Initial Value Problem in General Relativity

This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students who have taken a first course in general relativity, the article first discusses how to reformulate the spacetime fields and spacetime covariant field equations of Einstein's theory in terms of fields and field equations compatible with a 3+1 foliation of spacetime with spacelike hypersurfaces. It proceeds to discuss the arguments which show that the initial value problem for Einstein's theory is well-posed, in the sense that for any given set of initial data satisfying the Einstein constraint equations, there is a (maximal) spacetime solution of the full set of Einstein equations, compatible with the given set of data. The article then describes how to generate initial data sets which satisfy the Einstein constraints, using the conformal (and conformal thin sandwich) method, and using gluing techniques. The article concludes with comments regarding stability and long term behavior of solutions of Einstein's equations generated via the initial value problem.Comment: To appear as a chapter in "The Springer Handbook of Spacetime," edited by A. Ashtekar and V. Petkov. (Springer-Verlag, at Press

Constructing Solutions of the Einstein Constraint Equations

The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing solutions of the constraints and we recall what it tells us about the parameterization of the space of such solutions. One would like to know how to construct solutions which model particular physical phenomena. One useful step towards this goal is learning how to glue together known solutions of the constraint equations. We discuss recent results concerning such gluing.Comment: Write-up of my GR16 talk, 18 page

"That Shakespearian Rome! Work in Progress..." An Experiment in Intermedial Criticism

Il saggio tratta una sperimentazione di critica shakespeareana intermediale, presentata durante il convegno internazionale Shakespeare and Rome: Identity, Otherness, Empire (Università di Roma Tre, Rome, Italy, 2005). Il saggio descrive e discute i modi in cui il video interrogava, attraverso accorgimenti tecnici quali, per esempio, alternazione, sovrapposizione e sincronia, per combinare materiale provenienti da una vasta varietà di generi multimediali, la Roma di Shakespeare cinquecento anni dopo nei nostri tempi postmoderni e postcoloniali e multiculturali

Acceleration of heavy ions in the solar wind

The preferential acceleration and heating of solar wind heavy ions by the resonant cyclotron interaction were studied. It is concluded that this interaction is incapable of producing the observed differential speeds for reasonable solar wind parameters

"Financial Instability: A Recession Simulation on the U.S. Corporate Structure"

This study is a continuation of the empirical research on the impacts of debt; it argues that debt-usage is not neutral and that the currency of its cost is bankruptcy. A financially fragile economy is feared because of its potential harm. In the public sector the large and lingering deficit is not a problem in and of itself. It is only when future scenarios of budget item trade-offs or recession-fighting fiscal policy options are conjured up that the problem emerges. The same is true for the corporate debt. As long as the debt is incurred in an expanding economy, there is no economic problem. It is only when a contraction ensues that the problem emerges. The problem is encapsulated in bankruptcy and the costs that accompany it. Some of these costs are private and can be born by the managers and owners. However, in a recession this burden grows and spreads beyond the private; the costs become socialized. While previous researchers have indicated the extent of consumer and producer indebtedness, this study uses discriminant analysis to simulate the impact of a recession on the manufacturing sector so that a measure of our current financial vulnerability is produced. In the first section background material on the current financial structure of the United States is reviewed. The second section delineates the social costs of bankruptcy. The construction and characteristics of the discriminant function are specified in the third section. The fourth section details the simulation and its results.

Sketchy rendering for information visualization

We present and evaluate a framework for constructing sketchy style information visualizations that mimic data graphics drawn by hand. We provide an alternative renderer for the Processing graphics environment that redefines core drawing primitives including line, polygon and ellipse rendering. These primitives allow higher-level graphical features such as bar charts, line charts, treemaps and node-link diagrams to be drawn in a sketchy style with a specified degree of sketchiness. The framework is designed to be easily integrated into existing visualization implementations with minimal programming modification or design effort. We show examples of use for statistical graphics, conveying spatial imprecision and for enhancing aesthetic and narrative qualities of visual- ization. We evaluate user perception of sketchiness of areal features through a series of stimulus-response tests in order to assess users’ ability to place sketchiness on a ratio scale, and to estimate area. Results suggest relative area judgment is compromised by sketchy rendering and that its influence is dependent on the shape being rendered. They show that degree of sketchiness may be judged on an ordinal scale but that its judgement varies strongly between individuals. We evaluate higher-level impacts of sketchiness through user testing of scenarios that encourage user engagement with data visualization and willingness to critique visualization de- sign. Results suggest that where a visualization is clearly sketchy, engagement may be increased and that attitudes to participating in visualization annotation are more positive. The results of our work have implications for effective information visualization design that go beyond the traditional role of sketching as a tool for prototyping or its use for an indication of general uncertainty

"The Financially Fragile Firm: Is There a Case for It in the 1920s?"

This paper is an empirical investigation of Minsky's hypothesis in the U.S. consumer durables sector during the 1920s. The first section of the paper briefly describes Minsky's financial fragility hypothesis, while the second sketches a brief economic historical background of the 1920s in the U.S. The third section introduces the methodology utilized and the fourth presents the results of the analysis. In the conclusion the findings and their implications are summarized.

Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics

We show that sets of conformal data on closed manifolds with the metric in the positive or zero Yamabe class, and with the gradient of the mean curvature function sufficiently small, are mapped to solutions of the Einstein constraint equations. This result extends previous work which required the conformal metric to be in the negative Yamabe class, and required the mean curvature function to be nonzero.Comment: 15 page