Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups

Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and $\varepsilon$-spaces exhaust the class of $n$-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least ${1/2} n(n-1)+1$, for almost all values of $n$ [Patrangenaru V., Geom. Dedicata 102 (2003), 25-33]. We shall prove that the curvature tensor of these spaces satisfy several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov-Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and $\mathcal P$-spaces, and that $\varepsilon$-spaces are Ivanov-Petrova and curvature-curvature commuting manifolds

The twisted gradient flow coupling at one loop

We compute the one-loop running of the $SU(N)$ 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale $\tilde{l}$ given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the $\overline{\rm MS}$ scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of $\Lambda$ parameters between the two schemes. We analyze the $N$ dependence of the results and the possible implications for non-commutative gauge theories and volume independence.Comment: 52 pages, 12 figure

Synthesis and characterization of zirconium-antimony binary and interstitial ternary intermetallic compounds

A family of Zr[subscript]5Sb[subscript]3Z compounds, Z = C, O, Al, Si, P, S, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, have been synthesized in the Mn[subscript]5Si[subscript]3 structure. The Z element occupies the center of confacial trigonal antiprisms of zirconium atoms. Antimony can also occupy the interstitial site, and the binary compound has a homogeneity range Zr[subscript]5Sb[subscript]3.0 to Zr[subscript]5Sb[subscript]3.4.;The compounds were mainly prepared by arc-melting or powder sintering. Temperatures in excess of 1100° C were needed to provide adequate reaction rates for the sintering experiments. Isothermal vapor transport reactions, 1100 \u3c T \u3c1300° C, with iodine as a transporting agent were used to ensure complete reaction, but provided no single crystals. Reactions using Zn or In as a solvent yielded single crystals of a size suitable for physical property measurements. Structural refinements were carried out for the compounds Zr[subscript]5Sb[subscript]3Al, Zr[subscript]5Sb[subscript]3Si, Zr[subscript]5Sb[subscript]3S, Zr[subscript]5Sb[subscript]3Fe, Zr[subscript]5Sb[subscript]3(Fe[subscript]2/3In[subscript]1/3).;Extended-Huckel band calculations were carried out on Zr[subscript]5Sb[subscript]3, Zr[subscript]5Sb[subscript]3S, and Zr[subscript]5Sb[subscript]3Fe in order to rationalize the ability of Zr[subscript]5Sb[subscript]3 to interstitially incorporate this remarkable array of chemically diverse elements. A high density of states at the Fermi energy, low lying and strongly bonding ZrSb states in the Zr[subscript]5Sb[subscript]3 host, and the strong bonding interactions between zirconium and the interstitial element, combine to permit the extensive interstitial chemistry observed;The zirconium-antimony binary system was reinvestigated in the course of the Zr[subscript]5Sb[subscript]3Z study. Five new phases were identified: Zr[subscript]5Sb[subscript]3 ( Y[subscript]5Bi[subscript]3-type), ZrSb[subscript]1-x (FeSi-type), ZrSb (ZrSb-type), ZrSb[subscript]2 ( PbCl[subscript]2-type), and Zr[subscript]2Sb[subscript]3. The structure type of an additional compound was elucidated, Zr[subscript]2Sb ( La[subscript]2Sb-type). The unique structure type for ZrSb was determined by a single crystal X-ray diffraction experiment, and structural refinements were also carried out for Zr[subscript]5Sb[subscript]3 ( Y[subscript]5Bi[subscript]3 and Mn[subscript]5Si[subscript]3) and ZrSb[subscript]2 ( PbCl[subscript]2).;Extended-Huckel band calculations were carried out on the two ZrSb[subscript]2 structural polymorphs, PbCl[subscript]2 and ZrSb[subscript]2 types. The results indicate a slight increase in Sb-Sb bonding and a decrease in Sb-Zr bonding in the ZrSb[subscript]2 structure compared with those in the PbCl[subscript]2 modification. The results also imply that there is only a limited amount of charge transfer in these compounds, and a Zintl phase description is inappropriate. ftn * DOE Report IS-T-1298. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy

Analytic Development of a Reference Profile for the First Entry in a Skip Atmospheric Entry

This note shows that a feasible reference drag profile for the first entry portion of a skip entry can be generated as a polynomial expression of the velocity. The coefficients of that polynomial are found through the resolution of a system composed of m + 1 equations, where m is the degree of the drag polynomial. It has been shown that a minimum of five equations (m = 4) are required to establish the range and the initial and final conditions on velocity and flight path angle. It has been shown that at least one constraint on the trajectory can be imposed through the addition of one extra equation in the system, which must be accompanied by the increase in the degree of the drag polynomial. In order to simplify the resolution of the system of equations, the drag was considered as being a probability density function of the velocity, with the velocity as a distribution function of the drag. Combining this notion with the introduction of empirically derived constants, it has been shown that the system of equations required to generate the drag profile can be successfully reduced to a system of linear algebraic equations. For completeness, the resulting drag profiles have been flown using the feedback linearization method of differential geometric control as a guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. Satisfactory results were achieved when the gains in the error dynamics were changed at a certain point along the trajectory that is dependent on the velocity and the curvature of the drag as a function of the velocity. Future work should study the capacity to update the drag profile in flight when dispersions are introduced. Also, future studies should attempt to link the first entry, as presented and controlled in this note, with a more standard control concept for the second entry, such as the Apollo entry guidance, to try to assess the overall skip entry performance. A guidance law that includes an integral feedback term, as is the case in the actual Space Shuttle entry guidance and as is proposed in Ref 29, could be tried in future studies to assess whether its use results in an improvement of the tracking performance, and to evaluate the design needs when determining the control gains

The petroglyphs of cerro blanco of zonda (San Juan)

Recientes investigaciones en el Valle de Zonda (centro-sur de San Juan) permitieron descubrir un conjunto de petroglifos en una de las laderas del Cerro Blanco. La mayoría de las representaciones son figurativas (antropomorfos, camélidos, huellas de aves y felinos, serpientes, etc.). Su análisis y comparación indican que al menos una parte corresponden al período Aguada local. Asimismo, se discute la posible relación del sitio con el cercano canal matriz del sistema de riego prehispánico local y su importancia en el marco del proceso de integración regional que involucró al actual territorio de San Juan desde ca. 650 d.C.During recent research in the Zonda Valley (south-central San Juan) a group of petroglyphs was discovered on one of the slopes of Cerro Blanco. Most are figurative representations (anthropomorphs, camelids, birds and felines prints, snakes, etc.). Analysis and comparison of the figures indicate that at least a portion corresponds to the local Aguada period. The possible relationship of the site with the nearby main canal of the local prehispanic irrigation system, and its importance in the context of the regional integration process involving the territory of San Juan from ca. 650 A.D., are also discussed.Fil: Garcia, Eduardo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Juan. Centro de Investigaciones de la Geosfera y Biosfera; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Fisicas y Naturales; Argentin

Attitude determination with three-axis accelerometer for emergency atmospheric entry

Two algorithms are disclosed that, with the use of a 3-axis accelerometer, will be able to determine the angles of attack, sideslip and roll of a capsule-type spacecraft prior to entry (at very high altitudes, where the atmospheric density is still very low) and during entry. The invention relates to emergency situations in which no reliable attitude and attitude rate are available. Provided that the spacecraft would not attempt a guided entry without reliable attitude information, the objective of the entry system in such case would be to attempt a safe ballistic entry. A ballistic entry requires three controlled phases to be executed in sequence: First, cancel initial rates in case the spacecraft is tumbling; second, maneuver the capsule to a heat-shield-forward attitude, preferably to the trim attitude, to counteract the heat rate and heat load build up; and third, impart a ballistic bank or roll rate to null the average lift vector in order to prevent prolonged lift down situations. Being able to know the attitude, hence the attitude rate, will allow the control system (nominal or backup, automatic or manual) to cancel any initial angular rates. Also, since a heat-shield forward attitude and the trim attitude can be specified in terms of the angles of attack and sideslip, being able to determine the current attitude in terms of these angles will allow the control system to maneuver the vehicle to the desired attitude. Finally, being able to determine the roll angle will allow for the control of the roll ballistic rate during entry