New excited superdeformed bands in heavy Pb nuclei: Clue for an octupole softness near the N = 118 gap at large deformation

We report the identification of six new superdeformed (SD) bands in ^197,198Pb observed with the EUROBALL IV spectrometer. The results are interpreted in the framework of cranked Hartree-Fock calculations with approximate projection on the particle number by means of the Lipkin-Nogami method. A mixing between quasi-particle excitations and an octupole vibration is suggested in the two SD isotopes. We have estimated the ordering of the neutron valence orbitals and confirm indirectly a N = 118 SD gap. Received: 20 December 2000 / Accepted: 24 January 2001     

Antimatter and matter production in heavy ion collisions at CERN (The NEWMASS experiment NA52)

Besides the dedicated search for strangelets NA52 measures light (anti)particle and (anti)nuclei production over a wide range of rapidity. Compared to previous runs the statistics has been increased in the 1998 run by more than one order of magnitude for negatively charged objects at different spectrometer rigidities. Together with previous data taking at a rigidity of ?20 GeV/c we obtained $10^6 \bar p, 10^3 \bar d$ and two $\overline {^3 He} $ without centrality requirements. We measured nuclei and antinuclei (p, d, $\bar p,\bar d$ ) near midrapidity covering an impact parameter range of b ～ 2–12 fm. Our results strongly indicate that nuclei and antinuclei are mainly produced via the coalescence mechanism. However, the centrality dependence of the antibaryon to baryon ratios shows that antibaryons are diminished due to annihilation and breakup reactions in the hadron dense environment. The volume of the particle source extracted from coalescence models agrees with results from pion interferometry for an expanding source. The chemical and thermal freeze-out of nuclei and antinuclei appear to coincide with each other and with the thermal freeze-out of hadrons.     

Nonconcave Entropies in Multifractals and the Thermodynamic Formalism

We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy function yields the correct multifractal spectrum only when the latter is wholly concave. If the spectrum has no definite concavity, then the transform yields the concave envelope of the spectrum rather than the spectrum itself. Some mathematical and physical examples are given to illustrate this result, which lies at the root of the nonequivalence of the microcanonical and canonical ensembles. On a more positive note, we also show that the impossibility of expressing nonconcave multifractal spectra through Legendre-Fenchel transforms of free energies can be circumvented with the help of a generalized free energy function, which relates to a recently introduced generalized canonical ensemble. Analogies with the calculation of rate functions in large deviation theory are finally discussed. PACS numbers: 05.45.Df, 64.60.Ak, 65.40.Gr     

The linear search problem rides again

The Linear Search Problem concerns a search for a point in the real line by continuous motion starting at 0. The optimal turning points for such a search under the hypothesis that the location of the target is distributed normally about 0 have been approximated by mechanical calculation, but no proof has been given that there is only a single minimizing strategy or that the numbers calculated do indeed approximate that strategy. Plausible arguments have been made before, both by these authors and others. In this paper, the plausible arguments are supplanted by mathematical proofs. The research of the senior author has been supported by the Wisconsin Alumni Research Foundation. The research of the junior author has been supported by Hewlett Packard, Inc. under a Faculty Development Fellowship at Cornell University.     

Transmission of light through a random small-angle scattering medium

A theory of random small-angle scattering is presented. The photon dispersion partial differential equation is derived and the dispersion coefficient characterizing the medium is introduced. The equation is solved for a spatial impulse. The modulation transfer function and the contrast loss are derived as a funcion of spatial frequency, dispersion coefficient, and object-to-image distance. The limitation on resolution is shown by an indeterminancy relation based on the dispersion coefficient. The dispersion angle (rms value of scattering angle) is calculated as an example.     

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

High-dimensional partial differential equations (PDEs) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model. Such high-dimensional fully nonlinear PDEs are exceedingly difficult to solve as the computational effort for standard approximation methods grows exponentially with the dimension. In this work, we propose a new method for solving high-dimensional fully nonlinear second-order PDEs. Our method can in particular be used to sample from high-dimensional nonlinear expectations. The method is based on (1) a connection between fully nonlinear second-order PDEs and second-order backward stochastic differential equations (2BSDEs), (2) a merged formulation of the PDE and the 2BSDE problem, (3) a temporal forward discretization of the 2BSDE and a spatial approximation via deep neural nets, and (4) a stochastic gradient descent-type optimization procedure. Numerical results obtained using TensorFlow in Python illustrate the efficiency and the accuracy of the method in the cases of a 100-dimensional Black–Scholes–Barenblatt equation, a 100-dimensional Hamilton–Jacobi–Bellman equation, and a nonlinear expectation of a 100-dimensional G-Brownian motion.

     

On the resonant behavior of the16O+15N reaction

The ¹⁶ O+ ¹⁵ N reaction products have been studied by the γ-ray detection method in the CM energy range 15.5 to 36.1 MeV and by the kinematical coincidence method at energies ranging from E _CM =20.6 to 33.5MeV. The γ-ray yield excitation function of the ¹⁶O 3^? inelastic channel shows the existence of resonant structures. Two structures with ～ 1.6 MeV width are observed in the large angle elastic scattering excitation function, they are correlated with the resonances seen in the inelastic channel. Angular momentum assignments were made from the elastic backward angular distributions.     

High-spin structure in154Er

High spin states in the nucleus¹⁵⁴Er have been reinvestigated using the¹²³Sb(³⁵Cl, 4n) reaction and a variety of spectroscopic techniques including excitation functions,γ-γ coincidences,γ angular distribution and linear polarization measurements. From the measured energies, relative intensities and transition multipolarities a new level scheme has been deduced up to an excitation energy of ～12 MeV and spin 36. An interpretation of the experimental results is given in terms of the deformed Woods-Saxon orbitals. Gigantic backbending (superdeformation) effect is studied theoretically within the cranking model.     

In-flight test of a continuous laser remote sensing system

An airborne laser system for remote sensing has been developed and tested at flight altitudes from 500 to 1200 m. The system is based on two continuous-wave CO₂ lasers (output 3 W), tunable to different wavelengths, and detects the laser radiation scattered back from earth by heterodyne reception. The feasibility of the heterodyne reception technique under aircraft environment conditions was demonstrated, and man-made SF₆ clouds and different types of uncovered minerals were traced. The data obtained indicate that the measuring range of the system can be increased to satellite distance by using a larger telescope and a more powerful laser and by reducing the electrical bandwidth. The word was supported by the German Ministry of Science and Technology, represented by DFVLR-BPT under contract number 01 TL 026-AK/RT/WRT 2074.