The mathematics of functional differentiation under conservation constraint

The mathematics of K-conserving functional differentiation, with K being the integral of some invertible function of the functional variable, is clarified. The most general form for constrained functional derivatives is derived from the requirement that two functionals that are equal over a restricted domain have equal derivatives over that domain. It is shown that the K-conserving derivative formula is the one that yields no effect of K-conservation on the differentiation of K-independent functionals, which gives the basis for its generalization for multiple constraints. Connections with the derivative with respect to the shape of the functional variable and with the shape-conserving derivative, together with their use in the density-functional theory of many-electron systems, are discussed. Yielding an intuitive interpretation of K-conserving functional derivatives, it is also shown that K-conserving derivatives emerge as directional derivatives along K-conserving paths, which is achieved via a generalization of the Gateaux derivative for that kind of paths. These results constitute the background for the practical application of K-conserving differentiation.Comment: final version, published in J Math Chem; with an Appendix with the proof of (17) added, and some errata to [1] inserte

Functional differentiation under simultaneous conservation constraints (Constrained functional differentiation in statistical physics and hydrodynamics)

Analytical formulae for functional differentiation under simultaneous K-conservation constraints, with K the integral of some function of the functional variable, are derived, making the proper account for the simultaneous conservation of normalization and statistical averages, e.g., possible in functional differentiation in nonvariationally built physical theories, which gets particular relevance for nonequilibrium, time-dependent theories.Comment: final version, published in J Phys A; 14 pages; with (34)-(35) and a note after (10) added (to v3

Treatments of the exchange energy in density-functional theory

Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree-Fock equations, the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn-Sham equations, the Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn-Sham formulation of the Hartree-Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N=1,2,...), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.Comment: 19 pages; original manuscript from 2001 (v1) revised for publication, with presentation substantially improved, some errors corrected, plus an additional summarizing figure (Appendix B) include

A new approach to local hardness

The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in this way does not integrate to the (global) hardness - in contrast with the local softness, which integrates to the softness. It has also been shown recently that with the conventional formulae, the largest values of local hardness do not necessarily correspond to the hardest regions of a molecule. Here, in an attempt to fix these drawbacks, we propose a new approach to define and evaluate the local hardness. We define a local chemical potential, utilizing the fact that the chemical potential emerges as the additive constant term in the number-conserving functional derivative of the energy density functional. Then, differentiation of this local chemical potential with respect to the number of electrons leads to a local hardness that integrates to the hardness, and possesses a favourable property; namely, within any given electron system, it is in a local inverse relation with the Fukui function, which is known to be a proper indicator of local softness in the case of soft systems. Numerical tests for a few selected molecules and a detailed analysis, comparing the new definition of local hardness with the previous ones, show promising results.Comment: 30 pages (including 6 figures, 1 table

MAPPING LOCAL CLIMATE ZONES WITH A VECTOR-BASED GIS METHOD

In this study we determined Local Climate Zones in a South-Hungarian city, using vector-based and raster-based databases. We calculated seven of the originally proposed ten physical (geometric, surface cover and radiative) properties for areas which are based on the mobile temperature measurement campaigns earlier carried out in this city.As input data we applied 3D building database (earlier created with photogrammetric methods), 2D road database, topographic map, aerial photographs, remotely sensed reflectance information from RapidEye satellite image and our local knowledge about the area. The values of the properties were calculated by GIS methods developed for this purpose.We derived for the examined areas and applied for classification sky view factor, mean building height, terrain roughness class, building surface fraction, pervious surface fraction, impervious surface fraction and albedo.Six built and one land cover LCZ classes could be detected with this method on our study area. From each class one circle area was selected, which is representative for that class. Their thermal reactions were examined with the application of mobile temperature measurement dataset. The comparison was made in cases, when the weather was clear and calm and the surface was dry. We found that compact built-in types have more temperature surplus than open ones, and midrise types also have more than lowrise ones. According to our primary results, these categories provide a useful opportunity for intra- and inter-urban comparisons

LIINUS/SERPIL: a design study for interferometric imaging spectroscopy at the LBT

LIINUS/SERPIL is a design study to augment LBTs interferometric beam combiner camera LINC-NIRVANA with imaging spectroscopy. The FWHM of the interferometric main beam at 1.5 micron will be about 10 mas, offering unique imaging and spectroscopic capabilities well beyond the angular resolution of current 8-10m telescopes. At 10 mas angular scale, e.g., one resolution element at the distance of the Galactic Center corresponds to the average diameter of the Pluto orbit (79 AU), hence the size of the solar system. Taking advantage of the LBT interferometric beam with an equivalent maximum diameter of 23 m, LIINUS/SERPIL is an ideal precursor instrument for (imaging) spectrographs at extremely large full aperture telescopes. LIINUS/SERPIL will be built upon the LINC-NIRVANA hardware and LIINUS/SERPIL could potentially be developed on a rather short timescale. The study investigates several concepts for the optical as well as for the mechanical design. We present the scientific promises of such an instrument together with the current status of the design study.Comment: 12 pages, SPIE conference proceeding, Orlando, 200