We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for the Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modeling other physical phenomena where rare events play an important role.

A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the minimum number of trials. Here it will be shown that if the searcher must get very close to the target to find it, then the best search distribution is proportional to the square root of the target distribution regardless of dimension. For a Gaussian target distribution, the optimum search distribution is approximately a Gaussian with a standard deviation that varies inversely with how close the searcher must be to the target to find it. For a network where the searcher randomly samples nodes and looks for the fixed target along edges, the optimum is either to sample a node with probability proportional to the square root of the out-degree plus 1 or not to do so at all.

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function $F_{\mathrm{incoh}}(q,t)$ is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function $S(q,\omega )$, we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number $q$ we observe sound waves in the coherent scattering function $S(q,\omega )$ and the longitudinal current correlation function $C_{\mathrm{l}}(q,\omega )$. We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

By shearing electrorheological (ER) fluids between two concentric cylinders, we show a reversible shear thickening of ER fluids above a low critical shear rate (<1 s${}^{-1}$) and a high critical electric field strength ($>100$ V/mm), which can be characterized by a critical apparent viscosity. Shear thickening and electrostatic particle interaction-induced interparticle friction forces are considered to play an important role in the origin of lateral shear resistance of ER fluids, while the applied electric field controls the extent of shear thickening. The electric-field-controlled reversible shear thickening has implications for high-performance electrorheological -magnetorheological fluid design, clutch fluids with high friction forces triggered by applying a local electric field, other field-responsive materials, and intelligent systems.

The quantum and classical dynamics of particles kicked by a Gaussian attractive potential are studied. Classically, it is an open mixed system (the motion in some parts of the phase space is chaotic, and in some parts it is regular). The fidelity (Loschmidt echo) is found to exhibit oscillations that can be determined from classical considerations but are sensitive to phase space structures that are smaller than Planck’s constant. Families of quasienergies are determined from classical phase space structures. Substantial differences between the classical and quantum dynamics are found for time-dependent scattering. It is argued that the system can be experimentally realized by cold atoms kicked by a Gaussian light beam.

The structure of a relativistically hot, strongly magnetized jet is investigated at large distances from the source. Asymptotic equations are derived describing collimation and acceleration of the externally confined jet. Conditions are found for the transformation of the thermal energy into the fluid kinetic energy or into the Poynting flux. Simple scalings are presented for the jet collimation angle and Lorentz factors.

Previous work has demonstrated that combining mechanical vibration with magnetic interactions can result in the self-assembly of complex structures, albeit at low yield. Here we introduce a system where the yield of self-assembled structures is quantitatively predicted by a theoretical analysis. Millimeter-sized magnetic blocks, designed to form chains as their minimal energy state, are placed in a turbulent fluid flow. The distribution of chain lengths that form is quantitatively consistent with predictions, showing that the chain length distribution coincides with that of monomers or polymers in a thermal bath, with the turbulence strength parametrizing the effective temperature.

It has been recently shown that randomly charged surfaces can exhibit-long range electrostatic interactions even when they are net neutral. These forces depend on the specific realization of charge disorder and thus exhibit sample-to-sample fluctuations about their mean value. We analyze the fluctuations of these forces in the parallel slab configuration and in the sphere-plane geometry via the proximity force approximation. The fluctuations of the normal forces, which have a finite mean value, are computed exactly. Surprisingly, we also show that fluctuations in lateral forces are present, despite the fact that they have a zero mean, and that they have the same scaling behavior as the normal force fluctuations. The measurement of these lateral force fluctuations could help us to characterize the effects of charge disorder in experimental systems, leading to estimates of their magnitudes that are complementary to those given by normal force measurements.

Experimental and computational studies on the dynamics of millimeter-scale cylindrical liquid jets are presented. The influences of the modulation amplitude and the nozzle geometry on jet behavior have been considered. Laser Doppler anemometry (LDA) was used in order to extract the velocity field of a jet along its length, and to determine the velocity modulation amplitude. Jet shapes and breakup dynamics were observed via shadowgraph imaging. Aqueous solutions of glycerol were used for these experiments. Results were compared with Lagrangian finite-element simulations with good quantitative agreement.

An exact linear-response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low-frequency peak is seen that is higher than the zero-frequency response for large systems. For momentum nonconserving systems, there is no low-frequency peak. The momentum nonconserving system is expected to satisfy Fourier’s law; however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear-response simulation results for the same system is excellent.

The role of the wave form of periodic secondary excitations at controlling (suppressing and enhancing) escape from a potential well is investigated. We demonstrate analytically (by Melnikov analysis) and numerically that a judicious choice of the excitation’s wave form greatly improves the effectiveness of the escape-controlling excitations while keeping their amplitude and period fixed. These predictions are confirmed by an energy-based analysis that provides the same optimal values of the escape-controlling parameters. The example of a dissipative Helmholtz oscillator is used to illustrate the accuracy of these results.

We study the properties of classical and quantum strongly nonlinear chains by means of extensive numerical simulations. Due to strong nonlinearity, the classical dynamics of such chains remains chaotic at arbitrarily low energies. We show that the collective excitations of classical chains are described by sound waves whose decay rate scales algebraically with the wave number with a generic exponent value. The properties of the quantum chains are studied by the quantum Monte Carlo method and it is found that the low-energy excitations are well described by effective phonon modes with the sound velocity dependent on an effective Planck constant. Our results show that at low energies the quantum effects lead to a suppression of chaos and drive the system to a quasi-integrable regime of effective phonon modes.

Forecasting bifurcations before they occur is a significant challenge and an important need in several fields. Existing approaches detect bifurcations before they occur by exploiting the critical slowing down phenomenon. However, the perturbations used in those approaches are limited to being very small and this represents a significant drawback. Large levels of perturbation have not been used mainly because of a lack of an adequate formulation that is robust to experimental noise. This paper provides such a formulation, and discusses how this approach to forecasting bifurcations is more accurate, especially when the dynamics are far from the bifurcation. Both numerical and experimental results are presented to demonstrate the technique and highlight its advantages over other prediction methods.

Traditional random graph models of networks generate networks that are locally treelike, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly nontreelike neighborhoods that contain short loops, cliques, or other biconnected subgraphs. In this paper we propose and analyze a class of random graph models that incorporates general subgraphs, allowing for nontreelike neighborhoods while still remaining solvable for many fundamental network properties. Among other things we give solutions for the size of the giant component, the position of the phase transition at which the giant component appears, and percolation properties for both site and bond percolation on networks generated by the model.

We carry out a direct numerical simulation (DNS) study that reveals the effects of polymers on statistically steady, forced, homogeneous, and isotropic fluid turbulence. We find clear manifestations of dissipation-reduction phenomena: on the addition of polymers to the turbulent fluid, we obtain a reduction in the energy dissipation rate; a significant modification of the fluid-energy spectrum, especially in the deep-dissipation range; and signatures of the suppression of small-scale structures, including a decrease in small-scale vorticity filaments. We also compare our results with recent experiments and earlier DNS studies of decaying fluid turbulence with polymer additives.

We show that Fisher information $I$ and its weighted versions effectively measure the order $R$ of a large class of shift-invariant physical systems. This result follows from the assumption that $R$ decreases under small perturbations caused by a coarse graining of the system. The form found for $R$ is generally unitless, which allows the order for different phenomena to be compared objectively. The monotonic contraction properties of $R$ and $I$ in time imply that they are entropies, in addition to their usual status as information. This removes the need for data, and therefore an observer, in physical derivations based upon their use. Thus, this recognizes complementary scenarios to the participatory observer of Wheeler, where (now) physical phenomena can occur in the absence of an observer. Simple applications of the new order measure $R$ are discussed.

We propose a model for cyclically competing species on continuous space and investigate the effect of the interplay between the interaction range and mobility on coexistence. A transition from coexistence to extinction is uncovered with a strikingly nonmonotonic behavior in the coexistence probability. About the minimum in the probability, switches between spiral and plane-wave patterns arise. A strong mobility can either promote or hamper coexistence, depending on the radius of the interaction range. These phenomena are absent in any lattice-based model, and we demonstrate that they can be explained using nonlinear partial differential equations. Our continuous-space model is more physical and we expect the findings to generate experimental interest.

In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Here we present a mathematically consistent finite element approach to the simulation of Brownian polymer dynamics. The viscous damping forces are accounted for by an anisotropic friction model. By comparison with theoretical predictions and experimental data we demonstrate the reliability and efficiency of this method.

We study, using simulated experiments inspired by thin-film magnetic domain patterns, the feasibility of phase retrieval in x-ray diffractive imaging in the presence of intrinsic charge scattering given only photon-shot-noise limited diffraction data. We detail a reconstruction algorithm to recover the sample’s magnetization distribution under such conditions and compare its performance with that of Fourier transform holography. Concerning the design of future experiments, we also chart out the reconstruction limits of diffractive imaging when photon-shot-noise and the intensity of charge scattering noise are independently varied. This work is directly relevant to the time-resolved imaging of magnetic dynamics using coherent and ultrafast radiation from x-ray free-electron lasers and also to broader classes of diffractive imaging experiments which suffer noisy data, missing data, or both.

Interaction of light and ac electric fields with a nematic liquid crystal (NLC) doped with nanosized second-generation carbosilane codendrimers containing terminal azobenzene fragments has been studied. A first-order Freedericksz transition in the linearly polarized light, accompanied by an intrinsic bistability in a wide region, was observed. An additional ac electric field decreases the light-induced Freedericksz transition threshold and narrows the bistability region. Light illumination transforms the second-order electric-field-induced Freedericksz transition to a first-order one. The width of the bistability region increases with the light wave intensity. The theory of the interaction of light and ac electric fields with the dendrimer-doped NLCs is developed taking into account an additional (with respect to the undoped nematic host) dependence of the optical torque on the angle between the director and the light field.