An approach to F-theory

We consider BPS configurations in theories with two timelike directions from the perspective of the supersymmetry algebra. We show that whereas a BPS state in a theory with one timelike variable must have positive energy, in a theory with two times any BPS state must have positive angular momentum in the timelike plane, in that $Z_{0\tilde{0}}>0$, where $0$ and $\tilde{0}$ are the two timelike directions. We consider some generic BPS solutions of theories with two timelike directions, and then specialise to the study of the (10,2) dimensional superalgebra for which the spinor operators generate 2-forms and 6-forms. We argue that the BPS configurations of this algebra relate to F-theory in the same way that the BPS configurations of the eleven dimensional supersymmetry algebra relate to M-theory. We show that the twelve dimensional theory is one of fundamental 3-branes and 7-branes, along with their dual partners. We then formulate the new intersection rules for these objects. Upon reduction of this system we find the algebraic description of the IIB-branes and the M-branes. Given these correspondences we may begin an algebraic study of F-theory.Comment: 20 pages, no figures, late

Molecular and all solid DFT studies of the magnetic and chemical bonding properties within KM[Cr(CN)6_6] (M = V, Ni) complexes

A study at both the molecular and extended solid level in the framework DFT is carried out for KM[Cr(CN)$_6$] (M = V, Ni). From molecular calculations, the exchange parameters J are obtained, pointing to the expected magnetic ground states, i.e., antiferromagnetic for M = V with J = -296.5 cm$^{-1}$ and ferromagnetic for M = Ni with J = +40.5 cm$^{-1}$. From solid state computations the same ground states and J magnitudes are confirmed from energy differences. Furthermore an analysis of the site projected density of states and of the chemical bonding is developed in which the cyanide ion linkage is analyzed addressing some isomerism aspects.Comment: new results, 5 tables, 7 fig

Grain refinement of magnesium alloys: a review of recent research, theoretical developments and their application

This paper builds on the ‘‘Grain Refinement of Mg Alloys’’ published in 2005 and reviews the grain refinement research onMg alloys that has been undertaken since then with an emphasis on the theoretical and analytical methods that have been developed. Consideration of recent research results and current theoretical knowledge has highlighted two important factors that affect an alloy’s as-cast grain size. The first factor applies to commercial Mg-Al alloys where it is concluded that impurity and minor elements such as Fe and Mn have a substantially negative impact on grain size because, in combination with Al, intermetallic phases can be formed that tend to poison the more potent native or deliberately added nucleant particles present in the melt. This factor appears to explain the contradictory experimental outcomes reported in the literature and suggests that the search for a more potent and reliable grain refining technology may need to take a different approach. The second factor applies to all alloys and is related to the role of constitutional supercooling which, on the one hand, promotes grain nucleation and, on the other hand, forms a nucleation-free zone preventing further nucleation within this zone, consequently limiting the grain refinement achievable, particularly in low solute-containing alloys. Strategies to reduce the negative impact of these two factors are discussed. Further, the Interdependence model has been shown to apply to a broad range of casting methods from slow cooling gravity die casting to fast cooling high pressure die casting and dynamic methods such as ultrasonic treatment