Applications of the Gauss-Bonnet theorem to gravitational lensing

In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.Comment: 10 pages, 1 figure, IoP styl

Gaming with eutrophication: Contribution to integrating water quantity and quality management at catchment level

The Metropolitan Region of Sao Paulo (MRSP) hosts 18 million inhabitants. A complex system of 23 interconnected reservoirs was built to ensure its water supply. Half of the potable water produced for MRSP's population (35 m3/s) is imported from a neighbour catchment, the other half is produced within the Alto Tietê catchment, where 99% of the population lives. Perimeters of land use restriction were defined to contain uncontrolled urbanization, as domestic effluents were causing increasing eutrophication of some of these reservoirs. In the 90's catchment committees and sub committees were created to promote discussion between stakeholders and develop catchment plans. The committees are very well structured "on paper". However, they are not very well organised and face a lack of experience. The objective of this work was to design tools that would strengthen their discussion capacities. The specific objective of the AguAloca process was to integrate the quality issue and its relation to catchment management as a whole in these discussions. The work was developed in the Alto Tietê Cabeceiras sub-catchment, one of the 5 sub catchments of the Alto-Tietê. It contains 5 interconnected dams, and presents competitive uses such as water supply, industry, effluent dilution and irrigated agriculture. A RPG was designed following a companion modelling approach (Etienne et al., 2003). It contains a friendly game-board, a set of individual and collective rules and a computerized biophysical model. The biophysical model is used to simulate water allocation and quality processes at catchment level. It articulates 3 modules. A simplified nutrient discharge model permits the estimation of land use nutrient exportation. An arc-node model simulates water flows and associated nutrient charges from one point of the hydrographical network to another. The Vollenweider model is used for simulating specific reservoir dynamics. The RPG allows players to make individual and collective decisions related to water allocation and the management of its quality. Impacts of these decisions are then simulated using the biophysical model. Specific indicators of the game are then updated and may influence player's behaviour (actions) in following rounds. To introduce discussions on the management of water quality at a catchment level, an issue that is rarely explicitly dealt with, four game sessions were implemented involving representatives of basin committees and water and sanitation engineers. During the game session, the participants took advantage of the water quality output of the biophysical model to test management alternatives such as rural sewage collection or effluent dilution. The biophysical model accelerated calculations of flows and eutrophication rates that were then returned to the game board with explicit indicators of quantity and quality. Players could easily test decisions impacting on qualitative water processes and visualize the simulation results directly on the game board that was representing a friendly, virtual and simplified catchment. The Agualoca game proved its ability to turn complex water processes understandable for a non totally initiated public. This experience contributed to a better understanding of multiple-use water management and also of joint management of water quality and quantity. (Résumé d'auteur

Statistical-mechanical theory of the overall magnetic properties of mesocrystals

The mesocrystal showing both electrorheological and magnetorheological effects is called electro-magnetorheological (EMR) solids. Prediction of the overall magnetic properties of the EMR solids is a challenging task due to the coexistence of the uniaxially anisotropic behavior and structural transition as well as long-range interaction between the suspended particles. To consider the uniaxial anisotropy effect, we present an anisotropic Kirkwood-Fr\"{o}hlich equation for calculating the effective permeabilities by adopting an explicit characteristic spheroid rather than a characteristic sphere used in the derivation of the usual Kirkwood-Fr\"{o}hlich equation. Further, by applying an Ewald-Kornfeld formulation we are able to investigate the effective permeability by including the structural transition and long-range interaction explicitly. Our theory can reduce to the usual Kirkwood-Fr\"{o}hlich equation and Onsager equation naturally. To this end, the numerical simulation shows the validity of monitoring the structure of EMR solids by detecting their effective permeabilities.Comment: 14 pages, 1 figur

Magnetized strangelets at finite temperature

The main properties of magnetized strangelets, namely, their energy per baryon, radius and electric charge, are studied. Temperature effects are also taken into account in order to study their stability compared to the 56Fe isotope and non-magnetized strangelets using the liquid drop model. Massive quarks are considered with the aim to have a more realistic description for strangelets in the astrophysical context and the environment of heavy ion colliders, playing also an important role in the thermodynamical quantities of the quark gas. It is concluded that the presence of a magnetic field tends to stabilize more the strangelets, even when temperature effects are taken into account. Magnetized strangelets in a paired superconductor phase (magnetized color flavor locked phase) are also discussed. It is shown that they are more stable than ordinary magnetized strangelets for typical gap values of the order of O(100) MeV.Comment: 10 pages, 10 figures, discussion extended, new references adde

Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow

Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is non-standard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case

Cell-Free Synthesis of the Mitochondrial ADP/ATP Carrier Protein of Neurospora crassa

ADP/ATP carrier protein was synthesized in heterologous cell-free systems programmed with Neurospora poly(A)-containing RNA and homologous cell-free systems from Neurospora. The apparent molecular weight of the product obtained in vitro was the same as that of the authentic mitochondrial protein. The primary translation product obtained in reticulocyte lysates starts with formylmethionine when formylated initiator methionyl-tRNA (fMet-tRNAfMet) was present. The product synthesized in vitro was released from the ribosomes into the postribosomal supernatant. The evidence presented indicates that the ADP/ATP carrier is synthesized as a polypeptide with the same molecular weight as the mature monomeric protein and does not carry an additional sequence

A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page

Transport of Proteins into Mitochondria

The mitochondrial ADP/ATP carrier is an integral transmembrane protein of the inner membrane. It is synthesized on cytoplasmic ribosomes. Kinetic data suggested that this protein is transferred into mitochondria in a posttranslational manner. The following results provide further evidence for such a mechanism and provide information on its details. 1. In homologous and heterologous translation systems the newly synthesized ADP/ATP carrier protein is present in the postribosomal supernatant. 2. Analysis by density gradient centrifugation and gel filtration shows, that the ADP/ATP carrier molecules in the postribosomal fraction are present as soluble complexes with apparent molecular weights of about 120000 and 500000 or larger. The carrier binds detergents such as Triton X-100 and deoxycholate forming mixed micelles with molecular weights of about 200000–400000. 3. Incubation of a postribosomal supernatant of a reticulocyte lysate containing newly synthesized ADP/ATP carrier with mitochondria isolated from Neurospora spheroplasts results in efficient transfer of the carrier into mitochondria. About 20–30% of the transferred carrier are resistant to proteinase in whole mitochondria. The authentic mature protein is also largely resistant to proteinase in whole mitochondria and sensitive after lysis of mitochondria with detergent. Integrity of mitochondria is a prerequisite for translocation into proteinase resistant position. 4. The transfer in vitro into a proteinase-resistant form is inhibited by the uncoupler carbonyl-cyanide m-chlorophenylhydrazone but not the proteinase-sensitive binding. These observations suggest that the posttranslational transfer of ADP/ATP carrier occurs via the cytosolic space through a soluble oligomeric precursor form. This precursor is taken up by intact mitochondria into an integral position in the membrane. These findings are considered to be of general importance for the intracellular transfer of insoluble membrane proteins. They support the view that such proteins can exist in a water-soluble form its precursors and upon integration into the membrane undergo a conformational change. Uptake into the membrane may involve the cleavage of an additional sequence in some proteins, but this appears not to be a prerequisite as demonstrated by the ADP/ATP carrier protein

Antimatter and Matter Production in Heavy Ion Collisions at CERN (The NEWMASS Experiment NA52)

Besides the dedicated search for strangelets NA52 measures light (anti)particle and (anti)nuclei production over a wide range of rapidity. Compared to previous runs the statistics has been increased in the 1998 run by more than one order of magnitude for negatively charged objects at different spectrometer rigidities. Together with previous data taking at a rigidity of -20 GeV/c we obtained 10^6 antiprotons 10^3 antideuterons and two antihelium3 without centrality requirements. We measured nuclei and antinuclei (p,d,antiprotons, antideuterons) near midrapidity covering an impact parameter range of b=2-12 fm. Our results strongly indicate that nuclei and antinuclei are mainly produced via the coalescence mechanism. However the centrality dependence of the antibaryon to baryon ratios show that antibaryons are diminished due to annihilation and breakup reactions in the hadron dense environment. The volume of the particle source extracted from coalescence models agrees with results from pion interferometry for an expanding source. The chemical and thermal freeze-out of nuclei and antinuclei appear to coincide with each other and with the thermal freeze-out of hadrons.Comment: 12 pages, 8 figures, to appear in the proceedings of the conference on 'Fundamental Issues in Elementary Matter' Bad Honnef, Germany, Sept. 25-29, 200

Functions of several Cayley-Dickson variables and manifolds over them

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are proved in the new generalized form for functions of Cayley-Dickson variables instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated