We describe the evolution of a water drop saturated with NaCl and the growth of pure water droplets in a breath figure pattern (BF) condensing around it. This salty drop acts as a humidity sink, inhibiting the BF inside a ring at a distance $r=\delta$ from the sink center and slowing down BF growth outside the ring. The initial salty drop is taken either from a salt-saturated solution (type I experiment) or by placing an NaCl crystal on the substrate (type II experiment). The results are similar, provided that the initial time for type II evolution is taken at the end of the crystal dissolution. The evolution of the salty drop radius $R$ is deduced from the establishment of a three-dimensional hyperbolic concentration profile around the salty drop. This profile scales with $r/\delta$. Accounting for the salt concentration decrease with salty drop growth, $R$ is seen to grow as $t^5$. In the region $r>\delta$, water droplets nucleate and grow. The rate of evolution of the water droplets at constant $r/\delta$ can be used to determine the local water pressure. The corresponding data reasonably agree with a hyperbolic water vapor profile around the salty drop. These results can be applied to the growth of BF patterns to determine whether hyperbolic or linear water vapor profiles apply.

The phenomenological continuum model is used to study the director structure and dielectric response of the ferroelectric smectic-$A$ phase in thin planar cells. The frequency of the phase mode and the dielectric permittivity are calculated numerically as a function of the bias external DC electric field, cell thickness, the strength of polar surface anchoring, and the ratio between the bend and splay elastic constants. The theoretically obtained dependencies are in agreement with the recently reported experimental measurements, which show that in thin planar cells both the phase mode frequency and the dielectric permittivity decrease with increasing external bias electric field.

We study numerically and analytically first- and second-order phase transitions in neuronal networks stimulated by shot noise (a flow of random spikes bombarding neurons). Using an exactly solvable cortical model of neuronal networks on classical random networks, we find critical phenomena accompanying the transitions and their dependence on the shot noise intensity. We show that a pattern of spontaneous neuronal activity near a critical point of a phase transition is a characteristic property that can be used to identify the bifurcation mechanism of the transition. We demonstrate that bursts and avalanches are precursors of a first-order phase transition, paroxysmal-like spikes of activity precede a second-order phase transition caused by a saddle-node bifurcation, while irregular spindle oscillations represent spontaneous activity near a second-order phase transition caused by a supercritical Hopf bifurcation. Our most interesting result is the observation of the paroxysmal-like spikes. We show that a paroxysmal-like spike is a single nonlinear event that appears instantly from a low background activity with a rapid onset, reaches a large amplitude, and ends up with an abrupt return to lower activity. These spikes are similar to single paroxysmal spikes and sharp waves observed in electroencephalographic (EEG) measurements. Our analysis shows that above the saddle-node bifurcation, sustained network oscillations appear with a large amplitude but a small frequency in contrast to network oscillations near the Hopf bifurcation that have a small amplitude but a large frequency. We discuss an amazing similarity between excitability of the cortical model stimulated by shot noise and excitability of the Morris-Lecar neuron stimulated by an applied current.

The asymptotic behavior of a stochastic process subject to a colored noise is considered in the limit of vanishing correlation time of the noise. The interpretation of the multiplicative noise of the effective equation is investigated. The mathematically consistent formulation of the stochastic calculus for the limiting process is given. It differs in general from the Stratonovich one which is recovered when the colored noise obeys detailed balance or is a one-dimensional process.

We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.

We report on fingering and labyrinthine instabilities of the layer dislocation lines in freely suspended polar liquid-crystalline films. These polar fingerlike and labyrinth structures reversibly form upon a transition into a modulated phase. External electric fields of several kV/m applied in the film plane can reversibly influence the formation of the finger textures. We show that the labyrinthine pattern is intrinsically related to regular splay deformations of the polarization.

Chromonic liquid crystals are formed by molecules that spontaneously assemble into anisotropic structures in water. The ordering unit is therefore a molecular assembly instead of a molecule as in thermotropic liquid crystals. Although it has been known for a long time that certain dyes, drugs, and nucleic acids form chromonic liquid crystals, only recently has enough knowledge been gained on how to control their alignment so that studies of their fundamental liquid crystal properties can be performed. In this article, a simple method for producing planar alignment of the nematic phase in chromonic liquid crystals is described, and this in turn is used to create twisted nematic structures of both achiral and chiral chromonic liquid crystals. The optics of 90-degree twist cells allows the anchoring strength to be measured in achiral systems, which for this alignment technique is quite weak, about $3\times {10}^{-7}$ J/m${}^2$ for both disodium cromoglycate and Sunset Yellow FCF. The addition of a chiral amino acid to the system causes the chiral nematic phase to form, and similar optical measurements in 90-degree twist cells produce a measurement of the intrinsic pitch of the chiral nematic phase. From these measurements, the helical twisting power for $L$-alanine is found to be $(1.1\pm 0.4)\times {10}^{-2}$ $\mu$m${}^{-1}$ wt%${}^{-1}$ for 15 wt% disodium cromoglycate.

We analyze the dynamics of a relativistic particle moving in a uniform magnetic field and perturbed by a standing electrostatic wave. We show that a pulsed wave produces an infinite number of perturbative terms with the same winding number, which may generate islands in the same region of phase space. As a consequence, the number of isochronous island chains varies as a function of the wave parameters. We observe that in all the resonances, the number of chains is related to the amplitude of the various resonant terms. We determine analytically the position of the periodic points and the number of island chains as a function of the wave number and wave period. Such information is very important when one is concerned with regular particle acceleration, since it is necessary to adjust the initial conditions of the particle to obtain the maximum acceleration.

We present a method that optimizes the aspect ratio of a spatially anisotropic quantum lattice model during the quantum Monte Carlo simulation, and realizes the virtually isotropic lattice automatically. The anisotropy is removed by using the Robbins-Monro algorithm based on the correlation length in each direction. The method allows for comparing directly the value of the critical amplitude among different anisotropic models, and identifying the universality more precisely. We apply our method to the staggered dimer antiferromagnetic Heisenberg model and demonstrate that the apparent nonuniversal behavior is attributed mainly to the strong size correction of the effective aspect ratio due to the existence of the cubic interaction.

We study the full-counting statistics of current of large open systems through the application of random-matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating functions based on an expansion in terms of the inverse system size. We investigate how different symmetry properties and different counting schemes affect the results.

In a mixed-strategy game framework, each agent's strategy is defined by a real number; on the other hand, in a discrete strategy game framework, only binary strategies, either cooperation or defection, are allowed. In a spatial mixed-strategy game, with respect to the process for updating action (offer), either a synchronous or an asynchronous strategy update should be presumed. This study elucidates how stochastic perturbation that results from a synchronous or an asynchronous process for updating action significantly affects the enhancement of cooperation in an evolutionary process. Especially, when a synchronous process for updating action is assumed, the extent of cooperation increases with an increase in degree.

Using microscopic dynamical density functional theory, we calculate the dynamical formation of polycrystals by following the crystal growth around multiple crystalline seeds imposed to an undercooled fluid. Depending on the undercooling and the size ratio as well as the relative crystal orientation of two neighboring seeds, three possibilities of the final state emerge, namely no crystallization at all, formation of a monocrystal, or two crystallites separated by a curved grain boundary. Our results, which are obtained for two-dimensional hard disk systems using a fundamental-measure density functional, shed new light on the particle-resolved structure and growth of polycrystalline material in general.

Nanomotors convert chemical energy into mechanical motion. For a given motor type, the underlying chemical reaction that enables motility is typically well known, but the detailed, quantitative mechanism by which this reaction breaks symmetry and converts chemical energy to mechanical motion is often less clear, since it is difficult experimentally to measure important parameters such as the spatial distribution of chemical species around the nanorotor during operation. Without this information on how motor geometry affects motor function, it is difficult to control and optimize nanomotor behavior. Here we demonstrate how one easily observable characteristic of nanomotor operation—the visible trajectory of a nanorotor—can provide quantitative information about the role of asymmetry in nanomotor operation, as well as insights into the spatial distribution of motive force along the surface of the nanomotor, the motive torques, and the effective diffusional motion.

We propose a method to estimate $N_e$, the entanglement length, that incorporates both local and global topological characteristics of chains in a melt under equilibrium conditions. This estimate uses the writhe of the chains, the writhe of the primitive paths, and the number of kinks in the chains in a melt. An advantage of this method is that it works for both linear and ring chains, works under all periodic boundary conditions, does not require knowing the contour length of the primitive paths, and does not rely on a smooth set of data. We apply this method to linear finitely extendable nonlinear elastic chains and we observe that our estimates are consistent with those from other studies.

The anomalous responses of electrospun nanofibers and film fabricated of unfolded bovine serum albumin (BSA) under constant stress (creep) is observed. In contrast to typical creep behavior of viscoelastic materials demonstrating (after immediate elastic response) a time-dependent elongation, in case of low applied stresses ($<$1 MPa) the immediate elastic response of BSA samples is followed by gradual contraction up to $2\%$. Under higher stresses ($2\text{–}6$ MPa) the contraction phase changes into elongation; and in case of stresses above 7 MPa only elongation was observed, with no initial contraction. The anomalous creep behavior was not observed when the BSA samples were subjected to additional creep cycles independently on the stress level. The above anomaly, which was not observed before either for viscoelastic solids or for polymers, is related to specific protein features, namely, to the ability to fold. We hypothesize that the phenomenon is caused by folding of BSA macromolecules into dry molten globule states, feasible after cross-linked bonds break up, resulting from the applied external force.

We establish an agent-based model to study the impact of prey behavior on the hunting success of predators. The predators and prey are modeled as self-propelled particles moving in a three-dimensional domain and subject to specific sensing abilities and behavioral rules inspired by bat hunting. The predators randomly search for prey. The prey either align velocity directions with peers, defined as “interacting” prey, or swarm “independently” of peer presence; both types of prey are subject to additive noise. In a simulation study, we find that interacting prey using low noise have the maximum predation avoidance because they form localized large groups, while they suffer high predation as noise increases due to the formation of broadly dispersed small groups. Independent prey, which are likely to be uniformly distributed in the domain, have higher predation risk under a low noise regime as they traverse larger spatial extents. These effects are enhanced in large prey populations, which exhibit more ordered collective behavior or more uniform spatial distribution as they are interacting or independent, respectively.

We study the self-organization of binary cell mixtures in finite cubic lattices. Depending on the relative attractions between cell types, the binary mixture model generates four distinct cellular associations: complete sorting, shell-core sorting, partial mixing, and complete mixing of heterotypic cells. At the boundaries between these four phases, the cellular associations show large variations, representing phase transitions. We find that the partial mixing phase is highly tolerant to thermal fluctuations. Interestingly, human pancreatic islets, the micro-organs for glucose homeostasis, adapt the partial mixing phase consisting of $\alpha$ and $\beta$ cells.

A dissipative sandpile model is constructed and studied on small-world networks (SWNs). SWNs are generated by adding extra links between two arbitrary sites of a two-dimensional square lattice with different shortcut densities $\varphi$. Three regimes are identified: regular lattice (RL) for $\varphi \lesssim 2^{-12}$, SWN for $2^{-12}<\varphi <0.1$, and random network (RN) for $\varphi \ge 0.1$. In the RL regime, the sandpile dynamics is characterized by the usual Bak, Tang, and Weisenfeld (BTW)–type correlated scaling, whereas in the RN regime it is characterized by mean-field scaling. On SWNs, both scaling behaviors are found to coexist. Small compact avalanches below a certain characteristic size $s_c$ are found to belong to the BTW universality class, whereas large, sparse avalanches above $s_c$ are found to belong to the mean-field universality class. A scaling theory for the coexistence of two scaling forms on a SWN is developed and numerically verified. Though finite-size scaling is not valid for the dissipative sandpile model on RLs or on SWNs, it is found to be valid on RNs for the same model. Finite-size scaling on RNs appears to be an outcome of super diffusive sand transport and uncorrelated toppling waves.

We consider an idealized model in which individuals' changing opinions and their social network coevolve, with disagreements between neighbors in the network resolved either through one imitating the opinion of the other or by reassignment of the discordant edge. Specifically, an interaction between $x$ and one of its neighbors $y$ leads to $x$ imitating $y$ with probability $(1-\alpha )$ and otherwise (i.e., with probability $\alpha$) $x$ cutting its tie to $y$ in order to instead connect to a randomly chosen individual. Building on previous work about the two-opinion case, we study the multiple-opinion situation, finding that the model has infinitely many phase transitions (in the large graph limit with infinitely many initial opinions). Moreover, the formulas describing the end states of these processes are remarkably simple when expressed as a function of $\beta =\alpha /(1-\alpha )$.

A broad range of systems spanning biology, technology, and social phenomena may be represented and analyzed as complex networks. Recent studies of such networks using $k$-core decomposition have uncovered groups of nodes that play important roles. Here, we present $s$-core analysis, a generalization of $k$-core (or $k$-shell) analysis to complex networks where the links have different strengths or weights. We demonstrate the $s$-core decomposition approach on two random networks (ER and configuration model with scale-free degree distribution) where the link weights are (i) random, (ii) correlated, and (iii) anticorrelated with the node degrees. Finally, we apply the $s$-core decomposition approach to the protein-interaction network of the yeast Saccharomyces cerevisiae in the context of two gene-expression experiments: oxidative stress in response to cumene hydroperoxide (CHP), and fermentation stress response (FSR). We find that the innermost $s$-cores are (i) different from innermost $k$-cores, (ii) different for the two stress conditions CHP and FSR, and (iii) enriched with proteins whose biological functions give insight into how yeast manages these specific stresses.