Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local $C_{\infty v}$ symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals $\left(D_{\infty h}\right)$ in that it contains terms violating the $\mathbf{n}\to -\mathbf{n}$ symmetry. First we show that these ${\mathcal{Z}}_2$-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.

The dc electrical conductivity of double stranded DNA is investigated experimentally. Single DNA molecules are manipulated with subpiconewton force and deposited on gold nanoelectrodes by optical traps. The DNA is modified at its ends for specific bead attachments and along the chain to favor charge transfer between the DNA base pair stack and the electrodes. For an electrode separation of $70\mathrm{nm}$ we find, in aqueous environment, electrical resistances above $100\mathrm{G}\Omega$ indicating that even for weak stretching the double helix is almost insulating at this length scale.

We derive the second-order variation in the local static stress intensity factor of a tensile crack with a curved front. We then discuss the relevance of this result to the stability analysis of such fronts, and propose an equation of motion of planar crack fronts in heterogeneous media that contains two main ingredients—irreversibility of the propagation of the crack front and nonlinear effects.

We report a liquid-crystal pattern-formation experiment in which we break the lateral (translational) symmetry of a nematic medium with a laser-induced thermal gradient. The work is motivated by an improved measurement (reported here) of the temperature dependence of the electroconvection threshold voltage in planar-nematic 4-methoxybenzylidene-4-butylaniline. In contrast with other broken-symmetry-pattern studies that report a uniform drift, we observe a strip of counterpropagating rolls that collide at a sink point, and a strong temporally periodic amplitude modulation within a width of 3–4 rolls about the sink point. The time dependence of the amplitude at a fixed position is periodic but displays a nonsinusoidal relaxation-oscillation profile. After reporting experimental results based on spacetime contours and wave number profiles, along with a measurement of the change in the drift frequency with applied voltage at a fixed control parameter, we propose some potential guidelines for a theoretical model based on saddle-point solutions for Eckhaus-unstable states and coupled complex Ginzburg-Landau equations.

The fundamental dislocation processes of glide, climb, and annihilation are studied on diffusive time scales within the framework of a continuum field theory, the phase field crystal model. Glide and climb are examined for single edge dislocations subjected to shear and compressive strain, respectively, in a two-dimensional hexagonal lattice. It is shown that the natural features of these processes are reproduced without any explicit consideration of elasticity theory or ad hoc construction of microscopic Peierls potentials. Particular attention is paid to the Peierls barrier for dislocation glide or climb and the ensuing dynamic behavior as functions of strain rate, temperature, and dislocation density. It is shown that the dynamics are accurately described by simple viscous motion equations for an overdamped point mass, where the dislocation mobility is the only adjustable parameter. The critical distance for the annihilation of two edge dislocations as a function of separation angle is also presented.

Hydrophilic and hydrophobic aerosil particles immersed in S-(+)-[4-(2-methylbutyl) phenyl 4-$n$-octylbiphenyl-4-carboxylate] or [$p$-($n$-decyloxy) benzylidene-$p$-amino-(2-methylbutyl) cinnamate] compound have been studied by employing x-ray diffraction. The aerosil-induced relative layer compression $\Delta d$ has been measured in the smectic $A$ phase as a function of aerosil concentration $x$. $\Delta d\left(x\right)$ is shown to sensitively monitor the intermediate-rigid transition of the adaptive aerosil network. The dominant mechanism leading to the $\Delta d\left(x\right)$ profiles is the global establishment of the aerosil-induced molecular tilt in the smectic $A$ phase.

The dynamics of contact formation between different parts of a long chain molecule is of considerable interest in biology. The related processes of opening of a loop or closing to form a loop also are of considerable interest and have attracted the attention of experimentalists/theorists. For closing, results are available in the completely flexible limit. However, this limit is not realized in many cases. Recently, there have been investigations for the semiflexible case too. We develop an approach, which leads to an easy description of the dynamics, incorporating semiflexibility rigorously into account. With this approach, the dynamics of a semiflexible polymer ring formed by a weak bond between the two ends can be modeled as the escape of a particle over a barrier in a multidimensional potential energy surface. We then calculate the rate of opening using a multidimensional transition state theory. Effects of friction on the rate are also taken into account using the standard coupling to a bath of harmonic oscillators. We find that for shorter chains (i.e., semiflexible), the rate of opening is strongly length dependent and is well described by the equation $A(L∕l_p{)}^{\nu }\exp (B{l}_p∕L)$, with $L$ as the length, and $l_p$ as the persistence length, $A,B$ as the constants, and $\nu \approx 1.2$.

We show that spectral fluctuation of coexpression correlation matrices of yeast gene microarray profiles follows the description of the Gaussian orthogonal ensemble (GOE) of the random matrix theory (RMT) and removal of small values of the correlation coefficients results in a transition from the GOE statistics to the Poisson statistics of the RMT. This transition is directly related to the structural change of the gene expression network from a global network to a network of isolated modules.

A stochastic cellular automaton exhibiting a parity-conserving class transition has been investigated in the presence of quenched spatial disorder by large-scale simulations. Numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model. This opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state. For very strong disorder the model breaks up into blocks with exponential-size distribution and continuously changing critical exponents are observed. For strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model, in which residual particles survive the extinction. The critical dynamical behavior of this transition has been explored.

I report large-scale Monte Carlo studies of a one-dimensional height-restricted stochastic sandpile using the quasistationary simulation method. Results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly from those obtained using smaller systems, but are consistent with recent predictions derived from a Langevin equation for stochastic sandpiles [Ramasco et al., Phys. Rev. E 69, 045105(R) (2004)]. This suggests that apparent violations of universality in one-dimensional sandpiles are due to strong corrections to scaling and finite-size effects

We describe collaboration networks consisting of research projects funded by the European Union (EU) and the organizations involved in those projects. The networks are substantial in terms of size, complexity, and potential impact on research policies and national economies in the EU. In empirical determinations of the network properties, we observe characteristics similar to those of other collaboration networks, including scale-free degree distributions, small diameter, and high clustering. We present some plausible models for the formation and structure of networks with the observed properties.

We study computationally and experimentally the propagation of chemical pulses in complex geometries. The reaction of interest, CO oxidation, takes place on single crystal Pt(110) surfaces that are microlithographically patterned; they are also addressable through a focused laser beam, manipulated through galvanometer mirrors, capable of locally altering the crystal temperature and thus affecting pulse propagation. We focus on sudden changes in the domain shape (corners in a Y-junction geometry) that can affect the pulse dynamics; we also show how brief, localized temperature perturbations can be used to control reactive pulse propagation. The computational results are corroborated through experimental studies in which the pulses are visualized using reflection anisotropy microscopy.

A linear stability analysis is derived in self-imaging cavities for which the conditions for large Fresnel number are stated. In cases of both Fabry-Pérot and ring cavities a Hopf bifurcation is predicted at finite transverse wave number. The self-imaging Fabry-Pérot resonator operates as a longitudinal multimode cavity that invalidates the mean-field model. Above the bifurcation threshold, either vortex lattices, spirals, or targets occur, depending on the Fresnel number, the input intensity, and the mistunings. The time and spatial characteristics have different scales in the case of a self-imaging ring cavity, but the same sort of patterns are reported.

Finite-dimensional dynamical models for solitons of the cubic-quintic complex Ginzburg-Landau equation (CGLE) are derived. The models describe the evolution of the pulse parameters, such as the maximum amplitude, pulse width, and chirp. A clear correspondence between attractors of the finite-dimensional dynamical systems and localized waves of the continuous dissipative system is demonstrated. It is shown that stationary solitons of the CGLE correspond to fixed points, while pulsating solitons are associated with stable limit cycles. The models show that a transformation from a stationary soliton to a pulsating soliton is the result of a Hopf bifurcation in the reduced dynamical system. The appearance of moving fronts (kinks) in the CGLE is related to the loss of stability of the limit cycles. Bifurcation boundaries and pulse behavior in the regions between the boundaries, for a wide range of system parameters, are found from analysis of the reduced dynamical models. We also provide a comparison between various models and their correspondence to the exact results.

Porous polyethylene oxide–$b$–polyfluorooctylmethacrylate ($\mathrm{PEO}\text{−}b\text{−}\mathrm{PFOMA}$) diblock copolymer films were drop cast onto substrates from Freon (1,1,2-trichlorotrifluoroethane) in a humid atmosphere. The pores in the films exhibit long range hexagonal order in some cases, depending on the PFOMA-to-PEO molecular weight ratio. Films with the best ordered pores were formed with PFOMA-to-PEO ratios of $70\mathrm{kDa}:2\mathrm{kDa}$. The pores in the polymer films derive from water droplets that condense as Freon evaporates. The polymer stabilizes the water droplets, or “breath figures,” which act as an immiscible template that molds the porous film. Increased polymer hydrophobicity reduces the water wettability of the air/Freon interface, which in turn decreases water droplet nucleation, thus influencing the final pore size and spatial order in the polymer films. We describe how water droplet nucleation influences the final pore size and packing order in the polymer films.

We present a unified scaling theory for the optimal path connecting opposite edges of a disordered lattice of size $L$. Each bond of the lattice is assigned a cost $\exp \left(ar\right)$, where $r$ is a uniformly distributed random variable and $a$ is disorder strength. The optimal path minimizes the sum of the costs of the bonds along the path. We argue that for $L⪢a^{\nu }$, where $\nu$ is the correlation exponent of percolation, the path becomes equivalent to a directed polymer on an effective lattice consisting of blobs of size $\xi =a^{\nu }$. It is self-affined and characterized by the roughness exponent of directed polymers $\chi$. For $L⪡a^{\nu }$, or on the length scales below the blob size $\xi$, the path behaves as an optimal path in the strong disorder limit. It has a self-similar fractal shape with fractal dimension $d_{\mathrm{opt}}$. We derived the scaling relations for the length of the path, its transversal displacement, the average cost and its fluctuation. We test our scaling theoretical predictions by numerical simulations on a square lattice.

A simple model for simulating cross correlations of a many-assets market is discussed. Correlations between assets are initially considered within the context of the well-known one-factor model, in which a driving term common to all stocks is present. The results are compared to those of real market data corresponding to a set of 445 stocks taken from the Standard and Poors 500 index. The model is further extended by introducing a stochastic volatility within each time series using an autoregressive scheme. This artifical market reproduces the empirically observed fat tails in the distribution function of logarithmic price variations and, more important, leads to additional cross correlations between the time series, in better agreement with the real market behavior.

In this work, we present a lattice-Boltzmann model for the simulation of complex dissolution phenomena. We design boundary conditions to impose a fixed concentration or a surface flux for use in multicomponent lattice-Boltzmann models. These conditions can be applied to simulate complex reactive flow phenomena, e.g., in porous media. By combining the boundary conditions with a volume-of-fluid description of solid structures, the application area of the presented model is extended toward complex dissolution phenomena. The boundary conditions and the dissolution model are validated using benchmark problems with analytical solutions. The agreement is good in all tested cases.

A solution of the time-dependent Schrödinger equation is required in a variety of problems in physics and chemistry. These include atoms and molecules in time-dependent electromagnetic fields, time-dependent approaches to atomic collision problems, and describing the behavior of materials subjected to internal and external forces. We describe an approach in which the finite-element discrete variable representation (FEDVR) is combined with the real-space product (RSP) algorithm to generate an efficient and highly accurate method for the solution of the time-dependent linear and nonlinear Schrödinger equation. The FEDVR provides a highly accurate spatial representation using a minimum number of grid points $\left(N\right)$ while the RSP algorithm propagates the wave function in $O\left(N\right)$ operations per time step. Parallelization of the method is transparent and is implemented here by distributing one or two spatial dimensions across the available processors, within the message-passing-interface scheme. The complete formalism and a number of three-dimensional examples are given; its high accuracy and efficacy are illustrated by a comparison with the usual finite-difference method.

Absorbing boundary conditions are often employed in time-dependent mean-field calculations to cope with the problem of emitted particles which would otherwise return back onto the system and falsify the dynamical evolution. We scrutinize two widely used methods, imaginary potentials and gradual attenuation by a mask function. To that end, we consider breathing oscillations of a ${}^{16}\mathrm{O}$ nucleus computed on a radial one-dimensional grid in coordinate space. The most critical test case is the computation of resonance spectra in the (linear) domain of small amplitude motion. Absorbing bounds turn out to provide a reliable alternative to fully fledged continuum random phase approximation (RPA) calculations, although rather large absorbing bounds are required to simulate reliably well continuum conditions. We also investigate the computation of observables in the nonlinear domain. This regime turns out to be less demanding. Smaller absorbing margin suffice to achieve the wanted absorption effect.