Based on a copy number control model of bacterial plasmid, the internal noise near a given steady state is investigated by using the linear noise approximation. All the parameters are restricted to a certain region so that the time spent near the steady state is long enough and the absorbing state can be neglected. For the noise in the plasmid molecules, a transition occurs with increasing the noise in the signal molecules under certain conditions. A noise-reduction mechanism, noise suppression by noise, is found. More importantly, the critical condition for the occurrence of the noise-reduction effect is given in our theoretical treatment.

Nonstationary dynamical systems arise in applications, but little has been done in terms of the characterization of such systems, as most standard notions in nonlinear dynamics such as the Lyapunov exponents and fractal dimensions are developed for stationary dynamical systems. We propose a framework to characterize nonstationary dynamical systems. A natural way is to generate and examine ensemble snapshots using a large number of trajectories, which are capable of revealing the underlying fractal properties of the system. By defining the Lyapunov exponents and the fractal dimension based on a proper probability measure from the ensemble snapshots, we show that the Kaplan-Yorke formula, which is fundamental in nonlinear dynamics, remains valid most of the time even for nonstationary dynamical systems.

We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis. In previous work, we showed that, although the applied fields are stationary, they act like a terahertz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence, the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that, even in the presence of dissipation, deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally observable, signatures in the electron transport characteristics.

For a resonator in an electrostatic microelectromechanical system (MEMS), nonlinear coupling between applied electrostatic force and the mechanical motion of the resonator can lead to chaotic oscillations. Better performance of the device can be achieved when the oscillations are periodic with large amplitude. We investigate the nonlinear dynamics of a system of deformable doubly clamped beam, which is the core in many MEMS resonators, and propose a control strategy to convert chaos into periodic motions with enhanced output energy. Our study suggests that chaos control can lead to energy enhancement and consequently high performance of MEM devices.

A four-component dusty plasma consisting of electrons, ions, positively charged warm adiabatic dust, and negatively charged cold dust is considered. The basic features of the electrostatic solitary structures in such a four-component dusty plasma are investigated by the reductive perturbation method, which is valid for the small amplitude solitary waves, and by the pseudopotential approach which is valid for the arbitrary amplitude solitary waves. It is found that the presence of the positive dust component does not only significantly modify the basic properties of the solitary potential structures, but also causes the coexistence of the positive and negative solitary potential structures, which is an interesting feature shown in a dusty plasma with the dust of opposite polarity. The basic features and the underlying physics of the electrostatic solitary structures, which are relevant to cometary tails, upper mesosphere, Jupiter’s magnetosphere, etc., are briefly discussed.

We investigate the geographical effect on the synchronization of small-world oscillator networks. We construct small-world geographical networks by randomly adding links to one- and two-dimensional regular lattices, and we find that the synchronizability is a nonmonotonic function of both the coupling strength and the geographical distance of randomly added shortcuts. Our findings demonstrate that the geographical effect plays an important role in network synchronization, which may shed some light on the study of collective dynamics of complex networks.

Many of the core concepts and (especially field-theoretic) tools of statistical mechanics have developed within the context of thermodynamic equilibrium, where state variables are all taken to be charges, meaning that their values are inherently preserved under reversal of the direction of time. A principle concern of nonequilibrium statistical mechanics is to understand the emergence and stability of currents, quantities whose values change sign under time reversal. Whereas the correspondence between classical charge-valued state variables and their underlying statistical or quantum ensembles is quite well understood, the study of currents away from equilibrium has been more fragmentary, with classical descriptions relying on the asymmetric auxiliary-field formalism of Martin, Siggia, and Rose (and often restricted to the Markovian assumption of Doi and Peliti), while quantum descriptions employ a symmetric two-field formalism introduced by Schwinger and further clarified by Keldysh. In this paper we demonstrate that for quantum ensembles in which superposition is not violated by very strong conditions of decoherence, there is a large natural generalization of the principles and tools of equilibrium, which not only admits but requires the introduction of current-valued state variables. For these systems, not only do Martin-Siggia-Rose (MSR) and Schwinger-Keldysh (SK) field methods both exist, in some cases they provide inequivalent classical and quantum descriptions of identical ensembles. With these systems for examples, we can both study the correspondence between classical and quantum descriptions of currents, and also clarify the nature of the mapping between the structurally homologous but interpretationally different MSR and SK formalisms.

The crucial role of ambient correlations in determining thermodynamic behavior is established. A class of entangled states of two macroscopic systems is constructed such that each component is in a state of thermal equilibrium at a given temperature, and when the two are allowed to interact heat can flow from the colder to the hotter system. A dilute gas model exhibiting this behavior is presented. This reversal of the thermodynamic arrow is a consequence of the entanglement between the two systems, a condition that is opposite to molecular chaos and shown to be unlikely in a low-entropy environment. By contrast, the second law is established by proving Clausius’ inequality in a low-entropy environment. These general results strongly support the expectation, first expressed by Boltzmann and subsequently elaborated by others, that the second law is an emergent phenomenon which requires a low-entropy cosmological environment, one that can effectively function as an ideal information sink.

We have introduced a set of coupled fractional reaction-diffusion equations to model a multispecies system undergoing anomalous subdiffusion with linear reaction dynamics. The model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics. The effect of reactions is manifest in reaction modified spatiotemporal diffusion operators as well as in additive mean field reaction terms. One consequence of the nonseparability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species. The general solution is derived for the multispecies system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail. We have carried out Monte Carlo simulations corresponding to these special cases and we find excellent agreement with theory.

Recent experimental and theoretical studies of biomimetic membrane adhesions [Bruinsma et al., Phys. Rev. E 61, 4253 (2000); Boulbitch et al., Biophys. J. 81, 2743 (2001)] suggested that adhesion mediated by receptor interactions is due to the interplay between membrane undulations and a double-well adhesion potential, and should be a first-order transition. We study the nucleation of membrane adhesion by finding the minimum-energy path on the free energy surface constructed from the bending free energy of the membrane and the double-well adhesion potential. We find a nucleation free energy barrier around $20k_{\mathrm{B}}T$ for adhesion of flexible membranes, which corresponds to fast nucleation kinetics with a time scale of the order of seconds. For cell membranes with a larger bending rigidity due to the actin network, the nucleation barrier is higher and may require active processes such as the reorganization of the cortex network to overcome this barrier. Our scaling analysis suggests that the geometry of the membrane shapes of the adhesion contact is controlled by the adhesion length that is determined by the membrane rigidity, the barrier height, and the length scale of the double-well potential, while the energetics of adhesion is determined by the depths of the adhesion potential. These results are verified by numerical calculations.

Lipid rafts, defined as domains rich in cholesterol and sphingolipids, are involved in many important plasma membrane functions. Recent studies suggest that the way cells handle membrane cholesterol is fundamental in the formation of such lateral heterogeneities. We propose to model the plasma membrane as a nonequilibrium phase-separating system where cholesterol is dynamically incorporated and released. The model shows how cellular regulation of membrane cholesterol may determine the nanoscale lipid organization when the lipid mixture is close to a phase separation boundary, providing a plausible mechanism for raft formation in vivo.

An error measure, referred to as the hysteresis error, is developed from the Crooks fluctuation theorem to evaluate the sampling quality in free-energy calculations. Theory and the numerical free energy of hydration calculations are used to show that Hamiltonian replica exchange provides a direct route for minimizing the hysteresis error. Replica exchange swap probabilities yield the rate at which the hysteresis error falls with the simulation length, and this result can be used to decrease bias and statistical errors associated with free-energy calculations based on multicanonical simulations.

Plumes are typically formed when a continuous source of buoyancy is supplied at a localized source. We studied laminar plumes where buoyancy is supplied by an autocatalytic chemical reaction: The iodate-arsenous acid (IAA) reaction. The nonlinear kinetics of the IAA reaction produces a sharp propagating front at which buoyancy is produced by exothermicity and compositional change. When the reaction is initiated in an unconfined volume of reactant, a starting plume with a mushroom shaped head connected to the initiation point by a long conduit is formed. After the initial transient during the ascent of the head, we observed the emergence of a steady state in the conduit morphology and flow. Autocatalytic plumes were compared to nonreacting, compositionally buoyant plumes using the Gradient Echo Rapid Velocity and Acceleration Imaging Sequence (GERVAIS), an MRI velocimetric technique. Autocatalytic conduits had axisymmetric bimodal velocity profiles and cone-shaped morphologies, in contrast to the Gaussian profiles and cylindrical shapes of nonreacting conduits. The bimodal distribution for autocatalytic plumes is a consequence of the unique effect of entrainment in this system. Rather than the usual effect of entrainment in nonreacting plumes, where less buoyant fluid is incorporated into the plumes, entrainment in autocatalytic plumes provides a buoyancy flux along the entire conduit by means of chemical reaction, thereby delocalizing the buoyancy source.

Recent work has shown that torus formation in piecewise-smooth maps can take place through a special type of border-collision bifurcation in which a pair of complex conjugate multipliers for a stable cycle abruptly jump out of the unit circle. Transitions from an ergodic to a resonant torus take place via border-collision fold bifurcations. We examine the transition to chaos through torus destruction in such maps. Considering a piecewise-linear normal-form map we show that this transition, by virtue of the interplay of border-collision bifurcations with period-doubling and homoclinic bifurcations, can involve mechanisms that differ qualitatively from those described by Afraimovich and Shilnikov.

The effect of parameter diversity on coupled Chua systems is investigated. In the absence of diversity, the systems jump back and forth between two variable domains of a chaotic attractor, and the residence times within a single domain are uncertain. By introducing parameter diversity, a combined numerical and analytical approach indicates that the systems can jump regularly from one domain to another at an intermediate range of diversity, a signature of coherence resonance. Furthermore, the influences of coupling strength and the number of units are also considered. Our results provide a possibility for the control of chaos in spatially extended chaotic systems by the manipulation of parameter diversity.

The interaction of 32.5 and 6 nm ultrashort x-ray pulses with the solid materials ${\text{B}}_4\text{C}$, SiC, and Si is simulated with a nonlocal thermodynamic equilibrium radiation transfer code. We study the ionization dynamics as a function of depth in the material and modifications of the opacity during irradiation, and estimate the crater depth. Furthermore, we compare the estimated crater depth with experimental data, for fluences up to $2.2\text{J}/{\text{cm}}^2$. Our results show that, at 32.5 nm irradiation, the opacity changes by less than a factor of 2 for ${\text{B}}_4\text{C}$ and Si and by a factor of 3 for SiC, for fluences up to $200\text{J}/{\text{cm}}^2$. At a laser wavelength of 6 nm, the model predicts a dramatic decrease in opacity due to the weak inverse bremsstrahlung, increasing the crater depth for high fluences.

A simple explicit example of a Roberts-type dynamo is given in which the $\alpha$ effect of mean-field electrodynamics exists in spite of pointwise vanishing kinetic helicity of the fluid flow. In this way, it is shown that $\alpha$-effect dynamos do not necessarily require nonzero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition, numerical solutions of the original dynamo equations are given that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity.

We predict the existence of a special photonic band gap in a quasi-one-dimensional loop structure containing negative-index materials in the subwavelength regime. The mechanism of the formation for this special band gap is quite different from the so-called zero-average-index gaps in the one-dimensional structures, due to the parallel action of the loop. The parallel action enhances the impedance contrast between the two parts on either side of the interface in each unit cell, thus resulting in strong reflection which increases the width of the band gap. In addition, we show that even large band gaps could be obtained in multichannel structures.

A recently derived axisymmetric lattice Boltzmann model is evaluated numerically. The model incorporates a spatially and temporally varying source term into the evolution equation for the momentum distribution function on a two-dimensional Cartesian lattice. The precise form of the source term is derived through a Chapman-Enskog analysis so that the additional axisymmetric contributions in the Navier-Stokes equations are furnished when written in the cylindrical polar coordinate system. The validity of the model is confirmed by simulating Hagen-Poiseuille flow. Numerical predictions for the drag coefficient in Stokes’ flow over a sphere are presented and shown to be in excellent agreement with analytical results. At larger Reynolds numbers the numerical predictions are shown to approach an empirically derived formula for the drag coefficient.