We report the observation of a doubly periodic surface defect pattern in the liquid crystal 8CB, formed during the nematic–smectic-$A$ phase transition. The pattern results from the antagonistic alignment of the 8CB molecules, which is homeotropic at the surface and planar in the bulk of the sample cell. Within the continuum Landau–de Gennes theory of smectic liquid crystals, we find that the long period ($\approx$10 $\mu$m) of the pattern is given by the balance between the surface anchoring and the elastic energy of curvature wall defects. The short period ($\approx$1 $\mu$m) we attribute to a saddle-splay distortion, leading to a nonzero Gaussian curvature and causing the curvature walls to break up.

Rotational movement of isolated single cilia in mice embryo was investigated, which generates leftward fluid flow in the node cavity and plays an important role in left-right determination. The leftward unidirectional flow results from tilting of the rotational axis of the cilium to the posterior side. By combining computational fluid dynamics with experimental observations, we demonstrate that the leftward stroke can be more effective than expected for cases in which cilia tilting alone is considered with the no-slip condition under constant driving torque. Our results suggest that the driving torque is asymmetric.

We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of a non-Markovian generalized Langevin equation approach and associated multidimensional Markovian embedding dynamics. Viscoelastic deformations of the medium caused by the transport particle are modeled by a set of auxiliary Brownian quasiparticles elastically coupled to the transport particle and characterized by a hierarchy of relaxation times which obey a fractal scaling. The most slowly relaxing deformations which cannot immediately follow to the moving particle imprint long-range memory about its previous positions and cause subdiffusion and anomalous transport on a sufficiently long time scale. This anomalous behavior is combined with normal diffusion and transport on an initial time scale of overdamped motion. Anomalously slow directed transport in a periodic ratchet potential with broken space inversion symmetry emerges due to a violation of the thermal detailed balance by a zero-mean periodic driving and is optimized with frequency of driving, its amplitude, and temperature. Such optimized anomalous transport can be low dispersive and characterized by a large generalized Peclet number. Moreover, we show that overdamped subdiffusive ratchets can sustain a substantial load and do useful work. The corresponding thermodynamic efficiency decays algebraically in time since the useful work done against a load scales sublinearly with time following to the transport particle position, but the energy pumped by an external force scales with time linearly. Nevertheless, it can be transiently appreciably high and compare well with the thermodynamical efficiency of the normal diffusion overdamped ratchets on sufficiently long temporal and spatial scales.

We investigate a process of random walks of a point particle on a two-dimensional square lattice of size $n\times n$ with periodic boundary conditions. A fraction $p⩽20\%$ of the lattice is occupied by holes ($p$ represents macroporosity). A site not occupied by a hole is occupied by an obstacle. Upon a random step of the walker, a number of obstacles, $M$, can be pushed aside. The system approaches equilibrium in ${\left(n\ln n\right)}^2$ steps. We determine the distribution of $M$ pushed in a single move at equilibrium. The distribution $F\left(M\right)$ is given by $M^{\gamma }$ where $\gamma =-1.18$ for $p=0.1$, decreasing to $\gamma =-1.28$ for $p=0.01$. Irrespective of the initial distribution of holes on the lattice, the final equilibrium distribution of holes forms a fractal with fractal dimension changing from $a=1.56$ for $p=0.20$ to $a=1.42$ for $p=0.001$ (for $n=4,000$). The trace of a random walker forms a distribution with expected fractal dimension 2.

A viscous fluid flowing over plastic grains spontaneously generates single-thread channels. With time, these laminar analogues of alluvial rivers reach a reproducible steady state, showing a well-defined width and cross section. In the absence of sediment transport, their shape conforms with the threshold hypothesis which states that, at equilibrium, the combined effects of gravity and flow-induced stress maintain the bed surface at the threshold of motion. This theory explains how the channel selects its size and slope for a given discharge. In this light, laboratory rivers illustrate the similarity between the avalanche angle of granular materials and Shields's criterion for sediment transport.

Quantum chaotic scattering is referred to as the study of quantum behaviors of open Hamiltonian systems that exhibit transient chaos in the classical limit. Traditionally a central issue in this field is how the elements of the scattering matrix or their functions fluctuate as a system parameter, e.g., the electron Fermi energy, is changed. A tacit hypothesis underlying previous works was that the underlying classical phase-space structure remains invariant as the parameter varies, so semiclassical theory can be used to explain various phenomena in quantum chaotic scattering. There are, however, experimental situations where the corresponding classical chaotic dynamics can change characteristically with some physical parameter. Multiple-terminal quantum dots are one such example where, when a magnetic field is present, the classical chaotic-scattering dynamics can change between being nonhyperbolic and being hyperbolic as the Fermi energy is changed continuously. For such systems semiclassical theory is inadequate to account for the characteristics of conductance fluctuations with the Fermi energy. To develop a general framework for quantum chaotic scattering associated with variable classical dynamics, we use multi-terminal graphene quantum-dot systems as a prototypical model. We find that significant conductance fluctuations occur with the Fermi energy even for fixed magnetic field strength, and the characteristics of the fluctuation patterns depend on the energy. We propose and validate that the statistical behaviors of the conductance-fluctuation patterns can be understood by the complex eigenvalue spectrum of the generalized, complex Hamiltonian of the system which includes self-energies resulted from the interactions between the device and the semi-infinite leads. As the Fermi energy is increased, complex eigenvalues with extremely smaller imaginary parts emerge, leading to sharp resonances in the conductance.

We explore the phase diagram of the O($n$) loop model on the square lattice in the $(x,n)$ plane, where $x$ is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For $n\gg 2$ we find Ising-like phase transitions associated with the onset of a checkerboardlike ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one-half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of $n$ represents a softening of its particle-particle potentials. We also determine critical points in the range $-2\le n\le 2$. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the $n>2$ transition may continue into the dense phase of the $n\le 2$ loop model, or continue as a line of $n\le 2$ O($n$) multicritical points.

Unraveling the structure of complex biological networks and relating it to their functional role is an important task in systems biology. Here we attempt to characterize the functional organization of the large-scale metabolic networks of three microorganisms. We apply flux balance analysis to study the optimal growth states of these organisms in different environments. By investigating the differential usage of reactions across flux patterns for different environments, we observe a striking bimodal distribution in the activity of reactions. Motivated by this, we propose a simple algorithm to decompose the metabolic network into three subnetworks. It turns out that our reaction classifier, which is blind to the biochemical role of pathways, leads to three functionally relevant subnetworks that correspond to input, output, and intermediate parts of the metabolic network with distinct structural characteristics. Our decomposition method unveils a functional bow-tie organization of metabolic networks that is different from the bow-tie structure determined by graph-theoretic methods that do not incorporate functionality.

We present a study of the spatial correlation functions of a one-dimensional reaction-diffusion system in both equilibrium and out of equilibrium. For the numerical simulations we have employed the Gillespie algorithm dividing the system into cells to treat diffusion as a chemical process between adjacent cells. We find that the spatial correlations are spatially short ranged in equilibrium but become long ranged in nonequilibrium. These results are in good agreement with theoretical predictions from fluctuating hydrodynamics for a one-dimensional system and periodic boundary conditions.

This study investigates by experiment the dependence of the inertial-range exponent $m$ of the streamwise velocity spectrum on the external intermittency factor γ (≡ the fraction of time the flow is fully turbulent) and the mean shear $S$ in a turbulent square jet. Velocity measurements were made using hot-wire anemometry in the jet at 15 < $x$/$D_e$ < 40, where $D_e$ denotes the exit equivalent diameter, and for an exit Reynolds number of Re $=$ 50 000. The Taylor microscale Reynolds number $R_{\lambda }$ varies from about 70 to 450 in the present study. The TERA (turbulent energy recognition algorithm) method proposed by Falco and Gendrich [in Near-Wall Turbulence: 1988 Zoran Zariç Memorial Conference, edited by S. J. Kline and N. H. Afgan (Hemisphere Publishing Corp., Washington, DC, 1990), pp. 911–931] is discussed and applied to estimate the intermittency factor from velocity signals. It is shown that $m$ depends strongly on γ but negligibly on $S$. More specifically, $m$ varies with γ following $m=m_t+{\left(\ln {\gamma }^{-0.0173}\right)}^{1/2}$, where $m_t$ denotes the spectral exponent found in fully turbulent regions.

Test modes on turbulent magnetized plasmas are studied taking into account the stochastic ion trapping or eddying that characterizes the $\mathbf{E}\times \mathbf{B}$ drift in the background turbulence. It is shown that ion trapping provides an important physical mechanism for the complex nonlinear processes in drift turbulence evolution: generation of large-scale correlations and of zonal flow modes.

The efficiency of microscopic heat engines in a thermally heterogenous environment is considered. We show that—as a consequence of the recently discovered entropic anomaly—quasistatic engines, whose efficiency is maximal in a fluid at uniform temperature, have in fact vanishing efficiency in the presence of temperature gradients. For slow cycles the efficiency falls off as the inverse of the period. The maximum efficiency is reached at a finite value of the cycle period that is inversely proportional to the square root of the gradient intensity. The relative loss in maximal efficiency with respect to the thermally homogeneous case grows as the square root of the gradient. As an illustration of these general results, we construct an explicit, analytically solvable example of a Carnot stochastic engine. In this thought experiment, a Brownian particle is confined by a harmonic trap and immersed in a fluid with a linear temperature profile. This example may serve as a template for the design of real experiments in which the effect of the entropic anomaly can be measured.

A two-dimensional fractional Laplacian operator is derived and used to model nonlocal, nondiffusive transport. This integro-differential operator appears in the long-wavelength, fluid description of quantities undergoing non-Brownian random walks without characteristic length scale. To study bounded domains, a mask function is introduced that modifies the kernel in the fractional Laplacian and removes singularities at the boundary. Green's function solutions to the fractional diffusion equation are presented for the unbounded domain and compared to the one-dimensional Cartesian approximations. A time-implicit numerical integration scheme is presented to study fractional diffusion in a circular disk with azimuthal symmetry. Numerical studies of steady-state reveal temperature profiles in which the heat flux and temperature gradient are in the same direction, i.e., uphill transport. The response to off-axis heating, scaling of confinement time with system size, and propagation of cold pulses are investigated.

We examine the effect of spatial correlations on the phenomenon of real-space condensation in driven mass-transport systems. We suggest that in a broad class of models with a spatially correlated steady state, the condensate drifts with a nonvanishing velocity. We present a robust mechanism leading to this condensate drift. This is done within the framework of a generalized zero-range process (ZRP) in which, unlike the usual ZRP, the steady state is not a product measure. The validity of the mechanism in other mass-transport models is discussed.

We study the reduced dynamics of a pair of nondegenerate oscillators coupled collectively to a thermal bath. The model is related to the trilinear boson model where the idler mode is promoted to a field. Due to nonlinear coupling, the Markovian master equation for the pair of oscillators admits non-Gaussian equilibrium states, where the modes distribute according to the Bose-Einstein statistics. These states are metastable before the nonlinear coupling is taken over by linear coupling between the individual oscillators and the field. The Gibbs state for the individual modes lies in the subspace with infinite occupation quantum number. We present the time evolution of a few states to illustrate the behaviors of the system.

We have devised a lattice model to study force correlations in jamming granular solids in $d=2$ dimensions. We perform biased Monte Carlo simulations, favoring configurations with more bonds that bear no force, to “starve” the network of bonds and thereby control the distance from the isostatic point J. Increasingly long-ranged correlations are visible as point J is approached, not in the structure of the network of force-bearing bonds but in the spatial extent of perturbations of the force magnitudes consistent with a given starved network. The correlation length so defined diverges as the isostatic point is approached as a power law with an exponent of about $\xi \sim \delta Z^{-5}$. This divergence is much stronger than for the length scale of “soft modes” observed in jammed systems approaching point J from above.

We report an accurate Monte Carlo calculation of the phase diagram and clustering properties of the restricted primitive model with nonadditive hard-sphere diameters. At high density the positively nonadditive fluid shows more clustering than in the additive model and the negatively nonadditive fluid shows less clustering than in the additive model; at low density the reverse scenario appears. A negative nonadditivity tends to favor the formation of neutrally charged clusters starting from the dipole. A positive nonadditivity favors the pairing of like ions at high density. The critical point of the gas-liquid phase transition moves at higher temperatures and higher densities for a negative nonadditivity and at lower temperatures and lower densities for a positive nonadditivity. The law of corresponding states does not seem to hold strictly. Our results can be used to interpret recent experimental works on room temperature ionic liquids.

Melting and premelting phenomena in self-organized organic systems have been extensively explored in the literature, exploring distinct behaviors of different molecule lengths and morphologies. Nevertheless, the influence of the supramolecular assembly configuration on the occurrence of premelting remains poorly explored. Here we use phosphonic acids as model systems for self-organized molecular assemblies. These molecules exhibit long-range order on different types of substrates. The balance between chain-to-chain and head-to-head interactions leads to distinct types of stackings. Although their structural configurations are well understood, very little is known about their behavior near the melting transition. We show here that premelting occurs in lamellar structures and that its behavior depends directly on the ordered configuration assumed in the studied multilayers. Two molecules with different chain lengths were investigated: octadecyl phosphonic and octyl phosphonic acids. Although almost no dependence on the molecule length was observed, the occurrence of premelting is strongly influenced by their lamellar packing configuration. For tilted packings premelting is unfavored while in straight configurations, where alkyl chain interactions are weakened with respect to head-to-head interactions, strong premelting is observed. We find that the onset of premelting occurs at the domain boundaries with straight lamellar configurations and the domain sizes exhibit power law temperature dependences.

We examined the biaxial and antiferroelectric properties in the Smectic-$A{P}_A$ (Sm-$A{P}_A$) phase of bent-shaped DC-S-8. The biaxiality, which results from the existence of a secondary director, was well established from birefringence observations in the homeotropically aligned Sm-$A{P}_A$. By entering into Sm-$A{P}_A$ phase, the birefringence ($\Delta n$, difference between two refractive indices of short axes) continuously increased from 0 to 0.02 with decreasing temperature. The antiferroelectric switching and second harmonic generation (SHG) activity on the field-on state were also observed in the Sm-$A{P}_A$ phase, and the evaluated spontaneous polarization ($P_S$) value strongly depended on temperature. The temperature dependence of $\Delta n$ and $P_S$ resembles each other and follows Haller's approximation, showing that the biaxiality is due to polar packing in which the molecules are preferentially packed with their bent direction arranged in the same direction, and that the phase transition of Sm-$A{P}_A$ to Sm-$A$ is second order. The biaxiality was further examined in chiral Sm-$A{P}_A$${}^{*}$. Doping with chiral components induced the helical twisting of the secondary director in the Sm-$A{P}_A$${}^{*}$ phase, which was confirmed by observing the reflection of the circular dichroism (CD) bands in the homeotropically aligned cell. The helical pitch of Sm-$A{P}_A$${}^{*}$ is tunable in the range of 300–700 nm wavelength with a variation in the chiral content of 5 to 10 weight (wt)$\%$.

The present work studied the role of the polar group unconjugated oxygen on the inhibition of positronium (Ps) formation in two binary blends made from a set of chosen constituent polymers with polar and weakly polar groups (nonpolar). The polymer blend samples of PVC-EVA and PVC-SAN were investigated by coincidence Doppler broadening and positron lifetime techniques. The strong polar acetate group in the EVA contributed to positron annihilation with electrons of unconjugated oxygen (–C${}^{+}$=O${}^{-}$) as revealed by the momentum distribution curves peaking around 17 $P_L$ (10${}^{-3}$ $m_{0}c$). The ortho-Ps intensity indicated the unconjugated oxygen shows about a 28$\%$ Ps reduction even in the presence of a strong Ps inhibiting halogen (Cl${}^{-}$). In contrast, this effect was not seen in the PVC-SAN blends since SAN contains a weakly polar (nonpolar) acrylonitrile group (C≡N). Our results indicate the chlorine of PVC in the blends is a major contributor to Ps inhibition through the formation of a (Cl${}^{-}$-$e^{+)}$ bound state but the unconjugated oxygen in EVA of the PVC-EVA blend also plays a similar, but lesser, role.