Nonlocal Gravity: Modified Poisson's Equation

The recent nonlocal generalization of Einstein's theory of gravitation reduces in the Newtonian regime to a nonlocal and nonlinear modification of Poisson's equation of Newtonian gravity. The nonlocally modified Poisson equation implies that nonlocality can simulate dark matter. Observational data regarding dark matter provide limited information about the functional form of the reciprocal kernel, from which the original nonlocal kernel of the theory must be determined. We study this inverse problem of nonlocal gravity in the linear domain, where the applicability of the Fourier transform method is critically examined and the conditions for the existence of the nonlocal kernel are discussed. This approach is illustrated via simple explicit examples for which the kernels are numerically evaluated. We then turn to a general discussion of the modified Poisson equation and present a formal solution of this equation via a successive approximation scheme. The treatment is specialized to the gravitational potential of a point mass, where in the linear regime we recover the Tohline-Kuhn approach to modified gravity.Comment: 27 pages, 4 figures; v2: minor improvements, accepted for publication in J. Math. Phy

Magnetic Surfaces in Stationary Axisymmetric General Relativity

In this paper a new method is derived for constructing electromagnetic surface sources for stationary axisymmetric electrovac spacetimes endowed with non-smooth or even discontinuous Ernst potentials. This can be viewed as a generalization of some classical potential theory results, since lack of continuity of the potential is related to dipole density and lack of smoothness, to monopole density. In particular this approach is useful for constructing the dipole source for the magnetic field. This formalism involves solving a linear elliptic differential equation with boundary conditions at infinity. As an example, two different models of surface densities for the Kerr-Newman electrovac spacetime are derived.Comment: 15 page

High brightness inductively coupled plasma source for high current focused ion beam applications

A high brightnessplasmaion source has been developed to address focused ion beam(FIB) applications not satisfied by the liquid metal ion source (LMIS) based FIB. The plasmaFIB described here is capable of satisfying applications requiring high mill rates (>100μm³/s) with non-gallium ions and has demonstrated imaging capabilities with sub- 100-nm resolution. The virtual source size, angular intensity, mass spectra, and energy spread of the source have been determined with argon and xenon. This magnetically enhanced, inductively coupled plasmasource has exhibited a reduced brightness(βr) of 5.4×10³Am⁻²sr⁻¹V⁻¹, with a full width half maximum axial energy spread (ΔE) of 10eV when operated with argon. With xenon, βr=9.1×10³Am⁻²sr⁻¹V⁻¹ and ΔE=7eV. With these source parameters, an optical column with sufficient demagnification is capable of forming a sub-25-nm spot size at 30keV and 1pA. The angular intensity of this source is nominally three orders of magnitude greater than a LMIS making the source more amenable to creating high current focused beams, in the regime where spherical aberration dominates the LMIS-FIB. The source has been operated on a two lens ion column and has demonstrated a current density that exceeds that of the LMIS-FIB for current greater than 50nA. Source lifetime and current stability are excellent with inert and reactive gases. Additionally, it should be possible to improve both the brightness and energy spread of this source, such that the (βr/ΔE₂) figure-of-merit could be within an order of magnitude of a LMIS

Integral Equations for Heat Kernel in Compound Media

By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$ acquires a certain constant value. At the interface of the media the conditions are imposed which demand the continuity of the `temperature' and the `heat flows'. The integration in the equations is spread out only over the interface of the media. As a result the dimension of the initial problem is reduced by 1. The perturbation series for the integral equations derived are nothing else as the multiple scattering expansions for the relevant heat kernels. Thus a rigorous derivation of these expansions is given. In the one dimensional case the integral equations at hand are solved explicitly (Abel equations) and the exact expressions for the regarding heat kernels are obtained for diverse matching conditions. Derivation of the asymptotic expansion of the integrated heat kernel for a compound media is considered by making use of the perturbation series for the integral equations obtained. The method proposed is also applicable to the configurations when the same medium is divided, by a smooth compact surface, into internal and external regions, or when only the region inside (or outside) this surface is considered with appropriate boundary conditions.Comment: 26 pages, no figures, no tables, REVTeX4; two items are added into the Reference List; a new section is added, a version that will be published in J. Math. Phy

Multiple reflection expansion and heat kernel coefficients

We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the coefficients for Dirichlet and Neumann boundary conditions. Further, we calculate the heat kernel coefficients for the most general matching conditions on the surface of a sphere, including those cases corresponding to the presence of delta and delta prime background potentials. In the latter case, the multiple reflection expansion is shown to be non-convergent.Comment: 21 pages, corrected for some misprint

Macro-Climatic Distribution Limits Show Both Niche Expansion and Niche Specialization among C4 Panicoids

Grasses are ancestrally tropical understory species whose current dominance in warm open habitats is linked to the evolution of C4 photosynthesis. C4 grasses maintain high rates of photosynthesis in warm and water stressed environments, and the syndrome is considered to induce niche shifts into these habitats while adaptation to cold ones may be compromised. Global biogeographic analyses of C4 grasses have, however, concentrated on diversity patterns, while paying little attention to distributional limits. Using phylogenetic contrast analyses, we compared macro-climatic distribution limits among ~1300 grasses from the subfamily Panicoideae, which includes 4/5 of the known photosynthetic transitions in grasses. We explored whether evolution of C4 photosynthesis correlates with niche expansions, niche changes, or stasis at subfamily level and within the two tribes Paniceae and Paspaleae. We compared the climatic extremes of growing season temperatures, aridity, and mean temperatures of the coldest months. We found support for all the known biogeographic distribution patterns of C4 species, these patterns were, however, formed both by niche expansion and niche changes. The only ubiquitous response to a change in the photosynthetic pathway within Panicoideae was a niche expansion of the C4 species into regions with higher growing season temperatures, but without a withdrawal from the inherited climate niche. Other patterns varied among the tribes, as macro-climatic niche evolution in the American tribe Paspaleae differed from the pattern supported in the globally distributed tribe Paniceae and at family level.Fil: Aagesen, Lone. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Botánica Darwinion. Academia Nacional de Ciencias Exactas, Físicas y Naturales. Instituto de Botánica Darwinion; ArgentinaFil: Biganzoli, Fernando. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Métodos Cuantitativos y Sistemas de Información; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Bena, María Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Botánica Darwinion. Academia Nacional de Ciencias Exactas, Físicas y Naturales. Instituto de Botánica Darwinion; ArgentinaFil: Godoy Bürki, Ana Carolina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Botánica Darwinion. Academia Nacional de Ciencias Exactas, Físicas y Naturales. Instituto de Botánica Darwinion; ArgentinaFil: Reinheimer, Renata. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Agrobiotecnología del Litoral. Universidad Nacional del Litoral. Instituto de Agrobiotecnología del Litoral; ArgentinaFil: Zuloaga, Fernando Omar. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Botánica Darwinion. Academia Nacional de Ciencias Exactas, Físicas y Naturales. Instituto de Botánica Darwinion; Argentin

Geoantineutrino Spectrum, 3He/4He-ratio Distribution in the Earth's Interior and Slow Nuclear Burning on the Boundary of the Liquid and Solid Phases of the Earth's Core

The description problem of geoantineutrino spectrum and reactor antineutrino experimental spectrum in KamLAND, which takes place for antineutrino energy \~2.8 MeV, and also the experimental results of the interaction of uranium dioxide and carbide with iron-nickel and silicaalumina melts at high pressure (5-10 GP?) and temperature (1600-2200C) have motivated us to consider the possible consequences of the assumption made by V.Anisichkin and coauthors that there is an actinid shell on boundary of liquid and solid phases of the Earth's core. We have shown that the activation of a natural nuclear reactor operating as the solitary waves of nuclear burning in 238U- and/or 232Th-medium (in particular, the neutron- fission progressive wave of Feoktistov and/or Teller-Ishikawa-Wood) can be such a physical consequence. The simplified model of the kinetics of accumulation and burnup in U-Pu fuel cycle of Feoktistov is developed. The results of the numerical simulation of neutron-fission wave in two-phase UO2/Fe medium on a surface of the Earth's solid core are presented. The georeactor model of 3He origin and the 3He/4He-ratio distribution in the Earth's interior is offered. It is shown that the 3He/4He ratio distribution can be the natural quantitative criterion of georeactor thermal power. On the basis of O'Nions-Evensen-Hamilton geochemical model of mantle differentiation and the crust growth supplied by actinid shell on the boundary of liquid and solid phases of the Earth's core as a nuclear energy source (georeactor with power of 30 TW), the tentative estimation of geoantineutrino intensity and geoantineutrino spectrum on the Earth surface are given.Comment: 28 pages, 12 figures. Added text, formulas, figures and references. Corrected equations. Changed content of some section

Dynamic correlations in an ordered c(2×\times2) lattice gas

We obtain the dynamic correlation function of two-dimensional lattice gas with nearest-neighbor repulsion in ordered c(2$\times$2) phase (antiferromagnetic ordering) under the condition of low concentration of structural defects. It is shown that displacements of defects of the ordered state are responsible for the particle number fluctuations in the probe area. The corresponding set of kinetic equations is derived and solved in linear approximation on the defect concentration. Three types of strongly correlated complex jumps are considered and their contribution to fluctuations is analysed. These are jumps of excess particles, vacancies and flip-flop jumps. The kinetic approach is more general than the one based on diffusion-like equations used in our previous papers. Thus, it becomes possible to adequately describe correlations of fluctuations at small times, where our previous theory fails to give correct results. Our new analytical results for fluctuations of particle number in the probe area agree well with those obtained by Monte Carlo simulations.Comment: 10 pages, 7 figure

Observations of whistler mode waves with nonlinear parallel electric fields near the dayside magnetic reconnection separatrix by the Magnetospheric Multiscale mission

We show observations from the Magnetospheric Multiscale (MMS) mission of whistler mode waves in the Earth's low-latitude boundary layer (LLBL) during a magnetic reconnection event. The waves propagated obliquely to the magnetic field toward the X line and were confined to the edge of a southward jet in the LLBL. Bipolar parallel electric fields interpreted as electrostatic solitary waves (ESW) are observed intermittently and appear to be in phase with the parallel component of the whistler oscillations. The polarity of the ESWs suggests that if they propagate with the waves, they are electron enhancements as opposed to electron holes. The reduced electron distribution shows a shoulder in the distribution for parallel velocities between 17,000 and 22,000 km/s, which persisted during the interval when ESWs were observed, and is near the phase velocity of the whistlers. This shoulder can drive Langmuir waves, which were observed in the high-frequency parallel electric field data