Multiple scattering of light by atoms with internal degeneracy

An analytical microscopic theory for the resonant multiple scattering of light by cold atoms with arbitrary internal degeneracy is presented. It permits to calculate the average amplitude and the average intensity for one-photon states of the full transverse electromagnetic field in a dilute medium of unpolarized atoms. Special emphasis is laid upon an analysis in terms of irreducible representations of the rotation group. It allows to sum explicitly the ladder and maximally crossed diagrams, giving the average intensity in the Boltzmann approximation and the interference corrections responsible for weak localization and coherent backscattering. The exact decomposition into field modes shows that the atomic internal degeneracy contributes to the depolarization of the average intensity and suppresses the interference corrections. Static as well as dynamic quantities like the transport velocity, diffusion constants and relaxation times for all field modes and all atomic transitions are derived.Comment: Corrected minor errors. Slightly extended version of the article appeared in prin

Failure Analysis of Nickel-hydrogen Cell Subjected to Simulated Low Earth Orbit Cycling

A nickel-hydrogen cell completed 10,080 simulated low earth orbit charge/discharge cycles at depths-of-discharge ranging from 50 to 80 percent prior to failure. The cell is of the Air Force design, rated at 50 ampere-hours, 8.9 cm (3.5 inches) in diameter. Upon disassembly, the end of the polysulfone core supporting the electrode stack was found to have fractured. This allowed the electrode stack to expand. A massive short was found at the inner diameter of the electrodes centered roughly at plate set 34 to 37 from the positive end of the electrode stack. The damaged area extended through approximately one third of the electrode stack, with the effect becoming progressively less with distance from plate set 34 to 37. Measured thicknesses of the positive plates were significantly greater than the initial specification values. The postulated cause of failure is that positive plate growth caused fracture of the shoulder from the end of the polysulfone core on which the electrodes are mounted. The electrode stack relieved and pressure points were created at the area near the inner diameter of the plates at the tab attachment. A short occurred at a pressure point between opposing plates and propagated to other electrode sets due to thermal and mechanical stresses caused by the short

Extinction for two parabolic stochastic PDE's on the lattice

It is well known that, starting with finite mass, the super-Brownian motion dies out in finite time. The goal of this article is to show that with some additional work, one can prove finite time die-out for two types of systems of stochastic differential equations on the lattice Z^d. Our first system involves the heat equation on the lattice Z^d, with a nonlinear noise term u(t,x)^gamma dB_x(t), with 1/2 <= gamma < 1. The B_x are independent Brownian motions. When gamma = 1/2, the measure which puts mass u(t,x) at x is a super-random walk and it is well-known that the process becomes extinct in finite time a.s. Finite-time extinction is known to be a.s. false if gamma = 1. For 1/2 < gamma < 1, we show finite-time die-out by breaking up the solution into pieces, and showing that each piece dies in finite time. Our second example involves the mutually catalytic branching system of stochastic differential equations on Z^d, which was first studied by Dawson and Perkins. Roughly speaking, this process consists of 2 superprocesses with the continuous time simple random walk as the underlying spatial motion. Furthermore, each process stimulates branching and dying in the other process. By using a somewhat different argument, we show that, depending on the initial conditions, finite time extinction of one type may occur with probability 0, or with probability arbitrarily close to 1

NASA 50 amp hour nickel cadmium battery waste heat determination

A process for determining the waste heat generated in a 50-ampere-hour, nickel cadmium battery as a function of the discharge rate is described and results are discussed. The technique involved is essentially calibration of the battery as a heat transfer rate calorimeter. The tests are run at three different levels of battery activity, one at 40-watts of waste heat generated, one at 60, and one at 100. Battery inefficiency ranges from 14 to 18 percent at discharge rates of 284 to 588 watts, respectively and top-of-cell temperatures of 20 C

Hitting properties of parabolic s.p.d.e.'s with reflection

We study the hitting properties of the solutions $u$ of a class of parabolic stochastic partial differential equations with singular drifts that prevent $u$ from becoming negative. The drifts can be a reflecting term or a nonlinearity $cu^{-3}$, with $c>0$. We prove that almost surely, for all time $t>0$, the solution $u_t$ hits the level 0 only at a finite number of space points, which depends explicitly on $c$. In particular, this number of hits never exceeds 4 and if $c>15/8$, then level 0 is not hit.Comment: Published at http://dx.doi.org/10.1214/009117905000000792 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Entrepreneurship and Growth

In the year 2000 at a meeting in Lisbon, leaders of the European Union (EU) articulated a set of goals for the Union, which have come to be called the Lisbon Strategy or Lisbon Agenda. The agenda had three main goals: to promote growth through innovation, to create a learning economy, and to bring about social and environmental renewal. Exactly what the last goal implies is not clear, at least to me, but the intent and substance behind the first two certainly is. Research spending was to rise across the EU, university enrollments would rise with them, and a more friendly environment for innovation would be created as markets continued to be liberalized and integrated. The EU leaders meeting in Lisbon set the year 2010 as their goal for fulfilling this agenda. The year 2010 has come and gone. Today, growth rates in Europe are even lower than they were in 2000. Research and university budgets have been cut – sometimes drastically – across the EU. These developments are, of course, largely a response to the recent financial crisis and its impact on state finances. But the crisis would not have been nearly as severe as it has been, if EU countries had been well on their way to fulfilling the goals of the Lisbon Agenda when the crisis hit. The EU’s failure to come anywhere near meeting the goals set out in the year 2000 stems, I shall argue, to underlying structural factors and ideological perspectives, which constitute major obstacles to the kind of knowledge-based, innovative society that the EU leaders dreamed of in Lisbon more than a decade ago. This paper attempts to identify what these obstacles are.Entrepreneurship; Economic Growth; Human Capital; European Union