304,672 research outputs found
Horace Leonard March
No full text"45553. [obscured]WA Corp. Horace Leona[rd] March R A A F Darwin 194[obscured] Batchler."45553. [obscured]Western Australia. Corporal Horace Leona[rd] March. Royal Australian Air Force. Darwin 194[obscured]. Batchelor
Asymptotic form at large r of a third-order linear homogeneous differential equation for the ground-state electron density of the He atom
No full textIn earlier work a linear differential equation satified by the Schwartz ground-state electron density rho(R) for (non-relativistic) He-like atomic ions with large atomic number Z has been derived. Here, we utilize the asymptotic expansion at large r given by Amovilli and March for the neutral He atom. We thereby show that a linear differential equation of the same general shape as that satisfied by the Schwartz rho(r) again emerges for the neutral He atom itself, in the asymptotic limit of large r. We argue that essential input into the final differential equation for the He ground-state electron density will be the ionization potential plus the atomic polarizability
The exchange-correlation potential of DFT obtained from a semiempirically fine-tuned Hartree-Fock density for inhomogeneous electron liquids
No full textAbstract: The present authors have given an exact theory of the exchange-correlation potential V-xc(r) in terms of (i) the exact ground-state electron density n(r) and (ii) the idempotent Dirac density matrix gamma(r,r') generated by the DFT one-body potential V(r), having n(r) as its diagonal element. Here, we display two approximate consequences: (a) a form of V-xc(r) generated by the semiempirically fine-tuned HF density of Cordero et al. (N.A. Cordero, N.H. March, and J.A. Alonso, Phys. Rev. A 75, 052502 (2007)) and (b) the exchange-only potential V-x(r) determined solely by the HF ground state density for the Be atom
A form of the single-particle kinetic energy density of an inhomogeneous electron liquid from a combination of one-body potential and ground-state electron density
No full textAbstract: Gal and March have recently proposed a form of the single-particle kinetic energy density in density functional theory in terms of the one-body potential V(r) and the ground-state electron density n(r) generated thereby. Here, with a minor modification of the GM form, examples are given for (a) harmonic trapping and (b) a bare Coulomb potential. The case of the He atom is also considered, via the Chandrasekhar variational wave function. Finally, the use of the semiempirical fine-tuned Hartree-Fock n(r) for spherical atoms due to Cordero et al. is briefly referred to
Ornstein-Zernike function and Coulombic correlation in the homogeneous electron liquid
No full textAbstract: Adopting the original Ornstein-Zernike (OZ) definition of the direct correlation function c(r), the present study deals with the deviation Delta(r) of c(r) induced by Coulomb correlation in the homogeneous electron liquid beyond the OZ function c(FH)(r) for purely Fermi hole (FH) statistical correlations. It is first stressed that Delta(r) at large r is proportional to the Coulomb potential energy e(2)/r, suitably scaled with the plasma frequency. Both r space and k space formulations are presented. In k space, direct numerical use is made of inequalities due to Kugler [Phys. Rev. A 1, 1688 (1970)] by employing analytic representations of the pair correlations due to Gori-Giorgi [Phys. Rev. B 61, 7353 (2000)] as a function of the uniform electron density. Then, in r space, consideration is given to differential equations proposed by Dawson and March [Phys. Chem. Liq. 14, 131 (1984)] and also in the recent study of Nagy and Amovilli [J. Chem. Phys. 121, 6640 (2004)]. In both approaches, one-body potentials enter, into which Coulombic interelectronic repulsions are subsumed. Finally, Gaskell's [Proc. Phys. Soc. London 77, 1182 (1961)] variational ground-state wave function is shown to be related to the OZ direct correlation function in k space
Variational properties of a model for image segmentation with overlapping regions
No full textWe introduce a functional for image segmentation which takes into account the occlusions between objects in the image which are located at different depths in space. By minimizing the functional, we try to reconstruct both a piecewise smooth approximation of the input image g and the contours of the objects together with their hidden portions. Some variational properties of the involved functionals are then studied
An image segmentation variational model with free discontinuities and contour curvature
No full textWe introduce a functional for image segmentation which takes into account the transparencies (or shadowing) and the occlusions between objects located at different depths in space. By minimizing the functional, we try to reconstruct a piecewise smooth approximation of the input image, the contours due to transparencies, and the contours of the objects together with their hidden portions. The functional includes a Mumford-Shah type energy and a term involving the curvature of the contours. The variational properties of the functional are studied, as well as its approximation by Gamma-convergence. The comparison with the Nitzberg-Mumford variational model for segmentation with depth is also discussed
Monarch march [music] : op. 20 /
No full textFor piano.; Caption title.; Cover title: Monarch march, piano solo / by P.A. Quin.; Also available online http://nla.gov.au/nla.mus-an7411854
Approximation by Gamma-convergence of a curvature-depending functional in visual reconstruction
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