We investigate isotropic-isotropic, isotropic-nematic, and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom, and radial size ratios $\lambda$ up to 5. A fundamental measure density functional theory, previously used for the one-component model, is presented and results are compared against those from Onsager theory as a benchmark. For $\lambda \le 1.7$ the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of $\lambda$. For size ratios $\lambda \ge 2$, we find that demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of $\lambda$ than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles.

Broadband dielectric spectra of supercooled 1,2,6-hexanetriol are presented in order to reveal physical picture behind a glass transition of polyhydric alcohols. It has been reported so far that temperature dependences of $\alpha$ relaxation time for sugar alcohols exhibit systematic trend against number of carbon atoms or OH groups per molecule. However, because each molecule is composed of equal number of carbon atoms and OH groups in the case of the reported sugar alcohols, the more dominant parameter to govern the $\alpha$ relaxation dynamics has not been discussed. By using a chemical structure of the hexanetriol composed of the deferent number of carbon and OH, it is possible to determine the dominant parameter. From temperature dependence of $\alpha$ relaxation times, it is strongly supported that the number of OH groups is the dominant parameter. Furthermore, from an analysis of static dielectric constant, it is suggested that local hydrogen-bonding structure is similar among all polyhydric alcohols. From these two results, a simple picture of the origin of the systematic character is proposed.

We present the results of the experimental study of the two-port scattering matrix $\widehat{S}$ elastic enhancement factor $W_{S,\beta }$ for microwave irregular networks simulating quantum graphs with preserved and broken time reversal symmetry in the presence of moderate and strong absorption. In the experiment, quantum graphs with preserved time reversal symmetry were simulated by microwave networks which were built of coaxial cables and attenuators connected by joints. Absorption in the networks was controlled by the length of microwave cables and the use of microwave attenuators. In order to simulate quantum graphs with broken time reversal symmetry we used the microwave networks with microwave circulators. We show that the experimental results obtained for networks with moderate and strong absorption are in good agreement with the ones obtained within the framework of random matrix theory.

Starting from trace formulas for the tunneling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate complex-time paths. We show how this instantonlike approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunneling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunneling or resonant tunneling. Even though only one-dimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunneling.

We study effects of noise on pulse propagation in two bistable systems with flows: a chain of unidirectionally coupled neurons and a reaction-diffusion-convection equation with cubic nonlinearity. Pulse propagation in the systems is described by a common kinematical equation, which has exponential interaction between adjacent pulse fronts. The propagation length of pulses is then dealt with as a first passage time problem on it. We show that additive spatiotemporal noise increases the propagation length of unstable pulses and sustains pulse propagation. The mean propagation length of a single pulse increases infinitely in the presence of noise of infinitesimal strength. The propagation length of a pulse is distributed in a power-law form of exponent $-3/2$ as noise strength increases. A resonancelike behavior is also shown by bounding pulse width, and the mean propagation length is maximal at intermediate noise strength. Further, the proportion of survival pulses at some fixed length takes a maximum value at optimal noise strength.

We demonstrate an efficient and reliable method for wettability characterization by determining the contact angle $\theta$ which a liquid-vapor interface makes with a solid wall. The purpose is to overcome the difficulties, related to the curvature of the liquid-vapor interface, which make measurements of $\theta$ rather uncertain, especially on the micro- and nanoscale. The method employs a specially designed slitlike channel in contact with a reservoir whereby the wettability of one of the slit walls is to be examined whereas the other (auxiliary) wall is separated by half into a lyophilic and a lyophobic part so as to pin the incoming fluid and fix the one end of the liquid-vapor interface. In the present work, the physical background of the method is elucidated theoretically while the method’s applicability is demonstrated by molecular-dynamics simulation of a typical Lennard-Jones fluid, in contact with an atomistic wall. The wettability of the latter, as described by the corresponding contact angle $\theta$, is accurately determined by variation of the liquid-wall interaction in a very broad interval.

We have studied stable strata of gravity-induced phase separation in suspensions of synthetic Na-fluorohectorite clay in saline solutions. We have observed how the strata depend on clay concentration as well as on salt content. The mass distribution and density variation at the isotropic-nematic interface indicate that existing models and assumptions in existing simulations are able to relatively well account for the observed behavior. We suggest that discrepancies could be due to the high polydispersity and the irregular shape of our Na-fluorohectorite particles, as well as diffusive double-layer effects, which could result in a competition between nematic ordering and gelation. The dependence on ionic strength displays three main regimes irrespective of clay concentration. At low ionic strength ($\approx 0.1–5\text{mM}$ NaCl), the Debye screening length is longer than the van der Waals force range. In this regime, the particles repel each other electrostatically and entropy-driven Onsager-type nematic ordering may occur, although gelation effects could also play a role. For ionic strengths above about 5 mM, we believe that the van der Waals force comes into play and that particles attract each other locally according to the classical Derjaguin, Landau, Verwey, and Overbeek (DLVO) model of colloid interactions, resulting in a small-domain regime of attractive nematiclike ordering. In the third regime, for ionic strengths above $\approx 10\text{mM}$, the clay particles aggregate into larger assemblies, due to the dominant van der Waals force, and the observed birefringency is reduced. We have studied the nematic phase in detail between crossed polarizers and have found textures showing nematic Schlieren patterns. By rotating the polarizers as well as the samples, we have observed examples of disclinations of strengths $-1$, $-1/2$, and $+1$.

We investigate the structure of a tubular membrane adhering to a rigid cylindrical particle, in various radius ratios. Through a theoretical and numerical analysis of a free-energy model that uses Helfrich energy for the description of the membrane, we show that three distinct phases exist, depending on the ratio between radii of the membrane tube and the rigid cylinder and an adsorption parameter describing the attraction between the cylinder and tube surface. The adhesion transition from the desorbed to weakly adhered states is identified as a second-order phase transition; the wrapping transition from the weakly adhered to strongly adhered states is identified as a first-order phase transition.

When homoclinic orbits to an expanding periodic point exist, the point is called a snap-back repeller. Here, we consider the two-dimensional piecewise-linear map in canonical form, continuous and discontinuous, showing how snap-back repellers may be associated with robust chaotic attracting sets (not only with chaotic repellers). Examples are given both for the continuous and discontinuous maps.

Following a short report of our preliminary results [Sheeba et al., Phys. Rev. E 79, 055203(R) (2009)], we present a more detailed study of the effects of coupling delay in diffusively coupled phase oscillator populations. We find that coupling delay induces chimera and globally clustered chimera (GCC) states in delay coupled populations. We show the existence of multiclustered states that act as link between the chimera and the GCC states. A stable GCC state goes through a variety of GCC states, namely, periodic, aperiodic, long- and short-period breathers and becomes unstable GCC leading to global synchronization in the system, on increasing time delay. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.

We study the behavior of a magnetorheological fluid droplet confined to a Hele-Shaw cell in the presence of an applied radial magnetic field. Interfacial pattern formation is investigated by considering the competition among capillary, viscoelastic, and magnetic forces. The contribution of a magnetic field-dependent yield stress is taken into account. Linear stability analysis reveals the stabilizing role played by yield stress. On the other hand, a mode-coupling approach predicts that the resulting fingering structures should become less and less sharp as yield stress effects are increased. By employing a vortex-sheet formalism we have been able to identify a family of exact stationary solutions of the problem, unveiling the development of swollen polygonal patterns. A suggestive magnetically controlled shape transition in which the edges of the patterns change from convex to concave has been also identified.

This work considers the flow of a Newtonian fluid in a two-dimensional channel filled with an array of obstacles of distinct sizes that models an inhomogeneous medium. Obstacle sizes and positions are defined by the geometry of an Apollonian packing (AP). The radii of the circles are uniformly reduced by a factor $s<1$ for assemblies corresponding to the five first AP generations. The region of validity of Darcy’s law as a function of the channel Reynolds number is investigated for different values of $s$ and the dependency of the flow pattern and permeability with respect to porosity is established. Our results show that the semiempirical Kozeny-Carman scaling relation is satisfied provided the effects of the apparent porosity and $s$-dependent formation factor are properly considered.

The theory of elastic interaction of micrometer-sized axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self-energy of one colloidal particle and interaction energy between two particles in arbitrary confined nematic liquid crystals with strong anchoring condition on the bounding surfaces. Particular cases of dipole-dipole interaction in the homeotropic and planar nematic cell with thickness $L$ are considered and found to be exponentially screened on far distances with decay length ${\lambda }_{\text{dd}}=\frac{L}{\pi }$. It is predicted that bounding surfaces in the planar cell crucially change the attraction and repulsion zones of usual dipole-dipole interaction. As well it is predicted that the decay length in quadrupolar interaction is two times smaller than for the dipolar case in the homeotropic cell.

Anomalous diffusion of polymer chains in a polymer nanocomposite melt is investigated for different polymer-nanoparticle interaction strengths using stochastic molecular dynamics simulations. For spherical nanoparticles dispersed in a polymer matrix the results indicate that the chain motion exhibits three distinct regions of diffusion, the Rouse-like motion, an intermediate subdiffusive regime followed by a normal Fickian diffusion. The motion of the chain end monomers shows a scaling that can be attributed to the formation of strong “networklike” structures, which have been seen in a variety of polymer nanocomposite systems. Irrespective of the polymer-particle interaction strengths, these three regimes seem to be present with small deviations. Further investigation on dynamic structure factor shows that the deviations simply exist due to the presence of strong enthalpic interactions between the monomers with the nanoparticles, albeit preserving the anomaly in the chain diffusion. The time-temperature superposition principle is also tested for this system and shows a striking resemblance with systems near glass transition and biological systems with molecular crowding. The universality class of the problem can be enormously important in understanding materials with strong affinity to form either a glass, a gel or networklike structures.

In many cell types, calcium ion channels on the endoplasmic reticulum membrane occur in a clustered distribution. The channels generate either localized puffs, each comprising channels of only one cluster, or global calcium waves. In this work we model the calcium system as a two-dimensional lattice of active elements distributed regularly in an otherwise passive space. We address an important feature of the puff-wave transition, which is the difference in lifetime of puffs at a few hundred milliseconds and long-lived global waves with periods of several seconds. We show that such a lifetime difference between puffs and waves can be understood with strongly reduced ordinary differential equations modified by a time-scale factor that takes into account the coupling strength of active and passive regions determined by the ${\text{Ca}}^{2+}$ diffusion coefficient. Furthermore, we show that the point model can also describe very well the dependence of ${\text{Ca}}^{2+}$ oscillation characteristics on the cluster-cluster distance in the case of large diffusivity.

Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes. As the concentration of the transcription factor varies, the target genes thus undergo correlated changes, and this redundancy limits the ability of the cell to transmit information about input signals. We explore how interactions among the target genes can reduce this redundancy and optimize information transmission. Our discussion builds on recent work [Tkačik et al., Phys. Rev. E 80, 031920 (2009)], and there are connections to much earlier work on the role of lateral inhibition in enhancing the efficiency of information transmission in neural circuits; for simplicity we consider here the case where the interactions have a feed forward structure, with no loops. Even with this limitation, the networks that optimize information transmission have a structure reminiscent of the networks found in real biological systems.

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

The formation process of $s{p}^3$ hybridized carbon networks (i.e., diamondlike structures) in hydrogenated diamondlike carbon (DLC) films has been studied with the use of molecular-dynamics simulations. The processes simulated in this study are injections of hydrocarbon (${\text{CH}}_3$ and CH) beams into amorphous carbon (a-C) substrates. It has been shown that diamondlike $s{p}^3$ structures are formed predominantly at a subsurface level when the beam energy is relatively high, as in the “subplantation” process for hydrogen-free DLC deposition. However, for hydrogenated DLC deposition, the presence of abundant hydrogen at subsurface levels, together with thermal spikes caused by energetic ion injections, substantially enhances the formation of carbon-to-carbon $s{p}^3$ bonds. Therefore, the $s{p}^3$ bond formation process for hydrogenated DLC films essentially differs from that for hydrogen-free DLC films.