We study the dynamics of instability and pattern formation in a slender elastic thread that is continuously fed onto a surface moving at constant speed $V$ in its own plane. As $V$ is decreased below a critical value $V_c$, the steady “dragged catenary” configuration of the thread becomes unstable to sinusoidal meanders and thence to a variety of more complex patterns including biperiodic meanders, figures of 8, “W,” “two-by-one,” and “two-by-two” patterns, and double coiling. Laboratory experiments are performed to determine the phase diagram of these patterns as a function of $V$, the thread feeding speed $U$, and the fall height $H$. The meandering state is quantified by measuring its amplitude and frequency as functions of $V$, which are consistent with a Hopf bifurcation. We formulate a numerical model for a slender elastic thread that predicts well the observed steady shapes but fails to predict the frequency of the onset of meandering, probably because of slippage of the thread relative to the belt. A comparison of our phase diagram with the analogous diagram for a thread of viscous fluid falling on a moving surface reveals many similarities, but each contains several patterns that are not found in the other.

We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long time scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt-echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert-space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert-space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime.

Single and double-slit experiments are performed with two microwave billiards with the shapes of a rectangle and a quarter stadium, respectively. The classical dynamics of the former is regular, whereas that of the latter is chaotic. Microwaves can leave the billiards via slits in the boundary, forming interference patterns on a screen. The aim is to determine the effect of the billiard dynamics on their structure. For this the development of a method for the construction of a directed wave packet by means of an array of multiple antennas was crucial. The interference patterns show a sensitive dependence not only on the billiard dynamics but also on the initial position and direction of the wave packet.

Application of time-delayed feedback is a practical method of controlling bifurcations in reaction-diffusion systems. It has been shown that for a suitable feedback strength, time delay beyond a threshold may induce spatiotemporal instabilities. For an appropriate parameter space with differential diffusivities of the activator-inhibitor species, delayed feedback may generate Turing instability via a Hopf-Turing transition, resulting in stationary patterns. This is explored by a theoretical scheme in a photosensitive chlorine dioxide–iodine–malonic acid reaction-diffusion system where the delayed feedback is externally tuned by photoillumination intensity. Our analytical results corroborate with direct numerical simulations.

In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. These statistics can be evaluated on any reconstructed attractor, thereby allowing a direct comparison among different approaches: (uniform or nonuniform) delay vectors, PCA, Legendre coordinates, etc. It can also be used to select the most appropriate parameters of a reconstruction strategy. In the case of delay coordinates this translates into finding the optimal delay time and embedding dimension from the absolute minimum of the advocated cost function. Its definition is based on theoretical arguments on noise amplification, the complexity of the reconstructed attractor, and a direct measure of local stretch which constitutes an irrelevance measure. The proposed method is demonstrated on synthetic and experimental time series.

The observed flow enhancement in highly confining geometries is believed to be caused by fluid velocity slip at the solid wall surface. Here we present a simple and highly accurate method to predict this slip using equilibrium molecular dynamics. Unlike previous equilibrium molecular dynamics methods, it allows us to directly compute the intrinsic wall-fluid friction coefficient rather than an empirical friction coefficient that includes all sources of friction for planar shear flow. The slip length predicted by our method is in excellent agreement with the slip length obtained from direct nonequilibrium molecular dynamics simulations.

With the help of a model of magnetohydrodynamic (MHD) turbulence tested previously, we explore high Reynolds number regimes up to equivalent resolutions of ${6000}^3$ grid points in the absence of forcing and with no imposed uniform magnetic field. For the given initial condition chosen here, with equal kinetic and magnetic energy, the flow ends up being dominated by the magnetic field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy spectrum. However, the locally anisotropic magnetic field fluctuations perpendicular to the local mean field follow a Kolmogorov law. We find that the ratio of the eddy turnover time to the Alfvén time increases with wave number, contrary to the so-called critical balance hypothesis. Residual energy and helicity spectra are also considered; the role played by the conservation of magnetic helicity is studied, and scaling laws are found for the magnetic helicity and residual helicity spectra. We put these results in the context of the dynamics of a globally isotropic MHD flow that is locally anisotropic because of the influence of the strong large-scale magnetic field, leading to a partial equilibration between kinetic and magnetic modes for the energy and the helicity.

We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call $n$-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the $n$-foil knots the decay is described by power laws that range form $t^{-2/3}$ to $t^{-1/3}$, which can be as slow as the $t^{-1/3}$ behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like $t^{-1}$, which is somewhat slower than the previously obtained $t^{-3/2}$ behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above.

Transparency of a two-layer plasma structure in an external steady-state magnetic field, perpendicular to the wave incidence plane, is studied. The case of the p-polarized electromagnetic wave is considered. The electromagnetic wave is obliquely incident on the two-layer structure and is evanescent in both layers. The conditions for total transparency of the two-layer structure are found. The parametric dependencies of the transparency coefficient on the plasma slab widths, the magnitude of the wave number component, as well on the magnetic field magnitude are obtained.

The electron-ion temperature relaxation essentially affects both the laser absorption in coronal plasmas and the hot-spot formation in inertial confinement fusion (ICF). It has recently been reexamined for plasma conditions closely relevant to ICF implosions using either classical molecular-dynamics simulations or analytical methods. To explore the electron-ion temperature equilibration effects on ICF implosion performance, we have examined two Coulomb logarithm models by implementing them into our hydrocodes, and we have carried out hydrosimulations for ICF implosions. Compared to the Lee-More model that is currently used in our standard hydrocodes, the two models predict substantial differences in laser absorption, coronal temperatures, and neutron yields for ICF implosions at the OMEGA Laser Facility [Boehly et al. Opt. Commun. 133, 495 (1997)]. Such effects on the triple-picket direct-drive design at the National Ignition Facility (NIF) have also been explored. Based on the validity of the two models, we have proposed a combined model of the electron-ion temperature-relaxation rate for the overall ICF plasma conditions. The hydrosimulations using the combined model for OMEGA implosions have shown ∼6% more laser absorption, ∼6%–15% higher coronal temperatures, and ∼10% more neutron yield, when compared to the Lee-More model prediction. It is also noticed that the gain for the NIF direct-drive design can be varied by ∼10% among the different electron-ion temperature-relaxation models.

The use of Ewald summation schemes for calculating long-range Coulomb interactions, originally applied to ionic crystalline solids, is a very common practice in molecular simulations of charged fluids at present. Such a choice imposes an artificial periodicity which is generally absent in the liquid state. In this paper we propose a simple analytical $O\left(N^2\right)$ method which is based on Gauss’s law for computing exactly the Coulomb interaction between charged particles in a simulation box, when it is averaged over all possible orientations of a surrounding infinite lattice. This method mitigates the periodicity typical of crystalline systems and it is suitable for numerical studies of ionic liquids, charged molecular fluids, and colloidal systems with Monte Carlo and molecular dynamics simulations.

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential because different dynamical processes may be affected very differently by network topology. A full characterization of such systems thus requires a formalization that encompasses both aspects simultaneously, rather than relying only on the topological adjacency matrix. To achieve this, we introduce the concept of flow graphs, namely weighted networks where dynamical flows are embedded into the link weights. Flow graphs provide an integrated representation of the structure and dynamics of the system, which can then be analyzed with standard tools from network theory. Conversely, a structural network feature of our choice can also be used as the basis for the construction of a flow graph that will then encompass a dynamics biased by such a feature. We illustrate the ideas by focusing on the mathematical properties of generic linear processes on complex networks that can be represented as biased random walks and their dual consensus dynamics, and show how our framework improves our understanding of these processes.

We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction $p$ of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value $p_c\approx 10\%$, there is a dramatic decrease in the time $T_c$ taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when $p<p_c$, $T_c~\exp [\alpha (p)N]$, whereas for $p>p_c$, $T_c~\ln N$. We conclude with simulation results for Erdős-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

An ensemble of symmetric potential energy wells arranged at the vertices of a Fibonacci spiral can serve as the basis for an irreducibly two-dimensional thermal ratchet. Periodic rotation of the potential energy landscape through a three-step cycle drives trapped Brownian particles along spiral trajectories through the pattern. Which spiral is selected depends on the angular displacement at each step, with transitions between selected spirals arising at rational proportions of the golden angle. Fibonacci spiral ratchets therefore display an exceptionally rich range of transport properties, including inhomogeneous states in which different parts of the pattern induce motion in different directions. Both the radial and angular components of these trajectories can undergo flux reversal as a function of the scale of the pattern or the rate of rotation.

The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular dynamics of the particle determining the orientation of motion. In addition to a constant torque, the particle is supplemented by random torques, which are modeled as an Ornstein-Uhlenbeck process with given correlation time ${\tau }_c$. These nonvanishing correlations cause a persistence of the particles’ trajectories and a change of the effective spatial diffusion coefficient. We discuss the mean square displacement as a function of the correlation time and the noise intensity and detect a nonmonotonic dependence of the effective diffusion coefficient with respect to both correlation time and noise strength. A maximal diffusion behavior is obtained if the correlated angular noise straightens the curved trajectories, interrupted by small pirouettes, whereby the correlated noise amplifies a straightening of the curved trajectories caused by the constant torque.

Standard reservoir evaluations are based on Archie's law relating the average water saturation to the average electrical resistivity by $R_{\mathrm{ind}}=S_w^{-2}$. However, especially in the case of complex heterogeneous carbonates, deviation from Archie's law is observed and generally attributed to factors affecting the percolation or disconnectedness of the different phases (wetting films, microporosity, macropores) assuring electrical conductance. Pore-network models (PNM's) in combination with high-resolution computed microtomography (μ-CT) constitute a very effective tool to investigate the influence of the geometry and topology of the porous media on the spatial distribution of the conductive phase, and therefore on the shape of the resistivity index curve. An extended version of the classical PNM applicable to dual-porosity systems is presented. It combines the classical pore-network modeling applied on the macroporous space with the macroscopic properties of the microporous phase, supposing that the two pore systems act in parallel. Three-dimensional images provide information on the connectedness of the microporous phase, which is then included in the simulations. Electrical behavior of sandstone and two carbonates presenting distinct resistivity index curves were simulated and compared to measurements. Both Archie and “non-Archie” behavior were correctly reproduced, and the curve shape was explained considering percolation of the different phases.

Multiblock copolymer chains in implicit nonselective solvents are studied by using a Monte Carlo method, which employs a parallel tempering algorithm. Chains consisting of $120\hspace{0.5em}A$ and $120\hspace{0.5em}B$ monomers, arranged in three distinct microarchitectures: $(10-10){}_{12},\hspace{0.5em}(6-6){}_{20}$, and $(3-3){}_{40}$, collapse to globular states upon cooling, as expected. By varying both the reduced temperature $T^{*}$ and the compatibility between monomers $\omega$, numerous intraglobular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and $n$ clusters with $n>3$ (lamellar and other), which are reminiscent of the block copolymer nanophases for spherically confined geometries. Phase diagrams for various chains in the ($T^{*},\omega$) space are mapped. The structure factor $S(k)$, for a selected microarchitecture and $\omega$, is calculated. Since $S(k)$ can be measured in scattering experiments, it can be used to relate simulation results to an experiment. Self-assembly in those systems is interpreted in terms of competition between minimization of the interfacial area separating different types of monomers and minimization of contacts between chain and solvent. Finally, the relevance of this model to the protein folding is addressed.

Electron crystallography of 2D protein crystals provides a powerful tool for the determination of membrane protein structure. In this method, data is acquired in the Fourier domain as randomly sampled, uncoupled, amplitudes and phases. Due to physical constraints on specimen tilting, those Fourier data show a vast un-sampled “missing cone” of information, producing resolution loss in the direction perpendicular to the membrane plane. Based on the flexible language of projection onto sets, we provide a full solution for these problems with a projective constraint optimization algorithm that, for sufficiently oversampled data, produces complete recovery of unmeasured data in the missing cone. We apply this method to an experimental data set of Bacteriorhodopsin and show that, in addition to producing superior results compared to traditional reconstruction methods, full, reproducible, recovery of the missing cone from noisy data is possible. Finally, we present an automatic implementation of the refinement routine as open source, freely distributed, software that will be included in our 2dx software package.

Using first-principles calculations, we study electron transport through nucleotides inside a rectangular nanogap formed by two pairs of gold electrodes which are perpendicular and parallel to the nucleobase plane. We propose that this setup will enhance the nucleotide selectivity of tunneling signals to a great extent. Information from three electrical probing processes offers full nucleotide recognition, which survives the noise from neighboring nucleotides and configuration fluctuations.

Pairwise particle interactions arise in diverse physical systems ranging from insect swarms to self-assembly of nanoparticles. In the presence of long-range attraction and short-range repulsion, such systems can exhibit bound states. We use linear stability analysis of a ring equilibrium to classify the morphology of patterns in two dimensions. Conditions are identified that assure the well-posedness of the ring. In addition, weakly nonlinear theory and numerical simulations demonstrate how a ring can bifurcate to more complex equilibria including triangular shapes, annuli, and spot patterns with $N$-fold symmetry. Many of these patterns have been observed in nature, although a general theory has been lacking, in particular how small changes to the interaction potential can lead to large changes in the self-organized state.