We address the relaxation dynamics in hydrogen-bonded supercooled liquids near (but above) the glass transition, measured via broadband dielectric spectroscopy (BDS). We propose a theory based on decomposing the relaxation of the macroscopic dipole moment into contributions from hydrogen-bonded clusters of $s$ molecules, with $s_{\text{min}}\le s\le s_{\text{max}}$. The existence of $s_{\text{max}}$ is translated into a sum rule on the concentrations of clusters of size $s$. We construct the statistical mechanics of the supercooled liquid subject to this sum rule as a constraint, to estimate the temperature-dependent density of clusters of size $s$. With a theoretical estimate of the relaxation time of each cluster, we provide predictions for the real and imaginary parts of the frequency-dependent dielectric response. The predicted spectra and their temperature dependence are in accord with measurements, explaining a host of phenomenological fits like the Vogel-Fulcher fit and the stretched exponential fit. Using glycerol as a particular example, we demonstrate quantitative correspondence between theory and experiments. The theory also demonstrates that the $\alpha$ peak and the “excess wing” stem from the same physics in this material. The theory also shows that in other hydrogen-bonded glass formers the excess wing can develop into a $\beta$ peak, depending on the molecular material parameters (predominantly the surface energy of the clusters). We thus argue that $\alpha$ and $\beta$ peaks can stem from the same physics. We address the BDS in constrained geometries (pores) and explain why recent experiments on glycerol did not show a deviation from bulk spectra. Finally, we discuss the dc part of the BDS spectrum and argue why it scales with the frequency of the $\alpha$ peak, providing an explanation for the remarkable data collapse observed in experiments.

The “$\mathsf{V}$-shaped switching” mode in high polarization ferroelectric liquid crystals was studied with the aim of stabilizing the monostable bookshelf structure with the spontaneous polarization parallel to the glass plates. The director field in such cells was confirmed to be sensitive to both the liquid crystal properties and the cell parameters. In cells with only polyimide alignment layers, hysteresis free switching was never obtained, with bistable and asymmetric monostable structures compromising the zero-field dark state and preventing an ideal, hysteresis-free analog response. By incorporating a ${\mathrm{SiO}}_2$ layer between the ITO electrode and the polyimide, the undesired states were suppressed and essentially hysteresis-free switching was obtained for driving frequencies in the range $0.2–200\mathrm{Hz}$. Cells rubbed only on one side give more uniform alignment than cells rubbed on both sides but their inherent asymmetry shifts the long-term dark state away from $0\mathrm{V}$ and causes the response to gray level voltage modulation to be slightly asymmetric. The formation of different types of states as a function of the values of the surface parameters, and the observed stabilization of the $\mathsf{V}$-shaped switching structure by the dielectric surface layers, are in good agreement with an earlier analysis by Copic et al. [Phys. Rev. E 65, 021701 (2002)].

We investigate a longitudinally loaded elastic nanorod inside a cylindrical channel and show within the context of classical elasticity theory that the Euler buckling instability leads to a helical postbuckling form of the rod within the channel. The local pitch of the confined helix changes along the channel and so does the longitudinal force transmitted along the rod, diminishing away from the loaded end. This creates a possibility of jamming of the nanorod within the channel.

We study the microrheology of nanoparticle shells [A. D. Dinsmore et al., Science 298, 1006 (2002)] and viral capsids [I. L. Ivanovska et al., Proc. Natl. Acad. Sci. U.S.A. 101, 7600 (2004)] by computing the mechanical response function and thermal fluctuation spectrum of a viscoelastic spherical shell that is permeable to the surrounding solvent. We determine analytically the damped dynamics of bend and compression modes of the shell coupled to the solvent both inside and outside the sphere in the zero Reynolds number limit. We identify fundamental length and time scales in the system, and compute the thermal correlation function of displacements of antipodal points on the sphere and the mechanical response to pinching forces applied at these points. We describe how such a frequency-dependent antipodal correlation and/or response function, which should be measurable in new AFM-based microrheology experiments, can probe the viscoelasticity of these synthetic and biological shells constructed of nanoparticles.

From a study of the budding yeast cell cycle, we found that the cellular network evolves to have the least cost for realizing its biological function. We quantify the cost in terms of the dissipation or heat loss characterized through the steady-state properties: the underlying landscape and the associated flux. We found that the dissipation cost is intimately related to the stability and robustness of the network. With the least dissipation cost, the network becomes most stable and robust under mutations and perturbations on the sharpness of the response from input to output as well as self-degradations. The least dissipation cost may provide a general design principle for the cellular network to survive from the evolution and realize the biological function.

In this paper, we generalize a recently introduced expectation maximization (EM) method for graphs and apply it to content-based networks. The EM method provides a classification of the nodes of a graph, and allows one to infer relations between the different classes. Content-based networks are ideal models for graphs displaying any kind of community and/or multipartite structure. We show both numerically and analytically that the generalized EM method is able to recover the process that led to the generation of such networks. We also investigate the conditions under which our generalized EM method can recover the underlying content-based structure in the presence of randomness in the connections. Two entropies, $S_q$ and $S_c$, are defined to measure the quality of the node classification and to what extent the connectivity of a given network is content based. $S_q$ and $S_c$ are also useful in determining the number of classes for which the classification is optimal.

We study the dependence of friction on surface roughness, sliding velocity, and temperature. Expanding on the classic treatment of Greenwood and Williamson, we show that the fractal nature of a surface has little influence on the real area of contact and the static friction coefficient. A simple scaling argument shows that the static friction exhibits a weak anomaly $\mu \sim A_0^{-\chi /4}$, where $A_0$ is the apparent area and $\chi$ is the roughness exponent of the surface. We then develop a method to calculate atomic-scale friction between a microscopic asperity, such as the tip of a friction force microscope (FFM) and a solid substrate. This method, based on the thermal activation of the FFM tip, allows a quantitative extraction of all the relevant microscopic parameters and reveals a universal scaling behavior of atomic friction on velocity and temperature. This method is extended to include a soft atomic substrate in order to simulate FFM scans more realistically. The tip is connected with the support of the cantilever by an ideal spring and the substrate is simulated with a ball-spring model. The tip and substrate are coupled with repulsive potentials. Simulations are done at different temperatures and scanning velocities on substrates with different elastic moduli. Stick-slip motion of the tip is observed, and the numerical results of the friction force and distribution of force maxima match the theoretical framework.

We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated and derive analytic formulas for the joint nearest-neighbor degree probability distribution. Using those results we describe correlations in maximal entropy connected random graphs. We show that connected graphs are disassortative and that correlations are strongly related to the presence of one-degree nodes (leaves). We propose an efficient algorithm for generating connected random graphs. We illustrate our results with several examples.

We investigate the pattern formation produced by precipitated species during solvent evaporation through the numerical solution of a set of partial differential equations that account for the mechanisms of evaporation, diffusion, and precipitation. A pattern is formed because solvent evaporation provokes precipitation of species near the border of the system producing ringlike depositions from the edge to the center. Solvent evaporation is modeled as occurs with a liquid drop on a surface. The spacing between rings and its width are constant and roughly constant, respectively. Pattern formation follows the evaporation process inducing trends on pattern formation that are different to those produced by the precipitation of two species in a diffusive front (Liesegang rings). The spatial structure of rings under solvent evaporation is similar to those observed during solvent evaporation on two oppositely charged colloids and is attributable to the competition between precipitation and evaporation processes.

The current theory of alternating-current electro-osmosis (ACEO) is unable to explain the experimentally observed flow reversal of planar ACEO pumps at high frequency (above the peak, typically 10–100 kHz), low salt concentration $\left(1–1000\mu \text{M}\right)$, and moderate voltage (2–6 V), even taking into account Faradaic surface reactions, nonlinear double-layer capacitance, and bulk electrothermal flows. We attribute this failure to the breakdown of the classical Poisson-Boltzmann model of the diffuse double layer, which assumes a dilute solution of pointlike ions. In spite of low bulk salt concentration, the large voltage induced across the double layer leads to crowding of the ions and a related decrease in surface capacitance. Using several mean-field models for finite-sized ions, we show that steric effects generally lead to high-frequency flow reversal of ACEO pumps, similar to experiments. For quantitative agreement, however, an unrealistically large effective ion size (several nanometers) must be used, which we attribute to neglected correlation effects.

Approaching energy coupling in laser-irradiated metals, we point out the role of electron-electron collision as an efficient control factor for ultrafast optical absorption. The high degree of laser-induced electron-ion nonequilibrium drives a complex absorption pattern with consequences on the transient optical properties. Consequently, high electronic temperatures determine largely the collision frequency and establish a transition between absorptive regimes in solid and plasma phases. In particular, taking into account umklapp electron-electron collisions, we performed hydrodynamic simulations of the laser-matter interaction to calculate laser energy deposition during the electron-ion nonequilibrium stage and subsequent matter transformation phases. We observe strong correlations between optical and thermodynamic properties according to the experimental situations. A suitable connection between solid and plasma regimes is chosen in accordance with models that describe the behavior in extreme, asymptotic regimes. The proposed approach describes as well situations encountered in pump-probe types of experiments, where the state of matter is probed after initial excitation. Comparison with experimental measurements shows simulation results which are sufficiently accurate to interpret the observed material behavior. A numerical probe is proposed to analyze the transient optical properties of matter exposed to ultrashort pulsed laser irradiation at moderate and high intensities. Various thermodynamic states are assigned to the observed optical variation. Qualitative indications of the amount of energy coupled in the irradiated targets are obtained.

The dynamics of electrons in the presence of a positive ion is considered for conditions of weak electron-electron coupling but strong electron-ion coupling. The equilibrium electron density and the electric field time correlation functions are evaluated for semiclassical conditions using a classical statistical mechanics with a regularized electron-ion interaction for molecular dynamics simulation (MD). Results are reported for the autocorrelation function of the electron electric field at the ion for $0\le Z\le 40$, including conditions of strong electron-ion coupling. The electron stopping power and self-diffusion coefficient are determined from these results. Interpretation is provided by a theoretical analysis using the nonlinear Vlasov equation for the equilibrium structure, and a corresponding linear Vlasov equation for time correlation functions. The agreement of a simple mean field model with the semiclassical MD simulation is found to be quite good except for one state condition.

We study various solutions of the sine-Gordon model in $\left(1+1\right)$ dimensions. We use the Hirota method to construct some of them and then show that the wobble, discussed in detail in a recent paper by Kälberman, is one of such solutions. We concentrate our attention on a kink and its bound states with one or two breathers. We study their stability and some aspects of their scattering properties on potential wells and on fixed boundary conditions.

Some specific features and extensions of the continuous-time random-walk (CTRW) approach are analyzed in detail within the Markovian representation (MR) and CTRW-based non-Markovian stochastic Liouville equation (SLE). In the MR, CTRW processes are represented by multidimensional Markovian ones. In this representation the probability density function (PDF) $W\left(t\right)$ of fluctuation renewals is associated with that of reoccurrences in a certain jump state of some Markovian controlling process. Within the MR the non-Markovian SLE, which describes the effect of CTRW-like noise on the relaxation of dynamic and stochastic systems, is generalized to take into account the influence of relaxing systems on the statistical properties of noise. Some applications of the generalized non-Markovian SLE are discussed. In particular, it is applied to study two modifications of the CTRW approach. One of them considers cascaded CTRWs in which the controlling process is actually a CTRW-like one controlled by another CTRW process, controlled in turn by a third one, etc. Within the MR a simple expression for the PDF $W\left(t\right)$ of the total controlling process is obtained in terms of Markovian variants of controlling PDFs in the cascade. The expression is shown to be especially simple and instructive in the case of anomalous processes determined by the long-time tailed $W\left(t\right)$. The cascaded CTRWs can model the effect of the complexity of a system on the relaxation kinetics (in glasses, fractals, branching media, ultrametric structures, etc.). Another CTRW modification describes the kinetics of processes governed by fluctuating $W\left(t\right)$. Within the MR the problem is analyzed in a general form without restrictive assumptions on the correlations of PDFs of consecutive renewals. The analysis shows that fluctuations of $W\left(t\right)$ can strongly affect the kinetics of the process. Possible manifestations of this effect are discussed.

Ion transport in biological and synthetic nanochannels is characterized by phenomena such as ion current fluctuations and rectification. Recently, it has been demonstrated that nanofabricated synthetic pores can mimic transport properties of biological ion channels [P. Yu. Apel et al., Nucl. Instrum Methods Phys. Res. B 184, 337 (2001); Z. Siwy et al., Europhys. Lett. 60, 349 (2002)]. Here, the ion current rectification is studied within a reduced one-dimensional (1D) Poisson-Nernst-Planck (PNP) model of synthetic nanopores. A conical channel of a few nm to a few hundred nm in diameter, and of a few $\mu \text{m}$ long is considered in the limit where the channel length considerably exceeds the Debye screening length. The rigid channel wall is assumed to be weakly charged. A one-dimensional reduction of the three-dimensional problem in terms of corresponding entropic effects is put forward. The ion transport is described by the nonequilibrium steady-state solution of the 1D Poisson-Nernst-Planck system within a singular perturbation treatment. An analytic formula for the approximate rectification current in the lowest order perturbation theory is derived. A detailed comparison between numerical results and the singular perturbation theory is presented. The crucial importance of the asymmetry in the potential jumps at the pore ends on the rectification effect is demonstrated. This so constructed 1D theory is shown to describe well the experimental data in the regime of small-to-moderate electric currents.

Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior in nature, such as Gutenberg-Richter scaling. Because of the importance of long-range interactions in an elastic medium, we generalize the Burridge-Knopoff slider-block model to include variable range stress transfer. We find that the Burridge-Knopoff model with long-range stress transfer exhibits qualitatively different behavior than the corresponding long-range cellular automata models and the usual Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how quickly the friction force weakens with increasing velocity. Extensive simulations of quasiperiodic characteristic events, mode-switching phenomena, ergodicity, and waiting-time distributions are also discussed. Our results are consistent with the existence of a mean-field critical point and have important implications for our understanding of earthquakes and other driven dissipative systems.

We have performed a detailed dielectric investigation of the relaxational dynamics of glass-forming benzophenone. Our measurements cover a broad frequency range of $0.1\mathrm{Hz}\text{to}120\mathrm{GHz}$ and temperatures from far below the glass temperature well up into the region of the small-viscosity liquid. With respect to the $\alpha$ relaxation this material can be characterized as a typical molecular glass former with rather high fragility. A good agreement of the $\alpha$ relaxation behavior with the predictions of the mode coupling theory of the glass transition is stated. In addition, at temperatures below and in the vicinity of $T_g$ we detect a well-pronounced $\beta$ relaxation of Johari-Goldstein type, which with increasing temperature develops into an excess wing. We compare our results to literature data from optical Kerr effect and depolarized light scattering experiments, where an excess-wing-like feature was observed in the $1–100\mathrm{GHz}$ region. We address the question if the Cole-Cole peak, which was invoked to describe the optical Kerr effect data within the framework of the mode coupling theory, has any relation to the canonical $\beta$ relaxation detected by dielectric spectroscopy.

We have studied a sequence of anchoring transitions observed in nematic liquid crystals (NLCs) sandwiched between hydrophobic polyimide substrates treated with a plasma beam. There is a pronounced continuous transition from a homeotropic to a slightly tilted (nearly planar) alignment with the easy axis parallel to the incidence plane of the plasma beam (the zenithal transition) which takes place as the exposure dose increases. In NLCs with positive dielectric anisotropy, a further increase in the exposure dose results in in-plane reorientation of the easy axis by 90° (the azimuthal transition). This transition occurs through the twofold degenerate alignment characteristic of second-order anchoring transitions. In contrast to the critical behavior of anchoring, the contact angle of the NLC and water on the treated substrates declines monotonically with increasing exposure dose. It follows that the surface concentration of hydrophobic chains decreases continuously. The anchoring transitions under consideration are qualitatively interpreted by using a simple phenomenological model of competing easy axes which is studied by analyzing anchoring diagrams of generalized polar and nonpolar anchoring models.

Recent experiments show that external inplanar electric field can be employed to guide the molecular self-assembly in diblock copolymer (BCP) thin films to form lamellar nanostructures with potential applications in nanotechnology. We study this self-assembly process through a detailed coarse-grained phase-separation modeling. During the process, the free energy of the BCP films is modeled as the Ginzburg-Landau free energy with nonlocal interaction and electrostatic coupling. The resulting Cahn-Hilliard (CH) equation is solved using an efficient semi-implicit Fourier-spectral algorithm. Numerical results show that the morphology of order parameter formed in either symmetric or asymmetric BCP thin films is strongly influenced by the electric field. For symmetrical BCPs, highly ordered lamellar nanostructures evolved along the direction of the electric field. Phase nucleation and dislocation climbing in the BCP films predicted by the numerical simulation are in a good agreement with those observed in recent BCP electronanolithography. For asymmetrical BCPs, numerical simulation shows that nanodots are guided to align to the electric field. Furthermore, in the case of high electric field, nanodots formed in asymmetrical BCPs may further convert into highly ordered lamellar nanostructures (sphere-to-cylinder transition) parallel to the electric field. Effects of the magnitude of electric field, BCP asymmetry, and molecular interaction of BCPs on the self-assembly process are examined in detail using the numerical scheme developed in this study. The present study can be used for the prediction of the formation of nanostructures in BCP thin films and the quality control of BCP-based nanomanufacturing through optimizing the external electric fields.

We study the effect of noise for a physically realizable flow system with a hyperbolic chaotic attractor of the Smale-Williams type in the Poincaré cross section [Kuznetsov, Phys. Rev. Lett. 95, 144101 (2005)]. It is shown numerically that, by slightly varying the initial conditions on the attractor, one can obtain a uniform approximation of a noisy orbit by the trajectory of the system without noise, which is called the “shadowing” trajectory. We propose an algorithm for locating the shadowing trajectories in the system under consideration. Using this algorithm, we show that the mean distance between a noisy orbit and the approximating one does not depend essentially on the length of the time interval of observation, but only on the noise intensity. This dependence is nearly linear in a wide interval of the intensity of the noise. It is found that for weak noise the Lyapunov exponents do not depend noticeably on the noise intensity. However, in the case of strong noise the largest Lyapunov exponent decreases and even becomes negative, indicating the suppression of chaos by external noise.