League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest number of wins is declared to be the champion. The total number of games needed for the best team to win the championship with high certainty $T$ grows as the cube of the number of teams $N$, i.e., $T\sim N^3$. This number can be substantially reduced using preliminary rounds where teams play a small number of games and subsequently, only the top teams advance to the next round. When there are $k$ rounds, the total number of games needed for the best team to emerge as champion, $T_k$, scales as follows, $T_k\sim N^{{\gamma }_k}$ with ${\gamma }_k={[1-{(2∕3)}^{k+1}]}^{-1}$. For example, ${\gamma }_k=9∕5,27∕19,81∕65$ for $k=1,2,3$. These results suggest an algorithm for how to infer the best team using a schedule that is linear in $N$. We conclude that league format is an ineffective method of determining the best team, and that sequential elimination from the bottom up is fair and efficient.

We analyze the Bogoliubov spectrum of the Bose-Hubbard model with a finite number of sites and Bose particles by using a semiclassical approach. This approach allows us to take into account the finite-size effects responsible for evolution of the Bogoliubov spectrum into an irregular (chaotic) spectrum at higher energies. A manifestation of this transition for the excitation dynamics of the Bose-Hubbard system is discussed as well.

We study the response of two coupled FitzHugh-Nagumo systems to heterogeneous external inputs. The latter, modeled by periodic parametric stimuli, force the uncoupled excitable systems into a regime of chaotic firing. Due to parameter dispersion involved in randomly distributed amplitudes and/or phases of the external forces the units are nonidentical and their firing events will be asynchronous. Interest is focused on mutually synchronized spikings arising through the coupling. It is demonstrated that the phase difference of the two external forces crucially affects the onset of spike synchronization as well as the resulting degree of synchrony. For large phase differences the degree of spike synchrony is constricted to a maximal possible value and cannot be enhanced upon increasing the coupling strength. We even found that overcritically strong couplings lead to suppression of firing so that the units perform synchronous subthreshold oscillations. This effect, which we call “firing death,” is due to a coupling-induced modification of the excitation threshold impeding spiking of the units. In clear contrast, when only the amplitudes of the forces are distributed perfect spike synchrony is achieved for sufficiently strong coupling.

The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length $N=20$) we study the influence of various choices for the chain stiffness on the equation of state. Three techniques are applied and compared in order to critically assess their efficiency and accuracy: the “repulsive wall” method, the thermodynamic integration method (which rests on the feasibility of simulations in the grand canonical ensemble), and the recently advocated sedimentation equilibrium method, which records the density profile in an external (e.g., gravitationlike) field and infers, via a local density approximation, the equation of state from the hydrostatic equilibrium condition. We confirm the conclusion that the latter technique is far more efficient than the repulsive wall method, but we find that the thermodynamic integration method is similarly efficient as the sedimentation equilibrium method. For very stiff chains the onset of nematic order enforces the formation of an isotropic-nematic interface in the sedimentation equilibrium method leading to strong rounding effects and deviations from the true equation of state in the transition regime.

The Ludwig-Soret effect, the migration of a species due to a temperature gradient, has been extensively studied without a complete picture of its cause emerging. Here we investigate the dynamics of DNA and spherical particles subjected to a thermal gradient using a combination of Brownian dynamics and the lattice Boltzmann method. We observe that the DNA molecules will migrate to colder regions of the channel, an observation also made in experiments. In fact, the thermal diffusion coefficient found agrees quantitatively with the experimentally measured value. We also observe that the thermal diffusion coefficient decreases as the radius of the studied spherical particles increases. Furthermore, we observe that the thermal-fluctuation–fluid-momentum-flux coupling induces a gradient in the stress which leads to thermal migration in both systems.

Long-wavelength thermal fluctuations of lipid membranes are adequately described by the Helfrich elastic model. On the other hand, fluctuations of wavelengths comparable with bilayer thickness exhibit significant deviations from the prediction of the elastic model and are typically assumed to be dominated by microscopic surface tension due to protrusion of lipid molecules into the solvent. We present evidence that the short-wavelength modes of a lipid membrane are dominated by fluctuations of the tilt of lipid molecules with respect to the membrane normal rather than the microscopic surface tension. We obtain an expression for the spectral intensity of the thermal membrane fluctuations by appealing to the Hamm-Kozlov model, which accounts for both membrane bending and lipid tilt contributions to the total membrane energy but neglects the contributions of the microscopic surface tension. The tilt and the bending fluctuations obtained from our coarse-grained molecular dynamics simulations of a dipalmitoylphosphatidylcholine lipid bilayer show good agreement with the theory. Furthermore, the obtained tilt and bending moduli are in close agreement with experimentally determined values. The magnitude of the microscopic protrusion tension estimated from our simulations is significantly smaller than that of the tilt modulus. These results indicate that the membrane fluctuations can be adequately described by a macroscopic elastic model down to scales of interlipid distance provided one accounts for the tilt fluctuations.

Phospholipid dispersed in aqueous buffer above their critical micellar concentration form bilayers, which can spontaneously adopt closed metastable shapes with sizes ranging from a few hundred nanometers to few tens of micrometers. The equilibrium shapes of these vesicles are well described by the Canham-Evans-Helfrich curvature elastic energy. Their floppiness allows for thermal fluctuations to be easily detected, but no spontaneous shape transformation is usually observed for vesicles of spherical topological genus (i.e., shapes with no holes) because of strict geometrical constraints and/or energy barriers. This report shows that for a particular class of shapes with spherical topological genus (starfish vesicles), dramatic spontaneous shape transformations can occur due to the degeneracy of the shape solutions, as demonstrated by numerical calculations. These predictions are supported by experimental observations of a three-arm starfish vesicle undergoing spontaneous shape transformations similar to those predicted numerically.

We investigate the emergence of a structure in the correlation matrix of assets’ returns as the time horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New York, Paris, London, Milano) and with different methods. In addition to the usual correlations, we also analyze those obtained by subtracting the dynamics of the “center of mass” (i.e., the market mode). We find that when the center of mass is not removed the structure emerges, as the time horizon increases, from splitting a single large cluster into smaller ones. By contrast, when the market mode is removed the structure of correlations observed at the daily scale is already well defined at very high frequency ($5\min$ in the New York Stock Exchange). Moreover, this structure accounts for 80% of the classification of stocks in economic sectors. Similar results, though less sharp, are found for the other markets. We also find that the structure of correlations in the overnight returns is markedly different from that of intraday activity.

We analyze heat transfer and flow properties in laminar natural convection driven by a horizontal temperature gradient in a closed cavity and propose that for the classical scaling of heat transfer turbulence does not play a decisive role. Direct numerical simulations were performed with the Rayleigh number (Ra) from 1 to ${10}^8$ and the Prandtl number $\mathrm{Pr}=0.71$. In the laminar steady flow regime with the Ra approximately from ${10}^3$ to ${10}^7$, power-law scalings of heat transfer and maximum velocity with Ra have exponents of 0.31 and 0.54, respectively. The scalings agree well with results obtained in turbulent Rayleigh-Bernard convection, turbulent convection in laterally heated cavities and laminar convection in inclined enclosures, etc., which, with some simple physical arguments and reviews of the literature, leads us to propose that turbulence is not essential for the classical near $1∕3$ power-law scaling of Nu.

In microfluidic applications it has been observed that flows with spatial gradients in electrical conductivity are unstable under the application of sufficiently strong electric fields. These electrohydrodynamic instabilities can drive a nonlinear flow despite the low Reynolds number. Such flows hold promise as a simple mechanism for mixing fluids. In this work, the effect of a time periodic electric field on the instability is explored. The case where an electric field is applied across a diffuse interface of two fluids with varying electrical conductivity is considered. Frequency-dependent behavior is found only in the regime where the instability growth rates are very slow and cannot outpace mixing by molecular diffusion. Improving mixing by modulation of the electric body force is not a viable strategy in this geometry.

We use direct numerical simulation to study electrically driven convection in an annular thin film. The simulation models a laboratory experiment that consists of a weakly conducting, submicron thick liquid crystal film suspended between two concentric electrodes. The film is driven to convect by imposing a sufficiently large voltage across it. The flow is driven by a surface charge density inversion which is unstable to the imposed electrical force. This mechanism is closely analogous to the mass density inversion which is unstable to the buoyancy force in conventional, thermally driven Rayleigh-Bénard convection. The simulation uses a pseudospectral method with Chebyshev polynomials in the radial direction and Fourier modes in the azimuthal direction. The numerical results, which are in good agreement with previous experimental data and theoretical predictions, reveal several insights. The mode competition near a codimension-two point exhibits hysteresis. The primary bifurcation is supercritical for a broad range of fluid and geometrical parameters.

We study the dynamics of small droplets of polydimethylsiloxane silicone oil on a vertical, perfectly wetting, silicon wafer. Interference videomicroscopy allows us to capture the dynamics of these droplets. We use droplets with a volumes typically ranging from $100\text{to}500\mathrm{nl}$ (viscosities from $10\text{to}1000\mathrm{cSt}$) to understand long time derivations from classical solutions. Past researchers used one dimensional theory to understand the typical $t^{1∕3}$ scaling for the position of the tip of the droplet in time $t$. We observe this regime in experiment for intermediate times and discover a two-dimensional similarity solution of the shape of the droplet. However, at long times our droplets start to move more slowly down the plane than the $t^{1∕3}$ scaling suggests and we observe deviations in droplet shape from the similarity solution. We match experimental data with simulations to show these deviations are consistent with retarded van der Waals forcing which should become significant at the small heights observed.

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the Lévy type. In the stationary regime, the probability density of the work is found to have “fat” power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian. These tails lead to a strong violation of existing fluctuation theorems, as the ratio of the probabilities of positive and negative work fluctuations of equal magnitude behaves in a nonmonotonic way. Possible experiments that could probe these features are proposed.

A cell whose substrates were coated with the polyamic acid SE1211 (Nissan Chemical Industries) and baked at high temperatures was filled with a nematic liquid crystal in the isotropic phase. On cooling into the nematic phase, naturally occurring and temporally and thermally robust reverse tilt domains separated by thin filamentlike walls were observed. The properties of these structures are reported.

The rules governing cell division and differentiation are central to understanding the mechanisms of development, aging, and cancer. By utilizing inducible genetic labeling, recent studies have shown that the clonal population in transgenic mouse epidermis can be tracked in vivo. Drawing on these results, we explain how clonal fate data may be used to infer the rules of cell division and differentiation underlying the maintenance of adult murine tail-skin. We show that the rates of cell division and differentiation may be evaluated by considering the long-time and short-time clone fate data, and that the data is consistent with cells dividing independently rather than synchronously. Motivated by these findings, we consider a mechanism for cancer onset based closely on the model for normal adult skin. By analyzing the expected changes to clonal fate in cancer emerging from a simple two-stage mutation, we propose that clonal fate data may provide a novel method for studying the earliest stages of the disease.

The escape of a diffusing particle from a potential well is an important aspect of many dynamic processes in chemistry, physics, and biology, and such an escape process often involves finding a restricted region or patch in a multidimensional potential well. We study an idealized model of this process via simulation and analytic theory. By combining results from special cases having either high symmetry or zero potential, we obtain a simple formula for the first-contact time for a particle moving to a boundary patch in an arbitrary number of dimensions. We apply this formula in two, three, and six dimensions. The predicted dependences of the first-contact time on the well depth and patch size are compared to results from simulations, and close agreement is found. We extend the theory to calculate the first-contact time between two particles in separate harmonic potential wells. As an application of this extended theory, we calculate the first-contact time for two parallel semiflexible biopolymer filaments and compare these results to previous simulations.

We extend to the three-dimensional situation a recent proof of hyperbolicity of the exact (to all orders in Knudsen number) linear hydrodynamics obtained from Grad’s moment system [M. Colangeli, I. Karlin, M. Kröger, Phys. Rev. E 75, 051204 (2007)]. Proof of an $H$ theorem is also presented.

Many complex systems may be described by not one but a number of complex networks mapped on each other in a multi-layer structure. Because of the interactions and dependencies between these layers, the state of a single layer does not necessarily reflect well the state of the entire system. In this paper we study the robustness of five examples of two-layer complex systems: three real-life data sets in the fields of communication (the Internet), transportation (the European railway system), and biology (the human brain), and two models based on random graphs. In order to cover the whole range of features specific to these systems, we focus on two extreme policies of system’s response to failures, no rerouting and full rerouting. Our main finding is that multi-layer systems are much more vulnerable to errors and intentional attacks than they appear from a single layer perspective.

An end-grafted flexible polymer chain in three-dimensional space between two pistons undergoes an abrupt transition from a confined coil to a flowerlike conformation when the number of monomers in the chain, $N$, reaches a critical value. In two-dimensional (2D) geometry, excluded-volume interactions between monomers of a chain confined inside a strip of finite length $2L$ transform the coil conformation into a linear string of blobs. However, the blob picture raises questions about the nature of this escape transition. To check theoretical predictions based on the blob picture we study 2D single-polymer chains with excluded-volume interactions and with one end grafted in the middle of a strip of length $2L$ and width $H$ by simulating self-avoiding walks on a square lattice with the pruned-enriched Rosenbluth method. We estimate the free energy, the end-to-end distance, the number of imprisoned monomers, the order parameter, and its distribution. It is shown that in the thermodynamic limit of large $N$ and $L$ but finite $L∕N$, there is a small but finite jump in several average characteristics, including the order parameter. We also present a theoretical description based on the Landau free energy approach, which is in good agreement with the simulation results. Both simulation results and the analytical theory indicate that the 2D escape transition is a weak first-order phase transition.