Static black hole uniqueness and Penrose inequality

Under certain conditions, we give a new way to prove the uniqueness of static black hole in higher dimensional asymptotically flat spacetimes. In the proof, the Penrose inequality plays a key role in higher dimensions as well as four dimensions.Comment: 6 page

Particle Acceleration, Magnetic Field Generation, and Associated Emission in Collisionless Relativistic Jets

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., active galactic nuclei (AGNs), gamma-ray bursts (GRBs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations using injected relativistic electron-ion (electro-positron) jets show that acceleration occurs within the downstream jet. Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, other two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation from deflected electrons has different properties than synchrotron radiation which assumes a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: 4 pages, 3 figures, contributed talk at the workshop: High Energy Phenomena in Relativistic Outflows (HEPRO), Dublin, 24-28 September 2007. Fig. 3 is replaced by the correct versio

Particle acceleration in electron-ion jets

Weibel instability created in collisionless shocks is responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-ion jet fronts propagating into an ambient plasma without initial magnetic fields with a longer simulation system in order to investigate nonlinear stage of the Weibel instability and its acceleration mechanism. The current channels generated by the Weibel instability induce the radial electric fields. The z component of the Poynting vector (E x B) become positive in the large region along the jet propagation direction. This leads to the acceleration of jet electrons along the jet. In particular the E x B drift with the large scale current channel generated by the ion Weibel instability accelerate electrons effectively in both parallel and perpendicular directions.Comment: 2 pages, 1 figure, Proceedings for Astrophysical Sources of High Energy Particles and Radiation, AIP proceeding Series, eds . T. Bulik, G. Madejski and B. Ruda

Effect of anthocyanin composition in grape skin on anthocyanic vacuolar inclusion development and skin coloration

Berry skin coloration, the content and composition of anthocyanin and anthocyanic vacuolar inclusion (AVI) development were investigated in two black cultivars, Cabernet Sauvignon (Vitis vinifera) and Pione (V. vinifera × V. labrusca, 4x), and one red cv., Red Port (V. vinifera × V. labrusca). Pione had lower L* (lightness of the skin) and higher color index values than Cabernet Sauvignon, indicating that Pione had darker skin color than Cabernet Sauvignon. The two black cultivars had high contents of malvidin, while the major anthocyanidin of Red Port was cyanidin and delphinidin. This difference of anthocyanidin composition was responsible for the red color of Red Port. Whereas the anthocyanidin composition of the two black cultivars showed little difference, the percentage of acylated anthocyanins was markedly higher in Pione than in Cabernet Sauvignon. The diameter of AVIs was similar between Pione and Cabernet Sauvignon, but the density of AVIs was higher in cv. Pione. This difference in AVI development affects grape skin coloration. A comparison of the anthocyanin composition in isolated AVIs and that in whole cell tissue showed that in all three cultivars the percentage of acylated anthocyanins was high in the AVIs. In Pione skins the high percentage of acylated anthocyanins might result in many AVIs to be formed, and might be responsible for the dark coloration.

Convergence of the Allen-Cahn equation with Neumann boundary conditions

We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke's mean curvature flow with a generalized right angle condition on the boundary.Comment: 26 pages, 1 figur

3-D GRMHD and GRPIC Simulations of Disk-Jet Coupling and Emission

We investigate jet formation in black-hole systems using 3-D General Relativistic Particle-In-Cell (GRPIC) and 3-D GRMHD simulations. GRPIC simulations, which allow charge separations in a collisionless plasma, do not need to invoke the frozen condition as in GRMHD simulations. 3-D GRPIC simulations show that jets are launched from Kerr black holes as in 3-D GRMHD simulations, but jet formation in the two cases may not be identical. Comparative study of black hole systems with GRPIC and GRMHD simulations with the inclusion of radiate transfer will further clarify the mechanisms that drive the evolution of disk-jet systems.Comment: 3 pages, 1 figure, Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, edited by H. Kleinert, R.T. Jantzen and R. Ruffini, World Scientific, Singapore, 200

Relativistic Particle-In-Cell Simulation Studies of Prompt and Early Afterglows from GRBs

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks e.g. gamma-ray bursts (GRBs) active galactic nuclei (AGNs) and microquasars commonly exhibit power-law emission spectra. Recent PIC simulations of relativistic electron-ion (or electron-positron) jets injected into a stationary medium show that particle acceleration occurs within the downstream jet. In collisionless relativistic shocks particle (electron, positron and ion) acceleration is due to plasma waves and their associated instabilities (e.g. the Weibel (filamentation) instability) created in the shock region. The simulations show that the Weibel instability is responsible for generating and amplifying highly non-uniform small-scale magnetic fields. These fields contribute to the electron's transverse deflection behind the jet head. The resulting ``jitter'' radiation from deflected electrons has different properties compared to synchrotron radiation which assumes a uniform magnetic field. Jitter radiation may be important for understanding the complex time evolution and/or spectra in gamma-ray bursts, relativistic jets in general and supernova remnants.Comment: 19 pages,7 figures, contributed talk at Seventh European Workshop on Collisionless Shocks, Paris, 7- 9 November 2007. High resolution version can be obtained at http://gammaray.nsstc.nasa.gov/~nishikawa/shockws07.pd

Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products

Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional growth, and (ii) birth and death processes, leads to a generic power-law distribution with an exponent that depends on the characteristics of each ingredient. Here, we report the first complete empirical test of the theory and its application, based on the empirical analysis of the dynamics of market shares in the product market. We estimate directly the average growth rate of market shares and its standard deviation, the birth rates and the "death" (hazard) rate of products. We find that temporal variations and product differences of the observed power-law exponents can be fully captured by the theory with no adjustable parameters. Our results can be generalized to many systems for which the statistical properties revealed by power law exponents are directly linked to the underlying generating mechanism

Biologia da mosca-branca (Bemisia argentifolii) em tomate e repolho.

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