Author

# Mark Paul

Other affiliations: California Institute of Technology, University of California, Los Angeles

Bio: Mark Paul is an academic researcher from Virginia Tech. The author has contributed to research in topics: Rayleigh–Bénard convection & Cantilever. The author has an hindex of 21, co-authored 82 publications receiving 1624 citations. Previous affiliations of Mark Paul include California Institute of Technology & University of California, Los Angeles.

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##### Papers

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Virginia Tech

^{1}TL;DR: In this paper, a simplified version of the control system that is suitable for exact stochastic simulation of intrinsic noise caused by molecular fluctuations and extrinsic noise because of unequal division is presented.

Abstract: 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 the full reaction network has yet to be expressed in terms of elementary reaction steps. As a first step in this direction, we present a simplified version of the control system that is suitable for exact stochastic simulation of intrinsic noise caused by molecular fluctuations and extrinsic noise because of unequal division. The model is consistent with many characteristic features of noisy cell cycle progression in yeast populations, including the observation that mRNAs are present in very low abundance (≈1 mRNA molecule per cell for each expressed gene). For the control system to operate reliably at such low mRNA levels, some specific mRNAs in our model must have very short half-lives (<1 min). If these mRNA molecules are longer-lived (perhaps 2 min), then the intrinsic noise in our simulations is too large, and there must be some additional noise suppression mechanisms at work in cells.

160 citations

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Virginia Tech

^{1}TL;DR: The high-dimensional chaotic dynamics of the Lorenz-96 model is explored by computing the variation of the fractal dimension with system parameters and it is found that each wavelength of the deviation from extensive chaos contains on the order of two chaotic degrees of freedom.

Abstract: 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 atmosphere. First, we explore the spatiotemporal chaos limit by increasing the system size while holding the magnitude of the external forcing constant. Second, we explore the strong driving limit by increasing the external forcing while holding the system size fixed. As the system size is increased for small values of the forcing we find dynamical states that alternate between periodic and chaotic dynamics. The windows of chaos are extensive, on average, with relative deviations from extensivity on the order of 20%. For intermediate values of the forcing we find chaotic dynamics for all system sizes past a critical value. The fractal dimension exhibits a maximum deviation from extensivity on the order of 5% for small changes in system size and the deviation from extensivity decreases nonmonotonically with increasing system size. The length scale describing the deviations from extensivity is consistent with the natural chaotic length scale in support of the suggestion that deviations from extensivity are due to the addition of chaotic degrees of freedom as the system size is increased. We find that each wavelength of the deviation from extensive chaos contains on the order of two chaotic degrees of freedom. As the forcing is increased, at constant system size, the dimension density grows monotonically and saturates at a value less than unity. We use this to quantify the decreasing size of chaotic degrees of freedom with increased forcing which we compare with spatial features of the patterns.

151 citations

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TL;DR: 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 experiment.

Abstract: 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 experiment. We use this approach to investigate the fluid coupled motion of single and multiple cantilevers with experimentally motivated geometries.

123 citations

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TL;DR: A new model of the regulation of Cln and Clb‐dependent kinases is constructed, based on multisite phosphorylation of their target proteins and on positive and negative feedback loops involving the kinases themselves, which gives a quantitatively accurate account of the variability observed in the G1‐S transition in budding yeast.

Abstract: 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 of molecular fluctuations on cell-cycle progression in budding yeast cells, we have constructed a new model of the regulation of Cln- and Clb-dependent kinases, based on multisite phosphorylation of their target proteins and on positive and negative feedback loops involving the kinases themselves. To account for the significant role of noise in the transcription and translation steps of gene expression, the model includes mRNAs as well as proteins. The model equations are simulated deterministically and stochastically to reveal the bistable switching behavior on which proper cell-cycle progression depends and to show that this behavior is robust to the level of molecular noise expected in yeast-sized cells (∼50 fL volume). The model gives a quantitatively accurate account of the variability observed in the G1-S transition in budding yeast, which is governed by an underlying sizer+timer control system.

118 citations

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TL;DR: In this article, the authors use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, they analyze image time series of persistence diagrams from numerical simulations of two important problems in dynamics: Kolmogorov flow and Rayleigh-B enard convection.

86 citations

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01 Jan 1994

TL;DR: Micromachining technology was used to prepare chemical analysis systems on glass chips that utilize electroosmotic pumping to drive fluid flow and electrophoretic separation to distinguish sample components with no moving parts.

Abstract: Micromachining technology was used to prepare chemical analysis systems on glass chips (1 centimeter by 2 centimeters or larger) that utilize electroosmotic pumping to drive fluid flow and electrophoretic separation to distinguish sample components. Capillaries 1 to 10 centimeters long etched in the glass (cross section, 10 micrometers by 30 micrometers) allow for capillary electrophoresis-based separations of amino acids with up to 75,000 theoretical plates in about 15 seconds, and separations of about 600 plates can be effected within 4 seconds. Sample treatment steps within a manifold of intersecting capillaries were demonstrated for a simple sample dilution process. Manipulation of the applied voltages controlled the directions of fluid flow within the manifold. The principles demonstrated in this study can be used to develop a miniaturized system for sample handling and separation with no moving parts.

1,412 citations

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TL;DR: This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data and proposes a novel neural network architecture which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropic tensor.

Abstract: There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

1,159 citations

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TL;DR: The general issues that will be critical to the success of any type of next-generation mechanical biosensor are explained, such as the need to improve intrinsic device performance, fabrication reproducibility and system integration, and the need for a greater understanding of analyte-sensor interactions on the nanoscale.

Abstract: Mechanical interactions are fundamental to biology. Mechanical forces of chemical origin determine motility and adhesion on the cellular scale, and govern transport and affinity on the molecular scale. Biological sensing in the mechanical domain provides unique opportunities to measure forces, displacements and mass changes from cellular and subcellular processes. Nanomechanical systems are particularly well matched in size with molecular interactions, and provide a basis for biological probes with single-molecule sensitivity. Here we review micro- and nanoscale biosensors, with a particular focus on fast mechanical biosensing in fluid by mass- and force-based methods, and the challenges presented by non-specific interactions. We explain the general issues that will be critical to the success of any type of next-generation mechanical biosensor, such as the need to improve intrinsic device performance, fabrication reproducibility and system integration. We also discuss the need for a greater understanding of analyte–sensor interactions on the nanoscale and of stochastic processes in the sensing environment.

893 citations

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03 Apr 2009TL;DR: This paper provides a comprehensive overview of integrated piezoresistor technology with an introduction to the physics of Piezoresistivity, process and material selection and design guidance useful to researchers and device engineers.

Abstract: Piezoresistive sensors are among the earliest micromachined silicon devices. The need for smaller, less expensive, higher performance sensors helped drive early micromachining technology, a precursor to microsystems or microelectromechanical systems (MEMS). The effect of stress on doped silicon and germanium has been known since the work of Smith at Bell Laboratories in 1954. Since then, researchers have extensively reported on microscale, piezoresistive strain gauges, pressure sensors, accelerometers, and cantilever force/displacement sensors, including many commercially successful devices. In this paper, we review the history of piezoresistance, its physics and related fabrication techniques. We also discuss electrical noise in piezoresistors, device examples and design considerations, and alternative materials. This paper provides a comprehensive overview of integrated piezoresistor technology with an introduction to the physics of piezoresistivity, process and material selection and design guidance useful to researchers and device engineers.

789 citations

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TL;DR: In this paper, a model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behavior of the very large scale motions.

Abstract: A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating helical velocity response modes that are harmonic in the wall-parallel directions and in time, permitting comparison of our results to experimental data. The steady component of the velocity field that varies only in the wall-normal direction is identified as the turbulent mean profile. A singular value decomposition of the resolvent identifies the forcing shape that will lead to the largest velocity response at a given wavenumber–frequency combination. The hypothesis that these forcing shapes lead to response modes that will be dominant in turbulent pipe flow is tested by using physical arguments to constrain the range of wavenumbers and frequencies to those actually observed in experiments. An investigation of the most amplified velocity response at a given wavenumber–frequency combination reveals critical-layer-like behaviour reminiscent of the neutrally stable solutions of the Orr–Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely wall layers that scale with R+1/2 and critical layers where the propagation velocity is equal to the local mean velocity, one of which scales with R+2/3 in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall. The model reproduces inner scaling of the small scales near the wall and an approach to outer scaling in the flow interior. We use our analysis to make a first prediction that the appropriate scaling velocity for the very large scale motions is the centreline velocity, and show that this is in agreement with experimental results. Lastly, we interpret the wall modes as the motion required to meet the wall boundary condition, identifying the interaction between the critical and wall modes as a potential origin for an interaction between the large and small scales that has been observed in recent literature as an amplitude modulation of the near-wall turbulence by the very large scales.

594 citations