The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and antiparticle pair production and annihilation. In both cases, the fluctuation theorem is verified.

We consider models of financial markets in which all parties involved find incentives to participate. Strategies are evaluated directly by their virtual wealth. By tuning the price sensitivity and market impact, a phase diagram with several attractor behaviors resembling those of real markets emerge, reflecting the roles played by the arbitrageurs and trendsetters, and including a phase with irregular price trends and positive sums. The positive sumness of the players’ wealth provides participation incentives for them. Evolution and the bid-ask spread provide mechanisms for the gain in wealth of both the players and market makers. New players survive in the market if the evolutionary rate is sufficiently slow. We test the applicability of the model on real Hang Seng Index data over 20 years. Comparisons with other models show that our model has a superior average performance when applied to real financial data.

Experimentalists who measure the rupture force of a single molecular bond usually pull on that bond at a constant speed, keeping the loading rate $r=\frac{df}{dt}$ constant. The challenge is to extract the energy landscape of the interaction between the two molecules involved from the experimental rupture force distribution under several loading rates. This analysis requires the use of a model for the shape of this energy landscape. Several barriers can compose the landscape, though molecular bonds with a single barrier are often observed. The Bell model is commonly used for the analysis of rupture force measurements with bonds displaying a single barrier. It provides an analytical expression of the most likely rupture force which makes it very simple to use. However, in principle, it can only be applied to landscapes with extrema whose positions do not vary under force. Here, we evaluate the general relevance of the Bell model by comparing it with another analytical model for which the landscape is harmonic in the vicinity of its extrema. Similar shapes of force distributions are obtained with both models, making it difficult to confirm the validity of the Bell model for a given set of experimental data. Nevertheless, we show that the analysis of rupture force experiments on such harmonic landscapes with the Bell model provides excellent results in most cases. However, numerical computation of the distributions of the rupture forces on piecewise-linear energy landscapes indicates that the blind use of any model such as the Bell model may be risky, since there often exist several landscapes compatible with a given set of experimental data. Finally, we derive a universal relation between the range and energy of the bond and the force spectrum. This relation does not depend on the shape of the energy landscape and can thus be used to characterize unambiguously any one-barrier landscape from experiments. All the results are illustrated with the streptavidin-biotin bond.

Maintenance of cooperation was studied for a two-strategy evolutionary prisoner’s dilemma game where the players are located on a one-dimensional chain and their payoff comes from games with the nearest- and next-nearest-neighbor interactions. The applied host geometry makes it possible to study the impacts of two conflicting topological features. The evolutionary rule involves some noise affecting the strategy adoptions between the interacting players. Using Monte Carlo simulations and the extended versions of dynamical mean-field theory we determined the phase diagram as a function of noise level and a payoff parameter. The peculiar feature of the diagram is changed significantly when the connectivity structure is extended by extra links as suggested by Newman and Watts.

We report a transition from traveling to standing domain walls in a parametrically forced two-dimensional oscillatory Belousov-Zhabotinsky chemical reaction in 4:1 resonance. Our experimental results demonstrate spatiotemporal solutions not predicted by previous analytic results of the complex Ginzburg-Landau amplitude equation and numerical results from reaction-diffusion models. In addition to the stationary $\pi$ fronts at high forcing amplitudes, the 4:1 resonant patterns we observe include stationary $\pi ∕2$ fronts.

Linear and nonlinear counter-traveling waves in a fluid-filled annular cylinder with realistic no-slip boundary conditions uniformly heated from below and rotating about a vertical axis are investigated. When the gap of the annular cylinder is moderate, there exist two three-dimensional traveling waves driven by convective instabilities: a retrograde mode localized near the outer sidewall and a prograde mode adjacent to the inner sidewall with a different wave number, frequency and critical Rayleigh number. It is found that the retrogradely propagating mode is always more unstable and is marked by a larger azimuthal wave number. When the Rayleigh number is sufficiently large, both the counter-traveling modes can be excited and nonlinearly interacting, leading to an unusual nonlinear phenomenon in rotating Rayleigh-Bénard convection.

A hexagonal phase was found during the synthesis of interpenetrating polymer networks composed of polystyrene (PS) and poly(methyl methacrylate) (PMMA). By using confocal microscopy, it was found that the regularity of this hexagonal phase further increases upon de-cross-linking of the PS networks in the matrix phase by irradiation with shorter uv wavelengths. We conclude that the cooperation between the cross-link-induced suppression of phase separation and the elastic repulsion between the dispersed PMMA-rich domains is responsible for the emergence of this hexagonal phase.

The dynamics of a system formed by a finite number $N$ of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable. Several models based on truncation schemes of a hierarchy of stochastic equations for a set of fluctuating cumulant variables are presented. This hierarchy is derived using Itô stochastic calculus, and the noise terms in it are treated using an asymptotic approximation valid for large $N$. In addition, a simplified one-variable model based on an effective potential is also considered. These models are tested in the framework of the phenomenon of stochastic resonance. In turn, they are used to explain in simple terms the very large gains recently observed in these finite systems.

The shear-transformation-zone (STZ) theory of plastic deformation in glass-forming materials is reformulated in light of recent progress in understanding the roles played by the effective disorder temperature and entropy flow in nonequilibrium situations. A distinction between fast and slow internal-state variables reduces the theory to just two coupled equations of motion, one describing the plastic response to applied stresses and the other the dynamics of the effective temperature. The analysis leading to these equations contains, as a by-product, a fundamental reinterpretation of the dynamic yield stress in amorphous materials. In order to put all these concepts together in a realistic context, I conclude with a reexamination of the experimentally observed rheological behavior of a bulk metallic glass. That reexamination serves as a test of the STZ dynamics, confirming that system parameters obtained from steady-state properties such as the viscosity can be used to predict transient behaviors.

For many years it has been commonly accepted that electroconvection (EC) as primary instability in nematic liquid crystals for the “classical” planar geometry requires a positive anisotropy of the electric conductivity, ${\sigma }_a$, and a slightly negative dielectric anisotropy, ${ϵ}_a$. This firm belief was supported by many experimental and theoretical studies. Recent experiments, which have surprisingly revealed EC patterns at negative conduction anisotropy as well, have motivated the theoretical studies in this paper. It will be demonstrated that extending the common hydrodynamic description of nematics by the usually neglected flexoelectric effect allows for a simple explanation of EC in the “nonstandard” case ${\sigma }_a<0$.

Fluorescent proteins are frequently used as reporters for gene expression in living cells, either by being expressed in tandem with a protein of interest or through the creation of fusion proteins. The data yielded by the fluorescence output are of considerable interest in efforts to formulate quantitative models of cellular behavior underway in fields such as systems biology and synthetic biology. An often neglected aspect of these proteins, however, is their maturation: Before a fluorescent protein can generate a fluorescent signal, it must mature through a series of steps (folding, cyclization, and oxidation) that may take from many minutes to over a day. The presence of these maturation steps creates a distinction between the observed gene expression profile and the actual profile. We examine this effect through a simplified gene expression model and conclude that fluorescent protein maturation can have significant effects on estimates of both the mean protein levels and the variability in gene expression. The model shows that in many regimes, the observed variability will be increased by the maturation process, but indicates the existence of regimes in which the observed variability will actually be less than the true variability of the target protein. The latter effect arises from a low-pass filtering effect introduced by the chain of maturation reactions. The results suggest that the maturation of fluorescent proteins should be taken into account when using such proteins as quantitative indicators of gene expression levels.

A great part of the interest in complex networks has been motivated by the presence of structured, frequently nonuniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they provide the means to identify and classify several types of complex network, it becomes important to obtain meaningful measurements of the local network topology. In addition to traditional features such as the node degree, clustering coefficient, and shortest path, motifs have been introduced in the literature in order to provide complementary descriptions of the network connectivity. The current work proposes a different type of motif, namely, chains of nodes, that is, sequences of connected nodes with degree 2. These chains have been subdivided into cords, tails, rings, and handles, depending on the type of their extremities (e.g., open or connected). A theoretical analysis of the density of such motifs in random and scale-free networks is described, and an algorithm for identifying these motifs in general networks is presented. The potential of considering chains for network characterization has been illustrated with respect to five categories of real-world networks including 16 cases. Several interesting findings were obtained, including the fact that several chains were observed in real-world networks, especially the world wide web, books, and the power grid. The possibility of chains resulting from incompletely sampled networks is also investigated.

We investigate experimentally the detailed dynamics of how an existing microbubble $B_1$ is impacted and shattered by another nearby pulsed-laser-induced microbubble $B_2$, and the backward interaction on $B_2$ in a thin liquid layer. Mediated by the flow field, potential energy can be accumulated or lost through the alternate compression and expansion of the two bubbles. The symmetry breaking induced by the presence of the nearby counterbubble generates push-pull-type alternate forward and backward axial jetting on the compressed bubble associated with the elongated shape or even entrainment of the counterexpanding bubble into the jet-indented boundary. The strong penetrating axial jet through $B_1$, and its interplay with the transverse jets by the flow field surrounding $B_1$ in the first compression stage and the second expanding stage of $B_1$ lead to a complicated fragmentation pattern of $B_1$. Increasing the interbubble interaction by decreasing the interbubble distance causes $B_2$ to become entangled with $B_1$ through its entrainments into the backward axial jet-indented region of $B_2$, in the expansion phase of $B_2$. At the extreme of large laser energy for $B_2$, the leftward reexpansion of $B_1$ is suppressed. The strong shear flow field generates many tiny bubbles around the liquid-gas boundaries of the two axial jet-induced major daughter bubbles from $B_1$. The detailed interaction behaviors over a broad range of the energy of $B_2$, 0.14–$0.55\mu \text{J}$ (corresponding to the maximum bubble expansion energy), and of the interbubble distance (170–$500\mu \text{m}$) are presented and discussed.

We present mesoscopic fluid-wall interaction models for lattice Boltzmann (LB) model simulations of microscale flows. The exact solution of the slip velocity for the LB equation with the Bhatnagar-Gross-Krook collision operator is obtained for Poiseuille flow at finite Knudsen numbers. With a consistent definition of the Knudsen number, the slip coefficients of the LB equation with the standard D2Q9 scheme are found to be slightly larger than those of the Boltzmann equation with the same boundary condition, which makes the standard LB method remain quantitatively accurate only for small Knudsen numbers. By modifying the nonequilibrium energy flux or introducing the effective relaxation time, the LB method is analytically shown to reproduce the slip phenomena up to second order in the Knudsen number. For the standard LB method, the Knudsen layer is captured only with modification of the relaxation dynamics such as in the effective relaxation time model.

We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit algorithm. The first determinant state is identical to that of the Hartree-Fock theory. Calculations for a two-dimensional Hubbard model serve as a demonstration.

Recently Hu, Tung, Gao, and Cao [Phys. Rev. E 72, 056207 (2005)] investigated the 0-1 test for chaos. By looking at random data and at data stemming from the one-dimensional logistic map they concluded that the test is unreliable. We explain why their criticism is unfounded.

A bent-core mesogen containing a tetrathiafulvalene group is studied. The mesophase is an optically isotropic spongelike smectic phase without optical activity. The material responds to uv light in a peculiar way, showing photoconductivity and, in some circumstances, changing its mesomorphic properties. Under an electric field, large chiral domains are segregated from an initial racemic phase within a few minutes.

Experiments and computational simulations are carried out to study the behavior of a granular column in a silo whose walls are able to vibrate horizontally. The column is brought to a steady fluidized state and it behaves similar to a hydrostatic system. We study the dynamics of the granular discharge through openings at the bottom of the silo in order to search for a Torricelli-like behavior. We show that the flow rate scales with the wall induced shear rate, and at high rates, the granular bed indeed discharges similar to a viscous fluid.

Upon drying, colloidal suspensions undergo a phase transformation from a “liquid” to a “gel” state. With further solvent evaporation, tensile stresses develop in the gel, which ultimately leads to fractures. These generally manifest themselves in regular cracking patterns which reflect the physical conditions of the drying process. Here we show experimentally and theoretically how, in the case of a drying droplet of magnetic colloid (ferrofluid), an externally applied magnetic field modifies the stress in the gel and therefore the crack patterns. We find that the analysis of the shape of the cracks allows one to estimate the value of the gel Young’s modulus just before the crack nucleation.

We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially correlated stochastic force. A strong dissipation regime is described in which the ensemble-averaged fluctuations of the velocity exhibit transient oscillations that arise from memory effects. Also, we calculate generalized diffusion coefficients describing the transport of these particles and briefly discuss how they are affected by the magnetic field strength and correlation time. Our asymptotic results are extended to the general case of internal driving by correlated Gaussian stochastic forces with finite autocorrelation times.