A Renormalisation Group Study of Three Dimensional Turbulence

We study the three dimensional Navier-Stokes equation with a random Gaussian force acting on large wavelengths. Our work has been inspired by Polyakov's analysis of steady states of two dimensional turbulence. We investigate the time evolution of the probability law of the velocity potential. Assuming that this probability law is initially defined by a statistical field theory in the basin of attraction of a renormalisation fixed point, we show that its time evolution is obtained by averaging over small scale features of the velocity potential. The probability law of the velocity potential converges to the fixed point in the long time regime. At the fixed point, the scaling dimension of the velocity potential is determined to be ${-{4\over 3}}$. We give conditions for the existence of such a fixed point of the renormalisation group describing the long time behaviour of the velocity potential. At this fixed point, the energy spectrum of three dimensional turbulence coincides with a Kolmogorov spectrum.Comment: 8 pages , tex fil

Asymptotic behavior of the generalized Becker-D\"oring equations for general initial data

We prove the following asymptotic behavior for solutions to the generalized Becker-D\"oring system for general initial data: under a detailed balance assumption and in situations where density is conserved in time, there is a critical density $\rho_s$ such that solutions with an initial density $\rho_0 \leq \rho_s$ converge strongly to the equilibrium with density $\rho_0$, and solutions with initial density $\rho_0 > \rho_s$ converge (in a weak sense) to the equilibrium with density $\rho_s$. This extends the previous knowledge that this behavior happens under more restrictive conditions on the initial data. The main tool is a new estimate on the tail of solutions with density below the critical density

Gravitational microlensing and dark matter in the galactic halo

We present the basics of microlensing and give an overview of the results obtained so far. We also describe a scenario in which dark clusters of MACHOs (Massive Astrophysical Compact Halo Objects) and cold molecular clouds (mainly of $H_2$) naturally form in the halo at galactocentric distances larger than 10-20 kpc. Moreover, we discuss various experimental tests of this picture in particular a $\gamma$-ray emission from the clouds due to the scattering of high-energy cosmic-ray protons. Our estimate for the $\gamma$-ray flux turns out to be in remarkably good agreement with the recent discovery by Dixon et al. of a possible $\gamma$-ray emission from the halo using EGRET data.Comment: 14 pages, to appear in the proceedings of the 3K Cosmology Conference (Rome, october 1998), added references and minor change

Measurement of Inclusive f1(1285)f_1(1285) and f1(1420)f_1(1420) Production in ZZ Decays with the DELPHI Detector

Inclusive production of two $(K\bar K\pi)^0$ states in the mass region 1.22--1.56 GeV in $Z$ decay at LEP I has been observed by the DELPHI Collaboration. The measured masses and widths are $1274\pm4$ and $29\pm12$ MeV for the first peak and $1426\pm4$ and $51\pm14$ MeV for the second. A partial-wave analysis has been performed on the $(K\bar K\pi)^0$ spectrum in this mass range; the first peak is consistent with the quantum numbers $I^G(J^{PC})=0^+(0^{-+}/1^{++})$ and the second with $I^G(J^{PC})=0^+(1^{++})$. These measurements, as well as their total hadronic production rates per hadronic $Z$ decay, are consistent with the mesons of the type $n\bar n$, where $n=\{u,d\}$. They are very likely to be the $f_1(1285)$ and the $f_1(1420)$, respectively.Comment: 6 pages, 2 figures (in eps) talk given at XXXI International Symposium on Multiparticle Dynamics, Sep. 1-7, 2001, Datong China URL http://ismd31.ccnu.edu.cn

The Supermoduli Space of Matrix String Theory

We study matrix string scattering amplitudes and matrix string instantons on a marked Riemann surface in the limit of a vanishing string coupling constant. We give an explicit parameterization of the moduli space of such instantons. We also give a description of the set of fermionic supermoduli. The integration over the supermoduli leads to the inclusion of picture changing operators at the interaction points. Finally we investigate the large N limit of the measure on the instanton moduli space and show its convergence to the Weil-Petersson measure on the moduli space of marked Riemann surfaces.Comment: 30 Pages, Latex, 2 Postscript figure

An argument for the admissibility of execution impact evidence in pennsylvania

In 1991, the United States Supreme Court made a significant change to sentencing proceedings during capital trials. The Court ruled in Payne v. Tennessee that the Eighth Amendment does not prohibit “victim impact evidence,” testimony about the character of the murder victim and the impact of the death on the victim’s family. The Payne decision permits highly emotional testimony from family members to enter into the penalty phase of a death penalty trial