Embedding theorems of function classes, I

"Vegeu el resum a l'inici del document del fitxer adjunt."

Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

The work presented evaluates the statistical characteristics of regional bias and expected error in reconstructions of real positron emission tomography (PET) data of human brain fluoro-deoxiglucose (FDG) studies carried out by the maximum likelihood estimator (MLE) method with a robust stopping rule, and compares them with the results of filtered backprojection (FBP) reconstructions and with the method of sieves. The task of evaluating radioisotope uptake in regions-of-interest (ROIs) is investigated. An assessment of bias and variance in uptake measurements is carried out with simulated data. Then, by using three different transition matrices with different degrees of accuracy and a components of variance model for statistical analysis, it is shown that the characteristics obtained from real human FDG brain data are consistent with the results of the simulation studies.

Quantum dynamics of crystals of molecular nanomagnets inside a resonant cavity

It is found that crystals of molecular nanomagnets exhibit enhanced magnetic relaxation when placed inside a resonant cavity. A strong dependence of the magnetization curve on the geometry of the cavity has been observed, providing indirect evidence of the coherent microwave radiation by the crystals. A similar dependence has been found for a crystal placed between the Fabry-Perot superconducting mirrors.

Pulsed-field studies of the magnetization reversal in molecular nanomagnets

We report experimental studies of crystals of Mn12 molecular magnetic clusters in pulsed magnetic fields with sweep rates up to 410^3 T/s . The steps in the magnetization curve are observed at fields that are shifted with respect to the resonant field values. The shift systematically increases as the rate of the field sweep goes up. These data are consistent with the theory of the collective dipolar relaxation in molecular magnets.

Molecular dynamics study of orientational cooperativity in water

Recent experiments on liquid water show collective dipole orientation fluctuations dramatically slower than expected (with relaxation time >tation, the self-dipole randomization time tr, which is an upper limit on ta; we find that tr5ta. Third, to check if there are correlated domains of dipoles in water which have large relaxation times compared to the individual dipoles, we calculate the randomization time tbox of the site-dipole field, the net dipole moment formed by a set of molecules belonging to a box of edge Lbox. We find that the site-dipole randomization time tbox2.5ta for Lbox3 , i.e., it is shorter than the same quantity calculated for the self-dipole. Finally, we find that the orientational correlation length is short even at low T.

Quantum tunneling of domain walls in ferromagnets

We present a theoretical study of the quantum depinning of domain walls. Our approach extends earlier work by Stamp and confirms his suggestion that quantum tunneling of domain walls in ferromagnets may reveal itself at a macroscopic level in a manner similar to the Josephson effect in superconductors. The rate of tunneling of a domain wall through a barrier formed by a planar defect is calculated in terms of macroscopic parameters of the ferromagnet. A universal behavior of the WKB exponent in the limit of small barriers is demonstrated. The effect of dissipation on the tunneling rate is studied. It is argued that quantum diffusion of domain walls apparently explains a nonthermal magnetic relaxation observed in some materials at low temperatures.

Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization.

The liquid-liquid critical point scenario of water hypothesizes the existence of two metastable liq- uid phases low-density liquid (LDL) and high-density liquid (HDL) deep within the supercooled region. The hypothesis originates from computer simulations of the ST2 water model, but the stabil- ity of the LDL phase with respect to the crystal is still being debated. We simulate supercooled ST2 water at constant pressure, constant temperature, and constant number of molecules N for N ≤ 729 and times up to 1 μs. We observe clear differences between the two liquids, both structural and dynamical. Using several methods, including finite-size scaling, we confirm the presence of a liquid-liquid phase transition ending in a critical point. We find that the LDL is stable with respect to the crystal in 98% of our runs (we perform 372 runs for LDL or LDL-like states), and in 100% of our runs for the two largest system sizes (N = 512 and 729, for which we perform 136 runs for LDL or LDL-like states). In all these runs, tiny crystallites grow and then melt within 1 μs. Only for N ≤ 343 we observe six events (over 236 runs for LDL or LDL-like states) of spontaneous crystal- lization after crystallites reach an estimated critical size of about 70 ± 10 molecules.

Quantum tunneling of vortices in the Tl2CaBa2Cu2O8 superconductor

Magnetic-relaxation measurements of a Tl-based high-Tc superconductor show temperature-independent flux creep below 6 K. The effect is analyzed in terms of the overdamped quantum diffusion of two-dimensional vortices. Good agreement between theory and experiment is found.

Quantum decay of metastable states in small magnetic particles

We present an imaginary-time path-integral study of the problem of quantum decay of a metastable state of a uniaxial magnetic particle placed in the magnetic field at an arbitrary angle. Our findings agree with earlier results of Zaslavskii obtained by mapping the spin Hamiltonian onto a particle Hamiltonian. In the limit of low barrier, weak dependence of the decay rate on the angle is found, except for the field which is almost normal to the anisotropy axis, where the rate is sharply peaked, and for the field approaching the parallel orientation, where the rate rapidly goes to zero. This distinct angular dependence, together with the dependence of the rate on the field strength, provides an independent test for macroscopic spin tunneling.

Photometric and Halpha observations of LSI+61·303: detection of a 26 day V and JHK band modulation

We present new optical and infrared photometric observations and high resolution H α spectra of the periodic radio star LSI+61◦303. The optical photometric data set covers the time interval 1985-1993 and amounts to about a hundred nights. A period of ∼26 days is found in the V band. The infrared data also present evidence for a similar periodicity, but with higher amplitude of variation ((0.m 2). The spectroscopic observations include 16 intermediate and high dispersion spectra of LSI+61◦303 collected between January 1989 and February 1993. The H α emission line profile and its variations are analyzed. Several emission line parameters -- among them the H α EW and the width of the H α red hump -- change strongly at or close to radio maximum, and may exhibit periodic variability. We also observe a significant change in the peak separation. The H α profile of LSI+61◦303 does not seem peculiar for a Be star. However, several of the observed variations of the H α profile can probably be associated with the presence of the compact, secondary star.

Excitation modes of vortices in submicron magnetic disks

Classical and quantum theory of spin waves in the vortex state of a mesoscopic submicron magnetic disk have been developed with account of the finite mass density of the vortex. Oscillations of the vortex core resemble oscillations of a charged string in a potential well in the presence of the magnetic field. A conventional gyrotropic frequency appears as a gap in the spectrum of spin waves of the vortex. The mass of the vortex has been computed, and the result agrees with experimental findings. The finite vortex mass generates a high-frequency branch of spin waves. The effects of an external magnetic field and dissipation have been addressed.