The critical behavior of a random fiber bundle model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers nontrivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a nonuniversal behavior in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behavior for larger avalanches, a new behavior for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly, the prominence of nonuniversal behavior in avalanche size distribution depends on the system parameters.

The critical value of the reaction rate able to sustain the propagation of an invasive front is obtained for general non-Markovian biased random walks with reactions. From the Hamilton-Jacobi equation corresponding to the mean field equation we find that the critical reaction rate depends only on the mean waiting time and on the statistical properties of the jump length probability distribution function and is always underestimated by the diffusion approximation. If the reaction rate is larger than the jump frequency, invasion always succeeds, even in the case of maximal bias. Numerical simulations support our analytical predictions.

Much of the understanding of bulk liquids has progressed through study of the limiting case in which molecules interact via purely repulsive forces, such as a hard-core or “repulsive ramp” potential. In the same spirit, we report progress on the understanding of confined water by examining the behavior of waterlike molecules interacting with planar walls via purely repulsive forces and compare our results with those obtained for Lennard-Jones (LJ) interactions between the molecules and the walls. Specifically, we perform molecular dynamics simulations of 512 waterlike molecules interacting via the TIP5P potential and confined between two smooth planar walls that are separated by $1.1\mathrm{nm}$. At this separation, there are either two or three molecular layers of water, depending on density. We study two different forms of repulsive confinement, when the water-wall interaction potential is either (i) $1∕r^9$ or (ii) a WCA-like repulsive potential. We find that the thermodynamic, dynamic, and structural properties of the liquid in purely repulsive confinements qualitatively match those for a system with a pure LJ attraction to the wall. In previous studies that include attractions, freezing into monolayer or trilayer ice was seen for this wall separation. Using the same separation as these previous studies, we find that the crystal state is not stable with $1∕r^9$ repulsive walls but is stable with WCA-like repulsive confinement. However, by carefully adjusting the separation of the plates with $1∕r^9$ repulsive interactions so that the effective space available to the molecules is the same as that for LJ confinement, we find that the same crystal phases are stable. This result emphasizes the importance of comparing systems only using the same effective confinement, which may differ from the geometric separation of the confining surfaces.

The aging dynamics after shear rejuvenation in a glassy clay suspension have been investigated through dynamic light scattering (DLS). Two different aging regimes are observed: one is attained if the sample is rejuvenated before its gelation and one after the rejuvenation of the gelled sample. In the first regime, the application of shear fully rejuvenates the sample, as the system dynamics soon after shear cessation follow the same aging evolution characteristic of standard aging. In the second regime, aging proceeds very fast after shear rejuvenation, and classical DLS cannot be used. An original protocol to measure an ensemble-averaged intensity-correlation function is proposed and its consistency with classical DLS is verified. The fast aging dynamics of rejuvenated gelled samples exhibit a power-law dependence of the slow relaxation time on the waiting time.

An extension of the vector-wave theory of antiferroelectric bent-core liquid crystals to columnar and soft-crystalline mesophases is presented. We enumerate and describe the phases resulting from the condensation of one, two, and three vector waves in the isotropic liquid of bent-core molecules. Beside the one-dimensional $B2$ and smectic-$CP$ phases, 24 columnar and soft-crystalline orthorhombic, monoclinic, and triclinic phases can be stabilized when two or three waves have nonparallel wave vectors. Their symmetry groups, molecular arrangements, and phase diagrams are worked out and used to identify the structures of the main observed bent-core phases and their various subphases.

We present analytical solutions of the hydrodynamic resistance force a spherical particle experiences when it moves through a polymer solution containing nonadsorbing chains. Polymer depletion results in a reduced polymer concentration and fluid viscosity near the particle surface. The nonuniform physical properties in the fluid phase affect the transport behavior of a translating and rotating sphere as compared with the case of uniform properties. Based on Stokes’ stream function theory, we develop a simplified two-layer approximation by using a step function to represent the viscosity profile. The presence of the polymer solution is formulated in terms of correction functions to the translational and rotational friction of a sphere in a pure solvent. The results are in fair agreement with systematic measurements of the friction of a colloidal sphere when it moves through a polymer solution [Koenderink et al., Phys. Rev. E 69, 021804 (2004)]. The analysis also predicts an apparent slip length in terms of the viscosity ratio and thickness of the depletion layer.

It is well known that the hydrophobic effect is the major factor that drives a protein toward collapse and folding. We analyze the variation of the solvent-accessible surface area of amino acids in small fragments of protein $(3⩽N⩽45)$. In this way, we look into 5526 protein chains deposited in the Brookhaven Protein Data Bank. The accessible surface area behaves as a power law for $N⩾9$. The comparison between the loss of accessible area and the self-similar behavior gives us a measure of the possibility of an amino acid to have apolar or polar side chain. It is therefore possible to infer about amino acid hydrophobicity, i.e., if one amino acid has a hydrophobic side chain or if it has a hydrophilic one. Furthermore, the present findings indicate that the variation of the accessible surface area describes an alternative hydrophobicity scale.

In red blood cells there is a cortical cytoskeleton; a two-dimensional elastic network of membrane-attached proteins. We describe, using a simple model, how the metabolic activity of the cell, through the consumption of ATP, controls the stiffness of this elastic network. The unusual mechanical property of active strain softening is described and compared to experimental data. As a by-product of this activity there is also an active contribution to the amplitude of membrane fluctuations. We model this membrane as a field of independent “curvature motors,” and calculate the spectrum of active fluctuations. We find that the active cytoskeleton contributes to the amplitude of the membrane height fluctuations at intermediate wavelengths, as observed experimentally.

A simple flow network model of biological signal transduction is investigated. Networks with prescribed signal processing functions, robust against random node or link removals, are designed through an evolutionary optimization process. Statistical properties of large ensembles of such networks, including their characteristic motif distributions, are determined. Our analysis suggests that robustness against link removals plays the principal role in the architecture of real signal transduction networks and developmental genetic transcription networks.

We use theoretical principles to study how complex networks are topologically organized at large scale. Using spectral graph theory we predict the existence of four different topological structural classes of networks. These classes correspond, respectively, to highly homogenous networks lacking structural bottlenecks, networks organized into highly interconnected modules with low inter-community connectivity, networks with a highly connected central core surrounded by a sparser periphery, and networks displaying a combination of highly connected groups (quasicliques) and groups of nodes partitioned into disjoint subsets (quasibipartites). Here we show by means of the spectral scaling method that these classes really exist in real-world ecological, biological, informational, technological, and social networks. We show that neither of three network growth mechanisms—random with uniform distribution, preferential attachment, and random with the same degree sequence as real network—is able to reproduce the four structural classes of complex networks. These models reproduce two of the network classes as a function of the average degree but completely fail in reproducing the other two classes of networks.

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of the damped Benjamin-Ono equation. The structure of the dispersive shock is considered in this method.

We investigate the vorticity dynamics in a turbulent vortex using scattering of acoustic waves. Two ultrasonic beams are adjusted to probe simultaneously two spatial scales in a given volume of the flow, thus allowing a dual channel recording of the dynamics of coherent vorticity structures. Our results show that this allows one to measure the average energy transfer time between different spatial length scales, and that such transfer goes faster at smaller scales.

We present spectroscopic measurements of plasma parameters (electron density $n_{\mathrm{e}}$, electron temperature $T_{\mathrm{e}}$, gas temperature $T_{\mathrm{g}}$, underpopulation factor $b$) in the hot-core region in front of the cathode of a low-current, free-burning arc discharge in argon under atmospheric pressure. The discharge is operated in the hot-core mode, creating a hot cathode region with plasma parameters similar to high-current arcs in spite of the fact that we use comparatively low currents (less than $20\mathrm{A}$). We use continuum emission and (optically thin) line emission to determine $n_{\mathrm{e}}$ and $T_{\mathrm{e}}$. We apply relaxation measurements based on a power-interruption technique to investigate deviations from local thermodynamic equilibrium (LTE). These measurements let us determine the gas temperature $T_{\mathrm{g}}$. All measurements are performed side-on with charge-coupled-device cameras as detectors, so that all measured plasma parameters are spatially resolved after an Abel inversion. This yields the first ever spatially resolved observation of the non-LTE phenomena of the hot core in the near-cathode region of free-burning arcs. The results only partly coincide with previously published predictions and measurements in the literature.

The buckling of elastic bodies is a common phenomenon in the mechanics of solids. Wrinkling of membranes can often be interpreted as buckling under constraints that prohibit large-amplitude deformation. We present a combination of analytic calculations, experiments, and simulations to understand wrinkling patterns generated in a bilayer membrane. The model membrane is composed of a flexible spherical shell that is under tension and that is circumscribed by a stiff, essentially incompressible strip with bending modulus $B$. When the tension is reduced sufficiently to a value $\sigma$, the strip forms wrinkles with a uniform wavelength found theoretically and experimentally to be $\lambda =2\pi (B∕\sigma {)}^{1∕3}$. Defects in this pattern appear for rapid changes in tension. Comparison between experiment and simulation further shows that, with larger reduction of tension, a second generation of wrinkles with longer wavelength appears only when $B$ is sufficiently small.

We discuss the mechanism of fast and slow light generation when optical pulses propagate through a fiber taper coupled to an ultrahigh-$Q$ microsphere system in the time domain. Fast and slow light are explained as interference effects between ballistic light through the fiber and circulated light within the sphere. One of the striking effects predicted by this model is dynamic pulse splitting in the transmitted pulse at the critical coupling condition, where the coupling strength between the sphere and fiber equals the round-trip loss in the sphere. By realizing this critical coupling condition experimentally, we observed this dynamic pulse splitting effect.

We study tilings of the square lattice by linear trimers. For a cylinder of circumference $m$, we construct a conserved functional of the base of the tilings, and use this to block diagonalize the transfer matrix. The number of blocks increases exponentially with $m$. The dimension of the block corresponding to the largest eigenvalue is shown to grow as $(3∕2^{1∕3}{)}^m$. We numerically diagonalize this block for $m\le 27$, obtaining the estimate $S_{\infty }=0.158520\pm 0.000015$ for the entropy per site in the thermodynamic limit. We present numerical evidence that the continuum limit of the model has conformal invariance. We measure several scaling dimensions, including those corresponding to defects of monomers and $L$-shaped trimers. The trimer tilings of a plane admits a two-dimensional height representation. Monte Carlo simulations of the height variables show that the height-height correlations grows logarithmically at large separation, and the orientation-orientation correlations decay as a power law.

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential $\propto r^{-12}$ in $d=2$ dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width $D$) depends very sensitively on the precise boundary conditions at the two “walls” providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-)long range order is destroyed: The mean-square displacement of two particles $n$ lattice parameters apart in the $y$ direction along the walls then crosses over from the logarithmic increase (characteristic for $d=2$) to a linear increase with $n$ (characteristic for $d=1$). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width $D$ with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising and $XY$ models is made.

Colloidal particles that interact through strong, short-range, secondary attractions in liquids form irreversible “slippery” bonds that are not shear-rigid. Through event-driven simulations of slippery attractive spheres, we show that space-filling fractal clusters still emerge from the process of “slippery” diffusion-limited aggregation (DLA). Although slippery and classic DLA clusters have the same fractal dimension, $d_{\mathrm{f}}=2.5$, their average coordination numbers are quite different: $⟨z_{\mathrm{S}}⟩=6$ whereas $⟨z_{\mathrm{C}}⟩=2$. Local tetrahedral attractive jamming of the particles leads to a structure factor, $S\left(q\right)$, that exhibits dense cluster peaks at higher wave numbers, $q$, and a fractal power-law rise toward lower $q$.

Viscously damped particles driven past an evenly spaced array of potential energy wells or barriers may become kinetically locked in to the array, or else may escape from the array. The transition between locked-in and free-running states has been predicted to depend sensitively on the ratio between the particles’ size and the separation between wells. This prediction is confirmed by measurements on monodisperse colloidal spheres driven through arrays of holographic optical traps.