Norman H. Barth

The author finds the fourth-order gravitational action for manifolds with boundaries, and its associated boundary conditions, which is consistent with the action principle, and yields the correct field equations. A detailed analysis is given of how this is done. Relationships to the canonical formalism are pointed out. He discusses two types of bou...

For pt.I see ibid., vol.20, no.4, p.857-74 (1987). The author obtains useful relations for calculating the a(12)d/ asymptotic expansion coefficient for an associated heat kernel and elliptical operator of order greater than two in d dimensions. In the main relation he relates the a(12)d/ coefficients for two commuting elliptical operators and the a...

The authors generalise previous work (Christensen and Duff 1979) on a simple set of arbitrary spin field equations for fields propagating on curved manifolds without torsion. As a prelude to an extensive study of index theorems and anomalies in the case of non-zero torsion, new arbitrary spin field equations are developed and the consistency condit...

The author argues that it is possible to obtain the asymptotic expansion coefficients for an operator with torsion from the expansion coefficients for an operator without torsion. This is possible when both operators act on the same set of eigenfunctions in the same way, and therefore have the same spectrum. The author calculates in four dimensions...

An experiment design problem–-that of drifter cast strategy–-is discussed. Different optimization techniques used as part of preparations for the Semaphore-93 air-sea experiment, during which drifters were deployed, are examined. The oceanographic experiment objective was to sample a 500-km-square zone cantered at 33°N, 22°W in the Azores current a...

The seasonal cycle over the tropical Pacific simulated by eleven coupled ocean-atmosphere general circulation models (GCMs) is examined. Each model consists of a high resolution ocean GCM of either the tropical Pacific or near-global oceans, coupled to a moderate or high resolution atmospheric GCM, without the use of flux correction. The seasonal b...

The experiment design problem is explored in terms of time-dependent observational strategies. An example drawn from tracer studies is used to illustrate many of the issues. In particular, the optimization of an objective function, which characterizes the quality of an observational strategy, is carried out using a genetic algorithm (GA). Compariso...

The oceanographic experiment design problem is discussed in the context of several simple examples drawn from acoustic tomography. The optimization of an objective function—chosen to characterize the array design— is carried out using the technique of simulated annealing. A detailed description of this method and its implementation for the examples...

The mathematical formalism associated with a 2-dimensional inverse problem in radiation therapy treatment and planning is discussed. The formalism is extended to convex phantoms of arbitrary cross-section. Relations necessary to produce circularly symmetric dose distributions about any point within the phantom are obtained. The general case for a p...

The inverse problem in radiation therapy presents a solution for a fluence distribution based on the specification of a region of dose in a patient. We show results for one such solution based on the inversion of an integral over a function of the fluence profile of a rotating beam. We use Monte Carlo methods and numerical integrations to evaluate...

We have recently initiated a program for irradiating small, unresectable arteriovenous malformations (AVM's) in the brain. The treatments are delivered using a modified and carefully calibrated 6 MV linac. We are using high, single doses (15 to 25 Gy) with a goal of sclerosing the vessels and preventing hemorrhages. This technique, radiosurgery, is...

We report on a useful clinical method for precisely locating intracranial targets. Utilizing the BRW system, the technique is currently used in stereotaxic irradiation of arteriovenous malformations. An intracranial localizer box, with four radio-opaque markers on each face, surrounds the patient's head and is attached to the BRW Head Ring. Two loc...

The first part of a detailed analysis of the one-loop divergences of fourth-order gravity theories is presented. The functional-integral structure is determined and the three kinds of ghosts which appear are discussed. Field operators and gauge-fixing terms are derived and are found to be far more complicated than those of standard second-order the...

When the spacetime manifolds has no boundaries, total divergences, which arise after the variation of the action with respect to the metric, can always be set equal to zero using Gauss' Law, and thus do not contribute to the field equations. When boundaries are included in the manifold this is no longer true, and if the action is to be made station...