Duality Symmetries and G^{+++} Theories

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra

Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories

A description of the bosonic sector of ten-dimensional N=1 supergravity as a non-linear realisation is given. We show that if a suitable extension of this theory were invariant under a Kac-Moody algebra, then this algebra would have to contain a rank eleven Kac-Moody algebra, that can be identified to be a particular real form of very-extended D_8. We also describe the extension of N=1 supergravity coupled to an abelian vector gauge field as a non-linear realisation, and find the Kac-Moody algebra governing the symmetries of this theory to be very-extended B_8. Finally, we discuss the related points for the N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields

Dualisation of the D=7 Heterotic String

The dualisation and the first-order formulation of the D=7 abelian Yang-Mills supergravity which is the low energy effective limit of the D=7 fully Higssed heterotic string is discussed. The non-linear coset formulation of the scalars is enlarged to include the entire bosonic sector by introducing dual fields and by constructing the Lie superalgebra which generates the dualized coset element.Comment: 20 page

E11, generalised space-time and equations of motion in four dimensions

We construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at low levels in four dimensions. We include the fields for gravity, the scalars and the gauge fields as well as the duals of these fields. The generalised space-time, upon which the fields depend, consists of the usual coordinates of four dimensional space-time and Lorentz scalar coordinates which belong to the 56-dimensional representation of E7. We demand that the equations of motion are first order in derivatives of the generalised space-time and then show that they are essentially uniquely determined by the properties of the E11 Kac-Moody algebra and its first fundamental representation. The two lowest equations correctly describe the equations of motion of the scalars and the gauge fields once one takes the fields to depend only on the usual four dimensional space-time

Effects of Compressibility on the Maximum Lift Characteristics and Spanwise Load Distribution of a 12-Foot-Span Fighter-Type Wing of NACA 230-Series Airfoil Sections

Lift characteristics and pressure distribution for a NACA 230 wing were investigated for an angle of attack range of from -10 to +24 degrees and Mach range of from 0.2 to 0.7. Maximum lift coefficient increased up to a Mach number of 0.3, decreased rapidly to a Mach number of 0.55, and then decreased moderately. At high speeds, maximum lift coefficient was reached at from 10 to 12 degrees beyond the stalling angle. In high-speed stalls, resultant load underwent a moderate shift outward

The E_{11} origin of all maximal supergravities

Starting from the eleven dimensional E_{11} non-linear realisation of M-theory we compute all possible forms, that is objects with totally antisymmetrised indices, that occur in four dimensions and above as well as all the 1-forms and 2-forms in three dimensions. In any dimension D, the D-1-forms lead to maximal supergravity theories with cosmological constants and they are in precise agreement with the patterns of gauging found in any dimension using supersymmetry. The D-forms correspond to the presence of space-filling branes which are crucial for the consistency of orientifold models and have not been derived from an alternative approach, with the exception of the 10-dimensional case. It follows that the gaugings of supergravities and the spacetime-filling branes possess an eleven dimensional origin within the E_{11} formulation of M-theory. This and previous results very strongly suggest that all the fields in the adjoint representation of E_{11} have a physical interpretation.Comment: 54 page

Aging and Rejuvenation with Fractional Derivatives

We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index mu in the interval 2<mu <3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord, is given by ord=3-mu . A brand new system is characterized by the degree ord=mu -2. If the system is prepared at time -ta<0$ and the observation begins at time t=0, we derive the following scenario. For times 0<t<<ta the system is satisfactorily described by the fractional derivative with ord=3-mu . Upon time increase the system undergoes a rejuvenation process that in the time limit t>>ta yields ord=mu -2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.Comment: 11 pages, 4 figure

IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories

We show that IIA supergravity can be extended with two independent 10-form potentials. These give rise to a single BPS IIA 9-brane. We investigate the bosonic gauge algebra of both IIA and IIB supergravity in the presence of 10-form potentials and point out an intriguing relation with the symmetry algebra $E_{11}$, which has been conjectured to be the underlying symmetry of string theory/M-theory.Comment: 18 pages, section on IIA 9-branes added, references added; version to be publishe

Magnetic field configuration associated with solar gamma ray flares in June, 1991

The vector magnetic field configuration of the solar active region AR 6659 that produced very high levels of flare activity in Jun. 1991 is described. The morphology and evolution of the photospheric fields are described for the period 7-10 Jun., and the flares taking place around these dates and their locations relative to the photospheric fields are indicated. By comparing the observed vector field with the potential field calculated from the observed line-of-sight flux, we identify the nonpotential characteristics of the fields along the magnetic neutral lines where the flares were observed. These results are compared with those from the earlier study of gamma-ray flares

Longitudinal Aerodynamic Characteristics of a Wing-Body-Tail Model Having a Highly Tapered, Cambered 45 degree Swept Wing of Aspect Ratio 4 at Transonic Speeds

The longitudinal aerodynamic characteristics of a wing-body-horizontal-tail configuration designed for efficient performance at transonic speeds has been investigated at Mach numbers from 0.80 to 1.03 in the Langley 16-foot transonic tunnel. The effect of adding an outboard leading-edge chord-extension to the highly tapered 45 deg. swept wing was also obtained. The average Reynolds number for this investigation was 6.7 x 10(exp 6) based on the wing mean aerodynamic chord. The relatively low tail placement as well as the addition of a chord-extension achieved some alleviation of the pitchup tendencies of the wing-fuselage configuration. The maximum trimmed lift-drag ratio was 16.5 up to a Mach number of 0.9, with the moment center located at the quarter-chord point of the mean aerodynamic chord. For the untrimmed case, the maximum lift-drag ratio was approximately 19.5 up to a Mach number of 0.9