Quantum capping potentials with point charges: a simple QM/MM approach for the calculation of large-molecule NMR shielding tensors

A simple quantum-mechanics/molecular-mechanics (QM/MM) approach for calculating NMR shielding tensors (sigma) is presented. The method involves capping the QM region with quantum capping potentials (QCPs) and representing the MM region with point charges. Test calculations on simple systems without MM charges show that calculated sigma values improve relative to the full QM results with increasing distance between the capped bond and chromophore. Calculations on the histidine amino acid and cytosine monophosphate (CMP) nucleic acid show that the use of QCPs with point charges result in mean errors in the isotropic component of sigma that are less than 1.6 ppm. The results also reveal that, contrary to previous work, the explicit effect of point charges on sigma through coupling with gauge factors, as in the gauge including atomic orbital approach, is minimal for the CMP molecule. The present QM/MM approach for calculating sigma is easy to apply and requires no code modification.     

Two-kaon correlations in central Pb+Pb collisions at 158 a GeV/c

Two-particle interferometry of positive kaons is studied in Pb+Pb collisions at mean transverse momenta approximately 0.25 and 0.91 GeV/c. A three-dimensional analysis was applied to the lower p(T) data, while a two-dimensional analysis was used for the higher p(T) data. We find that the source-size parameters are consistent with the m(T) scaling curve observed in pion-correlation measurements in the same collisions, and that the duration time of kaon emission is consistent with zero within the experimental sensitivity.     

Chekenkov radiation of broad atmospheric showers (BAS) and analysis of ultra-high energy cosmic rays

A new method for analyzing BAS of cosmic rays is presented, along with calculation results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 24–32, September, 1986.     

Resonance Wave Expansions:¶Two Hyperbolic Examples

For scattering on the modular surface and on the hyperbolic cylinder, we show that the solutions of the wave equations can be expanded in terms of resonances, despite the presence of trapping. Expansions of this type are expected to hold in greater generality but have been understood only in non-trapping situations. Received: 1 October 1999 / Accepted: 24 January 2000     

Computing material collapse displacement fields on a cray X-MP/48 by the LP primal affine scaling algorithm

A pair of dual, highly degenerate linear programs modeling the static and kinematic principles of limit analysis are studied. They arise from mixed finite element discretizations of the continuous saddle point problem and piecewise linear approximations of the convex unbounded Mises set of admissible stresses. We use piecewise constant stresses and piecewise bilinear displacements, and present computational results with the Affine Scaling Algorithm a la Dikin (1967) and Karmarker (1984). Graphical displays are presented for material collapse fields of a rectangular solid with thin cuts under tension, in problem sizes up to 9000 variables and 7700 equations. To our knowledge, these stress fields have not been computed before.The research underlying this report was supported by NSF Grants ECS-8500940 at Carnegie-Mellon University and the University of Iowa and by ECS-8696087 at the University of Iowa. A preliminary version of this paper was presented at the Supercomputers and Large-Scale Optimization Workshop at the University of Minnesota, Minneapolis, May 16–18, 1988.     

Harmonic functions of polynomial growth on certain complete manifolds

Given a complete manifold with a particular structure at infinity, we give the dimension of the space of harmonic functions with prescribed polynomial growth.     

Growth peculiarities during vapor–liquid–solid growth of silicon nanowhiskers by electron-beam evaporation

One-dimensional (1D) silicon (Si) nanostructures were grown by electron-beam evaporation catalyzed by gold nanoparticles on silicon substrates following the vapor–liquid–solid growth mechanism. We report three strikingly different growth morphologies of the 1D Si nanostructures and discuss their formation. The morphology of the silicon nanostructures strongly depends on gold layer thickness, annealing temperature before deposition and growth temperature during the deposition. The formation of nanoscale silicon features such as nanobelts, nanowires and nanowhiskers was observed. The nanoscale silicon features were characterized by transmission and scanning electron microscopy using imaging, diffraction and energy-dispersive X-ray spectroscopy, atomic force microscopy and UV micro-Raman spectroscopy. PACS 68.37.Lp; 68.70.+w; 78.30.-j; 81.15.Jj     

Scattering theory for perturbed stratified media

We study the operatorH = -c ² x,y)Μx,y)∇ · Μ ^-1 (x,y)∇, wherec andΜ are perturbations of functionsc ₀(y) andΜ ₀(y) which depend only on the one-dimensional variabley. In particular, we study the spatial asymptotics of lim_ε↺0(H - (λ +iε)²)^-1 applied to functions which have compact support or are otherwise well-behaved at infinity and relate the scattering matrix to the asymptotics of the generalized eigenfunctions. We then prove a trace formula for the operatorH in terms of the scattering phase, and, in a very special situation, use the trace formula to find spectral asymptotics forH. Partially supported by an NSF Postdoctoral Fellowship and the University of Missouri Research Board.     

Self-injection length in La0.7Ca0.3MnO3-YBa2Cu3O7-δ ferromagnet-superconductor multilayer thin films

We have carried out extensive studies on the self-injection problem in barrierless heterojunctions between La_0.7Ca_0.3MnO₃ (LCMO) and YBa₂Cu₃O_7-δ (YBCO) thin films. The heterojunctions were formed in situ by sequentially growing LCMO and YBCO films on 〈100〉 LaAlO₃ (LAO) substrate using a pulsed laser deposition (PLD) system. YBCO micro-bridges with 64 μm width were patterned both on the LAO (control) and LCMO side of the substrate. Critical current, I _c, was measured at 77 K on both the control side as well as the LCMO side for different YBCO film thickness. It was observed that while the control side showed a J _c of ∼ 2 × 10⁶ A/cm², the LCMO side showed about half the value for the same thickness (1800 ?). The difference in J _c indicates that a certain thickness of YBCO has become ‘effectively’ normal due to self-injection. From the measurement of J _c at two different thicknesses (1800 ? and 1500 ?) of YBCO films both on the LAO as well as the LCMO side, the value of self-injection length (at 77 K) was estimated to be ∼ 900 ?. To the authors’ best knowledge, this is the first time that self-injection length has been quantified. A control experiment carried out with LaNiO₃ deposited by PLD on YBCO did not show any evidence of self-injection.     

Some Upper Bounds on the Number of Resonances for Manifolds with Infinite Cylindrical Ends

We prove some sharp upper bounds on the number of resonances associated with the Laplacian, or Laplacian plus potential, on a manifold with infinite cylindrical ends.