Using x-ray scattering, we have studied the nematic to smectic-$A$ phase transition of the liquid crystal butyloxybenzilidene-octylaniline confined in an aerosil network. We find that the disorder introduced by the aerosil network destroys the long-range nature of the phase transition, and that the transition becomes similar to that observed in a finite-size system, with finite low-temperature correlation lengths of the ordered moments and a power-law behavior of the order parameter with respect to the reduced temperature observable in a limited temperature range. We also show evidence for a systematic evolution of the effective order parameter critical exponent $\beta$ with increasing disorder.

The three-tailed amphiphile ferric stearate molecule, which forms a bimolecular layer on water surface with molecules in the lower and upper layers in different conformations, has been studied to understand transfer and growth of bimolecular films on the surface of hydrophilic silicon substrates. This bimolecular film forms a two-dimensional lattice on water with a slightly distorted hexagonal lattice where both the in-plane and out-of-plane domain sizes are small. The film also showed larger microscopic rigidity compared to its macroscopic mechanical response. This asymmetric bimolecular layer was found to be preserved when the film is transferred on the substrates at different values of surface pressures ranging from $1\mathrm{mN}∕\mathrm{m}$ to near-collapse $(55\mathrm{mN}∕\mathrm{m})$. Both the upper and lower layers become denser and interfaces between these layers become sharper with increase in deposition pressure but the growths have different natures. The lower layer of transferred film is dense from $1\mathrm{mN}∕\mathrm{m}$ and, except for a steplike increase between 20 and $30\mathrm{mN}∕\mathrm{m}$, changes slowly in density. The density of the upper molecular layer grows continuously with surface pressure.

A study is made of how active membrane proteins can modify the long wavelength mechanics of fluid membranes. The activity of the proteins is modelled as disturbing the protein surroundings through nonlocal force distributions of which a force-dipole distribution is the simplest example. An analytic expression describing how the activity modifies the force-balance equation for the membrane surface is obtained in the form of a moment expansion of the force distribution. This expression allows for further studies of the consequences of the activity for nonplanar membranes. In particular the active contributions to mechanical properties such as tension and bending moments become apparent. It is also explained how the activity can induce a hydrodynamic attraction between the active proteins in the membrane.

The fluctuation spectrum of a quasispherical vesicle with active membrane proteins is calculated. The activity of the proteins is modeled as the proteins pushing on their surroundings giving rise to nonlocal force distributions. Both the contributions from the thermal fluctuations of the active protein densities and the temporal noise in the individual active force distributions of the proteins are taken into account. The noise in the individual force distributions is found to become significant at short wavelengths.

Vortex multipoles—consisting of a core of vorticity closely surrounded by several smaller vorticity concentrations of opposite sign—are obtained from the evolution of vorticity in two-dimensional simulations. Using a meshless vortex method, we obtained triangular and square vortices, surrounded by three and four satellites, respectively. These structures have only been observed before to emerge from zero-circulation initial conditions. We also observed a pentagon vortex. Here, we obtain compound vortices of nonzero total circulation, and suggest a gamut of multipolar asymptotic solutions to the Navier-Stokes equations.

We experimentally study the propagation of a reaction front in a chain of counter-rotating vortices. The front is induced by an autocatalytic chemical reaction in an aqueous solution stirred by electroconvective means. The front propagates by getting quickly engulfed in a vortex and by slowly crossing the separatrix to the next vortex. Its mean velocity along the chain increases with the flow intensity but shows both a bending and a dependence on the vortex aspect ratio. We recover these features within a kinematic model of front propagation by seeking the quickest front path through a vortex.

A type of matter wave diffraction management is presented that leads to subdiffractive solitonlike structures. The proposed management technique uses two counter-moving, identical periodic potentials (e.g., optical lattices). For suitable lattice parameters, a different type of atomic bandgap structure appears in which the effective atomic mass becomes infinite at the lowest edge of an energy band. This way, normal matter-wave diffraction (proportional to the square of the atomic momentum) is replaced by fourth-order diffraction, and hence the evolution of the system becomes subdiffractive.

A multiphase-field model previously proposed by the authors is reformulated in a thermodynamically consistent form and extended to multicomponent systems. The phase-field and diffusion equations, derived from a free energy functional, are compared to those postulated in the previous model in the limit of a binary alloy. The constraint of local quasiequilibrium, which is equivalent to the postulate of equal diffusion potentials for coexisting phases, is deduced from a variational principle. Solute partitioning and evaluation of the thermodynamic driving force for phase transformation are done by numerical minimization of the free energy of the multiphase system using the Calphad approach. A local extrapolation scheme which enhances the computational efficiency for complex numerical simulations of technical alloys is presented. It is shown that this extrapolation scheme, used in a “multibinary” approximation, reproduces the former model without restriction to dilute solutions.

With the advancement in the information age, people are using electronic media more frequently for communications, and social relationships are also increasingly resorting to online channels. While extensive studies on traditional social networks have been carried out, little has been done on online social networks. Here we analyze the structure and evolution of online social relationships by examining the temporal records of a bulletin board system (BBS) in a university. The BBS dataset comprises of 1908 boards, in which a total of 7446 students participate. An edge is assigned to each dialogue between two students, and it is defined as the appearance of the name of a student in the from- and to-field in each message. This yields a weighted network between the communicating students with an unambiguous group association of individuals. In contrast to a typical community network, where intracommunities (intercommunities) are strongly (weakly) tied, the BBS network contains hub members who participate in many boards simultaneously but are strongly tied, that is, they have a large degree and betweenness centrality and provide communication channels between communities. On the other hand, intracommunities are rather homogeneously and weakly connected. Such a structure, which has never been empirically characterized in the past, might provide a new perspective on the social opinion formation in this digital era.

The notion of Granger causality between two time series examines if the prediction of one series could be improved by incorporating information of the other. In particular, if the prediction error of the first time series is reduced by including measurements from the second time series, then the second time series is said to have a causal influence on the first one. We propose a radial basis function approach to nonlinear Granger causality. The proposed model is not constrained to be additive in variables from the two time series and can approximate any function of these variables, still being suitable to evaluate causality. Usefulness of this measure of causality is shown in two applications. In the first application, a physiological one, we consider time series of heart rate and blood pressure in congestive heart failure patients and patients affected by sepsis: we find that sepsis patients, unlike congestive heart failure patients, show symmetric causal relationships between the two time series. In the second application, we consider the feedback loop in a model of excitatory and inhibitory neurons: we find that in this system causality measures the combined influence of couplings and membrane time constants.

Patterns can be used effectively to characterize dynamical orbits as regular or chaotic. The proposed method focuses on local, epochal characterization of orbits as opposed to global characterization usually employed by most established measures. The “patterns method” provides essentially a measure of chaos strength for every extremum of a signal. For this reason, it provides information about sticky epochs of chaotic orbits, as well as time-dependent orbits. This way it can be used to give extremely detailed pictures of the phase space of a system, as well as to provide characterizations early in the evolution of orbits. Moreover, the method applies generally; all that is required is a signal, of which an orbit is merely an example.

Lattice Boltzmann methods are of limited applicability for direct numerical simulation of turbulent flow due to instabilities in the zero viscosity limit. We observe that this is caused by an insufficient degree of Galilean invariance of the relaxation-type Lattice Boltzmann collision operator. The cascaded digital lattice Boltzmann automata described here, provides a method with which to achieve stable collision operators down to the limit of zero viscosity.

We present a model for pore stabilization in membranes without surface tension. Whereas an isolated pore is always unstable (since it either shrinks, tending to reseal, or grows without bound until membrane disintegration), it is shown that excluded volume interactions in a system of many pores can stabilize individual pores of a given size in a certain range of model parameters. For such a multipore membrane system, the distribution of pore size and associated pore lifetime are calculated within the mean-field approximation. We predict that, above the temperature $T_m$, when the effective line tension becomes negative, the membrane exhibits a dynamic sievelike porous structure.

We study the structure of the twist-grain-boundary phase of chiral liquid crystals by numerically minimizing the Landau–de Gennes free energy. We analyze the morphology of layers at the grain boundary, to better understand the mechanism of frustration between the smectic layer order and chirality. As the chirality increases, the layer compression energy strongly increases while the effective layer bending rigidity is reduced due to unlocking of the layer orientation and the director. This results in large deviation of the layer morphology from that of Scherk’s first minimal surface and linear stack of screw dislocations.

The effect of a high-frequency signal on the FitzHugh-Nagumo excitable model is analyzed. We show that the firing rate is diminished as the ratio of the high-frequency amplitude to its frequency is increased. Moreover, it is demonstrated that the excitable character of the system, and consequently the firing activity, is suppressed for ratios above a given threshold value. In addition, we show that the vibrational resonance phenomenon turns up for sufficiently large noise strength values.

Inclusion of solid particles drastically affects the pattern evolution of phase separation of a binary fluid mixture, via preferential wetting of one of the phases to the particles. Here we study this problem by numerical simulation, which incorporates interparticle hydrodynamic interactions properly. When particles favor one of the components of a mixture, wetting layers are quickly formed on the particle surfaces and all particles are eventually included into the more wettable phase. For immobile particles, domains of the more wettable phase are pinned to the particles and the domain growth is thus suppressed. For this case, the domain size at a certain phase-separation time decreases monotonically with increasing the particle concentration. For mobile particles, on the other hand, the reentrant morphological transformation is observed as a function of the particle concentration: With an increase in the particle concentration, the domain morphology of the more wettable phase sequentially changes from network, droplet to network. We found that the final morphological transition is induced by wetting-induced depletion interaction: Strong attractive interactions act among particles when the total volume of the more wettable phase is not enough to cover all the particles by wetting layers.

In this work we study the generation of respiratory patterns by oscine birds. We present a model capable of generating realistic respiratory patterns, during normal respiration and song production. The model accounts for the interaction between neural nuclei and air sac dynamics. We performed experiments in vivo in order to test the predictions of the model, measuring air sac pressure during song and normal respiration in canaries (Serinus canaria).

Understanding the topology of complex systems abstracted to networks is important for unraveling their functional capabilities. Many such networks follow the small-world and scale-free regimes. Several models of artificially growing networks lead to this observed network topology. Most previously proposed models for growing networks, such as rich-get-richer and duplication-divergence, produce realistic network topologies but do not consider the effects of exogenous forces such as optimization for adaptation in shaping network topology. It is likely that such forces have shaped complex systems throughout their evolution. To develop further insights into possible mechanisms that shape networks, a model that uses several previously proposed network growth algorithms was developed to grow networks that adapt under exogenous stress. A decision tree problem was used to generate a complex Boolean function. Growing networks were required to adapt to correctly decode this function using an evolutionary selection process. Under this growth regimen all growing network models are similarly adaptable. The newly added nodes tend to cluster into pathways emanating from few inputs, regardless of the growth algorithm. Distribution of redundant pathways from inputs to the output follow a power-law function with a scaling exponent $(\sim 1.3)$. Similar distribution of redundant pathways was observed from inputs in a cell signaling network and an air traffic control network. A flat distribution of redundant pathways from inputs was observed in growing networks that do not attempt to adapt. This analysis provides initial insights into distribution of pathways in naturally evolving complex systems that have defined input-output relationships.

The Glauber model is reconsidered based on a quantum formulation of the master equation. Unlike the conventional approach the temperature and the Ising energy are included from the beginning by introducing a Heisenberg-like picture of the second quantized operators. This method enables us to get an exact expression for the transition rate of a single flip process $w_i\left({\sigma }_i\right)$ which is in accordance with the principle of detailed balance. The transition rate differs significantly from the conventional one due to Glauber in the low-temperature regime. Here the behavior is controlled by the Ising energy and not by the microscopic time scale.