Vibrational Dynamics Studies by Nuclear Resonant Inelastic X-Ray Scattering

Nuclear resonant inelastic X-ray scattering of synchrotron radiation is being applied to ever widening areas ranging from geophysics to biophysics and materials science. Since its first demonstration in 1995 using the ⁵⁷Fe resonance, the technique has now been applied to materials containing ⁸³Kr, ¹⁵¹Eu, ¹¹⁹Sn, and ¹⁶¹Dy isotopes. The energy resolution has been reduced to under a millielectronvolt. This, in turn, has enabled new types of measurements like Debye velocity of sound, as well as the study of origins of non-Debye behavior in presence of other low-energy excitations. The effect of atomic disorder on phonon density of states has been studied in detail. The flux increase due to the improved X-ray sources, crystal monochromators, and time-resolved detectors has been exploited for reducing sample sizes to nano-gram levels, or using samples with dilute resonant nuclei like myoglobin, or even monolayers. Incorporation of micro-focusing optics to the existing experimental setup enables experiments under high pressure using diamond-anvil cells. In this article, we will review these developments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Low-lying states of trinuclear mixed-valence cluster: [Fe3S4]0

Low-lying energy states of the [Fe₃S₄]⁰ cluster have been calculated by taking into account the double exchange, superexchange and vibronic interaction. It was found that the adiabatic potential of the excited state withS=0 corresponds to the full delocalization of the “excess” charge. From the analysis of experimental data of Mössbauer spectroscopy and the temperature dependence of the magnetic susceptibility the double exchange parametert≥4000 cm^?1 and the vibronic interaction parameter λ₂/2k cm^?1 have been estimated.     

Jahn-teller chromium ions in CdF<Subscript>2</Subscript> and CaF<Subscript>2</Subscript> crystals: An EPR spectroscopic study in the frequency range 9.3–300 GHz

The bivalent chromium impurity centers in CdF₂ and CaF₂ crystals are investigated using electron paramagnetic resonance (EPR) in the frequency range 9.3–300 GHz. It is found that Cr²⁺ ions in the lattices of these crystals occupy cation positions and form [CrF₄F₄]^6? clusters whose magnetic properties at low temperatures are characterized by orthorhombic symmetry. The parameters of the electron Zeeman and ligand interactions of the Cr²⁺ ion with four fluorine ions in the nearest environment are determined. The initial splittings in the system of spin energy levels of the cluster are measured.     

Q operators for the simple quantum relativistic Toda Chain

We investigate the simple quantum relativistic Toda chain. The ultralocal simple Weyl algebra pair is associated with each site of the chain. Weyl’s q is considered to be inside a unit circle. Both independent Baxter operators Q are constructed explicitly as series in local Weyl generators. The operator-valued Wronskian of Q-s is also calculated.     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Creation of a donor-acceptor pair for studying intraprotein electron transfer with the participation of amino-acid derivatives of fullerene C60

Efficient quenching of eosin phosphorescence by amino-acid derivatives of fullerene (AADFs) such as C₆₀-alanine and C₆₀-glycine in aqueous solutions indicates the possibility of transferring electrons from eosin to fullerene upon collisions or in the exciplex state. To investigate electron transfer in the protein structure, we studied the process of incorporation of C₆₀-alanine and C₆₀-glycine into the heme pocket of myoglobin by controlling Förster quenching. The dissociation constant for the protein-AADF complex was estimated.     

Time-Cost Trade-Off Analysis in Some Constrained Assignment Problems

Several variations of two-dimensional (workers x jobs) and three-dimensional (workers x jobs x machines) time- as well as cost-minimizing assignment problems, which arise owing to (i) precedence relations of some form among the jobs or (ii) capacity restrictions on workers/machines imposed by the requirement that the surplus resources have to be fully employed, have been considered in the literature. In this paper, an algorithm is presented for time-cost trade-off analysis which is applicable to any general pair of such constrained problems. The algorithm is also illustrated by a numerical example.     

Long-term optimal operation of series parallel reservoirs for critical period with specified monthly generation and average monthly storage

We present in this paper an efficient approach for solving the problem of planning the long-term (multiyear) operation of a multireservoir hydroelectric power system for the critical period with a monthly variable load. This load is equal to a certain percentage of the total generation at the end of the year, subject to satisfying a number of constraints on the hydrosystem, using the minimum norm formulation.The proposed method is efficient in computing time and in calculating the total expected benefits from the system during the critical period. Numerical results are reported for a real system in operation consisting of two rivers. Each river has two series reservoirs.This work was supported by the Natural Science and Engineering Research Council of Canada, Grant No. A4146.