In English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics


Volume 50 No. 4 December 2001


Looking back beyond a half century; 187–194

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Measurement of time in nonrelativistic quantum and classical mechanics; 195–213

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Piret KUUSK and Madis KÕIV

Abstract. Possible theoretical frameworks for measurement of (arrival) time in nonrelativistic quantum mechanics are reviewed. It is argued that the ambiguity between indirect measurements by a suitably introduced time operator and direct measurements by a physical clock particle has a counterpart in the corresponding classical framework of measurement of the Newtonian time based on the Hamiltonian mechanics.

Key words: time, measurement, quantum mechanics, Hamiltonian dynamics.

Radiation field in an atmosphere subjected to cosine varying diffuse radiation; 214–226

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Tõnu VIIK and Indrek VURM

Abstract. The radiation field is calculated in an optically finite or semi-infinite, two-dimensional, plane-parallel, absorbing–emitting but nonscattering grey atmosphere subjected to diffuse cosine varying incident boundary radiation. We again approximate the kernel of the integral equation for the emissive power by a sum of exponents. After this approximation the integral equation can be solved exactly. The solution can be written in generalized x- and y-functions (or h- and g-functions in the semi-infinite case) which were introduced for a one-dimensional atmosphere. Since the radiation field in the case of diffuse incident radiation can be described as a superposition of solutions for the collimated case, we can find the accurate values for the source function and the radiative flux at arbitrary optical depths in the atmosphere. As in the case of collimated incident radiation, this approximation allowed of finding accurate numerical values for the source function and the radiative flux.

Key words: two-dimensional radiative transfer, X- and Y-functions, emissive power, radiative flux.

Electron paramagnetic resonance spectra of human tooth enamel with preferentially oriented nanocrystals; 227–246

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Abstract. Electron paramagnetic resonance spectra of a selected γ-irradiated human tooth enamel fragment expressed anisotropy that increased considerably after thermal annealing. By repeated irradiation, the spectrum of the fragment approached the disoriented (powder type) spectrum, but repeated thermal treating restored the anisotropy. The anisotropy is characteristic of an ensemble of hydroxyapatite nanocrystals, predominantly oriented with the hexagonal axis perpendicular to the outer surface of the tooth. A Monte Carlo spectral simulation, corresponding to the bulk arrangement of paramagnetic CO2 radicals possessing the  symmetry and normal distribution of y-axes (parallel to the O–O direction) in a space angle of 27° (± 5°) around the surface normal, gives a satisfactory agreement with the experimental spectra, whereas the agreement for alternative models with specific surface arrangement of the radicals is worse.

Key words: electron paramagnetic resonance, irradiated tooth enamel, CO2 radicals, spectral anisotropy, Monte Carlo simulation.

Contents of volume 50; 247–248