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

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

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

A lower bound for the mass of axisymmetric connected black hole data sets

We present a generalisation of the Brill-type proof of positivity of mass for axisymmetric initial data to initial data sets with black hole boundaries. The argument leads to a strictly positive lower bound for the mass of simply connected, connected axisymmetric black hole data sets in terms of the mass of a reference Schwarzschild metric

Solar Wind Turbulence and the Role of Ion Instabilities

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