Optimal bounds with semidefinite programming: an application to stress driven shear flows

We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing schemes, we do not consider the Euler--Lagrange equations for the minimizer. Instead, we use series expansions to formulate a finite dimensional semidefinite program (SDP) whose solution converges to that of the original variational problem. Our formulation accounts for the influence of all modes in the expansion, and the feasible set of the SDP corresponds to a subset of the feasible set of the original problem. Moreover, SDPs can be easily formulated when the fluid is subject to imposed boundary fluxes, which pose a challenge for the traditional methods. We apply this technique to compute rigorous and near-optimal upper bounds on the dissipation coefficient for flows driven by a surface stress. We improve previous analytical bounds by more than 10 times, and show that the bounds become independent of the domain aspect ratio in the limit of vanishing viscosity. We also confirm that the dissipation properties of stress driven flows are similar to those of flows subject to a body force localized in a narrow layer near the surface. Finally, we show that SDP relaxations are an efficient method to investigate the energy stability of laminar flows driven by a surface stress.Comment: 17 pages; typos removed; extended discussion of linear matrix inequalities in Section III; revised argument in Section IVC, results unchanged; extended discussion of computational setup and limitations in Sectios IVE-IVF. Submitted to Phys. Rev.

Single and Double Photoionization and Photodissociation of Toluene by Soft X-rays in Circumstellar Environment

The formation of polycyclic aromatic hydrocarbons (PAHs) and their methyl derivatives occurs mainly in the dust shells of asymptotic giant branch (AGB) stars. The bands at 3.3 and 3.4 $\mu$m, observed in infrared emission spectra of several objects, are attributed C-H vibrational modes in aromatic and aliphatic structures, respectively. In general, the feature at 3.3 $\mu$m is more intense than the 3.4 $\mu$m. Photoionization and photodissociation processes of toluene, the precursor of methylated PAHs, were studied using synchrotron radiation at soft X-ray energies around the carbon K edge with time-of-flight mass spectrometry. Partial ion yields of a large number of ionic fragments were extracted from single and 2D-spectra, where electron-ion coincidences have revealed the doubly charged parent-molecule and several doubly charged fragments containing seven carbon atoms with considerable abundance. \textit{Ab initio} calculations based on density functional theory were performed to elucidate the chemical structure of these stable dicationic species. The survival of the dications subjected to hard inner shell ionization suggests that they could be observed in the interstellar medium, especially in regions where PAHs are detected. The ionization and destruction of toluene induced by X-rays were examined in the T Dra conditions, a carbon-rich AGB star. In this context, a minimum photodissociation radius and the half-life of toluene subjected to the incidence of the soft X-ray flux emitted from a companion white dwarf star were determined.Comment: 11 pages, 4 figures, accept for publication in Ap

Accuracy of an eight-point tactile-electrode impedance method in the assessment of total body water.

OBJECTIVE: To establish the accuracy of an eight-polar tactile-electrode impedance method in the assessment of total body water (TBW). DESIGN: Transversal study. SETTING: University department. SUBJECTS: Fifty healthy subjects (25 men and 25 women) with a mean (s.d.) age of 40 (12) y. METHODS: TBW measured by deuterium oxide dilution; resistance (R) of arms, trunk and legs measured at frequencies of 5, 50, 250 and 500 kHz with an eight-polar tactile-electrode impedance-meter (InBody 3.0, Biospace, Seoul, Korea). RESULTS: An algorithm for the prediction of TBW from the whole-body resistance index at 500 kHz (height (2)/R(500) where R is the sum of the segmental resistances of arms, trunk and legs) was developed in a randomly chosen subsample of 35 subjects. This algorithm had an adjusted coefficient of determination (r2(adj)) of 0.81 (P<0.0001) and a root mean square error (RMSE) of 3.6 l (9%). Cross-validation of the predictive algorithm in the remaining 15 subjects gave an r2(adj) of 0.87 (P<0.0001) and an RMSE of 3.0 l (8%). The precision of eight-polar BIA, determined by measuring R three times a day for five consecutive days in a fasting subject, was < or =2.8% for all segments and frequencies. CONCLUSION: Eight-polar BIA is a precise method that offers accurate estimates of TBW in healthy subjects. This promising method should undergo further studies of precision and its accuracy in assessing extracellular water and appendicular body composition should be determined. SPONSORSHIP: Modena and Reggio Emilia University

Fabrication of three terminal devices by ElectroSpray deposition of graphene nanoribbons

Electrospray deposition (ESD) in ambient conditions has been used to deposit graphene nanoribbons (GNRs) dispersed in liquid phase on different types of substrates, including ones suitable for electrical transport. The deposition process was controlled and optimized by using Raman spectroscopy, Scanning Probe Microscopies and Scanning Electron Microscopy. When deposited on graphitic electrodes, GNRs were used as semi-conducting channel in three terminal devices showing gate tunability of the electrical current. These results suggest that ESD technique can be used as an effective tool to deposit chemically synthesized GNRs onto substrates of interest for technological applications

Photoelectrochemistry of Photosystem II in Vitro vs in Vivo.

Factors governing the photoelectrochemical output of photosynthetic microorganisms are poorly understood, and energy loss may occur due to inefficient electron transfer (ET) processes. Here, we systematically compare the photoelectrochemistry of photosystem II (PSII) protein-films to cyanobacteria biofilms to derive: (i) the losses in light-to-charge conversion efficiencies, (ii) gains in photocatalytic longevity, and (iii) insights into the ET mechanism at the biofilm interface. This study was enabled by the use of hierarchically structured electrodes, which could be tailored for high/stable loadings of PSII core complexes and Synechocystis sp. PCC 6803 cells. The mediated photocurrent densities generated by the biofilm were 2 orders of magnitude lower than those of the protein-film. This was partly attributed to a lower photocatalyst loading as the rate of mediated electron extraction from PSII in vitro is only double that of PSII in vivo. On the other hand, the biofilm exhibited much greater longevity (>5 days) than the protein-film (<6 h), with turnover numbers surpassing those of the protein-film after 2 days. The mechanism of biofilm electrogenesis is suggested to involve an intracellular redox mediator, which is released during light irradiation

EURADOS IC2012N: EURADOS 2012 intercomparison for whole-body neutron dosimetry

The European Radiation Dosimetry Group (EURADOS) IC2012n intercomparison for neutron dosemeters intended to measure personal dose equivalent, Hp(10), was performed in 2012. A total of 31 participants (27 individual monitoring services from Europe, 2 from Japan, 1 from Israel and 1 from USA) registered with 34 dosimetry systems. Participation was restricted to passive or active neutron dosemeters routinely used in individual monitoring of radiation workers. The dosimetry systems were based on thermoluminescence, polyallyldiglycol carbonate, optically stimulated luminescence, fission track detection and silicon diodes (electronic devices). The irradiation tests were chosen to provide the participants with useful information on their dosimetry systems, i.e. linearity, reproducibility, responses for different energies and angles and to simulated workplace fields. The paper will report and discuss the first analysis of the results of the EURADOS IC2012n intercompariso

Increased Adiposity, Dysregulated Glucose Metabolism and Systemic Inflammation in Galectin-3 KO Mice

PMCID: PMC3579848This 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

Semidefinite relaxation of a class of quadratic integral inequalities

We propose a novel technique to solve optimization problems subject to a class of integral inequalities whose integrand is quadratic and homogeneous with respect to the dependent variables, and affine in the parameters. We assume that the dependent variables are subject to homogeneous boundary conditions. Specifically, we derive rigorous relaxations of such integral inequalities in terms of semidefinite constraints, so a strictly feasible and near-optimal point for the original problem can be computed using semidefinite programming. Simple examples arising from the stability analysis of partial differential equations illustrate the potential of our method compared to existing techniques

The background method: Theory and computations

The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the background method can be formulated systematically within a broader "auxiliary function" framework for bounding mean quantities, and explain how symmetries of the flow and constraints such as maximum principles can be exploited. All ideas are presented in a general setting and are illustrated on Rayleigh-Bénard convection between stress-free isothermal plates. Second, we review a semidefinite programming approach and a timestepping approach to optimizing bounds computationally, revealing that they are related to each other through convex duality and low-rank matrix factorization. Open questions and promising directions for further numerical analysis of the background method are also outlined