Generalizing Optical Geometry

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz and Lasota 1997, Class. Quantum Grav. 14 (1997) A23). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson, Class. Quantum Grav. 23 (2006) 1) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity.Comment: 19 pages, 1 figure. A more general analysis is presented than in the former version. See also the companion papers arXiv:0708.2493, arXiv:0708.2533 and arXiv:0708.253

Degree growth of meromorphic surface maps

We study the degree growth of iterates of meromorphic selfmaps of compact Kahler surfaces. Using cohomology classes on the Riemann-Zariski space we show that the degrees grow similarly to those of mappings that are algebraically stable on some birational model.Comment: 17 pages, final version, to appear in Duke Math Journa

Singular semipositive metrics in non-Archimedean geometry

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or plurisubharmonic) metrics on L, and prove the analogue of the following two basic results in the complex case: the set of semipositive metrics is compact modulo constants, and each semipositive metric is a decreasing limit of smooth semipositive ones. In particular, for continuous metrics our definition agrees with the one by S.-W. Zhang. The proofs use multiplier ideals and the construction of suitable models of X over the valuation ring of K, using toroidal techniques.Comment: 49 pages, 1 figure. Accepted in the Journal of Algebraic Geometr

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure

Non-equilibrium dynamics in an interacting nanoparticle system

Non-equilibrium dynamics in an interacting Fe-C nanoparticle sample, exhibiting a low temperature spin glass like phase, has been studied by low frequency ac-susceptibility and magnetic relaxation experiments. The non-equilibrium behavior shows characteristic spin glass features, but some qualitative differences exist. The nature of these differences is discussed.Comment: 7 pages, 11 figure

A nonlinear Schr\"odinger equation for water waves on finite depth with constant vorticity

A nonlinear Schr\"odinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of weakly nonlinear wave packets is studied. It is demonstrated that vorticity modifies significantly the modulational instability properties of weakly nonlinear plane waves, namely the growth rate and bandwidth. At third order we have shown the importance of the coupling between the mean flow induced by the modulation and the vorticity. Furthermore, it is shown that these plane wave solutions may be linearly stable to modulational instability for an opposite shear current independently of the dimensionless parameter kh, where k and h are the carrier wavenumber and depth respectively

Fator de bioconcentração de poluentes orgânicos de lodos em laranjas.

O objetivo desse trabalho foi estimar o fator de bioconcentração de 19 poluentes orgânicos de lodos em laranjas, para indicar quais os poluentes que devem ser monitorados em laranjas cultivadas em solos tratados com lodos de esgoto provenientes de estações de tratamento do Estado de São Paulo. Para tanto, foram assumidos um cultivo hipotético de laranja em um solo tratado com lodo e utilizado o modelo Fruit Tree Model (FTM) para estimar o fator de bioconcentração. Foram utilizados os coeficientes de partição octanol-água dos poluentes, a taxa de transpiração e a biomassa das plantas de laranjeiras. Os coeficientes de partição caule-água e o fator de concentração no fluxo de transpiração foram calculados por meio de expressões que correlacionam cada um desses parâmetros com o coeficiente de partição octanol-água. Os poluentes indicados para monitoramento em laranja foram: 1,2-diclorobenzeno, 1,3-diclorobenzeno, 1,4-diclorobenzeno, 2,4-dinitrofenol, 3,3- diclorobenzidina e nitrobenzeno

Fator de bioconcentração de poluentes de lodo em laranjeiras.

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Numerical Simulation of the Kinetics of Radical Decay in Single-Pulse High-Energy Electron-Irradiated Polymer Aqueous Solutions

A new method for the numerical simulation of the radiation chemistry of aqueous polymer solutions is introduced. The method makes use of a deterministic approach combining the conventional homogeneous radiation chemistry of water with the chemistry of polymer radicals and other macromolecular species. The method is applied on single-pulse irradiations of aqueous polymer solutions. The speciation of macromolecular species accounts for the variations in the number of alkyl radicals per chain, molecular weight, and number of internal loops (as a consequence of an intramolecular radical-radical combination). In the simulations, the initial polymer molecular weight, polymer concentration, and dose per pulse (function of pulse length and dose rate during the pulse) were systematically varied. In total, 54 different conditions were simulated. The results are well in line with the available experimental data for similar systems. At a low polymer concentration and a high dose per pulse, the kinetics of radical decay is quite complex for the competition between intra- and intermolecular radical-radical reactions, whereas at a low dose per pulse the kinetics is purely second-order. The simulations demonstrate the limitations of the polymer in scavenging all the radicals generated by water radiolysis when irradiated at a low polymer concentration and a high dose per pulse. They also show that the radical decay of lower-molecular-weight chains is faster and to a larger extent dominated by intermolecular radical-radical reactions, thus explaining the mechanism behind the experimentally observed narrowing of molecular weight distributions

Balloon-borne radiometer measurement of Northern Hemisphere mid-latitude stratospheric HNO3 profiles spanning 12 years

Low-resolution atmospheric thermal emission spectra collected by balloon-borne radiometers over the time span of 1990–2002 are used to retrieve vertical profiles of HNO3, CFC-11 and CFC-12 volume mixing ratios between approximately 10 and 35 km altitude. All of the data analyzed have been collected from launches from a Northern Hemisphere mid-latitude site, during late summer, when stratospheric dynamic variability is at a minimum. The retrieval technique incorporates detailed forward modeling of the instrument and the radiative properties of the atmosphere, and obtains a best fit between modeled and measured spectra through a combination of onion-peeling and global optimization steps. The retrieved HNO3 profiles are consistent over the 12-year period, and are consistent with recent measurements by the Atmospheric Chemistry Experiment-Fourier transform spectrometer satellite instrument. This suggests that, to within the errors of the 1990 measurements, there has been no significant change in the HNO3 summer mid-latitude profile