The prewetting phenomena in a nematic liquid crystal confined to a droplet embedded in a spherical solid surface are discussed. This paper is based on Landau–de Gennes theory and Nobili-Durand surface energy. By using a Maxwell construction, we find that the first-order boundary-layer transition inside of droplet which vanishes completely below a critical radius $R_c$ when bulk nematic isotropic transition temperature is approached from above. We obtain a narrow temperature interval above the bulk nematic-isotropic phase transition which corresponds to nematic boundary layer inside of droplet. The interval length depends on surface potential and droplet radius. We also find that there is no critical radius for boundary transition when the nematic-isotropic transition temperature is approached from below.

In real situations, people are often faced with the option of voluntary contribution to achieve a collective goal, for example, building a dam or a fence, in order to avoid an unfavorable loss. Those who do not donate, however, can free ride on others’ sacrifices. As a result, cooperation is difficult to maintain, leading to an enduring collective-risk social dilemma. To address this issue, here we propose a simple yet effective theoretical model of threshold public goods game with collective risk and focus on the effect of risk on the emergence of social cooperation. To do this, we consider the population dynamics represented by replicator equation for two simplifying scenarios, respectively: one with fair sharers, who contribute the minimum average amount versus defectors and the other with altruists contributing more than average versus defectors. For both cases, we find that the dilemma is relieved in high-risk situations where cooperation is likely to persist and dominate defection in the population. Large initial endowment to individuals also encourages the risk-averse action, which means that, as compared to poor players (with small initial endowment), wealthy individuals (with large initial endowment) are more likely to cooperate in order to protect their private accounts. In addition, we show that small donation amount and small threshold (collective target) can encourage and sustain cooperation. Furthermore, for other parameters fixed, the impacts of group size act differently on the two scenarios because of distinct mechanisms: in the former case where the cost of cooperation depends on the group size, large size of group readily results in defection, while easily maintains cooperation in the latter case where the cost of cooperation is fixed irrespective of the group size. Our theoretical results of the replicator dynamics are in excellent agreement with the individual based simulation results.

A method for reconstructing the potential energy landscape of simple polypeptidic chains is described. We show how to obtain a faithful representation of the energy landscape in terms of a suitable directed graph. Topological and dynamical indicators of the graph are shown to yield an effective estimate of the time scales associated with both folding and equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined as a temperature-dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into “hubs” while redefining their connectivity. We show that the dynamical properties at large time scales are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to distinguish between “fast” and “slow” folders, one has to look at the kinetic properties of the corresponding directed graphs. In particular, we find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time while for the bad folder these time scales are comparable.

Heavy traffic congestion occurs daily at merging sections on a highway. For relieving this congestion, possibility of alternative configuration of vehicles on multiple-lane road at a merging area is discussed in this paper. This is the configuration where no vehicles move aside on the other lane. It has merit in making a smooth merging at an intersection or a junction due to the so-called “zipper effect.” We show, by developing a cellular automaton model for multiple lanes, that this configuration is achieved by simple local interactions between vehicles neighboring each other. The degree of the alternative configuration in terms of the spatial increase in parallel driving length is studied by using both numerical simulations and mean-field theory. We successfully construct a theoretical method for calculating this degree of the alternative configuration by using cluster approximation. It is shown that the theoretical results coincide with those of the simulations very well.

We investigate by direct numerical simulations the flow that rising bubbles cause in an originally quiescent fluid. We employ the Eulerian-Lagrangian method with two-way coupling and periodic boundary conditions. In order to be able to treat up to 288000 bubbles, the following approximations and simplifications had to be introduced, as done before, e.g., by Climent and Magnaudet, Phys. Rev. Lett. 82, 4827 (1999). (i) The bubbles were treated as point particles, thus (ii) disregarding the near-field interactions among them, and (iii) effective force models for the lift and the drag forces were used. In particular, the lift coefficient was assumed to be 1/2, independent of the bubble Reynolds number and the local flow field. The results suggest that large-scale motions are generated, owing to an inverse energy cascade from the small to the large scales. However, as the Taylor-Reynolds number is only in the range of 1, the corresponding scaling of the energy spectrum with an exponent of $-5/3$ cannot develop over a pronounced range. In the long term, the property of local energy transfer, characteristic of real turbulence, is lost and the input of energy equals the viscous dissipation at all scales. Due to the lack of strong vortices, the bubbles spread rather uniformly in the flow. The mechanism for uniform spreading is as follows. Rising bubbles induce a velocity field behind them that acts on the following bubbles. Owing to the shear, those bubbles experience a lift force, which makes them spread to the left or right, thus preventing the formation of vertical bubble clusters and therefore of efficient forcing. Indeed, when the lift is artificially put to zero in the simulations, the flow is forced much more efficiently and a more pronounced energy that accumulation at large scales (due to the inverse energy cascade) is achieved.

We probe the flow of two-dimensional (2D) foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction, and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate-dependent and inhomogeneous (shear-banded) velocity profiles, while monodisperse ordered foams are also shear banded but essentially rate independent. Second, we adapt a simple model [E. Janiaud, D. Weaire, and S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)] based on balancing the averaged drag forces between the bubbles and the top plate ${\overline{F}}_{bw}$ and the averaged bubble-bubble drag forces ${\overline{F}}_{bb}$ by assuming that ${\overline{F}}_{bw}\sim v^{2/3}$ and ${\overline{F}}_{bb}\sim {\left({\partial }_{y}v\right)}^{\beta }$, where $v$ and $\left({\partial }_{y}v\right)$ denote average bubble velocities and gradients. This model captures the observed rate-dependent flows for $\beta \approx 0.36$, and the rate independent flows for $\beta \approx 0.67$. Third, we perform independent rheological measurements of ${\overline{F}}_{bw}$ and ${\overline{F}}_{bb}$, both for ordered and disordered systems, and find these to be fully consistent with the forms assumed in the simple model. Disorder thus leads to a modified effective exponent $\beta$. Fourth, we vary the packing fraction $\varphi$ of the foam over a substantial range and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, the model describes flow profiles and rate dependence over the whole range of packing fractions with the same power-law exponents—only a dimensionless number $k$ that measures the ratio of the prefactors of the viscous drag laws is seen to vary with packing fraction. We find that $k\sim {\left(\varphi -{\varphi }_c\right)}^{-1}$, where ${\varphi }_c\approx 0.84$ corresponds to the 2D jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work shows that the presence of disorder qualitatively changes the effective bubble-bubble drag forces and suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power-law) rheology observed in a wide range of disordered materials.

Expressions for the yield of electron-positron pairs, their energy spectra, and production rates have been obtained in the interaction of multi-kJ pulses of high-intensity laser light interacting with solid targets. The Bethe-Heitler conversion of hard x-ray bremsstrahlung [D. A. Gryaznykh, Y. Z. Kandiev, and V. A. Lykov, JETP Lett. 67, 257 (1998); K. Nakashima and H. Takabe, Phys. Plasmas 9, 1505 (2002)] is shown to dominate over direct production (trident process) [E. P. Liang, S. C. Wilks, and M. Tabak, Phys. Rev. Lett. 81, 4887 (1998)]. The yields and production rates have been optimized as a function of incident laser intensity by the choice of target material and dimensions, indicating that up to $5\times {10}^{11}$ pairs can be produced on the OMEGA EP laser system [L. J. Waxer et al., Opt. Photonics News 16, 30 (2005)]. The corresponding production rates are high enough to make possible the creation of a pair plasma.

The permeability of solids has long been associated with a diffusive process involving activated mechanism as originally envisioned by Eyring. Tensile stress can affect the activation energy but definitive experiments of the diffusion rate of species through a stressed solid are lacking. Here we use core-shell (liquid core–solid shell) colloidal particles that are sensitive to osmotic pressure to follow the permeation of encapsulated probes at various stresses. We unambiguously show that the tensile stress applied on colloidal shells linearly reduces the local energy barrier for diffusion.

We study analytically a model of a two-dimensional partially directed flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an externally applied force. We find that the wall has a dramatic effect on the polymer. For wall attraction ${\epsilon }_1$ smaller than the nonsequential nearest-neighbor attraction $\epsilon$, the fraction of monomers at the wall is zero and the model is the same as that of a polymer without a wall. However, for ${\epsilon }_1$ greater than $\epsilon$, the fraction of monomers at the wall undergoes a first-order transition from unity at low temperature and small force, to zero at higher temperatures and forces. We present phase diagram for this transition. Our results are confirmed by Monte Carlo simulations.

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

We investigate the transport and separation of overdamped particles under the action of a uniform external force in a two-dimensional periodic energy landscape. Exact results are obtained for the deterministic transport in a square lattice of parabolic, repulsive centers that correspond to a piecewise-continuous linear-force model. The trajectories are periodic and commensurate with the obstacle lattice and exhibit phase-locking behavior in that the particle moves at the same average migration angle for a range of orientation of the external force. The migration angle as a function of the orientation of the external force has a Devil’s staircase structure. The first transition in the migration angle was analyzed in terms of a Poincare map, showing that it corresponds to a tangent bifurcation. Numerical results show that the limiting behavior for impenetrable obstacles is equivalent to the high Peclet number limit in the case of transport of particles in a periodic pattern of solid obstacles. Finally, we show how separation occurs in these systems depending on the properties of the particles.

Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently proposed multimodal pressure flow (MMPF) analysis that is based on Hilbert-Huang transform (HHT)—an advanced nonlinear decomposition algorithm. We considered three types of nonstationarities that are often presented in physical and physiological signals: (i) missing segments of data, (ii) linear and step-function trends embedded in data, and (iii) multiple chaotic oscillatory components at different frequencies in data. By generating two coupled oscillatory signals with an assigned phase shift, we quantify the change in the estimated phase shift after imposing artificial nonstationarities into the oscillatory signals. We found that all three types of nonstationarities affect the performances of the Fourier-based and the HHT-based phase analyses, introducing bias and random errors in the estimation of the phase shift between two oscillatory signals. We also provided examples of nonstationarities in real physiological data (cerebral blood flow and blood pressure) and showed how nonstationarities can complicate result interpretation. Furthermore, we propose certain strategies that can be implemented in the TFA and the MMPF methods to reduce the effects of nonstationarities, thus improving the performances of the two methods.

In the last few years we have witnessed the emergence, primarily in online communities, of new types of social networks that require for their representation more complex graph structures than have been employed in the past. One example is the folksonomy, a tripartite structure of users, resources, and tags—labels collaboratively applied by the users to the resources in order to impart meaningful structure on an otherwise undifferentiated database. Here we propose a mathematical model of such tripartite structures that represents them as random hypergraphs. We show that it is possible to calculate many properties of this model exactly in the limit of large network size and we compare the results against observations of a real folksonomy, that of the online photography website Flickr. We show that in some cases the model matches the properties of the observed network well, while in others there are significant differences, which we find to be attributable to the practice of multiple tagging, i.e., the application by a single user of many tags to one resource or one tag to many resources.

We investigate finite-size scaling aspects of disorder reaction-diffusion processes in one dimension utilizing both numerical and analytical approaches. The former averages the spectrum gap of the associated evolution operators by doubling their degrees of freedom, while the latter uses various techniques to map the equations of motion to a first-passage time process. Both approaches are consistent with nonuniversal dynamic exponents and with stretched exponential scaling forms for particular disorder realizations.

Granular surfaces subjected to forces due to rolling wheels develop ripples above a critical speed. The resulting pattern, known as washboard or corrugated road, is common on dry unpaved roads. We investigated this phenomenon theoretically and experimentally using laboratory-scale apparatus and beds of dry sand. A thick layer of sand on a circular track was forced by a rolling wheel on an arm whose weight and moment of inertia could be varied. We compared the ripples made by the rolling wheel to those made using a simple inclined plow blade. We investigated the dependence of the critical speed on various parameters and described a scaling argument that leads to a dimensionless ratio, analogous to the hydrodynamic Froude number, which controls the instability. This represents the crossover between conservative dynamic forces and dissipative static forces. Above onset wheel-driven ripples move in the direction of motion of the wheel, but plow-driven ripples move in the reverse direction for a narrow range of Froude numbers.

We show that a rich variety of nonequilibrium phases can be realized for interacting particles moving over a periodic substrate when the particles have effective internal orientational degrees of freedom. We specifically study driven colloidal molecular crystals where it has been established that $n$-merization produces effective orientational degrees of freedom. This system exhibits a polarization effect within the pinned phase, a remarkable variety of sliding phases, and has no single particle pinning regime. Similar dynamics should occur for other driven systems with effective orientational degrees of freedom such as sliding diatomic or higher-order states.

A series of mixtures comprising an antiferroelectric liquid-crystal host and a chiral dopant is described in which the layer spacing variation at the orthogonal smectic-$A^{\ast }$ $\left(\text{Sm}{A}^{\ast }\right)$ to tilted smectic-$C^{\ast }$ or smectic-$C_{\alpha }^{\ast }$ (${\text{Sm}C}^{\ast }$ or ${\text{Sm}C}_{\alpha }^{\ast }$) phase transition changes from the usual strong contraction in the pure system to one in which there is almost no layer spacing change observed across the transition for dopant concentrations of 7%. The nature of the orthogonal to tilted phase transition is examined using Raman spectroscopy, to determine the order parameters $⟨P_2⟩$ and $⟨P_4⟩$ in the ${\text{Sm}A}^{\ast }$ phase, and via a generalized Landau expansion to reveal the details of the phase transition itself. The results show that the value of $⟨P_2⟩$ at the orthogonal to tilted transition increases from around 0.6 to 0.7 as the dopant concentration increases, while $⟨P_4⟩$ remains constant at approximately 0.4 irrespective of dopant concentration. Further, the generalized Landau potential measurements prove that the transition is purely second order, while electro-optic measurements confirm that the tilt angle at the transition becomes smaller with increasing dopant concentration. The combined data show that the high-temperature tilted phase regime corresponds to a ${\text{Sm}C}_{\alpha }^{\ast }$ phase rather than the mechanism suggested by de Vries that is inferred by the layer spacing data alone. We demonstrate that the lower-temperature ${\text{Sm}C}_{\alpha }^{\ast }{\text{-Sm}C}^{\ast }$ phase transition is of first order. Further, the temperature range of the ${\text{Sm}C}_{\alpha }^{\ast }$ phase increases dramatically with concentration, from around 2 K in the pure system to around 21 K in the 8% doped mixture, showing that the chiral dopant plays a role in stabilizing this phase. Indeed, we particularly note that for the 8% doped mixture all other ${\text{Sm}C}^{\ast }$-like phases disappear and that the only tilted phase remaining is ${\text{Sm}C}_{\alpha }^{\ast }$. This implies that we are reporting a liquid-crystalline phase sequence, namely, $\text{cryst}{\text{.-Sm}C}_{\alpha }^{\ast }{\text{-Sm}A}^{\ast }\text{-iso}$., i.e., a direct transition between the ${\text{Sm}C}_{\alpha }^{\ast }$ phase and the crystalline phase.

Quantifying human group dynamics represents a unique challenge. Unlike animals and other biological systems, humans form groups in both real (offline) and virtual (online) spaces—from potentially dangerous street gangs populated mostly by disaffected male youths to the massive global guilds in online role-playing games for which membership currently exceeds tens of millions of people from all possible backgrounds, age groups, and genders. We have compiled and analyzed data for these two seemingly unrelated offline and online human activities and have uncovered an unexpected quantitative link between them. Although their overall dynamics differ visibly, we find that a common team-based model can accurately reproduce the quantitative features of each simply by adjusting the average tolerance level and attribute range for each population. By contrast, we find no evidence to support a version of the model based on like-seeking-like (i.e., kinship or “homophily”).

Recently a moving boundary approximation for the minimal model for negative streamer ionization fronts was extended with effects due to front curvature; this was done through a systematic solvability analysis. A central prediction of this analysis is the existence of a nonvanishing electric field in the streamer interior, whose value is proportional to the front curvature. In this paper we compare this result and other predictions of the solvability analysis with numerical simulations of the minimal model.

An exact analytical model for the interaction between an isolated shock wave and an isotropic turbulent vorticity field is presented. The interaction with a single-mode two-dimensional (2D) divergence-free vorticity field is analyzed in detail, giving the time and space evolutions of the perturbed quantities downstream. The results are generalized to study the interaction of a planar shock wave with an isotropic three-dimensional (3D) or 2D preshock vorticity field. This field is decomposed into Fourier modes, and each mode is assumed to interact independently with the shock front. Averages of the downstream quantities are made by integrating over the angles that define the orientation of the upstream velocity field. The ratio of downstream/upstream kinetic energies is in good agreement with existing numerical and experimental results for both 3D and 2D preshock vorticity fields. The generation of sound and the sonic energy flux radiated downstream from the shock front is also discussed in detail, as well as the amplification of transverse vorticity across the shock front. The anisotropy is calculated for the far downstream fields of both velocity and vorticity. All the quantities characteristic of the shock-turbulence interaction are reduced to closed-form exact analytical expressions. They are presented as explicit functions of the two parameters that govern the dynamics of the interaction: the adiabatic exponent $\gamma$ and the shock Mach number $M_1$. These formulas are further reduced to simpler exact asymptotic expressions in the limits of weak and strong shock waves $\left(M_1-1⪡1,M_1⪢1\right)$ and high shock compressibility of the gas $\left(\gamma \to 1\right)$.