The elastic response of a two-dimensional amorphous solid to induced local shear transformations, which mimic the elementary plastic events occurring in deformed glasses, is investigated via molecular-dynamics simulations. We show that for different spatial realizations of the transformation, despite relative fluctuations of order one, the long-time equilibrium response averages out to the prediction of the Eshelby inclusion problem for a continuum elastic medium. We characterize the effects of the underlying dynamics on the propagation of the elastic signal. A crossover from a propagative transmission in the case of weakly damped dynamics to a diffusive transmission for strong damping is evidenced. In the latter case, the full time-dependent elastic response is in agreement with the theoretical prediction, obtained by solving the diffusion equation for the displacement field in an elastic medium.

Close to a planar surface, lamellar structures are imposed upon otherwise bulk bicontinuous microemulsions. Thermally induced membrane undulations are modified by the presence of the rigid interface. While it has been shown that a pure membrane's dynamics are accelerated close to the interface, we observed nearly unchanged relaxation rates for membranes spiked with large amphiphilic diblock copolymers. An increase of the polymer concentration by a factor of 2–3 for the first and second surfactant membrane layers was observed. We interpret the reduced relaxation times as the result of an interplay between the bending rigidity and the characteristic distance of the first surfactant membrane to the rigid interface, which causes the hydrodynamic and steric interface effects described in Seifert's theory. The influence of these effects on decorated membranes yields a reduction of the frequencies and an amplification of the amplitudes of long-wavelength undulations, which are in accordance to our experimental findings.

We show that quasilocalized low-frequency modes in the vibrational spectrum can be used to construct soft spots, or regions vulnerable to rearrangement, which serve as a universal tool for the identification of flow defects in solids. We show that soft spots not only encode spatial information, via their location, but also directional information, via directors for particles within each soft spot. Single crystals with isolated dislocations exhibit low-frequency phonon modes that localize at the core, and their polarization pattern predicts the motion of atoms during elementary dislocation glide in two and three dimensions in exquisite detail. Even in polycrystals and disordered solids, we find that the directors associated with particles in soft spots are highly correlated with the direction of particle displacements in rearrangements.

The statistical mechanics of polymers grafted on surfaces has been the subject of intense research activity because of many potential applications. In this paper, we analytically investigate the conformational changes caused by a single crosslink on two ideal (Gaussian) chains grafted onto a rigid planar surface. Both the crosslink and the surface reduce the number of allowed configurations. In the absence of the hard substrate, the sole effect of the crosslink is a reduction in the effective Kuhn length of a tethered chain. The crosslink-induced shrinkage (collapse) of the grafted chains (mushrooms) turns out to be a reduction in the variance of the distribution of the height of the chain rather than a reduction of the height itself.

We revisit the “$\varepsilon$-intelligence” model of Tóth et al. [Phys. Rev. X 1, 021006 (2011)], which was proposed as a minimal framework to understand the square-root dependence of the impact of meta-orders on volume in financial markets. The basic idea is that most of the daily liquidity is “latent” and furthermore vanishes linearly around the current price, as a consequence of the diffusion of the price itself. However, the numerical implementation of Tóth et al. (2011) was criticized as being unrealistic, in particular because all the “intelligence” was conferred to market orders, while limit orders were passive and random. In this work, we study various alternative specifications of the model, for example, allowing limit orders to react to the order flow or changing the execution protocols. By and large, our study lends strong support to the idea that the square-root impact law is a very generic and robust property that requires very few ingredients to be valid. We also show that the transition from superdiffusion to subdiffusion reported in Tóth et al. (2011) is in fact a crossover but that the original model can be slightly altered in order to give rise to a genuine phase transition, which is of interest on its own. We finally propose a general theoretical framework to understand how a nonlinear impact may appear even in the limit where the bias in the order flow is vanishingly small.

We introduce a method for the numerical determination of the steady-state response of complex charged porous media to pressure, salt concentration, and electric potential gradients. The macroscopic fluxes of solvent, salt, and charge are computed within the framework of the Pore Network Model (PNM), which describes the pore structure of the samples as networks of pores connected to each other by channels. The PNM approach is used to capture the couplings between solvent and ionic flows which arise from the charge of the solid surfaces. For the microscopic transport coefficients on the channel scale, we take a simple analytical form obtained previously by solving the Poisson-Nernst-Planck and Stokes equations in a cylindrical channel. These transport coefficients are upscaled for a given network by imposing conservation laws for each pores, in the presence of macroscopic gradients across the sample. The complex pore structure of the material is captured by the distribution of channel diameters. We investigate the combined effects of this complex geometry, the surface charge, and the salt concentration on the macroscopic transport coefficients. The upscaled numerical model preserves the Onsager relations between the latter, as expected. The calculated macroscopic coefficients behave qualitatively as their microscopic counterparts, except for the permeability and the electro-osmotic coupling coefficient when the electrokinetic effects are strong. Quantitatively, the electrokinetic couplings increase the difference between the macroscopic coefficients and the corresponding ones for a single channel of average diameter.

We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$, respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for $n_t\in {\mathbb{Z}}^{+}$ and $n_p=1$, these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity, and we estimate the soliton lifetime in such a medium as a function of the toroidal winding number.

It is known that some kinds of bacteria swim by forming a bundle of their multiple flagella. However, the details of flagella synchronization as well as the swimming efficiency of such bacteria have not been fully understood. In this study, swimming of multiflagellated bacteria is investigated numerically by the boundary element method. We assume that the cell body is a rigid ellipsoid and the flagella are rigid helices suspended on flexible hooks. Motors apply constant torque to the hooks, rotating the flagella either clockwise or counterclockwise. Rotating all flagella clockwise, bundling of all flagella is observed in every simulated case. It is demonstrated that the counter rotation of the body speeds up the bundling process. During this procedure the flagella synchronize due to hydrodynamic interactions. Moreover, the results illustrated that during running the multiflagellated bacterium shows higher propulsive efficiency (distance traveled per one flagellar rotation) over a bacterium with a single thick helix. With an increasing number of flagella the propulsive efficiency increases, whereas the energetic efficiency decreases, which indicates that efficiency is something multiflagellated bacteria are assigning less priority to than to motility. These findings form a fundamental basis in understanding bacterial physiology and metabolism.

We present a numerical study of Rayleigh-Bénard convection disturbed by a longitudinal wind. Our results show that under the action of the wind, the vertical heat flux through the cell initially decreases, due to the mechanism of plume sweeping, and then increases again when turbulent forced convection dominates over the buoyancy. As a result, the Nusselt number is a nonmonotonic function of the shear Reynolds number. We provide simple models that capture with good accuracy all the dynamical regimes observed. We expect that our findings can lead the way to a more fundamental understanding of the complex interplay between mean wind and plume ejection in the Rayleigh-Bénard phenomenology.

We study $n$-pulse interaction in fast collisions of $N$ solitons of the cubic nonlinear Schrödinger (NLS) equation in the presence of generic weak nonlinear loss. We develop a generalized reduced model that yields the contribution of the $n$-pulse interaction to the amplitude shift for collisions in the presence of weak $(2m+1)$-order loss, for any $n$ and $m$. We first employ the reduced model and numerical solution of the perturbed NLS equation to analyze soliton collisions in the presence of septic loss $(m=3)$. Our calculations show that the three-pulse interaction gives the dominant contribution to the collision-induced amplitude shift already in a full-overlap four-soliton collision, and that the amplitude shift strongly depends on the initial soliton positions. We then extend these results for a generic weak nonlinear loss of the form $G\left(\right|\psi {|}^2)\psi$, where $\psi$ is the physical field and $G$ is a Taylor polynomial of degree $m_c$. Considering $m_c=3$, as an example, we show that three-pulse interaction gives the dominant contribution to the amplitude shift in a six-soliton collision, despite the presence of low-order loss. Our study quantitatively demonstrates that $n$-pulse interaction with high $n$ values plays a key role in fast collisions of NLS solitons in the presence of generic nonlinear loss. Moreover, the scalings of $n$-pulse interaction effects with $n$ and $m$ and the strong dependence on initial soliton positions lead to complex collision dynamics, which is very different from that observed in fast NLS soliton collisions in the presence of cubic loss.

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological $\epsilon$-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be $\epsilon$-machines, irrespective of estimated transition probabilities. Properties of $\epsilon$-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

In a recent paper [Vaikuntanathan and Jarzynski, Phys. Rev. E 83, 061120 (2011)], a model was introduced whereby work could be extracted from a thermal bath by measuring the energy of a particle that was thermalized by the bath and manipulating the potential of the particle in the appropriate way, depending on the measurement outcome. If the extracted work is $W_{\text{extracted}}$ and the work $W_{\text{erasure}}$ needed to be dissipated in order to erase the measured information in accordance with Landauer's principle, it was shown that $W_{\text{extracted}}\le W_{\text{erasure}}$ in accordance with the second law of thermodynamics. Here we extend this work in two directions: First, we discuss how accurately the energy should be measured. By increasing the accuracy one can extract more work, but at the same time one obtains more information that has to be deleted. We discuss what are the appropriate ways of optimizing the balance between the two and find optimal solutions. Second, whenever $W_{\text{extracted}}$ is strictly less than $W_{\text{erasure}}$ it means that an irreversible step has been performed. We identify the irreversible step and propose a protocol that will achieve the same transition in a reversible way, increasing $W_{\text{extracted}}$ so that $W_{\text{extracted}}=W_{\text{erasure}}$.

We present direct measurements of the evolution of the segmental-level microstructure of a stable shear-banding polymerlike micelle solution during flow startup and cessation in the plane of flow. These measurements provide a definitive, quantitative microstructural understanding of the stages observed during flow startup: an initial elastic response with limited alignment that yields with a large stress overshoot to a homogeneous flow with associated micellar alignment that persists for approximately three relaxation times. This transient is followed by a shear (kink) band formation with a flow-aligned low-viscosity band that exhibits shear-induced concentration fluctuations and coexists with a nearly isotropic band of homogenous, highly viscoelastic micellar solution. Stable, steady banding flow is achieved only after approximately two reptation times. Flow cessation from this shear-banded state is also found to be nontrivial, exhibiting an initial fast relaxation with only minor structural relaxation, followed by a slower relaxation of the aligned micellar fluid with the equilibrium fluid's characteristic relaxation time. These measurements resolve a controversy in the literature surrounding the mechanism of shear banding in entangled wormlike micelles and, by means of comparison to existing literature, provide further insights into the mechanisms driving shear-banding instabilities in related systems. The methods and instrumentation described should find broad use in exploring complex fluid rheology and testing microstructure-based constitutive equations.

Saturated random packing of particles built of two identical, relatively shifted spheres in two- and three-dimensional flat and homogeneous space was studied numerically using a random sequential adsorption algorithm. The shift between centers of spheres varied from $0.0$ to $8.0$ sphere diameters. Numerical simulations allowed the determination of random sequential adsorption kinetics, the saturated random coverage ratio, as well as the available surface function and density autocorrelation function.

Self-folding is the autonomous folding of two-dimensional shapes into three-dimensional forms in response to an external stimulus. This paper focuses on light-induced self-folding of prestrained polymer sheets patterned with black ink. The ink absorbs the light and the resulting heat induces the polymer beneath the ink to relax faster than the rest of the sheet. A simple geometric model captures both the folding angle and folding kinetics associated with this localized shrinkage. The model assumes that (1) the polymer in contact with the ink shrinks at a rate determined by the temporal temperature profile of the hinge surface; (2) the bottom of the sheet, which is cooler, does not shrink considerably; and (3) a linear gradient of strain relaxation exists across the film between these two extremes. Although there are more complex approaches for modeling folding, the appeal of this model is its simplicity and ease of use. Measurements of the macroscopic, thermally driven shrinkage behavior of the sheets help predict the kinetics of folding by determining how fast the top of the hinge shrinks as a function of temperature and time. These measurements also provide information about the temperature required to induce folding and offer indirect measurement of the glass transition temperature of the polymer that comprises the sheet.

We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.

The Lagrange-mesh method is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. With a basis of Lagrange functions involving associated Laguerre polynomials related to the Gauss quadrature, the method is applied to the Dirac equation. The potential may possess a $1/r$ singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers $n+1$ of mesh points, where $n$ is the principal quantum number. Numerically exact mean values of powers $-2$ to 3 of the radial coordinate $r$ can also be obtained with $n+2$ mesh points. For the Yukawa potential, a 15-digit agreement with benchmark energies of the literature is obtained with 50 or fewer mesh points.

Typically the force between paramagnetic particles in a uniform magnetic field is described using the dipolar model, which is inaccurate when particles are in close proximity to each other. Instead, the exact force between paramagnetic particles can be determined by solving a three-dimensional Laplace's equation for magnetostatics under specified boundary conditions and calculating the Maxwell stress tensor. The analytical solution to this multi-boundary-condition Laplace's equation can be obtained by using a solid harmonics expansion in conjunction with the Hobson formula. However, for a multibody system, finite truncation of the Hobson formula does not lead to convergence of the expansion at all points, which makes the approximation physically unrealistic. Here we present a numerical method for solving this Laplace's equation for magnetostatics. This method uses a smoothed representation to replace all the boundary conditions. A two-step propagation is used to dramatically accelerate the calculation without losing accuracy. Using this method, we calculate the force between two paramagnetic particles in a uniform and a rotational external field and compare our results with other models. Furthermore, the many-body effects for three-particle, ten-particle, and 24-particle systems are examined using the same method. We also calculate the interaction between particles with different magnetic susceptibilities and particle diameters. The Laplace's equation solver method described in this article that is used to determine the force between paramagnetic particles is shown to be very useful for dynamic simulations for both two-particle systems and a large cluster of particles.