The internal structure of porous materials is of importance in many areas such as medicine, chemical engineering, and petrophysics. While diffraction methods such as x ray are widely used to study the internal pore space, these methods suffer from the loss of the phase information in the detected signals. Recently, an advanced diffusive diffraction NMR method was proposed [F. B. Laun et al., Phys. Rev. Lett. 107, 048102 (2011)] which is predicted to preserve the phase information, thus overcoming this severe limitation of diffraction methods in general. Here we provide experimental confirmation that the suggested approach is indeed able to acquire the diffractive signal including its phase which allows the direct image reconstruction of the pore space, averaged over all pores. We furthermore prove that this approach may combine the advantages of magnetic resonance imaging, namely, its robust and straightforward image reconstruction via a Fourier transformation with the much improved spatial resolution of pulsed gradient spin echo NMR.

We consider the dynamics of small tracer particles in turbulent quantum fluids. The complicated interaction processes of vortex filaments, the quantum constraints on vorticity, and the varying influence of both the superfluid and the normal fluid on the tracer particle effectively lead to a superstatistical Langevin-like model that in a certain approximation can be solved analytically. An analytic expression for the probability density function of velocity $v$ of the tracer particle is derived that exhibits not only the experimentally observed $v^{-3}$ tails but also the correct behavior near the center of the distribution, in excellent agreement with experimental measurements and numerical simulations. Our results are universal and do not depend on details of the quantum fluid.

In the presence of wave dissipation, phase-space structures emerge in nonlinear Vlasov dynamics. Our theory gives a simple relation between the growth of these coherent structures and that of the wave energy. The structures can drive the wave by direct momentum exchange, which explains the existence of nonlinear instabilities in both barely unstable and linearly stable (subcritical) regimes. When dissipation is modeled by a linear term in the field equation, simple expressions of a single-hole growth rate and of the initial perturbation threshold are in agreement with numerical simulations.

When an object needs to be found in a random environment by a team of searchers, we obtain a formula for the total number of searchers needed if at least $k$ of them must find the object by some large time $S$. We then compute the energy consumed by the $N$ searchers if they are all stopped as soon as $k$ are successful, and we show that the energy consumed decreases as $N$ increases. We also consider the case in which the successful ones stop but the unsuccessful ones continue until a time-out or until they are destroyed by some other “natural” cause, and in this case we see that the energy consumed increases with $N$ as one might expect. The transform-based analysis used assumes that the searchers’ motion is described by diffusion processes, that the search space is infinite and homogeneous, that searchers can be destroyed or become permanently lost as they proceed, and that a time-out mechanism is used so that any searcher that exceeds this time-out and has not succeeded in its quest will be removed and replaced by a new searcher that behaves stochastically and independently of its predecessor.

We propose a Langevin equation for systems in an environment with nonuniform temperature. At odds with an older proposal, ours admits a locally Maxwellian steady state, local equipartition holds, and for detailed-balanced (reversible) systems statistical and physical entropies coincide. We describe its thermodynamics, which entails a generalized version of the first law and Clausius's characterization of reversibility. Finally, we show that a Brownian particle constrained into a smooth curve behaves according to our equation, as if experiencing nonuniform temperature.

Defects in liquid crystals are used to model topological entities ranging from Skyrmions in high-energy physics to early-universe cosmic strings, as well as find practical applications in self-assembly of diffraction gratings and in scaffolding of plasmonic nanoparticles, but they are hard to control and organize into three-dimensional lattices. We laterally scan focused laser beams to produce periodic arrays of twist-stabilized defects forming either linear (fingers) or axially symmetric (torons) configurations in partially polymerizable liquid crystal films. Polymerization allows for stabilization of these structures and the formation of three-dimensional arrays of defects by stacking of the thin cholesteric films on top of each other. In the process of fabrication of such arrays, we polymerize the liquid crystal film with an array of torons or fingers and then sequentially produce and photopolymerize new liquid crystal layers on top of it, thus obtaining a three-dimensional structure of twist-stabilized defects in a layer-by-layer fashion. Templating by the polymerized layer spontaneously yields ordered organization of fingers and torons in the new cholesteric layer, thus enabling a three-dimensional ordered structure of defects. Nondestructive three-dimensional imaging of director fields by use of three-photon excitation fluorescence polarizing microscopy reveals the nature of topological singularities and physical underpinnings behind the observed templating effect. Three-dimensional patterning of defects templates the self-assembly of plasmonic nanoparticles into individual singularities and their arrays, laying the groundwork for potential applications in nanophotonics, plasmonics, metamaterial fabrication, and nanoscale energy conversion.

External torques affect the trajectories of swimming microorganisms. We calculate analytically the effective three-dimensional diffusivity of a spherical active particle subject to both a constant external torque and thermal noise. We find that the presence of a torque renders the effective diffusive behavior anisotropic. The analytical results are compared with Brownian dynamics simulations and we obtain excellent agreement. For steady swimmers an external torque always decreases the effective swimmer diffusivity whereas it may be enhanced for time-reversible swimmers.

We propose a simple model for a binary decision making process on a graph, motivated by modeling social decision making with cooperative individuals. The model is similar to a random field Ising model or fiber bundle model, but with key differences in behavior on heterogeneous networks. For many types of disorder and interactions between the nodes, we predict with mean field theory discontinuous phase transitions that are largely independent of network structure. We show how these phase transitions can also be understood by studying microscopic avalanches and describe how network structure enhances fluctuations in the distribution of avalanches. We suggest theoretically the existence of a “glassy” spectrum of equilibria associated with a typical phase, even on infinite graphs, so long as the first moment of the degree distribution is finite. This behavior implies that the model is robust against noise below a certain scale and also that phase transitions can switch from discontinuous to continuous on networks with too few edges. Numerical simulations suggest that our theory is accurate.

In this paper we study synchronization of random clustered networks consisting of Kuramoto oscillators. More specifically, by developing a mean-field analysis, we find that the presence of cycles of order 3 does not play an important role with regard to network synchronization, showing that the synchronization of random clustered networks can be described by tree-based theories, even for high values of clustering. In order to support our findings, we provide numerical simulations considering clustered and nonclustered networks, which are in good agreement with our theoretical results.

In the present work, we consider a framework for characterizing electro-osmotic flows in topographically complicated porous media and derive an effective up-scaled transport parameter to quantify this. We term this parameter the electro-permeability, which characterizes the electro-osmotic flow through composite porous media in analogy with Darcy's law. The electro-permeability tensor, thus introduced, serves a simple means of relating the volume flow rate with the applied electric field without going into the intricacies of the microstructure of the porous domain. First, we consider cases where the solid fractions have a fractal dimension generated by the Mandelbrot set, purely for the sake of demonstration. Based on such considerations, we employ the method of homogenization to obtain the effective electro-permeability parameter from the numerical simulations executed over a representative volume element. Our derived electro-permeability tensor components exhibit functional relationships with the solid or liquid fraction as well as the topography of the porous medium. Having established these functional relationships, we evaluate the tensor components for a binary composite porous medium in which one constituent has markedly high ζ potential than the other constituent, for illustration with potential relevance in microfluidics. We establish the sensitivity of the electro-permeability tensor on the domain morphology, solid fraction, ratio of solid fractions of the two phases having the two different ζ potential values, and the ζ potential contrast and compare it with equivalent Darcy permeability for the same. We thus provide a simple mathematical framework that may be immensely helpful for devising a computationally efficient way of characterizing electro-osmosis through topographically complicated porous media.

We investigate two-dimensional turbulence within the instanton formalism, which determines the most probable field in a stochastic classical field theory starting from the Martin-Siggia-Rose path integral. We perform an approximate analysis of these equations based on a variational ansatz using elliptical vortices. The results are evolution equations for the positions and the shapes of the vortices. We solve these ordinary differential equations numerically. The extremal action for the two-point statistics is determined by the merging of two elliptical vortices. We discuss the relationship of this dynamical system to the inverse cascade process of two-dimensional turbulence.

Weak nonlinear low-frequency modes in a two-component electron-ion dissipative quantum plasma are investigated. The dissipation arises due to the electron-ion collision. It is found that a standard perturbative approach leads to a new nonlinear equation for the dynamics of the finite amplitude wave. The quantum diffraction effect in the presence of collisions introduces a dissipative effect. The numerical solutions of this novel equation predict the existence of weak shock structures.

Optical properties of a composite material made of ferromagnetic metal nanoparticles embedded in a dielectric host are studied. We constructed an effective dielectric tensor of the composite material taking into account the orientational distribution of nanoparticle magnetic moments in external magnetic field. A nonlinear dependence of the optical rotation on magnetic field resulting from the reorientation of nanoparticles is demonstrated. The theoretical findings were applied to the magneto-optical experimental data of cobalt ferromagnetic nanoparticles embedded in a dielectric liquid host. The dependence of the Faraday rotation on Co-based ferromagnetic nanoparticles was measured as a function of the external magnetic field, varying the size of nanoparticles and the wavelength of light. The proposed approach enables quantitative determination of the magnetic moment and the plasma frequency of a single nanoparticle, and from this the size of the nonmagnetic shell of magnetic nanoparticles.

We study the competitive RSOS-BD model focusing on the validity of the Kardar-Parisi-Zhang (KPZ) ansatz $h\left(t\right)=v_{\infty }t+{\left(\Gamma t\right)}^{\beta }\chi$ and the universality of the height distributions (HDs) near the point where the model has Edwards-Wilkinson (EW) scaling. Using numerical simulations for long times, we show that the system is asymptotically KPZ, as expected, for values of the probability of the RSOS component very close to $p=p_c\approx 0.83$. Namely, the growth exponents converge to ${\beta }_{\mathrm{KPZ}}=1/3$ and the HDs converge to the GOE Tracy-Widom distribution; however, the convergence seems to be faster in the last ones. While the EW-KPZ crossover appears in the roughness scaling in a broad range of probabilities $p$ around $p_c$, a Gaussian-GOE crossover is not observed in the HDs into the same interval, possibly being restricted to values of $p$ very close to $p_c$. These results improve recent ones reported by de Assis et al. [Phys. Rev. E 86, 051607 (2012)], where, based on smaller simulations, the KPZ scaling was argued to break down in a broad range of $p$ around $p_c$.

We report on observations of the flow of plastic particles floating on the surface of water in a rectangular channel. The system is driven by moving one wall of the channel at a constant velocity. The opposite side of the channel is open, and the particles are pushed into a region free of material. During the flow, video of the particle motions is captured, and the average force on the pushing wall is measured. We have studied particle shapes that are both circular disks and rectangular bars. We find that when the rectangular bars form a layer at the side walls of the channel (whether or not the central region is filled with disks or additional rectangular bars), the system exhibits sudden increases and decreases in the average force on the driving wall. This behavior is consistent with the existence of jamming in the system. We report on the shape and velocity dependence of these force fluctuations, and the evidence that buckling of the rectangular blocks at the wall is responsible for generating the jamming dynamics.

We study the nonsteady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units. We compute the time-dependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, nonuniversal microscopic time regime, we find a nontrivial long crossover towards the nonsteady macroscopic critical regime. This “mesoscopic” time regime is robust under changes of the microscopic disorder, including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms, yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale ($L\simeq 2^{25}$) simulations for the nonsteady dynamics of the continuum displacement quenched Edwards-Wilkinson equation, getting accurate and consistent depinning exponents for this class: $\beta =0.245\pm 0.006$, $z=1.433\pm 0.007$, $\zeta =1.250\pm 0.005$, and $\nu =1.333\pm 0.007$. Our study may explain numerical discrepancies (as large as $30\%$ for the velocity exponent $\beta$) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.

The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solid-state physics and materials science, its percolation properties have received little attention. We investigate several nonuniversal percolation properties on this lattice using Monte Carlo simulation. We show that the percolation threshold is $p_c^{\text{bond}}=0.18602\pm 0.00002$ for bonds and $p_c^{\text{site}}=0.26240\pm 0.00005$ for sites. The number of clusters at the threshold per site is $n_c^{\text{bond}}=0.28458\pm 0.00005$ and $n_c^{\text{site}}=0.03998\pm 0.00005$. The stacked triangular lattice is a convenient choice to study the RGB model [Schrenk et al., Sci. Rep. 2, 751 (2012)]. We present results on this model and its scaling behavior at the percolation threshold.

Spin-glass phases and phase transitions for $q$-state clock models and their $q\to \infty$ limit the $XY$ model, in spatial dimension $d=3$, are studied by a detailed renormalization-group study that is exact for the $d=3$ hierarchical lattice and approximate for the cubic lattice. In addition to the now well-established chaotic rescaling behavior of the spin-glass phase, each of the two types of spin-glass phase boundaries displays, under renormalization-group trajectories, their own distinctive chaotic behavior. These chaotic renormalization-group trajectories subdivide into two categories, namely as strong-coupling chaos (in the spin-glass phase and, distinctly, on the spin-glass–ferromagnetic phase boundary) and as intermediate-coupling chaos (on the spin-glass–paramagnetic phase boundary). We thus characterize each different phase and phase boundary exhibiting chaos by its distinct Lyapunov exponent, which we calculate. We show that, under renormalization group, chaotic trajectories and fixed distributions are mechanistically and quantitatively equivalent. The phase diagrams of arbitrary even $q$-state clock spin-glass models in $d=3$ are calculated. These models, for all non-infinite $q$, have a finite-temperature spin-glass phase. Furthermore, the spin-glass phases exhibit a universal ordering behavior, independent of $q$. The spin-glass phases and the spin-glass–paramagnetic phase boundaries exhibit universal fixed distributions, chaotic trajectories and Lyapunov exponents. In the $XY$ model limit, our calculations indicate a zero-temperature spin-glass phase.

We employ a recent technique for building complex networks from time series data to construct a directed network embodying time structure to collate the predictive properties of individual granular sensors in a series of biaxial compression tests. For each grain, we reconstruct a static predictive model. This combines a subset selection algorithm and an information theory fitting criterion that selects which other grains in the assembly are best placed to predict a given grain's local stress throughout loading history. The local stress of a grain at each time step is summarized by the magnitude of its particle load vector. A directed network is constructed by representing each grain as a node, and assigning an in-link to a grain from another grain if the latter is selected within the best predictive model of the first grain. The grains with atypically large out-degree are thus the most responsible for predicting the stress history of the other grains: These turn out to be only a few grains which reside inside shear bands. Moreover, these “smart grains” prove to be strongly linked to the mechanism of force chain buckling and intermittent rattler events. That only a small number of grain sensors situated in the shear band are required to accurately capture the rheological response of all other grains in the assembly underlines the crucial importance of nonlocal interactions, espoused by extended continuum theories which posit nonlocal evolution laws. Findings here cast the spotlight on two specific mechanisms as being key to the formulation of robust evolution laws in deforming granular materials under compression and shear: the long held mechanism for energy dissipation of force chain buckling and the sudden switch in roles that a rattler plays as it enters in and out of force chains.

The relation between liquid-liquid phase transitions and waterlike density anomalies in core-softened potentials of fluids was investigated in an exactly solvable one-dimensional lattice model and in a three-dimensional fluid with a Fermi-like potential, the latter by molecular dynamics. Both systems were shown to present three liquid phases, two liquid-liquid phase transitions closely connected to two distinct regions of anomalous density increase. We propose that an oscillatory behavior observed on the thermal expansion coefficient as a function of pressure can be used as a signature of the connection between the liquid-liquid phase transition and density anomaly.