Unusually high differential attenuation at C band: Results from a two-year analysis of the French Trappes polarimetric radar data

The differential phase (ΦDP) measured by polarimetric radars is recognized to be a very good indicator of the path integrated by rain. Moreover, if a linear relationship is assumed between the specific differential phase (KDP) and the specific attenuation (AH) and specific differential attenuation (ADP), then attenuation can easily be corrected. The coefficients of proportionality, γH and γDP, are, however, known to be dependent in rain upon drop temperature, drop shapes, drop size distribution, and the presence of large drops causing Mie scattering. In this paper, the authors extensively apply a physically based method, often referred to as the “Smyth and Illingworth constraint,” which uses the constraint that the value of the differential reflectivity ZDR on the far side of the storm should be low to retrieve the γDP coefficient. More than 30 convective episodes observed by the French operational C-band polarimetric Trappes radar during two summers (2005 and 2006) are used to document the variability of γDP with respect to the intrinsic three-dimensional characteristics of the attenuating cells. The Smyth and Illingworth constraint could be applied to only 20% of all attenuated rays of the 2-yr dataset so it cannot be considered the unique solution for attenuation correction in an operational setting but is useful for characterizing the properties of the strongly attenuating cells. The range of variation of γDP is shown to be extremely large, with minimal, maximal, and mean values being, respectively, equal to 0.01, 0.11, and 0.025 dB °−1. Coefficient γDP appears to be almost linearly correlated with the horizontal reflectivity (ZH), differential reflectivity (ZDR), and specific differential phase (KDP) and correlation coefficient (ρHV) of the attenuating cells. The temperature effect is negligible with respect to that of the microphysical properties of the attenuating cells. Unusually large values of γDP, above 0.06 dB °−1, often referred to as “hot spots,” are reported for 15%—a nonnegligible figure—of the rays presenting a significant total differential phase shift (ΔϕDP > 30°). The corresponding strongly attenuating cells are shown to have extremely high ZDR (above 4 dB) and ZH (above 55 dBZ), very low ρHV (below 0.94), and high KDP (above 4° km−1). Analysis of 4 yr of observed raindrop spectra does not reproduce such low values of ρHV, suggesting that (wet) ice is likely to be present in the precipitation medium and responsible for the attenuation and high phase shifts. Furthermore, if melting ice is responsible for the high phase shifts, this suggests that KDP may not be uniquely related to rainfall rate but can result from the presence of wet ice. This hypothesis is supported by the analysis of the vertical profiles of horizontal reflectivity and the values of conventional probability of hail indexes.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Numerical Methods for Stiff Two-Point Boundary Value Problems

We consider the two-point boundary value problem for stiff systems of ordinary differential equations. For systems that can be transformed to essentially diagonally dominant form with appropriate smoothness conditions, a priori estimates are obtained. Problems with turning points can be treated with this theory, and we discuss this in detail. We give robust difference approximations and present error estimates for these schemes. In particular we give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable so that the system will satisfy the correct smoothness conditions. Numerical examples are presented for both linear and nonlinear problems.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

Insulin resistance determines a differential response to changes in dietary fat modification on metabolic syndrome risk factors: the LIPGENE study

Background: Previous data support the benefits of reducing dietary saturated fatty acids (SFAs) on insulin resistance (IR) and other metabolic risk factors. However, whether the IR status of those suffering from metabolic syndrome (MetS) affects this response is not established. OBJECTIVE: Our objective was to determine whether the degree of IR influences the effect of substituting high-saturated fatty acid (HSFA) diets by isoenergetic alterations in the quality and quantity of dietary fat on MetS risk factors. DESIGN: In this single-blind, parallel, controlled, dietary intervention study, MetS subjects (n = 472) from 8 European countries classified by different IR levels according to homeostasis model assessment of insulin resistance (HOMA-IR) were randomly assigned to 4 diets: an HSFA diet; a high-monounsaturated fatty acid (HMUFA) diet; a low-fat, high-complex carbohydrate (LFHCC) diet supplemented with long-chain n-3 polyunsaturated fatty acids (1.2 g/d); or an LFHCC diet supplemented with placebo for 12 wk (control). Anthropometric, lipid, inflammatory, and IR markers were determined. RESULTS: Insulin-resistant MetS subjects with the highest HOMA-IR improved IR, with reduced insulin and HOMA-IR concentrations after consumption of the HMUFA and LFHCC n-3 diets (P < 0.05). In contrast, subjects with lower HOMA-IR showed reduced body mass index and waist circumference after consumption of the LFHCC control and LFHCC n-3 diets and increased HDL cholesterol concentrations after consumption of the HMUFA and HSFA diets (P < 0.05). MetS subjects with a low to medium HOMA-IR exhibited reduced blood pressure, triglyceride, and LDL cholesterol levels after the LFHCC n-3 diet and increased apolipoprotein A-I concentrations after consumption of the HMUFA and HSFA diets (all P < 0.05). CONCLUSIONS: Insulin-resistant MetS subjects with more metabolic complications responded differently to dietary fat modification, being more susceptible to a health effect from the substitution of SFAs in the HMUFA and LFHCC n-3 diets. Conversely, MetS subjects without IR may be more sensitive to the detrimental effects of HSFA intake. The metabolic phenotype of subjects clearly determines response to the quantity and quality of dietary fat on MetS risk factors, which suggests that targeted and personalized dietary therapies may be of value for its different metabolic features.

Discontinuous local semiflows for Kurzweil equations leading to LaSalle`s invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle`s invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle`s invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. All rights reserved.

Evaluation of the light polymerization efficiency of copolymers used in dental formulations by differential scanning calorimetry

Different compositions of visible-light-curable triethylene glycol dimethacrylate/bisglycidyl methacrylate copolymers used in dental resin formulations were prepared through copolymerization photoinitiated by a camphorquinone/ethyl 4-dimethylaminobenzoate system irradiated with an Ultrablue IS light-emitting diode. The obtained copolymers were evaluated with differential scanning calorimetry. From the data for the heat of polymerization, before and after light exposure, obtained from exothermic differential scanning calorimetry curves, the light polymerization efficiency or degree of conversion of double bonds was calculated. The glass-transition temperature also was determined before and after photopolymerization. After the photopolymerization, the glass-transi-tion temperature was not well defined because of the breadth of the transition region associated with the properties of the photocured dimethacrylate. The glass-transition temperature after photopolymerization was determined experimentally and compared with the values determined with the Fox equation. In all mixtures, the experimental value was lower than the calculated value. Scanning electron microscopy was used to analyze the morphological differences in the prepared copolymer structures. (C) 2007 Wiley Periodicals, Inc.

Copper determination in ethanol fuel by differential pulse anodic stripping voltammetry at a solid paraffin-based carbon paste electrode modified with 2-aminothiazole organofunctionalized silica

Solid paraffin-based carbon paste electrodes modified with 2-aminothiazole organofunctionalized silica have been applied to the anodic stripping determination of copper ions in ethanol fuel samples without any sample treatment. The proposed method comprised four steps: (1) copper ions preconcentration at open circuit potential directly in the ethanol fuel sample; (2) exchange of the solution and immediate cathodic reduction of the absorbate at controlled potential; (3) differential pulse anodic stripping voltammetry; (4) electrochemical surface regeneration by applying a positive potential in acid media. Factors affecting the preconcentration, reduction and stripping steps were investigated and the optimum conditions were employed to develop the analytical procedure. Using a preconcentration time of 20 min and reduction time of 120 s at -0.3 V versus Ag/AgCl(sat) a linear range from 7.5 x 10(-8) to 2.5 x 10(-6) mol L(-1) with detection limit of 3.1 x 10(-8) mol L(-1) was obtained. Interference studies have shown a decrease in the interference effect according to the sequence: Ni > Zn > Cd > Pb > Fe. However, the interference effects of these ions have not forbidden the application of the proposed method. Recovery values between 98.8 and 102.3% were obtained for synthetic samples spiked with known amounts of Cu(2+) and interfering metallic ions. The developed electrode was successfully applied to the determination of Cu(2+) in commercial ethanol fuel samples. The results were compared to those obtained by flame atomic absorption spectroscopy by using the F-test and t-test. Neither F-value nor t-value have exceeded the critical values at 95% confidence level, confirming that there are no significant differences between the results obtained by both methods. (c) 2006 Elsevier B.V. All rights reserved.

Differential organotin sensitivity in two Leucozonia species from a ship traffic area in southeastern Brazil

Tributyltin exposure is the primary cause of imposex development in gastropods, making them excellent bioindicators. The present research represents the first examination of butyltin (BT) contamination in surface sediments associated with imposex in Leucozonia nassa and L. ocellata in a harbour complex area in Espirito Santo, southeastern Brazil. The objectives of this study were to evaluate the organotin pollution in the area and to assess the sensitivity of both species to BT pollution through imposex development. Specimens were collected between 2007 and 2010 and the sediments were sampled in 2007. Imposex intensity was evaluated based on the percentage of imposexed females, the relative penis length index (RPLI) and the average value of the vas deferens sequence index (VDSI). BTs were analysed using gas chromatography equipped with a pulsed flame photometric detector (PFPD). The results demonstrated the occurrence of elevated concentrations of BTs in the sediment ranging from 383.7 to 7172.9 ng Sn g(-1), indicating a severe contamination of the area, which was confirmed by the biological monitoring results. Our findings also indicated that L. ocellata is a less sensitive species than L. nassa and that this differential sensitivity plays a key role in the distributions of the populations of both species in the studied area.

Measurement of the inclusive 3-jet production differential cross section in proton-proton collisions at 7 TeV and determination of the strong coupling constant in the TeV range

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Simultaneous optical signal-to-noise ratio and differential group delay monitoring based on degree of polarization measurements in optical communications systems

We present a simultaneous optical signal-to-noise ratio (OSNR) and differential group delay (DGD) monitoring method based on degree of polarization (DOP) measurements in optical communications systems. For the first time in the literature (to our best knowledge), the proposed scheme is demonstrated to be able to independently and simultaneously extract OSNR and DGD values from the DOP measurements. This is possible because the OSNR is related to maximum DOP, while DGD is related to the ratio between the maximum and minimum values of DOP. We experimentally measured OSNR and DGD in the ranges from 10 to 30 dB and 0 to 90 ps for a 10 Gb/s non-return-to-zero signal. A theoretical analysis of DOP accuracy needed to measure low values of DGD and high OSNRs is carried out, showing that current polarimeter technology is capable of yielding an OSNR measurement within 1 dB accuracy, for OSNR values up to 34 dB, while DGD error is limited to 1.5% for DGD values above 10 ps. For the first time to our knowledge, the technique was demonstrated to accurately measure first-order polarization mode dispersion (PMD) in the presence of a high value of second-order PMD (as high as 2071 ps(2)). (C) 2012 Optical Society of America

Determination of the intrinsic kinetic parameters of sulfide-oxidizing autotrophic denitrification in differential reactors containing immobilized biomass

Nitrogen removal coupled with sulfide oxidation has potential for the treatment of effluents from anaerobic reactors because they contain sulfide, which can be used as an endogenous electron donor for denitrification. This work evaluated the intrinsic kinetics of sulfide-oxidizing autotrophic denitrification via nitrate and nitrite in systems containing attached cells. Differential reactors were fed with nitrified synthetic domestic sewage and different sulfide concentrations. The intrinsic kinetic parameters of nitrogen removal were determined when the mass transfer resistance was negligible. This bioprocess could be described by a half-order kinetic model for biofilms. The half-order kinetic coefficients ranged from 0.425 to 0.658 mg N-1/2 L-1/2 h(-1) for denitrification via nitrite and from 0.190 to 0.609 mg N-1/2 L-1/2 h(-1) for denitrification via nitrate. In this latter, the lower value was due to the use of electrons donated from intermediary sulfur compounds whose formation and subsequent consumption were detected. (C) 2011 Elsevier Ltd. All rights reserved.

Differential regulation of PGC-1α expression in rat liver and skeletal muscle in response to voluntary running

Abstract Background The beneficial actions of exercise training on lipid, glucose and energy metabolism and insulin sensitivity appear to be in part mediated by PGC-1α. Previous studies have shown that spontaneously exercised rats show at rest enhanced responsiveness to exogenous insulin, lower plasma insulin levels and increased skeletal muscle insulin sensitivity. This study was initiated to examine the functional interaction between exercise-induced modulation of skeletal muscle and liver PGC-1α protein expression, whole body insulin sensitivity, and circulating FFA levels as a measure of whole body fatty acid (lipid) metabolism. Methods Two groups of male Wistar rats (2 Mo of age, 188.82 ± 2.77 g BW) were used in this study. One group consisted of control rats placed in standard laboratory cages. Exercising rats were housed individually in cages equipped with running wheels and allowed to run at their own pace for 5 weeks. At the end of exercise training, insulin sensitivity was evaluated by comparing steady-state plasma glucose (SSPG) concentrations at constant plasma insulin levels attained during the continuous infusion of glucose and insulin to each experimental group. Subsequently, soleus and plantaris muscle and liver samples were collected and quantified for PGC-1α protein expression by Western blotting. Collected blood samples were analyzed for glucose, insulin and FFA concentrations. Results Rats housed in the exercise wheel cages demonstrated almost linear increases in running activity with advancing time reaching to maximum value around 4 weeks. On an average, the rats ran a mean (Mean ± SE) of 4.102 ± 0.747 km/day and consumed significantly more food as compared to sedentary controls (P < 0.001) in order to meet their increased caloric requirement. Mean plasma insulin (P < 0.001) and FFA (P < 0.006) concentrations were lower in the exercise-trained rats as compared to sedentary controls. Mean steady state plasma insulin (SSPI) and glucose (SSPG) concentrations were not significantly different in sedentary control rats as compared to exercise-trained animals. Plantaris PGC-1α protein expression increased significantly from a 1.11 ± 0.12 in the sedentary rats to 1.74 ± 0.09 in exercising rats (P < 0.001). However, exercise had no effect on PGC-1α protein content in either soleus muscle or liver tissue. These results indicate that exercise training selectively up regulates the PGC-1α protein expression in high-oxidative fast skeletal muscle type such as plantaris muscle. Conclusion These data suggest that PGC-1α most likely plays a restricted role in exercise-mediated improvements in insulin resistance (sensitivity) and lowering of circulating FFA levels.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.