Mark R. Paul

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The stochastic response of nanoscale oscillators of arbitrary geometry immersed in a viscous fluid is studied. Using the fluctuation-dissipation theorem, it is shown that deterministic calculations of the governing fluid and solid equations can be used in a straightforward manner to directly calculate the stochastic response that would be measured in(More)
The DNA replication-division cycle of eukaryotic cells is controlled by a complex network of regulatory proteins, called cyclin-dependent kinases, and their activators and inhibitors. Although comprehensive and accurate deterministic models of the control system are available for yeast cells, reliable stochastic simulations have not been carried out because(More)
In order for the cell's genome to be passed intact from one generation to the next, the events of the cell cycle (DNA replication, mitosis, cell division) must be executed in the correct order, despite the considerable molecular noise inherent in any protein-based regulatory system residing in the small confines of a eukaryotic cell. To assess the effects(More)
Many physiological characteristics of living cells are regulated by protein interaction networks. Because the total numbers of these protein species can be small, molecular noise can have significant effects on the dynamical properties of a regulatory network. Computing these stochastic effects is made difficult by the large timescale separations typical of(More)
We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. First, we show that, in the absence of the mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean(More)
We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by Lorenz to study fundamental issues regarding the forecasting of spatially extended chaotic systems such as the(More)
The stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence of the noise force is determined from the fluctuation-dissipation(More)
The results of an analysis of turbulent pipe flow based on a Karhunen-Loève decomposition are presented. The turbulent flow is generated by a direct numerical simulation of the Navier-Stokes equations using a spectral element algorithm at a Reynolds number Reτ = 150. This simulation yields a set of basis functions that captures 90% of the energy after 2,453(More)
We numerically explore gyrotactic bioconvection in large spatially extended domains of finite depth using parameter values from available experiments with the unicellular alga Chlamydomonas nivalis. We numerically integrate the three-dimensional, time-dependent continuum model of Pedley et al. [J. Fluid Mech. 195, 223 (1988)] using a high-order, parallel,(More)
The free-living aquatic bacterium, Caulobacter crescentus, exhibits two different morphologies during its life cycle. The morphological change from swarmer cell to stalked cell is a result of changes of function of two bi-functional histidine kinases, PleC and CckA. Here, we describe a detailed molecular mechanism by which the function of PleC changes(More)