A recently proposed consistent Bhatnagar-Gross-Krook-type approach for reversible bimolecular chemical reactions, well suited to deal with collision dominated gas mixtures in which mechanical and chemical relaxation times are of the same order of magnitude (fast reactions), is discussed. The model recovers essential features of the chemical process such as mass action law at equilibrium and reactive $H$ theorem. The hydrodynamic limit, at both Euler and Navier-Stokes levels, is derived by a Chapman-Enskog procedure, in terms of the relevant hydrodynamic variables, and compared to the corresponding limits holding in the nonreactive and in the slowly reactive cases. In particular, results show that reactive corrections to transport coefficients cannot be neglected for fast reactions.

Fluid transport in microfluidic systems typically is laminar due to the low Reynolds number characteristic of the flow. The inclusion of suspended polymers imparts elasticity to fluids, allowing instabilities to be excited when substantial polymer stretching occurs. For high molecular weight polymer chains we find that flow velocities achievable by standard electro-osmotic pumping are sufficient to excite extensional instabilities in dilute polymer solutions. We observe a dependence in measured fluctuations on polymer concentration which plateaus at a threshold corresponding to the onset of significant molecular crowding in macromolecular solutions; plateauing occurs well below the overlap concentration. Our results show that electro-osmotic flows of complex fluids are disturbed from the steady regime, suggesting potential for enhanced mixing and requiring care in modeling the flow of complex liquids such as biopolymer suspensions.

Relation among various expressions of the complex admittance for quantum systems in contact with heat reservoir is studied. Exact expressions of the complex admittance are derived in various types of formulations of equations of motion under contact with heat reservoir. Namely, the complex admittance is studied in the relaxation method and the external-field method. In the former method, the admittance is calculated using the Kubo formula for quantum systems in contact with heat reservoir in no external driving fields, while in the latter method the admittance is directly calculated from equations of motion with external driving terms. In each method, two types of equation of motions are considered, i.e., the time-convolution (TC) equation and time-convolutionless (TCL) equation. That is, the full of the four cases are studied. It is turned out that the expression of the complex admittance obtained by using the relaxation method with the TC equation exactly coincides with that obtained by using the external-field method with the TC equation, while other two methods give different forms. It is also explicitly demonstrated that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the system-reservoir interaction. The formulas necessary for the higher-order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the $n\text{th}$ order approximation are given. By transforming inverse-temperature integrals into time integrals, the admittances are also given in the formulas with time-integrals alone. To characterize the TC and TCL methods, we study the expressions of the admittances of two exactly solvable models. Each exact form of admittance is compared with the results of the two methods in the lowest Born approximation. It is found that depending on the model, either of TC and TCL would be the better method.

The response of an overdamped bistable system driven by a Gaussian white noise and perturbed by a weak monochromatic signal is studied analytically. The perturbation theory is employed to calculate the nonlinear coherent response in the leading order of the amplitude of the weak signal. Simple analytic formulas for the linear and the nonlinear responses have been derived in low noise and low-frequency regime and the results based on the derived formulas are compared with the numerical results.

We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the piecewise linear intermittent map. Thus, we provide a framework to understand a unified characterization of intermittency and also present the Lyapunov exponent for renewal processes. This method is applied to the occurrence of earthquakes using the Japan Meteorological Agency and the National Earthquake Information Center catalog. By analyzing the return map of interevent times, we find that interevent times are not independent and identically distributed random variables but that the conditional probability distribution functions in the tail obey the Weibull distribution.

The slow compaction of a tapped granular packing is reminiscent of the low-temperature dynamics glasses. Here, I study the dynamics of granular compaction by means of a volumetric spectroscopy. While the specific packing volume $v$ displays glassy aging and memory effects at low tapping amplitudes $\Gamma$, the dynamic volumetric susceptibility ${\tilde{\chi }}_v=\partial v/\partial \Gamma$ displays minimal glassy effects, and its frequency spectrum gives no indication of a rapidly growing time scale. These features are contrast sharply with that found in the dielectric and magnetic susceptibilities of structural and spin glasses. Instead, ${\tilde{\chi }}_v$ appears to exhibit the behavior of a dynamic configurational specific heat, such as that obtained from computer simulations of spin-glass models. This suggests that the glassy dynamics of granular compaction is controlled by statistically rare processes that diverge from the typical dynamics of the system. From modifications of the dynamical spectrum by finite system size, I suggest that these glassy processes derive from large-scale collective particle rearrangements.

Magnetic-field-induced surface reorientation of nematic liquid crystals on polyethyl-methacrylate films is studied. The experiments indicate that the time scale of director gliding expands from a fraction of a second to several hours. A power-law distribution function of relaxation times provides very good agreement between measurements and calculated gliding curves. From the model an upper limit of the extrapolation length can be extracted, which points to a surprisingly strong equilibrium azimuthal anchoring of the liquid crystal on the polymer layer.

The study of mechanical unfolding, through the combined efforts of atomic force microscopy and simulation, is yielding fresh insights into the free-energy landscapes of proteins. Thus far, experiments have been mostly analyzed with one-dimensional models of the free-energy landscape. We show that as the two ends of a protein, filamin, are pulled apart at a speed tending to zero, the measured mechanical strength plateaus at $\sim 30\text{pN}$ instead of going toward zero, deviating from the Bell model. The deviation can only be explained by a switch between parallel pathways. Insightful analysis of mechanical unfolding kinetics needs to account for the multidimensionality of the free-energy landscapes of proteins, which are crucial for understanding the behavior of proteins under the small forces experienced in vivo.

Single-cell experiments of simple regulatory networks can markedly differ from cell population experiments. Such differences arise from stochastic events in individual cells that are averaged out in cell populations. For instance, while individual cells may show sustained oscillations in the concentrations of some proteins, such oscillations may appear damped in the population average. In this paper we investigate the role of RNA stochastic fluctuations as a leading force to produce a sustained excitatory behavior at the single-cell level. As opposed to some previous models, we build a fully stochastic model of a negative feedback loop that explicitly takes into account the RNA stochastic dynamics. We find that messenger RNA random fluctuations can be amplified during translation and produce sustained pulses of protein expression. Motivated by the recent appreciation of the importance of noncoding regulatory RNAs in post-transcription regulation, we also consider the possibility that a regulatory RNA transcript could bind to the messenger RNA and repress translation. Our findings show that the regulatory transcript helps reducing gene expression variability both at the single-cell level and at the cell population level.

An exact, analytic solution for a simple electrostatic model applicable to biomolecular recognition is presented. In the model, a layer of high-dielectric constant material (representative of the solvent, water), whose thickness may vary separates two regions of low-dielectric constant material (representative of proteins, DNA, RNA, or similar materials), in each of which is embedded a point charge. For identical charges, the presence of the screening layer always lowers the energy compared to the case of point charges in an infinite medium of low-dielectric constant. Somewhat surprisingly, the presence of a sufficiently thick screening layer also lowers the energy compared to the case of point charges in an infinite medium of high-dielectric constant. For charges of opposite sign, the screening layer always lowers the energy compared to the case of point charges in an infinite medium of either high or low dielectric constant. The behavior of the energy leads to a substantially increased repulsive force between charges of the same sign. The attractive force between charges of opposite signs is weaker than in an infinite medium of low dielectric constant material but stronger than in an infinite medium of high dielectric constant material. The presence of this behavior, which we name asymmetric screening, in the simple system presented here confirms the generality of the behavior that was established in a more complicated system of an arbitrary number of charged dielectric spheres in an infinite solvent.

We propose a coevolutionary game to study cooperative behavior in the presence of catastrophic phenomenon. We incorporate tolerance to elimination of individuals in network games where individuals update their strategies synchronously, and there are no birth of individuals and stochastic effects. We find that an avalanchelike death process can arise when defection strategies exist and individuals are vulnerable to deficiency of profits. Strikingly, we observe that, after such a cascading process terminates, cooperators are the sole survivors regardless of the game types and of the connection patterns among individuals as determined by the network topology. Cooperation thus becomes the optimal strategy and absolutely outperforms defection. Our results can yield insights into evolution of cooperation in the presence of catastrophic events in social and natural systems.

We study the properties of the Google matrix of an Ulam network generated by intermittency maps. This network is created by the Ulam method which gives a matrix approximant for the Perron-Frobenius operator of dynamical map. The spectral properties of eigenvalues and eigenvectors of this matrix are analyzed. We show that the PageRank of the system is characterized by a power law decay with the exponent $\beta$ dependent on map parameters and the Google damping factor $\alpha$. Under certain conditions the PageRank is completely delocalized so that the Google search in such a situation becomes inefficient.

By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi-golden rule regime. The calculated quantum corrections can be viewed as arising from a static random perturbation acting on nearly self-retracing interfering paths, and hence will be suppressed for time-varying perturbations. Moreover, using trajectory-based methods we show a relation, recently obtained in RMT, between the fidelity amplitude and the cross-form factor for parametric level correlations. Beyond RMT, we compute Ehrenfest-time effects on the fidelity amplitude. Furthermore our semiclassical approach allows for a unified treatment of the fidelity, both in the Fermi-golden rule and Lyapunov regimes, demonstrating that quantum corrections are suppressed in the latter.

We have studied the soliton propagation through a segment containing random pointlike scatterers. In the limit of small concentration of scatterers when the mean distance between the scatterers is larger than the soliton width, a method has been developed for obtaining the statistical characteristics of the soliton transmission through the segment. The method is applicable for any classical particle traversing through a disordered segment with the given velocity transformation after each act of scattering. In the case of weak scattering and relatively short disordered segment the transmission time delay of a fast soliton is mostly determined by the shifts of the soliton center after each act of scattering. For sufficiently long segments the main contribution to the delay is due to the shifts of the amplitude and velocity of a fast soliton after each scatterer. Corresponding crossover lengths for both cases of light and heavy solitons have been obtained. We have also calculated the exact probability density function of the soliton transmission time delay for a sufficiently long segment. In the case of weak identical scatterers the latter is a universal function which depends on a sole parameter—the mean number of scatterers in a segment.

In this work we present a mechanism to detect the presence of an external electric field of either weak or large amplitude by means of the decay process from an unstable state, described by a bistable potential, of an electrically charged Brownian particle embedded in a uniform electromagnetic field. Since the detection process takes place around the initial unstable state of the bistable potential, our theoretical description is given in the linear approximation of the aforementioned potential. The decay process is characterized through the statistics of the passage time distribution calculated by means of two theoretical approaches relying on the overdamped Langevin equation: one is the quasideterministic approach valid for large times and used for the detection of weak signals, whereas the other one is the rotational approach, valid for intermediate times and adequate for the detection of large electric-field amplitudes.

A class of probabilistic models for cascading failure propagation in interconnected systems is proposed. The models are able to represent important physical characteristics of realistic load-redistribution mechanisms, e.g., that the load increments after a failure depend on the load of the failing element and that they may be distributed nonuniformly among the remaining elements. In the limit of large system sizes, the models are solved analytically in terms of generalized branching processes, and the failure propagation properties of a prototype example are analyzed in detail.

The $p$-state clock model is studied, for general values of $p$, from simulations using a heat-bath single spin flipping Monte Carlo method, and a mapping of the corresponding spinlike configurations to a solid-on-solid growth model. The growth exponents are calculated. From the dynamics generated by this far from equilibrium kinetic roughening of the surface one is able to characterize the corresponding equilibrium magnetic properties of the original model, such as the high temperature Berezinskii-Koserlitz-Thouless (BKT) transitions, the low-temperature long-range ordered phase transitions, as well as the conventional second-order phase transitions. The present method suggests that for $p\ge 5$ the high-temperature phase transition is indeed a BKT one, whose value is the same as that for $p\to \infty$ ($XY$ model), while the low-temperature phase transition has a first-order character.

We study the elasto-plastic behavior of materials made of individual (discrete) objects such as a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities such as the elastic strain of the structure, the yield strain, and the yield function. The past history of the sample plays no explicit role except through its effect on these statistical quantities. They suffice to relate the discrete scale with the collective global scale. At this global scale, the material behaves as a continuous medium; it is described with tensors such as elastic strain, stress, and velocity gradient. We write the differential equations which predict their elastic and plastic behavior in both the general case and the case of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3. We suggest practical applications including the following: when to choose a scalar formalism rather than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a high, yield strain.

Biroli et al.’s extension of the standard mode-coupling theory to inhomogeneous equilibrium states [G. Biroli, J. P. Bouchaud, K. Miyazaki, and D. R. Reichman, Phys. Rev. Lett. 97, 195701 (2006)] allowed them to identify a characteristic length scale that diverges upon approaching the mode-coupling transition. We present a numerical investigation of this length scale. To this end we derive and numerically solve equations of motion for coefficients in the small $q$ expansion of the dynamic susceptibility ${\chi }_{\mathbf{q}}\left(\mathbf{k};t\right)$ that describes the change of the system’s dynamics due to an external inhomogeneous potential. We study the dependence of the characteristic length scale on time, wave vector, and on the distance from the mode-coupling transition. We verify scaling predictions of Biroli et al. In addition, we find that the numerical value of the diverging length scale qualitatively agrees with lengths obtained from four-point correlation functions. We show that the diverging length scale has very weak $k$ dependence, which contrasts with very strong $k$ dependence of the $q\to 0$ limit of the susceptibility, ${\chi }_{\mathbf{q}=0}\left(\mathbf{k};t\right)$. Finally, we compare the diverging length obtained from the small $q$ expansion to that resulting from an isotropic approximation applied to the equation of motion for the dynamic susceptibility ${\chi }_{\mathbf{q}}\left(\mathbf{k};t\right)$.

A simulation study was made of the effects of strong electric fields on the morphology of a Nafion®-like ionomer at various levels of hydration. The results of united-atom molecular-dynamics computations showed a self-organization of the side chain terminal groups into cylindrical clusters. The walls of these clusters contain the sulfonate dipoles, while the interior holds the majority of the water molecules. These cylindrical structures then align to form an hexatic array aligned along the direction of the applied electric field. The hexatic morphology persists after the removal of the field. A calculation by means of the Kirkwood coupling parameter method shows the Helmholtz free energy of the hexatic morphology of the poled membrane to be lower than that of the initial isotropic material, even in the absence of the applied field.