave energy density and wave momentum density. The wave amplitude in steady state is obtained in terms of a simple spatial integration of the driving current. The contribution from the spatial derivative of the dielectric response is found to be important. The analytical predictions are verified through comparison with $\delta f$ particle-in-cell computations of electron Bernstein wave propagation, thus showing applicability to kinetic systems.

Proton trapping and acceleration by an electron bubble-channel structure in laser interaction with high-density plasma is investigated by using three-dimensional particle-in-cell simulations. It is shown that protons can be trapped, bunched, and efficiently accelerated for appropriate laser and plasma parameters, and the proton acceleration is enhanced if the plasma consists mainly of heavier ions such as tritium. The observed results are analyzed and discussed in terms of a one-dimensional analytical three-component-plasma wake model.

Volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is a time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data by assuming that it is described by a hidden Markov process which together with the price forms a two-dimensional diffusion process. We derive a maximum-likelihood estimate of the volatility path valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are that (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model, (ii) the estimated volatility is related to trading volume by a power law of the form $\sigma \propto V^{0.55}$, and (iii) future returns are proportional to the current volatility, which suggests some degree of predictability for the size of future returns.

The asymptotic stability of spatiotemporal chaos is difficult to determine, since transient spatiotemporal chaos may be extremely long lived. A master stability analysis reveals that the asymptotic state of transient spatiotemporal chaos in the Gray-Scott system and in the Bär-Eiswirth system is characterized by negative transverse Lyapunov exponents on the attractor of the invariant synchronization manifold. The average lifetime of transient spatiotemporal chaos depends on the number of transverse directions that are unstable along a typical excitation cycle.

The postprocesses that occur in coelectrospun polymer nanofibers are investigated. The high rate of solvent evaporation during the electrospinning of fibers results in such a rapid formation of the shell of the tubular nanofibers, that the polymer molecules composing the fibers are in a nonequilibrium state. This stretched state of macromolecules is assumed to be stabilized in a solid matrix, and can account for the anomalous properties of the nanofibers. During this processing stage a considerable amount of solvent remains inside the tubular nanofibers. The evaporation of the solvent continues for several minutes, and is accompanied by further evolution of the nanofibers in both their microstates and macrostates. In this paper, we examine possible macrostate modifications of the nanofibers, such as radial buckling. The theoretical model which describes the kinetics of the solvent evaporation is found to be in good agreement with experimental observations. Thus, the physical parameters of the system in question can be estimated, and the conditions of fiber shell instability that produce buckling of the tubular nanofibers can also be predicted.

Visualization experiments of rate-controlled immiscible displacement of oil by water are performed on a model porous medium of controlled fractional wettability, fabricated by mixing water-wet glass microspheres with strongly oil-wet polytetrafluoroethylene microspheres and packing them between two transparent glass plates. The growth pattern is video recorded and the transient response of the pressure drop across the pore network is measured for various fractions of oil-wet particles. The space-averaged capillary pressure coincides to the pressure drop measured across the porous medium. The oscillating transient signal of the capillary pressure is analyzed with multilevel wavelets to produce the best level wavelet details or best level capillary pressure spectrum (BLCPS) by minimizing the “entropy” of wavelet approximation. Invasion of water in oil-wet areas is reflected in high-frequency and low-amplitude fluctuations of the BLCPS. Correspondingly, invasion of water in water-wet areas is associated with low-frequency and high-amplitude fluctuations of the BLCPS. The displacement growth pattern is reflected in the “energy” and “frequency” of the BLCPS which along with the time-averaged capillary pressure are correlated with two parameters quantifying the spatial variation of wettability over the porous medium: the frontal wettability of the active interface of the fluids before each invasion step and the regional wettability of the area invaded by the displacing fluid.

Microfluidic chips have been fabricated in Pyrex glass to study electrokinetic pumping generated by a low-voltage ac bias applied to an in-channel asymmetric metallic electrode array. A measurement procedure has been established and followed carefully resulting in a high degree of reproducibility of the measurements over several days. A large coverage fraction of the electrode array in the microfluidic channels has led to an increased sensitivity allowing for pumping measurements at low bias voltages. Depending on the ionic concentration a hitherto unobserved reversal of the pumping direction has been measured in a regime, where both the applied voltage and the frequency are low, $V_{\mathrm{rms}}<1.5\mathrm{V}$ and $f<20\mathrm{kHz}$, compared to previously investigated parameter ranges. The impedance spectrum has been thoroughly measured and analyzed in terms of an equivalent circuit diagram to rule out trivial circuit explanations of our findings. Our observations agree qualitatively, but not quantitatively, with theoretical electrokinetic models published in the literature.

The dynamics and linear stability of a liquid film flowing over a locally heated surface are studied using a long-wave lubrication analysis. The temperature gradient at the leading edge of the heater induces a gradient in surface tension that opposes the gravitationally driven flow and leads to the formation of a pronounced capillary ridge. The resulting free-surface shapes are computed, and their stability to spanwise perturbations is analyzed for a range of Marangoni numbers, substrate inclination angles, and temperature profiles. Instability is predicted above a critical Marangoni number for a finite band of wave numbers separated from zero, which is consistent with published results from experiment and direct numerical simulation. An energy analysis is used to gain insight into the effect of inclination angle on the instability. Because the spatial nonuniformity of the base state gives rise to nonnormal linearized operators that govern the evolution of perturbations, a nonmodal, transient analysis is used to determine the maximum amplification of small perturbations to the film. The structure of optimal perturbations of different wave numbers is computed to elucidate the regions of the film that are most sensitive to perturbations, which provides insight into ways to stabilize the flow. The results of this analysis are contrasted to those for noninertial coating flows over substrates with topographical features, which exhibit similar capillary ridges but are strongly stable to perturbations.

The reflection of plane waves on a perfectly reflecting surface is a well-known phenomenon in physics. This particular case of the famous Snell-Descartes laws, also called mirror reflection, is valid only for linear waves. For nonlinear shock waves, it is known that this law breaks for sufficiently grazing angles. This paper provides some experimental evidence of this phenomenon for amplitude more than 100 times as small as in previous measurements in air. This is achieved by means of ultrasonic periodic shock waves in water. For grazing angles (typically from 0° to 7°) three different patterns exhibiting strong differences with the mirror law can be observed. The first one is the nonlinear regular reflection for which the incident shock and the reflected one merge on the rigid surface but the incident and reflected angles are different. The second pattern looks similar to the Mach reflection in aerodynamics. In this case, three shocks are present: the incident and reflected shocks merge just above the rigid surface into a third one connected to the rigid surface. In the third pattern, only the incident shock is visible. These experimental results are successfully compared with a theory through accurate numerical simulations.

In this work, the electromagnetic interaction of plane waves with infinitely long metamaterial-coated conducting cylinders is considered. Different from “conjugate” pairing of double-positive (DPS) and double-negative (DNG) or epsilon-negative (ENG) and mu-negative (MNG) concentric cylinders, achieving transparency and maximizing scattering are separately achieved by covering perfect electric conductor (PEC) cylinders with simple (i.e., homogeneous, isotropic, and linear) metamaterial coatings. The appropriate constitutive parameters of such metamaterials are investigated for Transverse Magnetic (TM) and in particular for Transverse Electric (TE) polarizations. For TE polarization it is found out that the metamaterial-coating permittivity has to be in the $0<{\epsilon }_c<{\epsilon }_0$ interval to achieve transparency, and in the $-{\epsilon }_0<{\epsilon }_c<0$ interval to achieve scattering maximization. However, unlike the “conjugate” pairing of DPS-DNG or ENG-MNG cases, when the transparency for metamaterial-coated PEC cylinders are considered, the analytically found relation between ${\epsilon }_c$ and the ratio of core-coating radii, $\gamma$, should be modified in a sense that scattering from the PEC core is canceled by the coating. Furthermore, replacing $\epsilon$ by $\mu$ (and vice versa) does not lead to the same conclusions for TM polarization unless the PEC cylinder is replaced by a perfect magnetic conductor (PMC) cylinder. On the other hand, scattering maximization can also be achieved in the TM polarization case when coating permeability ${\mu }_c<0$, whereas transparency requires large $\mid {\mu }_c\mid$ for this polarization. Numerical results in the form of normalized monostatic and bistatic echo widths, which demonstrate the transparency and scattering maximization phenomena, are given and possible application areas are discussed.

We show that the frequency range of the zero averaged refractive index gap in a photonic heterostructure containing negative-index materials can be enlarged owing to the property that its lower and upper frequency edges depend on the thickness ratio of the positive- and negative-index materials. Compared to the zero averaged refractive index gap of a single photonic crystal, the frequency range of the zero averaged refractive index gaps in a photonic heterostructure can be notably enlarged. Moreover, it is shown that the band edge of the zero averaged refractive index gap is determined not only by the TM polarization but also by the TE polarization, which is obviously different from the omnidirectional band gaps in conventional photonic crystals, whose bandwidth is determined by the TM polarization.