Analytical results for a Fokker-Planck equation in the small noise limit

We present analytical results for the lowest cumulants of a stochastic process described by a Fokker-Planck equation with nonlinear drift. We show that, in the limit of small fluctuations, the mean, the variance and the covariance of the process can be expressed in compact form with the help of the Lambert W function. As an application, we discuss the interplay of noise and nonlinearity far from equilibrium.Comment: 5 pages, 4 figure

Enhancement of the stability of genetic switches by overlapping upstream regulatory domains

We study genetic switches formed from pairs of mutually repressing operons. The switch stability is characterised by a well defined lifetime which grows sub-exponentially with the number of copies of the most-expressed transcription factor, in the regime accessible by our numerical simulations. The stability can be markedly enhanced by a suitable choice of overlap between the upstream regulatory domains. Our results suggest that robustness against biochemical noise can provide a selection pressure that drives operons, that regulate each other, together in the course of evolution.Comment: 4 pages, 5 figures, RevTeX

Stability Properties of Nonhyperbolic Chaotic Attractors under Noise

We study local and global stability of nonhyperbolic chaotic attractors contaminated by noise. The former is given by the maximum distance of a noisy trajectory from the noisefree attractor, while the latter is provided by the minimal escape energy necessary to leave the basin of attraction, calculated with the Hamiltonian theory of large fluctuations. We establish the important and counterintuitive result that both concepts may be opposed to each other. Even when one attractor is globally more stable than another one, it can be locally less stable. Our results are exemplified with the Holmes map, for two different sets of parameter, and with a juxtaposition of the Holmes and the Ikeda maps. Finally, the experimental relevance of these findings is pointed out.Comment: Phys.Rev. Lett., to be publishe

Robust Trapped-Ion Quantum Logic Gates by Continuous Dynamical Decoupling

We introduce a novel scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac-Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit couplings.Comment: Slightly longer than the published versio

Symmetry Relations for Trajectories of a Brownian Motor

A Brownian Motor is a nanoscale or molecular device that combines the effects of thermal noise, spatial or temporal asymmetry, and directionless input energy to drive directed motion. Because of the input energy, Brownian motors function away from thermodynamic equilibrium and concepts such as linear response theory, fluctuation dissipation relations, and detailed balance do not apply. The {\em generalized} fluctuation-dissipation relation, however, states that even under strongly thermodynamically non-equilibrium conditions the ratio of the probability of a transition to the probability of the time-reverse of that transition is the exponent of the change in the internal energy of the system due to the transition. Here, we derive an extension of the generalized fluctuation dissipation theorem for a Brownian motor for the ratio between the probability for the motor to take a forward step and the probability to take a backward step

A "partitioned leaping" approach for multiscale modeling of chemical reaction dynamics

We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic framework. The technique correctly accounts for stochastic noise at significantly reduced computational cost, requires the definition of only three model-independent parameters and is particularly well-suited for simulating systems containing widely disparate species populations. We present the theoretical foundations of partitioned leaping, discuss various options for its practical implementation and demonstrate the utility of the method via illustrative examples.Comment: v4: 12 pages, 5 figures, final accepted version. Error found and fixed in Appendi

Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis

An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models

Stability of adhesion clusters under constant force

We solve the stochastic equations for a cluster of parallel bonds with shared constant loading, rebinding and the completely dissociated state as an absorbing boundary. In the small force regime, cluster lifetime grows only logarithmically with bond number for weak rebinding, but exponentially for strong rebinding. Therefore rebinding is essential to ensure physiological lifetimes. The number of bonds decays exponentially with time for most cases, but in the intermediate force regime, a small increase in loading can lead to much faster decay. This effect might be used by cell-matrix adhesions to induce signaling events through cytoskeletal loading.Comment: Revtex, 4 pages, 4 Postscript files include

Escaping from nonhyperbolic chaotic attractors

We study the noise-induced escape process from chaotic attractors in nonhyperbolic systems. We provide a general mechanism of escape in the low noise limit, employing the theory of large fluctuations. Specifically, this is achieved by solving the variational equations of the auxiliary Hamiltonian system and by incorporating the initial conditions on the chaotic attractor unambiguously. Our results are exemplified with the H{\'e}non and the Ikeda map and can be implemented straightforwardly to experimental data.Comment: replaced with published versio

Analysis of nucleation using mean first-passage time data from molecular dynamics simulation

We introduce a method for the analysis of nucleation using mean first-passage time (MFPT) statistics obtained by molecular dynamics simulation. The method is based on the Becker-Döring model for the dynamics of a nucleation-mediated phase change and rigorously accounts for the system size dependence of first-passage statistics. It is thus suitable for the analysis of systems in which the separation between time scales for nucleation and growth is small, due to either a small free energy barrier or a large system size. The method is made computationally practical by an approximation of the first-passage time distribution based on its cumulant expansion. Using this approximation, the MFPT of the model can be fit to data from molecular dynamics simulation in order to estimate valuable kinetic parameters, including the free energy barrier, critical nucleus size, and monomer attachment pre-factor, as well as the steady-state rates of nucleation and growth. The method is demonstrated using a case study on nucleation of n-eicosane crystals from the melt. For this system, we found that the observed distribution of first-passage times do not follow an exponential distribution at short times, rendering it incompatible with the assumptions made by some other methods. Using our method, the observed distribution of first-passage times was accurately described, and reasonable estimates for the kinetic parameters and steady-state rates of nucleation and growth were obtained