Random-walk theory for localization

A continuous-time random-walk theory has been developed for Anderson localization. On a continuous time scale random walks are performed along extended (i.e., propagating) and localized (i.e., trap) states. Complete information of disorder is contained in a distribution function called “hopping time distribution function” ψ_nm(t), which gives the probability per unit time for transition from state m to state n in time t. The “stay-put” probability ??(t = ∞), which is the probability to rediscover an excitation at a site “0” at time t = ∞ if it was there at t = 0, is obtained in terms of ψ_nm(t). Appropriate forms for ψ_nm(t) are constructed which are in conformity with the photoconductivity experiments on dispersive transport, and ??(∞) are calculated. The results indicate that the entire spectrum consists of three regimes, namely, those of (i) “diffusion,” (ii) “weak diffusion,” and (iii) “no diffusion,” which, respectively, designate the extension, the power-law localization, and the exponential localization of states. The results also shed light on the question of “continuous or discontinuous (?)” transition across the mobility edge.     

The biosynthesis of nornuciferine-I(2-methoxy-6aα-aporphine-1-ol)

The incorporation of (±)-norcoclaurine, (±)-coclaurine, (±)-N-methylcoclairine, (±)-N-methylnorcoclaurine into nornuciferine-I in Croton sparsiflorus morong has been studied, and the specific utilization of the (±)-N-methylcoclaurine demonstrated. The evidence supports the direct oxidative coupling of (+)-(S)-N-methylcoclaurine to give N-methylcrotsparine, which in turn is shown to be a specific precursor of nornuciferine-I. The experiments also show that N-methylcrotsparine is reduced to N-methylcrotsparinol and it is N-methylcrotsparinol-I which is preferentially dehydrated and rearranged to nornuciferine-I.     

Fcc-hcp phase coexistence in Al at high pressures: Explanation in terms of density of states

The density of states (DOS) of fcc and hcp structures of Al has been calculated for normal and high pressures. It has been found that the DOS of both structures, near the Fermi level, is similar over a range of compressed volumes close to the fcc-hcp transition volume (V/V₀∼0.53). This similarity is the reason for the reported coexistence of fcc-hcp phases over a wide range of pressures near the fcc-hcp phase transition. All calculations have been performed using the FP-LAPW method with GGA.     

An X-band time domain electron paramagnetic resonance spectrometer

A computer-controlled X-band time domain electron paramagnetic resonance (EPR) spectrometer, with a time resolution of the order of 0.5μsec, has been constructed with many of the crucial microwave components designed and fabricated by the Microwave Engineering Group of TIFR. The spectrometer operates either in a microwave power pulsed mode for determination of spin-lattice relaxation times by the saturation recovery technique or in the kinetic mode for determination of the time dependence of EPR signal after laser excitation. It has an automatic frequency control, an automatic phase control and, most importantly, a field-frequency lock which ensures good stability of the EPR line positions enabling signal averaging for extended periods. The constructional details of the spectrometer and its performance in both the modes are described here by reporting results on certain typical systems.     

Experiment aimed at the study of 252Cf binary and ternary fission

A new experiment devoted to the fission of ²⁵²Cf is described. It continued a series of our experiments based on correlation measurements of γ rays emitted by fission fragment pairs. The measurements of γ-γ and γ-γ-γ coincidences were done at Gammasphere with closed ²⁵²Cf sources. The open source was used for the first time in the last experiment. Fission fragment detectors were arranged in the center hole of Gammasphere. Correlations between fission fragment masses, total kinetic energy, and γ rays were observed. The first, preliminary results of data analysis are discussed. The text was submitted by the authors in English.     

Capacity and entry issues in online exchanges

With the advent of open standards and Internet technologies, the number of sellers who can participate in online exchanges is greatly increased. We model the competition between identical sellers vying for the same business, and find that there exists a mixed-strategy equilibrium in prices. The results help us understand the dynamics between a seller’s capacity and his motivation to participate in an auction.     

Mutually unbiased bases

After a brief review of the notion of a full set of mutually unbiased bases in an N-dimensional Hilbert space, we summarize the work of Wootters and Fields (W K Wootters and B C Fields, Ann. Phys. 191, 363 (1989)) which gives an explicit construction for such bases for the case N=p ^r , where p is a prime. Further, we show how, by exploiting certain freedom in the Wootters-Fields construction, the task of explicitly writing down such bases can be simplified for the case when p is an odd prime. In particular, we express the results entirely in terms of the character vectors of the cyclic group G of order p. We also analyse the connection between mutually unbiased bases and the representations of G.     

Maximum-likelihood approach to strain imaging using ultrasound

A maximum-likelihood (ML) strategy for strain estimation is presented as a framework for designing and evaluating bioelasticity imaging systems. Concepts from continuum mechanics, signal analysis, and acoustic scattering are combined to develop a mathematical model of the ultrasonic waveforms used to form strain images. The model includes three-dimensional (3-D) object motion described by affine transformations, Rayleigh scattering from random media, and 3-D system response functions. The likelihood function for these waveforms is derived to express the Fisher information matrix and variance bounds for displacement and strain estimation. The ML estimator is a generalized cross correlator for pre- and post-compression echo waveforms that is realized by waveform warping and filtering prior to cross correlation and peak detection. Experiments involving soft tissuelike media show the ML estimator approaches the Cramer-Rao error bound for small scaling deformations: at 5 MHz and 1.2% compression, the predicted lower bound for displacement errors is 4.4 microns and the measured standard deviation is 5.7 microns.