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

Food Chain Disruptions and Trade: The Importance of North American Market Integration

Food Consumption/Nutrition/Food Safety, International Relations/Trade,

Preparation of monotectic alloys having a controlled microstructure by directional solidification under dopant-induced interface breakdown

Monotectic alloys having aligned spherical particles of rods of the minor component dispersed in a matrix of the major component are prepared by forming a melt containing predetermined amounts of the major and minor components of a chosen monotectic system, providing in the melt a dopant capable of breaking down the liquid solid interface for the chosen alloy, and directionally solidfying the melt at a selected temperature gradient and a selected rate of movement of the liquid-solid interface (growth rate). Shaping of the minor component into spheres or rods and the spacing between them are controlled by the amount of dopant and the temperature gradient and growth rate values. Specific alloy systems include Al Bi, Al Pb and Zn Bi, using a transition element such as iron

The WTO and U.S. Domestic Support in the Food Conservation, and Energy Act of 2008

Agricultural and Food Policy, International Relations/Trade, F13, Q18,

The Maine Civil Rights Act: History, Enforcement, Application, and Analysis

Since the passage of the “Maine Civil Rights Act” (MCRA, Act) in 1989, the Maine Department of the Attorney General has made enforcement of that civil “hate crime” law one of its highest priorities. According to one statistic, “more than 125 people have been prosecuted in Maine\u27s civil courts on hate crime charges since 1994,” and only two of those actions have been lost by the State. The Attorney General at the time of this writing, Andrew Ketterer, has stated that he takes the perpetration of hate crimes seriously, and that it has been important to him “that the message gets out that Maine will not tolerate the abuse of its minority citizens.” The breadth of the term “Maine Civil Rights Act” is a bit misleading because although the Act protects civil rights, it does so only in narrow circumstances. Unlike the broader Maine Human Rights Act, the Maine Civil Rights Act is intended to apply only to situations in which there is violence or threats of violence or damage to property or threats of damage to property that are motivated by bias against categories identified by the legislature. This Comment will explore the Maine Civil Rights Act in detail. The primary purpose of this writing is to provide practitioners of law in Maine with information about the Act

Hot-water aquifer storage: A field test

The basic water injection cycle used in a large-scale field study of heat storage in a confined aquifer near Mobile, Alabama is described. Water was pumped from an upper semi-confined aquifer, passed through a boiler where it was heated to a temperature of about 55 C, and injected into a medium sand confined aquifer. The injection well has a 6-inch (15-cm) partially-penetrating steel screen. The top of the storage formation is about 40 meters below the surface and the formation thickness is about 21 meters. In the first cycle, after a storage period of 51 days, the injection well was pumped until the temperature of the recovered water dropped to 33 c. At that point 55,300 cubic meters of water had been withdrawn and 66 percent of the injected energy had been recovered. The recovery period for the second cycle continued until the water temperature was 27.5 C and 100,100 cubic meters of water was recovered. At the end of the cycle about 90 percent of the energy injected during the cycle had been recovered

Trade Creation and Trade Diversion in the North American Free Trade Agreement: The Case of Agricultural Sector

This paper examines the impact of the U.S.-Mexico trade agreement under NAFTA. The results suggest that U.S. agricultural imports from Mexico have been responsive to tariff rate reductions applied to Mexican products. A 1 percent decrease in tariff rates is associated with an increase in U.S. agricultural imports from Mexico by 3.96 percent in the first six years of NAFTA and by 1.07 percent in the last six years of NAFTA. US imports from Mexico have also been attributable to the pre-NAFTA tariff rates. Overall, the results indicate that the U.S.-Mexico trade agreement under NAFTA has been trade creating rather than trade diverting.International Relations/Trade,

Fractional spins and static correlation error in density functional theory

Electronic states with fractional spins arise in systems with large static correlation (strongly correlated systems). Such fractional-spin states are shown to be ensembles of degenerate ground states with normal spins. It is proven here that the energy of the exact functional for fractional-spin states is a constant, equal to the energy of the comprising degenerate pure spin states. Dramatic deviations from this exact constancy condition exist with all approximate functionals, leading to large static correlation errors for strongly correlated systems, such as chemical bond dissociation and band structure of Mott insulators. This is demonstrated with numerical calculations for several molecular systems. Approximating the constancy behavior for fractional spins should be a major aim in functional constructions and should open the frontier for DFT to describe strongly correlated systems. The key results are also shown to apply in reduced density-matrix functional theory.Comment: 6 pages, 4 figure