Exact Nonperturbative Unitary Amplitudes for 1->N Transitions

I present an extension to arbitrary N of a previously proposed field theoretic model, in which unitary amplitudes for $1->8$ processes were obtained. The Born amplitude in this extension has the behavior $A(1->N)^{tree}\ =\ g^{N-1}\ N!$ expected in a bosonic field theory. Unitarity is violated when $|A(1->N)|>1$, or when $N>\N_crit\simeq e/g.$ Numerical solutions of the coupled Schr\"odinger equations shows that for weak coupling and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}. The very small size of the coefficient 1/\g2 , indicative of a very weak exponential suppression, is not in accord with standard discussions based on saddle point analysis, which give a coefficient $\sim 1.\$ The weak dependence on $N$ could have experimental implications in theories where the exponential suppression is weak (as in this model). Non-perturbative contributions to few-point correlation functions in this theory would arise at order $K\ \simeq\ \left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}$in an expansion in powers of$\g2.$Comment: 11 pages, 3 figures (not included

Fungal speciation using quantitative polymerase chain reaction (QPCR) in patients with and without chronic rhinosinusitis.

Objectives/hypothesisThe objectives of this study were to determine the mycology of the middle meatus using an endoscopically guided brush sampling technique and polymerase chain reaction laboratory processing of nasal mucous; to compare the mycology of the middle meatus in patients with sinus disease with subjects without sinus disease; to compare the responses on two standardized quality-of-life survey forms between patients with and without sinusitis; and to determine whether the presence of fungi in the middle meatus correlates with responses on these data sets.Study designThe authors conducted a single-blind, prospective, cross-sectional study.MethodsPatients with sinus disease and a control group without sinus disease were enrolled in the study. A disease-specific, validated Sinonasal Outcomes Test survey (SNOT-20) was completed by the subjects and a generalized validated Medical Outcomes Short Form 36 Survey (SF-36) was also completed. An endoscopically guided brush sampling of nasal mucous was obtained from the middle meatus. Fungal specific quantitative polymerase chain reaction (QPCR) was performed on the obtained sample to identify one of 82 different species of fungus in the laboratory. Statistical analysis was used to categorize the recovered fungal DNA and to crossreference this information with the outcomes surveys.ResultsThe fungal recovery rate in the study was 45.9% in patients with sinus disease and 45.9% in control subjects. Patients with chronic rhinosinusitis had a mean SNOT-20 score of 1.80 versus the control group mean score of 0.77 (P < .0001). SF-36 data similarly showed a statistically significant difference between diseased and control populations with controls scoring a mean of 80.37 and patients with chronic rhinosinusitis scoring a mean of 69.35 for a P value of .02. However, no statistical significance could be ascribed to the presence or absence of fungi recovered, the type of fungi recovered, or the possible impact of fungi on the quality-of-life survey results.ConclusionThe recovery rate of fungi from the middle meatus of patients with chronic rhinosinusitis and a control population without chronic rhinosinusitis is 45.9% using QPCR techniques. No direct causation with regard to fungal species or presence was proven; however, a species grouping for future studies is proposed based on trends in this data and other reports. Disease-specific outcomes surveys revealed a statistically significant difference between the two groups

Stationary generalized Kerr-Schild spacetimes

In this paper we have applied the generalized Kerr-Schild transformation finding a new family of stationary perfect-fluid solutions of the Einstein field equations. The procedure used combines some well-known techniques of null and timelike vector fields, from which some properties of the solutions are studied in a coordinate-free way. These spacetimes are algebraically special being their Petrov types II and D. This family includes all the classical vacuum Kerr-Schild spacetimes, excepting the plane-fronted gravitational waves, and some other interesting solutions as, for instance, the Kerr metric in the background of the Einstein Universe. However, the family is much more general and depends on an arbitrary function of one variable.Comment: 21 pages, LaTeX 2.09. To be published in Journal of Mathematical Physic

Techniques for the realization of ultrareliable spaceborne computers Interim scientific report

Error-free ultrareliable spaceborne computer

Evaluation of hyperelastic models for unidirectional short fibre reinforced materials using a representative volume element with refined boundary conditions

The simulation of a short fibre reinforced structure by means of the FEM requires the knowledge of the material behaviour at every Gauss point. In order to obtain such information, a representative volume element (RVE) containing unidirectional short fibres is analysed in the presented work. In order to cover the complete anisotropic effect of the fibres, deformations with different angles to the fibre direction have to be conducted. In contrast to other works, this task is tackled using the application of periodic boundary conditions to the RVE in tensorial form, which enables a simple access to consider varying fibre angles with one and the same RVE. As the RVE’s average response represents the homogenised behaviour at a macroscopic material point, the material models’ parameters can be identified by fitting them to stress-strain curves obtained from simulations with the RVE. The findings of these analyses are used to assess the applicability of several hyperelastic models describing transversal isotropic materials under consideration of large deformations. For example it is shown, that the formulation of mixed invariants with the isochoric right Cauchy-Green tensor is insufficient to reproduce the RVE’s behaviour at purely volumetric deformations. Both the modelling and the calculations are carried out with the commercial FEMsoftware ABAQUS. Insight is given to the implementation of the boundary conditions as well as the underlying constitutive equations

Design of a fault tolerant airborne digital computer. Volume 1: Architecture

This volume is concerned with the architecture of a fault tolerant digital computer for an advanced commercial aircraft. All of the computations of the aircraft, including those presently carried out by analogue techniques, are to be carried out in this digital computer. Among the important qualities of the computer are the following: (1) The capacity is to be matched to the aircraft environment. (2) The reliability is to be selectively matched to the criticality and deadline requirements of each of the computations. (3) The system is to be readily expandable. contractible, and (4) The design is to appropriate to post 1975 technology. Three candidate architectures are discussed and assessed in terms of the above qualities. Of the three candidates, a newly conceived architecture, Software Implemented Fault Tolerance (SIFT), provides the best match to the above qualities. In addition SIFT is particularly simple and believable. The other candidates, Bus Checker System (BUCS), also newly conceived in this project, and the Hopkins multiprocessor are potentially more efficient than SIFT in the use of redundancy, but otherwise are not as attractive

Artificial Intelligence

Contains a report on a research project.M.I.T. Research Laboratory of ElectronicsM.I.T. Computation Cente

General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry

The Hamiltonian formulation of general relativity on a null surface is established in the teleparallel geometry. No particular gauge conditons on the tetrads are imposed, such as the time gauge condition. By means of a 3+1 decomposition the resulting Hamiltonian arises as a completely constrained system. However, it is structurally different from the the standard Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the basic field quantities are tetrads that transform under the global SO(3,1) and the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra

Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing

We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her with the previously found constraints, these form a sufficient number of second class constraints so that the phase space is reduced to one pair of canonically conjugate variables: \Ac_2\and\Sc^2. The formalism is related to both the Bondi-Sachs and the Newman-Penrose methods of studying the gravitational field at null infinity. Asymptotic solutions in the vicinity of null infinity which exclude logarithmic behavior require the connection to fall off like $1/r^3$ after the Minkowski limit. This, of course, gives the previous results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off more slowly leads to logarithmic behavior which leaves null infinity intact, allows for meaningful gravitational radiation, but the peeling theorem does not extend to $\Psi_1$ in the terminology of Newman-Penrose. The conclusions are in agreement with those of Chrusciel, MacCallum, and Singleton. This work was begun as a preliminary study of a reduced phase space for quantization of general relativity.Comment: magnification set; pagination improved; 20 pages, plain te

Differential Forms and Wave Equations for General Relativity

Recently, Choquet-Bruhat and York and Abrahams, Anderson, Choquet-Bruhat, and York (AACY) have cast the 3+1 evolution equations of general relativity in gauge-covariant and causal ``first-order symmetric hyperbolic form,'' thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation which governs the light-speed propagation of the extrinsic curvature tensor. Along a similar line, we construct a related wave equation which, as the key equation in a system, describes vacuum general relativity. Whereas the approach of AACY is based on tensor-index methods, the present formulation is written solely in the language of differential forms. Our approach starts with Sparling's tetrad-dependent differential forms, and our wave equation governs the propagation of Sparling's 2-form, which in the ``time-gauge'' is built linearly from the ``extrinsic curvature 1-form.'' The tensor-index version of our wave equation describes the propagation of (what is essentially) the Arnowitt-Deser-Misner gravitational momentum.Comment: REVTeX, 26 pages, no figures, 1 macr