The polarized reflection and absorption spectra of perylene crystals in monomeric and dimeric forms

The electronic absorption spectra of perylene crystals in the α- and β-forms were measured by the normal incidence reflection method in the spectral region from 20 000 to 60 000 cm^?1. From the absorption spectrum polarized perpendicular to [1$\text{1}$0] axis of the α-form crystal, the bands around 24 000 cm^?1 were determined to be polarized along the long molecular axis. Two strong bands with different polarizations were observed around 50 000 cm^?1 for each of the α- and β-perylene crystals and were assigned to the transitions to the ¹B_2u and ¹B_3u states. The observed polarized absorption spectra as a whole were consistent with the theoretical results by Hummel and Ruedenberg and the reflection method was found to be suitable to the polarized absorption measurement of strong bands of crystals. The observed factor-group splittings were compared with the theoretical values, the oriented gas model being found to be applicable to the β-form crystal.     

A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

Spacetime correlation functions of dynamic speckles produced by a series of moving phase screens

Spacetime correlation functions of the time-varying speckle intensity have been evaluated for the case where speckle patterns are produced in the Fresnel diffraction region by light propagating through a series of moving random-phase screens. The correlation functions are given by a set of recursion formulae which are useful for numerical computations. Three statistical quantities relating to the motion of speckle patterns are derived to examine the relationship between the velocity distribution of the phase screens and the temporal behaviour of resultant speckle patterns. It is found that the velocity differences between the phase screens have a strong effect on both the decorrelation of speckle patterns and the fluctuating speed of the speckle intensity.     

SDiff(2) Toda equation — Hierarchy,Tau function,and symmetries

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-Kähler version, however now based upon a symplectic structure on a cylinderS ¹×R. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.     

An anomalous emission excited near the absorption edge of pyrene crystals

Emission spectra and decay times of the fluorescence excited at the absorption edge region in pyrene crystals were measured. At liquid nitrogen temperature, the fluorescence under the excitation at 390 nm is considered as the excimer emission and its band peak shifts a little to the short wavelength in comparison with that of the excimer emission under the excitation at 360 nm. The emission decay times under the excitation at the 390 nm and 360 nm are about 155 ns and 180 ns, respectively, at liquid nitrogen temperature. The former decay time changes its value abruptly near 127 K. This abrupt change of the decay time may be due to the phase transition in pyrene crystals.     

Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for ``infinite-dimensional second-order cone programs.' We consider as an example a long-step primal-dual algorithm based on the Nesterov-Todd direction. It is shown that this algorithm can be generalized along with complexity estimates to the infinite-dimensional situation under consideration. An application is given to an important problem of control theory: multi-criteria analytic design of the linear regulator. The calculation of the Nesterov-Todd direction requires in this case solving one matrix differential Riccati equation plus solving a finite-dimensional system of linear algebraic equations on each iteration. The number of equations and unknown variables of this algebraic system is m+1, where m is a number of quadratic performance criteria. Key words.polynomial-time primal-dual interior-point methods – JB-algebras – infinite-dimensional problems – optimal control problemsThis author was supported in part by DMS98-03191 and DMS01-02698.This author was supported in part by the Grant-in-Aid for Scientific Research (C) 11680463 of the Ministry of Education, Culture, Sports, Science and Technology of Japan.Mathematics Subject Classification (1991):90C51, 90C48, 34H05, 49N05     

Migration of excimers in pyrene crystals

Emission decay times of the new excimer were measured for undoped and perylene doped pyrene crystals. From the decay times obtained, the temperature dependence of the diffusion coefficient of the excimers was deduced by assuming a model in which two electronic states of the new excimer are involved in the energy transfer process. Within this model, it was found that in the upper excimer state the excimers migrated by a hopping process, while in the lower excimer state they migrated as free excimer excitons while undergoing phonon scattering.     

Structure in the emission from pyrene evaporated films

Emission spectra and decay times of fluorescence of pyrene thin films prepared by evaporation onto substrates at liquid nitrogen temperature were measured. Structure in the emission from films warmed slowly up to higher temperature is found to the higher energy side of the excimer emission band. The decay time is about 410 ns at temperatures between 110 K and 210 K. But the emission from the film warmed up to a temperature above 210 K shows only the excimer emission. These results are discussed in relation to an amorphous structure in the pyrene evaporated thin film.     

Evaluating the equivalence of verbal scales and question stems to be used in English and Japanese noise annoyance questions

Two experiments were conducted to evaluate the equivalence of noise annoyance scales and questions recommended by Team 6 (Community Response to Noise) of ICBEN for English and Japanese, two strikingly different languages. The first experiment was conducted with bilingual subjects in order to test a key assumption of the method established by ICBEN Team 6 for the development of equivalent noise annoyance scales: subjects who speak different languages interpret the concept of “highest degree” of annoyance similarly. The results indicate that English- and Japanese-speaking subjects do interpret the “highest degree” similarly. The second experiment tested for effects of wording differences. English- and Japanese-speaking subjects were presented with noise annoyance questions of one of three format types. The first type was similar to the question format recommended by ICBEN Team 6. It focused on the degree to which a given noise would “bother, disturb, or annoy” the subject. The second asked subjects to evaluate the “bothersome, annoying, or disturbing” quality of the noise. The third asked how much the noise would “worry, irritate, or concern” the subject. No significant difference was found in responses to the three formats when subjects evaluated noise in laboratory conditions.     

Effect of Comatic Aberration on the Propagation Characteristics of Laguerre--Gaussian Beams

Seidel comatic aberration is an important cause of deformation for a Laguerre--Gaussian (LG) beam. In addition, mono-axial comatic aberration, whose phase modulation depends only on one transverse coordinate, is also an important cause of beam deformation. Deformation of an LG beam by such aberrations is analyzed through numerical simulation based on the angular spectrum method. It is also shown that for holographically generated LG beams quadratic spatial variation of grating pitch can produce seidel and mono-axial comatic aberrations. An example of an experimentally generated LG beam with mono-axial comatic aberration is reported.