Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on “soft” quasi-two-dimensional dusty plasma clusters. Our model does not contain external drive or plasma interactions that serve to drive the system away from thermodynamic equilibrium. The grains are confined by an external potential, interact via static Yukawa forces, and are subject to stochastic heating and dissipation from neutrals. One remarkable feature is emergence of leptokurtic probability distributions of grain displacements $\xi \left(\tau \right)$ on time scales $\tau <{\tau }_{\Delta }$, where ${\tau }_{\Delta }$ is the time at which the standard deviation $\sigma \left(\tau \right)\equiv {⟨{\xi }^2\left(\tau \right)⟩}^{1/2}$ approaches the mean intergrain distance $\Delta$. Others are development of humps in the distributions on multiples of $\Delta$, anomalous Hurst exponents, and transitions from leptokurtic toward Gaussian displacement distributions on time scales $\tau >{\tau }_{\Delta }$. The latter is a signature of intermittency, here interpreted as a transition from bursty transport associated with hopping on intermediate time scales to vortical flows on longer time scales. These intermittency features are quantitatively modeled by a single-particle Itô-Langevin stochastic equation with a nonlinear drift term.

The local electric-field distribution has been investigated in a core-shell cylindrical metamaterial structure under the illumination of a uniform incident optical field. The structure consists of a homogeneous dielectric core, a shell of graded metal-dielectric metamaterial, embedded in a uniform matrix. In the quasistatic limit, the permittivity of the metamaterial is given by the graded Drude model. The local electric potentials and hence the electric fields have been derived exactly and analytically in terms of hypergeometric functions. Our results showed that the peak of the electric field inside the cylindrical shell can be confined in a desired position by varying the frequency of the optical field and the parameters of the graded profiles. Thus, by fabricating graded metamaterials, it is possible to control electric-field distribution spatially. We offer an intuitive explanation for the gradation-controlled electric-field distribution.

The deformation of dense random fiber networks is important in a variety of applications including biological and nonliving systems. In this paper it is shown that semiflexible fiber networks exhibit long-range power-law spatial correlations of the density and elastic properties. Hence, the stress and strain fields measured over finite patches of the network are characterized by similar spatial correlations. The scaling is observed over a range of scales bounded by a lower limit proportional to the segment length and an upper limit on the order of the fiber length. If the fiber bending stiffness is reduced below a threshold, correlations are lost. The issue of solving boundary value problems defined on large domains of random fiber networks is also addressed. Since the direct simulation of such systems is impractical, the network is mapped into an equivalent continuum with long-range correlated elastic moduli. A technique based on the stochastic finite element method is used to solve the resulting stochastic continuum problem. The method provides the moments of the distribution function of the solution (e.g., of the displacement field). It performs a large dimensionality reduction which is based on the scaling properties of the underlying elasticity of the material. Two examples are discussed in closure.

We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector. The algorithm, a Monte Carlo implementation of a deterministic one we recently benchmarked, is an extension of the power method. In the implementation presented, we used a basic Monte Carlo splitting and termination method called the comb, incorporated the weight cancellation method of Arnow et al., and exploited a sampling method, the sewing method, that does a large state space sampling as a succession of small state space samplings. We illustrate the effectiveness of the algorithm by its determination of the two largest eigenvalues of the transfer matrices for variously sized two-dimensional, zero-field Ising models. While very likely useful for other transfer-matrix problems, the algorithm is however quite general and should find application to a larger variety of problems requiring a few dominant eigenvalues of a matrix.

A method based on a modified Newton-Raphson scheme is presented to estimate parameters of a nonlinear dynamical system from the time series data of the variables. The method removes some of the problems associated with the standard synchronization based methods. An important achievement of this method is that it is possible to determine the exact form of dynamical equations for systems with quadratic nonlinearity.

While slowly turning the ends of a single molecule of DNA at constant applied force, a discontinuity was recently observed at the supercoiling transition when a small plectoneme is suddenly formed. This can be understood as an abrupt transition into a state in which stretched and plectonemic DNA coexist. We argue that there should be discontinuities in both the extension and the torque at the transition and provide experimental evidence for both. To predict the sizes of these discontinuities and how they change with the overall length of DNA, we organize a phenomenological theory for the coexisting plectonemic state in terms of four parameters. We also test supercoiling theories, including our own elastic rod simulation, finding discrepancies with experiment that can be understood in terms of the four coexisting state parameters.

We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for the height profile of a growing interface. In one dimension we find that the transition pathway between different height configurations is determined by the nucleation and subsequent propagation of facets or steps, corresponding to moving domain walls or growth modes in the underlying noise-driven Burgers equation. This transition scenario is in accordance with recent analytical studies of the one-dimensional Kardar-Parisi-Zhang equation in the asymptotic weak noise limit. We also briefly discuss transitions in two dimensions.

The anomalous exponents governing the long-wavelength behavior of the flat phase of physical crystalline membranes are calculated within a self-consistent screening approximation (SCSA) applied to second order expansion in $1/d_C$ ($d_C$ is the codimension), extending the seminal work of Le Doussal and Radzihovsky [Phys. Rev. Lett. 69, 1209 (1992)]. In particular, the bending rigidity is found to harden algebraically in the long-wavelength limit with an exponent $\eta =0.789\dots$, which is used to extract the elasticity softening exponent ${\eta }_u=0.422\dots$, and the roughness exponent $\zeta =0.605\dots$. The scaling relation ${\eta }_u=2-2\eta$ is proven to hold to all orders in SCSA. Further, applying the SCSA to an expansion in $1/d_C$, is found to be essential, as no solution to the self-consistent equations is found in a two-bubble level, which is the naive second-order expansion. Surprisingly, even though the expansion parameter for physical membrane is $1/d_C=1$, the SCSA applied to second-order expansion deviates only slightly from the first order, increasing $\zeta$ by mere 0.016. This supports the high quality of the SCSA for physical crystalline membranes, as well as improves the comparison to experiments and numerical simulations of these systems. The prediction of SCSA applied to first order expansion for the Poisson ratio is shown to be exact to all orders.

Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic [Berezinskii-Kosterlitz-Thouless (BKT)] geometric order, occurs in the phase diagram in addition to the ordinary (compact) percolating phase and the nonpercolating phase. It is found that no connection exists between, on the one hand, the onset of this geometric BKT behavior and, on the other hand, the onsets of the highly clustered small-world character of the network and of the thermal BKT transition of the Ising model on this network. Nevertheless, both geometric and thermal BKT behaviors have inverted characters, occurring where disorder is expected, namely, at low bond probability and high temperature, respectively. This may be a general property of long-range networks.

A pair of two-level systems initially prepared in different thermal states and coupled to an external reversible work source do not in general reach a common temperature at the end of a unitary work extraction process. We define an effective temperature for the final nonequilibrium but passive state of the bipartite quantum system and analyze its properties.

The effect of noise on the solid-to-liquid transition of a dense granular assembly under planar shear is studied numerically using soft-particle molecular dynamics simulations in two dimensions. We focus on small systems in a thin planar Couette cell, examining the bistable region while increasing shear, with varying amounts of random noise, and determine statistics of the shear required for fluidization. In the absence of noise, the threshold value of the shear stress depends on the preparation of the system and has a broad distribution. However, adding force fluctuations both lowers the mean threshold value of the shear stress and decreases its variability. This behavior is interpreted as thermoactivated escape through a fluctuating barrier.

We report the nematic and smectic ordering in an aqueous suspension of monolayer $\alpha$-Zirconium phosphate platelets possessing a high polydispersity in diameter but uniform thickness. We observe an isotropic-nematic transition as the platelet volume fraction increases, followed by the formation of a smectic, an elusive phase that has been rarely seen in discotic liquid crystals. The smectic phase is characterized by x-ray diffraction high-resolution transmission electron microscopy, and optical microscopy. The phase equilibria in this highly polydisperse suspension are rationalized in terms of a theoretical approach based on density-functional theory.

We study random graph models for directed acyclic graphs, a class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models roughly analogous to the fixed edge number and fixed edge probability variants of traditional undirected random graphs. We calculate a number of properties of these models, including particularly the probability of connection between a given pair of vertices, and compare the results with real-world acyclic network data finding that theory and measurements agree surprisingly well—far better than the often poor agreement of other random graph models with their corresponding real-world networks.

An alternative approach to determining embedding dimension when reconstructing dynamic systems from a noisy time series is proposed. The available techniques of determining embedding dimension (the false nearest-neighbor method, calculation of the correlation integral, and others) are known [H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, New York, 1997)] to be inefficient, even at a low noise level. The proposed approach is based on constructing a global model in the form of an artificial neural network. The required amount of neurons and the embedding dimension are chosen so that the description length should be minimal. The considered approach is shown to be appreciably less sensitive to the level and origin of noise, which makes it also a useful tool for determining embedding dimension when constructing stochastic models.

Thermal transpiration is a rarefied gas flow driven by a wall temperature gradient and is a promising mechanism for gas pumping without moving parts, known as the Knudsen pump. Obtaining temperature measurements along capillary walls in a Knudsen pump is difficult due to extremely small length scales. Meanwhile, simplified analytical models are not applicable under the practical operating conditions of a thermal transpiration device, where the gas flow is in the transitional rarefied regime. Here, we present a coupled gas-phonon heat transfer and flow model to study a closed thermal transpiration system. Discretized Boltzmann equations are solved for molecular transport in the gas phase and phonon transport in the solid. The wall temperature distribution is the direct result of the interfacial coupling based on mass conservation and energy balance at gas-solid interfaces and is not specified a priori unlike in the previous modeling efforts. Capillary length scales of the order of phonon mean free path result in a smaller temperature gradient along the transpiration channel as compared to that predicted by the continuum solid-phase heat transfer. The effects of governing parameters such as thermal gradients, capillary geometry, gas and phonon Knudsen numbers and, gas-surface interaction parameters on the efficiency of thermal transpiration are investigated in light of the coupled model.

A new fundamentally based formulation of nonlocal effects in the rapid pressure-strain correlation in turbulent flows has been obtained. The resulting explicit form for the rapid pressure-strain correlation accounts for nonlocal effects produced by spatial variations in the mean-flow velocity gradients and is derived through Taylor expansion of the mean velocity gradients appearing in the exact integral relation for the rapid pressure-strain correlation. The integrals in the resulting series expansion are solved for high- and low-Reynolds number forms of the longitudinal correlation function $f\left(r\right)$, and the resulting nonlocal rapid pressure-strain correlation is expressed as an infinite series in terms of Laplacians of the mean strain rate tensor. This formulation is used to obtain a nonlocal transport equation for the turbulence anisotropy that is expected to provide improved predictions of the anisotropy in strongly inhomogeneous flows.

Within the frame work of classic electromagnetic theory, a general electrical boundary condition describing the induced-charge electrokinetic phenomena at the liquid-dielectric interface is proposed in the present study. Two well-known limiting cases, i.e., perfectly insulating and perfectly polarizable wall boundary conditions, can be recovered from the present electrical boundary condition. By utilizing the proposed boundary condition, the induced-charge electro-osmosis (ICEO) flow in an infinitely long microchannel patterned with two symmetric polarizable dielectric blocks is investigated analytically. Fourier transform method is invoked to solve a biharmonic equation, which governs the (ICEO) flow field described by the stream function. Dimensionless parameters are introduced, and their effects on flow characteristics are analyzed. It is found that an increase in polarizability of the dielectric block enhances the slip velocity on its surface and thus induces a pair of counter-rotating vortices. Also, increasing the natural zeta potential on the upstream and downstream of the insulating microchannel walls leads to extinction of the vortex near the upstream insulating microchannel and suppression of the vortex near the downstream insulating microchannel.

Taking the approach via a special variable separation, some features of the $\left(3+1\right)$-dimensional multisolitonic solutions, including the embedded soliton, the taperlike soliton, the plateau-type soliton, and the rectangle soliton, were revealed in this study thanks to the intrusion of the appropriate boundary conditions and/or their initial qualifications. Some physical properties, such as the spatiotemporal evolution, wave form structure, and interactive phenomena with or without the background waves of multisolitons are discussed, especially in the two-soliton case. It is found that different interactive behaviors of solitary waves take place under different parameter conditions of collision in this system. It is verified that the elastic interaction phenomena exist in this $\left(3+1\right)$-dimensional integrable model. Furthermore, in other types of nonlinear systems, the abundant $\left(3+1\right)$-dimensional multisolitonic solutions were also investigated.

Considering a two-dimensional lattice of weakly coupled waveguides, where each waveguide may carry two orthogonal modes of dipolar character, we present a nonlinear discrete vector model for the study of Kerr optical solitons with profiles having a reduced symmetry relative to the underlying lattice. We describe analytically and numerically existence and stability properties of such states in square and triangular lattices and also reveal directional mobility properties of two-dimensional gap solitons which were recently observed in experiment. The model also describes one-site peaked discrete vortices corresponding to experimentally observed “second-band” vortex lattice solitons, for which oscillatory instabilities are predicted. We also introduce a concept of “rotational Peierls-Nabarro barrier” characterizing the minimum energy needed for rotation of stable dipole modes and compare numerically translational and rotational energy barriers in regimes of good mobility.

We investigate theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators; the two types of resonators used have different resonant frequencies caused by unequal slit sizes. We use the rotating-wave approximation and construct several types of breather excitations both for the energy-conserving as well as dissipative-driven case; we corroborate these approximate results trough numerically exact computations. We demonstrate that discrete breathers can appear spontaneously in the dissipative-driven system as a result of a fundamental instability.