A Streamwise Constant Model of Turbulence in Plane Couette Flow

Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behavior of fully turbulent plane Couette flow using a streamwise constant projection of the Navier Stokes equations. This results in a two-dimensional, three velocity component ($2D/3C$) model. We first use a steady state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity profile. Simulations of the $2D/3C$ model under small amplitude Gaussian forcing of the cross-stream components are compared to DNS data. The results indicate that a streamwise constant projection of the Navier Stokes equations captures salient features of fully turbulent plane Couette flow at low Reynolds numbers. A system theoretic approach is used to demonstrate the presence of large input-output amplification through the forced $2D/3C$ model. It is this amplification coupled with the appropriate nonlinearity that enables the $2D/3C$ model to generate turbulent behaviour under the small amplitude forcing employed in this study.Comment: Journal of Fluid Mechanics 2010, in pres

Density flow over networks: A mean-field game theoretic approach

A distributed routing control algorithm for dynamic networks has recently been presented in the literature. The networks were modeled using time evolution of density at network edges and the routing control algorithm allowed edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We borrow the idea and rearrange the density model to recast the problem within the framework of mean-field games. The contribution of this paper is three-fold. First, we provide a mean-field game formulation of the problem at hand. Second, we illustrate an extended state space solution approach. Third, we study the stochastic case where the density evolution is driven by a Brownian motion

Feedback control architecture and the bacterial chemotaxis network.

PMCID: PMC3088647This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to 'reset' (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a 'cascade control' feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance

Measurements of high-energy neutron-induced fission of (nat)Pb and (209)Bi

This is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License 3.0, which permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided the original work is properly citedThe CERN Neutron Time-Of-Flight (n_TOF) facility is well suited to measure low cross sections as those of neutron-induced fission in subactinides. The cross section ratios of (nat)Pb and (209)Bi relative to (235)U and (238)U were measured using PPAC detectors and a fragment coincidence method that allows us to identify the fission events. The present experiment provides first results for neutron-induced fission up to 1 GeV. Good agreement is found with previous experimental data below 200 MeV. The comparison with proton-induced fission indicates that the limiting regime where neutron-induced and proton-induced fission reach equal cross sections is close to 1 GeV

Measurement of the (90,91,92,93,94,96)Zr(n,gamma) and (139)La(n,gamma) cross sections at n_TOF

Open AccessNeutron capture cross sections of Zr and La isotopes have important implications in the field of nuclear astrophysics as well as in the nuclear technology. In particular the Zr isotopes play a key role for the determination of the neutron density in the He burning zone of the Red Giant star, while the (139)La is important to monitor the s-process abundances from Ba up to Ph. Zr is also largely used as structural materials of traditional and advanced nuclear reactors. The nuclear resonance parameters and the cross section of (90,91,92,93,94,96)Zr and (139)La have been measured at the n_TOF facility at CERN. Based on these data the capture resonance strength and the Maxwellian-averaged cross section were calculated

Measurement of the neutron capture cross section of the s-only isotope 204Pb from 1 eV to 440 keV

The neutron capture cross section of 204Pb has been measured at the CERN n_TOF installation with high resolution in the energy range from 1 eV to 440 keV. An R-matrix analysis of the resolved resonance region, between 1 eV and 100 keV, was carried out using the SAMMY code. In the interval between 100 keV and 440 keV we report the average capture cross section. The background in the entire neutron energy range could be reliably determined from the measurement of a 208Pb sample. Other systematic effects in this measurement could be investigated and precisely corrected by means of detailed Monte Carlo simulations. We obtain a Maxwellian average capture cross section for 204Pb at kT=30 keV of 79(3) mb, in agreement with previous experiments. However our cross section at kT=5 keV is about 35% larger than the values reported so far. The implications of the new cross section for the s-process abundance contributions in the Pb/Bi region are discussed.Comment: 8 pages, 3 figures, article submitted to Phys. Rev.

New measurement of neutron capture resonances of 209Bi

The neutron capture cross section of Bi209 has been measured at the CERN n TOF facility by employing the pulse-height-weighting technique. Improvements over previous measurements are mainly because of an optimized detection system, which led to a practically negligible neutron sensitivity. Additional experimental sources of systematic error, such as the electronic threshold in the detectors, summing of gamma-rays, internal electron conversion, and the isomeric state in bismuth, have been taken into account. Gamma-ray absorption effects inside the sample have been corrected by employing a nonpolynomial weighting function. Because Bi209 is the last stable isotope in the reaction path of the stellar s-process, the Maxwellian averaged capture cross section is important for the recycling of the reaction flow by alpha-decays. In the relevant stellar range of thermal energies between kT=5 and 8 keV our new capture rate is about 16% higher than the presently accepted value used for nucleosynthesis calculations. At this low temperature an important part of the heavy Pb-Bi isotopes are supposed to be synthesized by the s-process in the He shells of low mass, thermally pulsing asymptotic giant branch stars. With the improved set of cross sections we obtain an s-process fraction of 19(3)% of the solar bismuth abundance, resulting in an r-process residual of 81(3)%. The present (n,gamma) cross-section measurement is also of relevance for the design of accelerator driven systems based on a liquid metal Pb/Bi spallation target.Comment: 10 pages, 5figures, recently published in Phys. Rev.

Resonance capture cross section of 207Pb

The radiative neutron capture cross section of 207Pb has been measured at the CERN neutron time of flight installation n_TOF using the pulse height weighting technique in the resolved energy region. The measurement has been performed with an optimized setup of two C6D6 scintillation detectors, which allowed us to reduce scattered neutron backgrounds down to a negligible level. Resonance parameters and radiative kernels have been determined for 16 resonances by means of an R-matrix analysis in the neutron energy range from 3 keV to 320 keV. Good agreement with previous measurements was found at low neutron energies, whereas substantial discrepancies appear beyond 45 keV. With the present results, we obtain an s-process contribution of 77(8)% to the solar abundance of 207Pb. This corresponds to an r-process component of 23(8)%, which is important for deriving the U/Th ages of metal poor halo stars.Comment: 7 pages, 3 figures, to be published in Phys. Rev.

Locally Optimal Reach Set Over-approximation for Nonlinear Systems

Safety verification of embedded systems modeled as hybrid systems can be scaled up by employing simulation-guided reach set over-approximation techniques. Existing methods are applicable only to restricted classes of systems, overly conservative, or computationally expensive. We present new techniques to compute a locally optimal bloating factor based on discrepancy functions, which allow construction of reach set over-approximations from simulation traces for general nonlinear systems. The discrepancy functions are critical for tools like C2E2 to verify bounded time safety properties for complex hybrid systems with nonlinear continuous dynamics. The new discrepancy function is computed using local bounds on a matrix measure under an optimal metric such that the exponential change rate of the discrepancy function is minimized. The new technique is less time consuming and less conservative than existing techniques and does not incur significant computational overhead. We demonstrate the effectiveness of our approach by comparing the performance of a prototype implementation with the state-of-the-art reachability analysis tool Flow*.National Science Foundation/CCF 1422798Ope

Measurement of the radiative neutron capture cross section of 206Pb and its astrophysical implications

The (n, gamma) cross section of 206Pb has been measured at the CERN n_TOF facility with high resolution in the energy range from 1 eV to 600 keV by using two optimized C6D6 detectors. In the investigated energy interval about 130 resonances could be observed, from which 61 had enough statistics to be reliably analyzed via the R-matrix analysis code SAMMY. Experimental uncertainties were minimized, in particular with respect to (i) angular distribution effects of the prompt capture gamma-rays, and to (ii) the TOF-dependent background due to sample-scattered neutrons. Other background components were addressed by background measurements with an enriched 208Pb sample. The effect of the lower energy cutoff in the pulse height spectra of the C6D6 detectors was carefully corrected via Monte Carlo simulations. Compared to previous 206Pb values, the Maxwellian averaged capture cross sections derived from these data are about 20% and 9% lower at thermal energies of 5 keV and 30 keV, respectively. These new results have a direct impact on the s-process abundance of 206Pb, which represents an important test for the interpretation of the cosmic clock based on the decay of 238U.Comment: 11 pages, 8 figures, paper to be submitted to Phys. Rev.