Algebraic structure of stochastic expansions and efficient simulation

We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration schemes that are more accurate than the corresponding stochastic Taylor approximation, independent of the governing vector fields and to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is one example. Herein we: show that the natural context to study stochastic integrators and their properties is the convolution shuffle algebra of endomorphisms; establish a new whole class of efficient integrators; and then prove that, within this class, the sinhlog integrator generates the optimal efficient stochastic integrator at all orders.Comment: 19 page

Large current noise in nanoelectromechanical systems close to continuous mechanical instabilities

We investigate the current noise of nanoelectromechanical systems close to a continuous mechanical instability. In the vicinity of the latter, the vibrational frequency of the nanomechanical system vanishes, rendering the system very sensitive to charge fluctuations and, hence, resulting in very large (super-Poissonian) current noise. Specifically, we consider a suspended single-electron transistor close to the Euler buckling instability. We show that such a system exhibits an exponential enhancement of the current noise when approaching the Euler instability which we explain in terms of telegraph noise.Comment: 11 pages, 12 figures; v2: minor changes, published versio

The governing bodies of Lutheran secondary schools in Australia : an exploratory study

The governing bodies of Lutheran secondary colleges and schools in Australia are comprised of a cross-section of community-minded people, who have accepted the invitation to serve as college council members. The council members bring a range of experiences and expertise to the task they have accepted. This paper profiles the membership of college councils. It reports, to a limited degree, the alignment or otherwise of the way councils operate against the expectation of the By-laws of the Lutheran Church of Australia in regard to the operation of college councils. The paper also explores the views of both council members and principals on some issues, and uncovers the degree of difference or similarity in these views. The research method used for the study is the survey technique. Questionnaires were sent to the principals, council members and council chairpersons of all the Lutheran secondary colleges in Australia, except one. The research reveals that there are a significant number of issues of organisation and behaviours of Councils on which there are quite differing views, both between Councils, between individual council members, and between councils and principals

Dynamic model of gene regulation for the lac operon

Gene regulatory network is a collection of DNA which interact with each other and with other matter in the cell. The lac operon is an example of a relatively simple genetic network and is one of the best-studied structures in the Escherichia coli bacteria. In this work we consider a deterministic model of the lac operon with a noise term, representing the stochastic nature of the regulation. The model is written in terms of a system of simultaneous first order differential equations with delays. We investigate an analytical and numerical solution and analyse the range of values for the parameters corresponding to a stable solution

Dimer diffusion in a washboard potential

The transport of a dimer, consisting of two Brownian particles bounded by a harmonic potential, moving on a periodic substrate is investigated both numerically and analytically. The mobility and diffusion of the dimer center of mass present distinct properties when compared with those of a monomer under the same transport conditions. Both the average current and the diffusion coefficient are found to be complicated non-monotonic functions of the driving force. The influence of dimer equilibrium length, coupling strength and damping constant on the dimer transport properties are also examined in detail.Comment: Final revised version. 7 pages, 6 figure

Spatiotemporal Fluctuation Induced Transition in a Tumor Model with Immune Surveillance

We report on a simple model of spatial extend anti-tumor system with a fluctuation in growth rate, which can undergo a nonequilibrium phase transition. Three states as excited, sub-excited and non-excited states of a tumor are defined to describe its growth. The multiplicative noise is found to be double-face: The positive effect on a non-excited tumor and the negative effect on an excited tumor.Comment: 8pages,5figure

Positive-P phase space method simulation in superradiant emission from a cascade atomic ensemble

The superradiant emission properties from an atomic ensemble with cascade level configuration is numerically simulated. The correlated spontaneous emissions (signal then idler fields) are purely stochastic processes which are initiated by quantum fluctuations. We utilize the positive-P phase space method to investigate the dynamics of the atoms and counter-propagating emissions. The light field intensities are calculated, and the signal-idler correlation function is studied for different optical depths of the atomic ensemble. Shorter correlation time scale for a denser atomic ensemble implies a broader spectral window needed to store or retrieve the idler pulse.Comment: To be published in Phys. Rev.