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- Debashis Barik, William T Baumann, Mark R Paul, Bela Novak, John J Tyson
- Molecular systems biology
- 2010

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)

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)

- M R Paul, M C Cross, P F Fischer, H S Greenside
- Physical review letters
- 2001

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power law is found to arise from quasidiscontinuous changes in the slope of the time series of… (More)

- K-H Chiam, M R Paul, M C Cross, H S Greenside
- Physical review. E, Statistical, nonlinear, and…
- 2003

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)

- N. Hashemi, H. Dankowicz, M. R. Paul
- 2008

We study the nonlinear dynamics of a tapping mode atomic force microscope with tip-surface interactions that include attractive, repulsive, and capillary force contributions using numerical techniques tailored for hybrid or discontinuous dynamical systems that include forward-time simulation with event handling and numerical pseudo-arclength continuation.… (More)

- M R Paul, M C Cross, P F Fischer
- Physical review. E, Statistical, nonlinear, and…
- 2002

Pattern formation in Rayleigh-Bénard convection in a large-aspect-ratio cylinder with a radial ramp in the plate separation is studied analytically and numerically by performing numerical simulations of the Boussinesq equations. A horizontal mean flow and a vertical large scale counterflow are quantified and used to understand the pattern wave number. Our… (More)

The results of an analysis of turbulent pipe flow based on a Karhunen-Lò eve 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,… (More)

- J D Scheel, M R Paul, M C Cross, P F Fischer
- Physical review. E, Statistical, nonlinear, and…
- 2003

Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These simulations reproduce traveling waves observed experimentally. Traveling waves are studied near threshold by using the complex Ginzburg-Landau equation (CGLE): a mode analysis enables the CGLE… (More)

- M R Paul, M I Einarsson, P F Fischer, M C Cross
- Physical review. E, Statistical, nonlinear, and…
- 2007

Using large-scale numerical calculations we explore spatiotemporal chaos in Rayleigh-Bénard convection for experimentally relevant conditions. We calculate the spectrum of Lyapunov exponents and the Lyapunov dimension describing the chaotic dynamics of the convective fluid layer at constant thermal driving over a range of finite system sizes. Our results… (More)

- Kartik Subramanian, Mark R. Paul, John J. Tyson
- PLoS Computational Biology
- 2013

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)