Essential countability of treeable equivalence relations

We establish a dichotomy theorem characterizing the circumstances under which a treeable Borel equivalence relation E is essentially countable. Under additional topological assumptions on the treeing, we in fact show that E is essentially countable if and only if there is no continuous embedding of E1 into E. Our techniques also yield the first classical proof of the analogous result for hypersmooth equivalence relations, and allow us to show that up to continuous Kakutani embeddability, there is a minimum Borel function which is not essentially countable-to-one

Declining interstitial transsudation in man

Results and methodology of experimentation dealing with declining interstitial transsudation are discussed. Concepts of the formation of interstitial fluids are in agreement with measurements of calf volume in normal young women, in horizontal recumbency or after horizontal immersion. The volume of the calf is reduced when the hydrostatic pressure of the blood column is diminished under the phlebostatic level and when the external pressure is increased by the hydrostatic pressure of a water bath

Comparison between high-energy proton and charged pion induced damage in Lead Tungstate calorimeter crystals

A Lead Tungstate crystal produced for the electromagnetic calorimeter of the CMS experiment at the LHC was cut into three equal-length sections. The central one was irradiated with 290 MeV/c positive pions up to a fluence of (5.67 +- 0.46)x10^13 /cm^2, while the other two were exposed to a 24 GeV/c proton fluence of (1.17 +- 0.11) x 10^13/ cm^2. The damage recovery in these crystals, stored in the dark at room temperature, has been followed over two years. The comparison of the radiation-induced changes in light transmission for these crystals shows that damage is proportional to the star densities produced by the irradiation.Comment: 7 pages, 4 figure

First results on radiation damage in PbWO4 crystals exposed to a 20 GeV/c proton beam

We have exposed seven full length production quality crystals of the electromagnetic calorimeter (ECAL) of the CMS detector to a 20 GeV/c proton beam at the CERN PS accelerator. The exposure was done at fluxes of 10**12 p/cm**2/h and 10**13 p/cm**2/h and integral fluences of 10**12 p/cm**2 and 10**13 p/cm**2 were reached at both rates. The light transmission of the crystals was measured after irradiation and suitable cooling time for induced radioactivity to decrease to a safe level. First results of these measurements are shown. The possible damage mechanisms are discussed and simulations based on one possible model are presented. The implications for long-term operation of CMS are discussed and it is shown that in the whole barrel and at least most of the ECAL endcap hadron damage alone - even if cumulative - should not cause the crystals to fail the CMS specification of an induced absorption coefficient muIND < 1.5 /m during the first 10 years of LHC operation.Comment: 5 pages, to be published in Proc. ICATPP Conference on Astroparticle, Particle, Space Physics, Detectors and Medical Physics Applications (Como, Italy, 6 to 10 October 2003

Ab initio calculation of H + He+^+ charge transfer cross sections for plasma physics

The charge transfer in low energy (0.25 to 150 eV/amu) H($nl$) + He$^+(1s)$ collisions is investigated using a quasi-molecular approach for the $n=2,3$ as well as the first two $n=4$ singlet states. The diabatic potential energy curves of the HeH$^+$ molecular ion are obtained from the adiabatic potential energy curves and the non-adiabatic radial coupling matrix elements using a two-by-two diabatization method, and a time-dependent wave-packet approach is used to calculate the state-to-state cross sections. We find a strong dependence of the charge transfer cross section in the principal and orbital quantum numbers $n$ and $l$ of the initial or final state. We estimate the effect of the non-adiabatic rotational couplings, which is found to be important even at energies below 1 eV/amu. However, the effect is small on the total cross sections at energies below 10 eV/amu. We observe that to calculate charge transfer cross sections in a $n$ manifold, it is only necessary to include states with $n^{\prime}\leq n$, and we discuss the limitations of our approach as the number of states increases.Comment: 14 pages, 10 figure

Deformations of modules of differential forms

We study non-trivial deformations of the natural action of the Lie algebra $\mathrm{Vect}({\mathbb R}^n)$ on the space of differential forms on ${\mathbb R}^n$. We calculate abstractions for integrability of infinitesimal multi-parameter deformations and determine the commutative associative algebra corresponding to the miniversal deformation in the sense of \cite{ff}.Comment: Published by JNMP at http://www.sm.luth.se/math/JNM

Towards Laser Control of Open Quantum Systems: Memory Effects

Laser control of Open Quantum Systems (OQS) is a challenging issue as compared to its counterpart in isolated small size molecules, basically due to very large numbers of degrees of freedom to be accounted for. Such a control aims at appropriately optimizing decoherence processes of a central two-level system (a given vibrational mode, for instance) towards its environmental bath (including, for instance, all other normal modes). A variety of applications could potentially be envisioned, either to preserve the central system from decaying (long duration molecular alignment or orientation, qubit decoherence protection) or, to speed up the information flow towards the bath (efficient charge or proton transfers in long chain organic compounds). Achieving such controls require some quantitative measures of decoherence in relation with memory effects in the bath response, actually given by the degree of non-Markovianity. Characteristic decoherence rates of a Spin-Boson model are calculated using a Nakajima-Zwanzig type master equation with converged HEOM expansion for the memory kernel. It is shown that, by adequately tuning the two-level transition frequency through a controlled Stark shift produced by an external laser field, non-Markovianity can be enhanced in a continuous way leading to a first attempt towards the control of OQS

Control of molecular dynamics with zero-area fields: Application to molecular orientation and photofragmentation

The constraint of time-integrated zero-area on the laser field is a fundamental, both theoretical and experimental requirement in the control of molecular dynamics. By using techniques of local and optimal control theory, we show how to enforce this constraint on two benchmark control problems, namely molecular orientation and photofragmentation. The origin and the physical implications on the dynamics of this zero-area control field are discussed.Comment: 19 pages, 7 figure