We study nematic electrohydrodynamic convection (EHC) under excitation with superimposed harmonic wave forms. Within the standard model for EHC, a time reversal of the excitation does not affect threshold voltages and pattern wavelengths obtained in a linear stability analysis. This was confirmed in experiments with superimposed square waves [Heuer et al., Phys. Rev. E 78, 036218 (2008)]. We show here that this symmetry with respect to time reversal of the excitation breaks down close to the transition from the conduction regime to the dielectric regime. The EHC standard model without flexoelectric terms fails to predict quantitatively correct threshold curves and wavelengths in a certain parameter range below the transition. This is an indication that a more elaborate description of the EHC mechanism is necessary in this range. We suggest that the weak electrolyte model has to be employed for a correct description. This is in accordance with observations of traveling rolls and of localized structures at onset of the convection in earlier experiments described in literature.

The length distributions of polymer fragments subjected to an elongational-flow-induced scission are profoundly affected by the fluid flow and the polymer bond strengths. In this paper, laminar elongational flow was used to induce chain scission of a series of circumference-programmed DNA nanotubes. The DNA nanotubes served as a model system for semiflexible polymers with tunable bond strength and cross-sectional geometry. The expected length distribution of fragmented DNA nanotubes was calculated from first principles by modeling the interplay between continuum hydrodynamic elongational flow and the molecular forces required to overstretch multiple DNA double helices. Our model has no-free parameters; the only inferred parameter is obtained from DNA mechanics literature, namely, the critical tension required to break a DNA duplex into two single-stranded DNA strands via the overstretching B-S DNA transition. The nanotube fragments were assayed with fluorescence microscopy at the single-molecule level and their lengths are in agreement with the scission theory.

Exact traveling wave and soliton solutions, including the bright-bright and dark-dark soliton pairs, are found for the system of two coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients, by employing the homogeneous balance principle and the F-expansion technique. A kind of shape-changing soliton collision is identified in the system. The collision is essentially elastic between the two solitons with opposite velocities. Our results demonstrate that the dynamics of solitons can be controlled by selecting the diffraction, nonlinearity, and gain coefficients.

A phase field crystal (PFC) density functional for binary mixtures is coarse grained and a formalism for calculating the simultaneous concentration, temperature, and density dependence of the surface energy anisotropy of a solid-liquid interface is developed. The methodology systematically relates bulk free energy coefficients arising from coarse graining to thermodynamic data, while gradient energy coefficients are related to molecular properties. Our coarse-grained formalism is applied to the determination of surface energy anisotropy in two-dimensional Zn-Al films, a situation relevant for quantitative phase field simulations of dendritic solidification in zinc coatings.

Three bent-core liquid-crystal compounds presenting the unusual columnar B1 to tilted polar smectic ($\text{Sm-}CP$ or B2) phase transition are studied through small-angle x-ray diffraction on aligned samples. The well-established character of the smectic phase helps to characterize the structural changes during the transition. A mechanism for this transition is proposed, which accounts for the low enthalpy usually observed in this process. The B1 phase is found to possess a great degree of lamellarization, with pseudosmectic ferroelectric layers along the crystallographic (11) planes. As a consequence of these observations a distribution of the block polarizations in the columnar structure is proposed.

We present a Green’s function-based perturbative approach to solving nonlinear reaction-diffusion problems in networks of endothelial cells. We focus on a single component $\left({\text{Ca}}^{2+}\right)$, piecewise nonlinear model of endoplasmic calcium dynamics and trans-membrane diffusion. The decoupling between nonlinear reaction dynamics and the linear diffusion enables the calculation of the diffusion part of the Green’s function for network of cells with nontrivial topologies. We verify analytically and then numerically that our approach leads to the known transition from propagation of calcium front to failure of propagation when the diffusion rate is varied relative to the reaction rates. We then derive the Green’s function for a semi-infinite chain of cells with various boundary conditions. We show that the calcium dynamics of cells in the vicinity of the end of the semi-infinite chain is strongly dependent on the boundary conditions. The behavior of the semi-infinite chain with absorbing boundary conditions, a simple model of a multicellular structure with an end in contact with the extracellular matrix, suggests behavioral differentiation between cells at the end and cells embedded within the chain.

We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension $d_g=\text{ln}3/\text{ln}2$, with the aim to probe for scaling behavior and to study the systematic dependence of the critical exponents on the dimension and structure of the lattices. We show that the scaling law $D\left(2-\tau \right)=d_w$ generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where $d_w=2$. Furthermore, we observe that the lattice dimension $d_g$, the fractal dimension of the random walk on the lattice $d_w$, and the critical exponent $D$ form a plane in three-dimensional parameter space, i.e., they obey the linear relationship $D=0.632\left(3\right)d_g+0.98\left(1\right)d_w-0.49\left(3\right)$.

The $q$-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the transfer matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of temperature for different number of states, $q$. Different scaling functions in temperature and $q$ are proposed. A quantitative agreement is found between results from both methods. No critical behavior is observed in the thermodynamic limit for any number of states.

In this paper an approach to identify delay phenomena from time series is developed. We show that it is possible to perform a reliable time delay identification by using quantifiers derived from information theory, more precisely, permutation entropy and permutation statistical complexity. These quantifiers show clear extrema when the embedding delay $\tau$ of the symbolic reconstruction matches the characteristic time delay ${\tau }_S$ of the system. Numerical data originating from a time delay system based on the well-known Mackey-Glass equations operating in the chaotic regime were used as test beds. We show that our method is straightforward to apply and robust to additive observational and dynamical noise. Moreover, we find that the identification of the time delay is even more efficient in a noise environment. Our permutation approach is also able to recover the time delay in systems with low feedback rate or high nonlinearity.

The nonlinear development of monotonic and oscillatory long-wave Marangoni instabilities in a heated horizontal layer of a liquid, containing an insoluble surfactant on its surface, is investigated. By means of asymptotic expansions, weakly nonlinear amplitude equations, which govern the evolution of disturbances near the instability threshold, are derived. It turns out that both kinds of instabilities are subcritical; therefore, the asymptotic analysis does not allow us to find any stable supercritical regimes. In the case of sufficiently small concentration of the surfactant, where only monotonic instability is possible, the preferred kind of hexagons is predicted.

The large scale behavior of the simplest non-mean-field spin-glass system is analyzed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the $ϵ$-expansion technique with two independent methods. The techniques presented show how the underlying ideas of the renormalization group apply also in this disordered model, in such a way that an $ϵ$-expansion can be consistently set up. By pushing such calculation to high orders in $ϵ$, a consistent non-mean-field theory for such disordered system could be established, giving a substantial contribution the development of a predictive theory for real spin glasses.

In colloidal crystals of spheres, dislocation motion is unrestricted. On the other hand, recent studies of relaxation in crystals of colloidal dimer particles have demonstrated that the dislocation dynamics in such crystals are reminiscent of glassy systems. The observed glassy dynamics arise as a result of dislocation cages formed by certain dimer orientations. In the current study, we use experiments and simulations to investigate the transition that arises when a pure sphere crystal is doped with an increasing concentration of dimers. Specifically, we focus on both dislocation caging and vacancy motion. Interestingly, we find that any nonzero fraction of dimers introduces finite dislocation cages, suggesting that glassy dynamics are present for any mixed crystal. However, we have also identified a vacancy-mediated uncaging mechanism for releasing dislocations from their cages. This mechanism is dependent on vacancy diffusion, which slows by orders of magnitude as the dimer concentration is increased. We propose that in mixed crystals with low dimer concentrations vacancy diffusion is fast enough to uncage dislocations and delay the onset of glassy dislocation dynamics.

We figured out periodic undulations of lamellae “zigzags” in liquid crystals under confinement by glass and patterned silicon hybrid cell, but in the absence of applied fields. The optical and internal structures of zigzags have been investigated from mesoscopic scale to molecular level by convoluting real and reciprocal space probes, such as polarized light microscopy, scanning electron microscopy, and microbeam x-ray diffraction. The homeotropic anchoring happens at air/liquid crystal, while planar one appears at glass or patterned silicon surfaces. The wetting and displacement of lamellae near the glass surface give rise to tilting and bending in the stacking of lamellae. This can provide a solution for the origin of periodic zigzags: asymmetric strain exerted to lamellae at two-dimensional glass surface and one-dimensional-like pattern. This can give a hint for potential photonic applications such as optical gratings and modulators due to its high periodicity.

The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation compared to the inclusion size. Two-dimensional compressive stresses in the membrane make the coupling coefficients decay asymptotically as $1/r^2$ with interparticle distance $r$. For the common case, where the distance to the substrate is of submicrometer scale, we present expressions for the coupling between distant disklike inclusions, which are valid for arbitrary inclusion size. We calculate the effect of inclusions on the response of the membrane and the associated corrections to the coupling diffusion coefficients to leading order in the concentration of inclusions. While at short distances the response is modified as if the membrane were a two-dimensional suspension, the large-distance response is not renormalized by the inclusions.

The peeling of adhesive tape is known to proceed with a stick-slip mechanism and produces a characteristic ripping sound. The peeling also produces light and when peeled in a vacuum, even X-rays have been observed, whose emissions are correlated with the slip events. Here we present direct imaging of the detachment zone when Scotch tape is peeled off at high speed from a solid surface, revealing a highly regular substructure, during the slip phase. The typical 4-mm-long slip region has a regular substructure of transverse $220\mu \text{m}$ wide slip bands, which fracture sideways at speeds over 300 m/s. The fracture tip emits waves into the detached section of the tape at $\sim 100\text{m}/\text{s}$, which promotes the sound, so characteristic of this phenomenon.

We introduce a model that allows for the prediction of the permeability of self-affine rough channels (one-dimensional fracture) and two-dimensional fractures over a wide range of apertures. In the lubrication approximation, the permeability shows three different scaling regimes. For fractures with a large mean aperture or an aperture small enough to the permeability being close to disappearing, the permeability scales as the cube of the aperture when the zero level of the aperture is set to coincide with the disappearance of the permeability. Between these two regimes, there is a third regime where the scaling is due to the self-affine roughness. For rough channels, the exponent is found to be $3-1/H$, where $H$ is the Hurst exponent. For two-dimensional fractures, it is necessary to introduce an equivalent aperture $b_c$ to make the scaling regime apparent. $b_c$ is defined as the hydraulic aperture of the most restrictive barrier crossing the fracture normal to the flow direction. This regime is characterized by an exponent higher than that for the one-dimensional case: it is 2.25 for $H=0.8$ and 2.16 for $H=0.3$.

We predict the existence of gray (dark) solitary waves in negative-index materials on the basis of a derived higher-order nonlinear Schrödinger equation. The conditions for the formation of three cases of gray solitary waves and exact analytical expressions are presented. Furthermore, we investigate the properties of these gray solitary waves in negative-index materials. The results show that the higher-order linear and nonlinear effects play a crucial role for the formation and properties of the second and third cases of gray solitary waves.

The application of the lattice Boltzmann method in two-phase flows is often restricted by the numerical instability at low viscosities. In this work, a multirelaxation-time (MRT) lattice Boltzmann model (LBM) is developed using the interaction potential approach. With the MRT collision term and a general force term, the new MRT model is able to significantly enhance the numerical stability at low viscosities, without appreciable increase in computation time or memory use. Advanced force formulation using the multirange potential can also be readily incorporated into the current MRT scheme. Numerical tests are first performed in two dimensions under equilibrium conditions. The MRT model is able to reduce the lowest stable viscosity by an order of magnitude compared to the single relaxation time LBM. In addition, the spurious velocity at the gas-liquid interface can also be significantly decreased by tuning the adjustable relaxation parameters. Then two sets of three-dimensional simulations are conducted to investigate the buoyant rise of a gas bubble in a low-viscosity liquid. In particular, millimeter air bubble in water, which is difficult for traditional two-phase LBM due to both low viscosity and high-surface tension, is successfully simulated using the MRT technique developed in this study. The simulated bubble shape and velocity are compared with the experimental results and empirical correlations in the literature, and the satisfactory agreement proves the validity of the MRT-LBM for two-phase flows.

Spin transport in the anisotropic Heisenberg chain is typically investigated theoretically with respect to the finiteness of transport coefficients only. Assuming their finiteness at high temperatures, we develop a concrete quantitative picture of the diffusion constant/(dc-)conductivity as a function of both the anisotropy parameter $\Delta$ and the spin quantum number $s$, going beyond the most commonly considered case $s=1/2$. Using this picture, we enable the comparison of finite transport coefficients from complementary theoretical methods on a quantitative level, having more significance than the finiteness alone. Our method is essentially based on an application of the time-convolutionless projection operator technique to current autocorrelations. This technique, although being a perturbation theory in $\Delta$, is found to be applicable, even if $\Delta$ is not small. This finding supports the applicability to a wider class of strongly interacting many-particle quantum systems.