Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

Diffusion and activation of n-type dopants in germanium

The diffusion and activation of $n$-type impurities (P and As) implanted into $p$-type Ge(100) substrates were examined under various dose and annealing conditions. The secondary ion mass spectrometry profiles of chemical concentrations indicated the existence of a sufficiently high number of impurities with increasing implanted doses. However, spreading resistance probe profiles of electrical concentrations showed electrical concentration saturation in spite of increasing doses and indicated poor activation of As relative to P in Ge. The relationships between the chemical and electrical concentrations of P in Ge and Si were calculated, taking into account the effect of incomplete ionization. The results indicated that the activation of P was almost the same in Ge and Si. The activation ratios obtained experimentally were similar to the calculated values, implying insufficient degeneration of Ge. The profiles of P in Ge substrates with and without damage generated by Ge ion implantation were compared, and it was clarified that the damage that may compensate the activated $n$-type dopants has no relationship with the activation of P in Ge.Comment: 6 pages, 4 figure

Binary Bose-Einstein Condensate Mixtures in Weakly and Strongly Segregated Phases

We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two distinct phases: the weakly segregated phase characterized by a `penetration depth' and the strongly segregated phase characterized by a healing length. In the weakly segregated phase the symmetry of the shape of each condensate will not take that of the trap because of the finite surface tension, but its total density profile still does. In the strongly segregated phase even the total density profile takes a different symmetry from that of the trap because of the mutual exclusion of the condensates. The lower critical condensate-atom number to observe the complete phase segregation is discussed. A comparison to recent experimental data suggests that the weakly segregated phase has been observed.Comment: minor change

Synthesis of hexahydrofuro[3,2-c]quinoline, a martinelline type analogue and investigation of its biological activity

2015-2016 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

A time frequency analysis of wave packet fractional revivals

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.Comment: 9 pages, 4 figure

Density Modulations and Addition Spectra of Interacting Electrons in Disordered Quantum Dots

We analyse the ground state of spinless fermions on a lattice in a weakly disordered potential, interacting via a nearest neighbour interaction, by applying the self-consistent Hartree-Fock approximation. We find that charge density modulations emerge progressively when r_s >1, even away from half-filling, with only short-range density correlations. Classical geometry dependent "magic numbers" can show up in the addition spectrum which are remarkably robust against quantum fluctuations and disorder averaging.Comment: 4 pages, 3 eps figure

Critical properties of loop percolation models with optimization constraints

We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional bond percolation. In contrast to this an optimization constraint for the loop configurations, which then have to minimize a particular generic energy function, leads to a percolation transition that constitutes a new universality class, for which we report the critical exponents. Implication for the physics of solid-on-solid and vortex glass models are discussed.Comment: 8 pages, 8 figure