The effect of the geomagnetic field on cosmic ray energy estimates and large scale anisotropy searches on data from the Pierre Auger Observatory

We present a comprehensive study of the influence of the geomagnetic field on the energy estimation of extensive air showers with a zenith angle smaller than 60 degrees, detected at the Pierre Auger Observatory. the geomagnetic field induces an azimuthal modulation of the estimated energy of cosmic rays up to the similar to 2% level at large zenith angles. We present a method to account for this modulation of the reconstructed energy. We analyse the effect of the modulation on large scale anisotropy searches in the arrival direction distributions of cosmic rays. At a given energy, the geomagnetic effect is shown to induce a pseudo-dipolar pattern at the percent level in the declination distribution that needs to be accounted for.

Estimates of hourly diffuse radiation on tilted surfaces in southeast of brazil

The global radiation incident on a tilted surfaces consists of components direct, diffuse and reflected from the ground. On a hourly database, the direct radiation can be calculated by geometric projections (ratio of the incidence angle to the solar zenith angle). The reflected radiation has a small effect on calculations and may be calculated with an isotropic model. Both components presents dependence of measures in incidence or horizontal surface. The great difficulty is to evaluate the diffuse radiation by variations of circumsolar, brightness horizontal, isotropic and anisotropic subcomponents. This study evaluated twenty models to estimate hourly diffuse radiation incident on tilted surfaces at 12.85° (latitude - 10°), 22.85° (latitude) and 32.85° (latitude + 10°) facing to North, under different cloudiness sky conditions, in Botucatu, São Paulo State, Brazil (22°53' S, 48°26' W and 786 m above the mean sea level). In contrast, models for estimating the diffuse component show major differences, which justify the validation for local calibrations. There is a decrease of the maximum total radiation scattered with increasing atmospheric transmissivity and inclination angle. The best results are obtained by anisotropic models: Ma and Iqbal, Hay, Reindl et al. and Willmott; isotropic: Badescu and Koronakis, and the Circumsolar model. The increase of the inclination angle allows for a reduction in the performance of statistical parametric models for estimating the hourly diffuse radiation.

A snapshot of suspended sediment and fluid mud occurrence in a mixed-energy embayment, Tijucas Bay, Brazil

Along the southern Brazilian coast, Tijucas Bay is known for its unique muddy tidal flats associated with chenier plains. Previous field observations pointed to very high suspended sediment concentrations (SSCs) in the inner parts of the bay, and in the estuary of the Tijucas River, suggesting the presence of fluid mud. In this study, the occurrences of suspended sediments and fluid mud were examined during a larger-scale, high-resolution 2-day field campaign on 1-2 May 2007, encompassing survey lines spanning nearly 80 km, 75 water sampling stations for near-bottom density estimates, and ten sediment sampling stations. Wave refraction modeling provided qualitative wave energy estimates as a function of different incidence directions. The results show that SSC increases toward the inner bay near the water surface, but seaward near the bottom. This suggests that suspended sediment is supplied by the local rivers, in particular the Tijucas. Near-surface SSCs were of the order of 50 mg l(-1) close to the shore, but exceeded 100 mg l(-1) near the bottom in the deeper parts of the bay. Fluid mud thickness and location given by densimetry and echo-sounding agreed in some places, although being mostly discordant. The best agreement was observed where wave energy was high during the campaign. The discrepancy between the two methods may be an indication for the existence of fluid mud, which is recorded by one method but not the other. Agreement is considered to be an indication of fluidization, whereas disagreement indicates more consolidation. Wave modeling suggests that waves from the ENE and SE are the most effective in supplying energy to the inner bay, which may induce the liquefaction of mud deposits to form fluid mud. Nearshore mud resuspension and weak horizontal currents result in sediment-laden offshore flow, which explains the higher SSCs measured in the deeper parts of the bay, besides providing a mechanism for fine-sediment export to the inner shelf.

Hyperbolic-like estimates for higher order equations

The main goal of this paper is to derive long time estimates of the energy for the higher order hyperbolic equations with time-dependent coefficients. in particular, we estimate the energy in the hyperbolic zone of the extended phase space by means of a function f (t) which depends on the principal part and on the coefficients of the terms of order m - 1. Then we look for sufficient conditions that guarantee the same energy estimate from above in all the extended phase space. We call this class of estimates hyperbolic-like since the energy behavior is deeply depending on the hyperbolic structure of the equation. In some cases, these estimates produce a dissipative effect on the energy. (C) 2012 Elsevier Inc. All rights reserved.

I. The structure and properties of closed circular duplex DNA. II. Chemically interacting systems at equilibrium in a buoyant density gradient

I. The binding of the intercalating dye ethidium bromide to closed circular SV 40 DNA causes an unwinding of the duplex structure and a simultaneous and quantitatively equivalent unwinding of the superhelices. The buoyant densities and sedimentation velocities of both intact (I) and singly nicked (II) SV 40 DNAs were measured as a function of free dye concentration. The buoyant density data were used to determine the binding isotherms over a dye concentration range extending from 0 to 600 µg/m1 in 5.8 M CsCl. At high dye concentrations all of the binding sites in II, but not in I, are saturated. At free dye concentrations less than 5.4 µg/ml, I has a greater affinity for dye than II. At a critical amount of dye bound I and II have equal affinities, and at higher dye concentration I has a lower affinity than II. The number of superhelical turns, τ, present in I is calculated at each dye concentration using Fuller and Waring's (1964) estimate of the angle of duplex unwinding per intercalation. The results reveal that SV 40 DNA I contains about -13 superhelical turns in concentrated salt solutions.

The free energy of superhelix formation is calculated as a function of τ from a consideration of the effect of the superhelical turns upon the binding isotherm of ethidium bromide to SV 40 DNA I. The value of the free energy is about 100 kcal/mole DNA in the native molecule. The free energy estimates are used to calculate the pitch and radius of the superhelix as a function of the number of superhelical turns. The pitch and radius of the native I superhelix are 430 Å and 135 Å, respectively.

A buoyant density method for the isolation and detection of closed circular DNA is described. The method is based upon the reduced binding of the intercalating dye, ethidium bromide, by closed circular DNA. In an application of this method it is found that HeLa cells contain in addition to closed circular mitochondrial DNA of mean length 4.81 microns, a heterogeneous group of smaller DNA molecules which vary in size from 0.2 to 3.5 microns and a paucidisperse group of multiples of the mitochondrial length.

II. The general theory is presented for the sedimentation equilibrium of a macromolecule in a concentrated binary solvent in the presence of an additional reacting small molecule. Equations are derived for the calculation of the buoyant density of the complex and for the determination of the binding isotherm of the reagent to the macrospecies. The standard buoyant density, a thermodynamic function, is defined and the density gradients which characterize the four component system are derived. The theory is applied to the specific cases of the binding of ethidium bromide to SV 40 DNA and of the binding of mercury and silver to DNA.

Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Numerical Methods for Non-Stationary Stokes Flow

We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.

Dynamics of the interaction between body fluid and Ti cp: the influence of surface functionalization in the first stages of osseointegration

INTRODUCTION: Regenerative therapies using biomaterials require accurate information on interactions between the implanted material and the human body. To improve the process of bone regeneration it is necessary to obtain a better understanding of the influence of the surfaces on the early stages of osseointegration. This work aims to investigate the dynamic interaction between simulated body fluid (SBF) and titanium surfaces (Ti cp) immediately after their first contact. METHODS: Ti cp samples were passed through physicochemical treatments after immersion in acid solution, alkaline solution and solutions containing TiO2 and Ca2+, to obtain three different surfaces. These were characterized by electron microscopy and free energy estimates. The evaluation of the interaction with SBF was performed by measuring the dynamic contact angles after contacting the surfaces. RESULTS: The effects of SBF wettability were more significant on surfaces according to high energy estimates. A comparative analysis of the three types of surfaces showed that fluid spreading was greater in samples with greater polar components, indicating that the surface nature influences interactions in the early stages of osseointegration. CONCLUSION: The results indicate the influence of polar interactions in the dynamic wettability of the SBF. It is possible that these interactions can also influence cellular viability on surfaces. Based on these results, new experiments are being designed to improve the presented methodology as a tool for the evaluation of biomaterials without the need for in vivo experiments.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Energy inequalities and error estimates for axisymmetric torsion of thin elastic shells of revolution

The problem motivating this investigation is that of pure axisymmetric torsion of an elastic shell of revolution. The analysis is carried out within the framework of the three-dimensional linear theory of elastic equilibrium for homogeneous, isotropic solids. The objective is the rigorous estimation of errors involved in the use of approximations based on thin shell theory.

The underlying boundary value problem is one of Neumann type for a second order elliptic operator. A systematic procedure for constructing pointwise estimates for the solution and its first derivatives is given for a general class of second-order elliptic boundary-value problems which includes the torsion problem as a special case.

The method used here rests on the construction of “energy inequalities” and on the subsequent deduction of pointwise estimates from the energy inequalities. This method removes certain drawbacks characteristic of pointwise estimates derived in some investigations of related areas.

Special interest is directed towards thin shells of constant thickness. The method enables us to estimate the error involved in a stress analysis in which the exact solution is replaced by an approximate one, and thus provides us with a means of assessing the quality of approximate solutions for axisymmetric torsion of thin shells.

Finally, the results of the present study are applied to the stress analysis of a circular cylindrical shell, and the quality of stress estimates derived here and those from a previous related publication are discussed.

The energy density of jellyfish: Estimates from bomb-calorimetry and proximate-composition

Two techniques are described to calculate energy densities for the bell, gonad and oral arm tissues of three scyphozoan jellyfish (Cyanea capillata, Rhizostoma octopus and Chrysaora hysoscella). First, bomb-calorimetry was used, a technique that is readily available and inexpensive. However, the reliability of this technique for gelatinous material is contentious. Second, further analysis involving the more labour intensive proximate-composition analysis (protein, fat and carbohydrate) was carried out on two species (C capillata and R. octopus). These proximate data were subsequently converted to energy densities. The two techniques (bomb-calorimetry and proximate-composition) gave very similar estimates of energy density. Differences in energy density were found both amongst different species and between different tissues of the same species. Mean ( +/- S.D.) energy density estimates for whole animals from bomb-calorimetry were 0.18 +/- 0.05, 0.11 +/- 0.04, and 0.10 +/- 0.03 kJ g wet mass(-1) for C. capillata, R. octopus, and C. hysoscella respectively. The implications of these low energy densities for species feeding on jellyfish are discussed. (c) 2007 Elsevier B.V. All rights reserved.

Energy substitutability in transition agriculture: estimates and implications for Hungary

Subsidised energy prices in pre-transition Hungary had led to excessive energy intensity in the agricultural sector. Transition has resulted in steep input price increases. In this study, Allen and Morishima elasticities of substitution are estimated to study the effects of these price changes on energy use, chemical input use, capital formation and employment. Panel data methods, Generalised Method of Moments (GMM) and instrument exogeneity tests are used to specify and estimate technology and substitution elasticities. Results indicate that indirect price policy may be effective in controlling energy consumption. The sustained increases in energy and chemical input prices have worked together to restrict energy and chemical input use, and the substitutability between energy, capital and labour has prevented the capital shrinkage and agricultural unemployment situations from being worse. The Hungarian push towards lower energy intensity may be best pursued through sustained energy price increases rather than capital subsidies. (C) 2003 Elsevier B.V. All rights reserved.

Wild bird feeding in a large UK urban area: characteristics and estimates of energy input and individuals supported

Wild bird feeding is popular in domestic gardens across the world. Nevertheless, there is surprisingly little empirical information on certain aspects of the activity and no year-round quantitative records of the amounts and nature of the different foods provided in individual gardens. We sought to characterise garden bird feeding in a large UK urban area in two ways. First, we conducted face-to-face questionnaires with a representative cross-section of residents. Just over half fed birds, the majority doing so year round and at least weekly. Second, a two-year study recorded all foodstuffs put out by households on every provisioning occasion. A median of 628 kcal/garden/day was given. Provisioning level was not significantly influenced by weather or season. Comparisons between the data sets revealed significantly less frequent feeding amongst these ‘keen’ feeders than the face-to-face questionnaire respondents, suggesting that one-off questionnaires may overestimate provisioning frequency. Assuming 100% uptake, the median provisioning level equates to sufficient supplementary resources across the UK to support 196 million individuals of a hypothetical average garden-feeding bird species (based on 10 common UK garden-feeding birds’ energy requirements). Taking the lowest provisioning level recorded (101 kcal/day) as a conservative measure, 31 million of these average individuals could theoretically be supported.

A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.