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A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron WavesMar 08 2012We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating through this marginally stable plasma will ... More

Waveless Approximation Theories of GravityFeb 20 2007The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability -- are associated ... More

Spatial Confinement of the IBEX Ribbon: A Dominant Turbulence MechanismApr 08 2014The narrow ribbon of enhanced energetic neutral atom flux observed by the Interstellar Boundary Explorer (IBEX) spacecraft has prompted numerous ideas to explain its structure and properties. One of these ideas is the "neutral solar wind" scenario, which ... More

On the dynamics of generators of Cauchy horizonsJan 17 1994We discuss various features of the dynamical system determined by the flow of null geodesic generators of Cauchy horizons. Several examples with non--trivial (``chaotic'', ``strange attractors'', etc.) global behaviour are constructed. Those examples ... More

Kolmogorov versus Iroshnikov-Kraichnan spectra: Consequences for ion heating in the solar windJun 02 2011Whether the phenomenology governing MHD turbulence is Kolmogorov or Iroshnikov-Kraichnan (IK) remains an open question, theoretically as well as observationally. The ion heating profile observed in the solar wind provides a quantitative, if indirect, ... More

The Effect of Magnetic Turbulence Energy Spectra and Pickup Ions on the Heating of the Solar WindJun 02 2011In recent years, a phenomenological solar wind heating model based on a turbulent energy cascade prescribed by the Kolmogorov theory has produced reasonably good agreement with observations on proton temperatures out to distances around 70 AU, provided ... More

Stochastic Heating, Differential Flow, and the Alpha-to-Proton Temperature Ratio in the Solar WindJul 30 2013We extend previous theories of stochastic ion heating to account for the motion of ions along the magnetic field. We derive an analytic expression for the ion-to-proton perpendicular temperature ratio in the solar wind for any ion species, assuming that ... More

Empirical Estimate of the Shape of the Upstream Heliopause from IBEX-Lo Helium Measurements: Preliminary ResultsNov 27 2017We present a simplified model of the outer heliosheath to help interpret the observations of interstellar neutral helium by the IBEX-Lo instruments. We assume that the measured particles are composed of the superposition of a primary beam population, ... More

Non-Maxwellian Proton Velocity Distributions in Nonradiative ShocksApr 23 2008The Balmer line profiles of nonradiative supernova remnant shocks provide the means to measure the post-shock proton velocity distribution. While most analyses assume a Maxwellian velocity distribution, this is unlikely to be correct. In particular, neutral ... More

Quasilinear Consequences of Turbulent Ion Heating by Magnetic Moment BreakingDec 12 2018The fast solar wind emerging from coronal holes is likely heated and accelerated by the dissipation of magnetohydrodynamic turbulence, but the specific kinetic mechanism resulting in the perpendicular ion heating required by observations is not understood. ... More

Self-Consistent Ion Cyclotron Anisotropy-Beta Relation for Solar Wind ProtonsJul 03 2013We derive a set of self-consistent marginally stable states for a system of ion-cyclotron waves propagating parallel to the large-scale magnetic field through a homogeneous proton-electron plasma. The proton distributions and the wave dispersions are ... More

Draping of the Interstellar Magnetic Field over the Heliopause - A Passive Field ModelApr 02 2015As the local interstellar plasma flows past our heliosphere, it is slowed and deflected around the magnetic obstacle of the heliopause. The interstellar magnetic field, frozen into this plasma, then becomes draped around the heliopause in a characteristic ... More

The Coronal Physics Investigator (CPI) Experiment for ISS: A New Vision for Understanding Solar Wind AccelerationApr 19 2011In February 2011 we proposed a NASA Explorer Mission of Opportunity program to develop and operate a large-aperture ultraviolet coronagraph spectrometer called the Coronal Physics Investigator (CPI) as an attached International Space Station (ISS) payload. ... More

Initial Value Problem in General RelativityApr 07 2013This 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 ... More

Constructing Solutions of the Einstein Constraint EquationsMar 13 2002The 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 ... More

General Relativity, Time and DeterminismOct 20 2016Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational phenomena, both ... More

On Strong Cosmic CensorshipMay 24 2015For almost half of the one hundred year history of Einstein's theory of general relativity, Strong Cosmic Censorship has been one of its most intriguing conjectures. The SCC conjecture addresses the issue of the nature of the singularities found in most ... More

General Relativity and Gravitation: A Centennial PerspectiveSep 19 2014To commemorate the 100th anniversary of general relativity, the International Society on General Relativity and Gravitation (ISGRG) commissioned a Centennial Volume, edited by the authors of this article. We jointly wrote introductions to the four Parts ... More

Resonant Interactions Between Protons and Oblique Alfvén/Ion-Cyclotron WavesDec 28 2009Resonant interactions between ions and Alfv\'en/ion-cyclotron (A/IC) waves may play an important role in the heating and acceleration of the fast solar wind. Although such interactions have been studied extensively for "parallel" waves, whose wave vectors ... More

Critical behavior in Ricci flowJun 07 2003We use numerical techniques to study the formation of singularities in Ricci flow. Comparing the Ricci flows corresponding to a one parameter family of initial geometries on S^3 with varying amounts of S^2 neck pinching, we find critical behavior at the ... More

Degenerate neckpinches in mean curvature flow on noncompact hypersurfacesMar 05 2016Mar 13 2016We study the formation of Type-II singularities in mean curvature flows of rotationally symmetric noncompact embedded hypersurfaces. Using analytic techniques based on formal matched asymptotics and the construction of upper and lower barrier solutions ... More

Symmetries of Cosmological Cauchy Horizons with Non-Closed OrbitsJul 25 2018We consider analytic, vacuum spacetimes that admit compact, non-degenerate Cauchy horizons. Many years ago we proved that, if the null geodesic generators of such a horizon were all \textit{closed} curves, then the enveloping spacetime would necessarily ... More

Proof-Carrying Hardware via IC3Oct 15 2014Proof-carrying hardware (PCH) is an approach to achieving safety of dynamically reconfigurable hardware, transferring the idea of proof-carrying code to the hardware domain. Current PCH approaches are, however, either limited to combinational and bounded ... More

Existence and Blowup Results for Asymptotically Euclidean Initial Data Sets Generated by the Conformal MethodSep 02 2016For each set of (freely chosen) seed data, the conformal method reduces the Einstein constraint equations to a system of elliptic equations, the conformal constraint equations. We prove an admissibility criterion, based on a (conformal) prescribed scalar ... More

Power Law Inflation with ElectromagnetismOct 29 2012We generalize Ringstr\"om's global future causal stability results (Ringstr\"om 2009) for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein-Maxwell-scalar field system. In particular, after noting ... More

Symmetries of Higher Dimensional Black HolesMay 10 2008We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension $n\geq 4$ contains a non-degenerate horizon with compact cross sections that are transverse to the stationarity generating Killing vector field ... More

The Modelling of Degenerate Neck Pinch Singularities in Ricci Flow by Bryant SolitonsSep 04 2007In earlier work, carrying out numerical simulations of the Ricci flow of families of rotationally symmetric geometries on $S3$, we have found strong support for the contention that (at least in the rotationally symmetric case) the Ricci flow for a ``critical'' ... More

On the area of the symmetry orbits in $T^2$ symmetric spacetimesApr 04 2003Feb 03 2004We obtain a global existence result for the Einstein equations. We show that in the maximal Cauchy development of vacuum $T^2$ symmetric initial data with nonvanishing twist constant, except for the special case of flat Kasner initial data, the area of ... More

Asymptotic Behavior in Polarized {\bf T}$^2$-symmetric Vacuum SpacetimesSep 27 2017We use Fuchsian Reduction to study the behavior near the singularity of a class of solutions of Einstein's vacuum equations. These solutions admit two commuting spacelike Killing fields like the Gowdy spacetimes, but their twist does not vanish. The spacetimes ... More

Convergence of Ricci flow on $\mathbb{R}^2$ to flat spaceAug 16 2009We prove that, starting at an initial metric $g(0)=e^{2u_0}(dx^2+dy^2)$ on $\mathbb{R}^2$ with bounded scalar curvature and bounded $u_0$, the Ricci flow $\partial_t g(t)=-R_{g(t)}g(t)$ converges to a flat metric on $\mathbb{R}^2$.

Spherically symmetric dynamical horizonsDec 15 2005We determine sufficient and necessary conditions for a spherically symmetric initial data set to satisfy the dynamical horizon conditions in the spacetime development. The constraint equations reduce to a single second order linear master equation, which ... More

The Constraint EquationsMay 17 2004We review the properties of the constraint equations, from their geometric origin in hypersurface geometry through to their roles in the Cauchy problem and the Hamiltonian formulation of the Einstein equations. We then review properties of the space of ... More

Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-upMar 05 2016May 07 2017We study the phenomenon of Type-II curvature blow-up in mean curvature flows of rotationally symmetric noncompact embedded hypersurfaces. Using analytic techniques based on formal matched asymptotics and the construction of upper and lower barrier solutions ... More

SOHO CTOF Observations of Interstellar He+ Pickup Ion Enhancements in Solar Wind Compression RegionsApr 21 2003We present a recent analysis with 1996 SOHO CELIAS CTOF data, which reveals correlations of He+ pickup ion fluxes and spectra with the magnetic field strength and solar wind density. The motivation is to better understand the ubiquitous large variations ... More

Asymptotic Behavior of Polarized and Half-Polarized U(1) symmetric Vacuum SpacetimesMar 12 2002We use the Fuchsian algorithm to study the behavior near the singularity of certain families of U(1) Symmetric solutions of the vacuum Einstein equations (with the U(1) isometry group acting spatially). We consider an analytic family of polarized solutions ... More

Areal Foliation and AVTD Behavior in T^2 Symmetric Spacetimes with Positive Cosmological ConstantJan 09 2007Feb 19 2007We prove a global foliation result, using areal time, for T^2 symmetric spacetimes with a positive cosmological constant. We then find a class of solutions that exhibit AVTD behavior near the singularity.

Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint EquationsOct 15 1996We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of ... More

Singularity Formation in 2+1 Wave MapsJun 27 2001We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.

Half polarized U(1) symmetric vacuum spacetimes with AVTD behaviorJun 10 2005In a previous work, we used a polarization condition to show that there is a family of U(1) symmetric solutions of the vacuum Einstein equations such that each exhibits AVTD (Asymptotic Velocity Term Dominated) behavior in the neighborhood of its singularity. ... More

Non CMC Conformal Data Sets Which Do Not Produce Solutions of the Einstein Constraint EquationsNov 18 2003The conformal formulation provides a method for constructing and parametrizing solutions of the Einstein constraint equations by mapping freely chosen sets of conformal data to solutions, provided a certain set of coupled, elliptic determined PDEs (whose ... More

Global existence for wave maps with torsionJul 25 2000Wave maps (i.e. nonlinear sigma models) with torsion are considered in 2+1 dimensions. Global existence of smooth solutions to the Cauchy problem is proven for certain reductions under a translation group action: invariant wave maps into general targets, ... More

Ultraviolet Coronagraph Spectroscopy: A Key Capability for Understanding the Physics of Solar Wind AccelerationNov 10 2010Understanding the physical processes responsible for accelerating the solar wind requires detailed measurements of the collisionless plasma in the extended solar corona. Some key clues about these processes have come from instruments that combine the ... More

Toward a deeper understanding of Visualization through keyword analysisAug 13 2014We present the results of a comprehensive analysis of visualization paper keywords supplied for 4366 papers submitted to five main visualization conferences. We describe main keywords, topic areas, and 10-year historic trends from two datasets: (1) the ... More

Cosmological spacetimes not covered by a constant mean curvature slicingOct 09 1997We show that there exist maximal globally hyperbolic solutions of the Einstein-dust equations which admit a constant mean curvature Cauchy surface, but are not covered by a constant mean curvature foliation.

[Plasma 2020 Decadal] Disentangling the Spatiotemporal Structure of Turbulence Using Multi-Spacecraft DataMar 13 2019This white paper submitted for 2020 Decadal Assessment of Plasma Science concerns the importance of multi-spacecraft missions to address fundamental questions concerning plasma turbulence. Plasma turbulence is ubiquitous in the universe, and it is responsible ... More

Topologically general U(1) symmetric Einstein spacetimes with AVTD behaviorFeb 24 2005We use Fuchsian methods to show that, for any two dimensional manifold $\Sigma^2$, there is a large family of U(1) symmetric solutions of the vacuum Einstein equations on the manifold $\Sigma \times S^1 \times \mathbb{R}$, each of which has AVTD behavior ... More

Second-Order Renormalization Group Flow of Three-Dimensional Homogeneous GeometriesMay 29 2012We study the behavior of the second order Renormalization Group flow on locally homogeneous metrics on closed three-manifolds. In the cases $\mathbb R^3$ and $\text{SO}(3)\times \R$, the flow is qualitatively the same as the Ricci flow. In the cases $\text{H}(3)$ ... More

Gluing and wormholes for the Einstein constraint equationsSep 13 2001Jul 26 2002We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations. This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this handle ... More

Gluing Initial Data Sets for General RelativitySep 10 2004We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically ... More

On the topology of vacuum spacetimesJun 12 2002Oct 10 2002We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary compact manifold ... More

Ricci Flow in Two DimensionsMar 24 2011Ricci flow on two dimensional surfaces is far simpler than in the higher dimensional cases. This presents an opportunity to obtain much more detailed and comprehensive results. We review the basic facts about this flow, including the original results ... More

Linear stability of homogeneous Ricci solitonsJun 30 2006Nov 02 2006As a step toward understanding the analytic behavior of Type-III Ricci flow singularities, i.e. immortal solutions that exhibit |Rm|<C/t curvature decay, we examine the linearization of an equivalent flow at fixed points discovered recently by Baird--Danielo ... More

Mixmaster Behavior in Inhomogeneous Cosmological SpacetimesDec 12 1997Mar 11 1998Numerical investigation of a class of inhomogeneous cosmological spacetimes shows evidence that at a generic point in space the evolution toward the initial singularity is asymptotically that of a spatially homogeneous spacetime with Mixmaster behavior. ... More

Applications of theorems of Jean Leray to the Einstein-scalar field equationsNov 02 2006The Einstein-scalar field theory can be used to model gravitational physics with scalar field matter sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the Einstein-scalar ... More

A gluing construction for non-vacuum solutions of the Einstein constraint equationsJan 26 2005We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical fields such ... More

The Einstein-scalar field constraints on asymptotically Euclidean manifoldsJun 20 2005We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because ... More

Non-Kahler Ricci flow singularities that converge to Kahler-Ricci solitonsMar 08 2017May 15 2018We investigate Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities with the property that parabolic rescalings at the singularities converge to singularity models taking the form of shrinking Kahler-Ricci solitons. ... More

Ricci flow on locally homogeneous closed 4-manifoldsFeb 08 2005We discuss the Ricci flow on homogeneous 4-manifolds. After classifying these manifolds, we note that there are families of initial metrics such that we can diagonalize them and the Ricci flow preserves the diagonalization. We analyze the long time behavior ... More

Degenerate neckpinches in Ricci flowAug 21 2012In earlier work, we derived formal matched asymptotic profiles for families of Ricci flow solutions developing Type-II degenerate neckpinches. In the present work, we prove that there do exist Ricci flow solutions that develop singularities modeled on ... More

Ricci flow on asymptotically conical surfaces with nontrivial topologyMar 26 2010As part of the general investigation of Ricci flow on complete surfaces with finite total curvature, we study this flow for surfaces with asymptotically conical (which includes as a special case asymptotically Euclidean) geometries. After establishing ... More

Stability Within $T^2$-Symmetric Expanding SpacetimesDec 19 2018We prove a nonpolarised analogue of the asymptotic characterization of $T^2$-symmetric Einstein Flow solutions completed recently by LeFloch and Smulevici. In this work, we impose a condition weaker than polarisation and so our result applies to a larger ... More

Convergence Stability for Ricci FlowMay 01 2018The principle of convergence stability for geometric flows is the combination of the continuous dependence of the flow on initial conditions, with the stability of fixed points. It implies that if the flow from an initial state $g_0$ exists for all time ... More

Construction of N-body time-symmetric initial data sets in general relativitySep 06 2009Given a collection of N asymptotically Euclidean ends with zero scalar curvature, we construct a Riemannian manifold with zero scalar curvature and one asymptotically Euclidean end, whose boundary has a neighborhood isometric to the disjoint union of ... More

Oscillatory approach to the singularity in vacuum spacetimes with $T^2$ isometryApr 16 2001May 02 2003We use qualitative arguments combined with numerical simulations to argue that, in the approach to the singularity in a vacuum solution of Einstein's equations with $T^2$ isometry, the evolution at a generic point in space is an endless succession of ... More

The constraint equations for the Einstein-scalar field system on compact manifoldsOct 10 2006Dec 11 2006We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, ... More

Timelike Minimal Submanifolds of General Co-dimension in Minkowski SpaceTimeDec 01 2005We consider the timelike minimal surface problem in Minkowski spacetimes and show local and global existence of such surfaces having arbitrary dimension $\geq 2$ and arbitrary co-dimension, provided they are initially close to a flat plane.

Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe MetricsOct 03 2007Feb 15 2008We 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 ... More

A geometric introduction to the 2-loop renormalization group flowDec 20 2013The Ricci flow has been of fundamental importance in mathematics, most famously though its use as a tool for proving the Poincar\'e Conjecture and Thurston's Geometrization Conjecture. It has a parallel life in physics, arising as the first order approximation ... More

Short-time existence for the second order renormalization group flow in general dimensionsJan 07 2014We prove local existence for the second order Renormalization Group flow initial value problem on closed Riemannian manifolds $(M,g)$ in general dimensions, for initial metrics whose sectional curvatures $K_P$ satisfy the condition $1+\alpha K_P > 0$, ... More

Non-Kahler Ricci flow singularities modeled on Kahler-Ricci solitonsMar 08 2017Mar 05 2019We investigate Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities and present evidence in favor of a conjecture that parabolic rescalings at the singularities converge to singularity models that are shrinking Kahler-Ricci ... More

Formal matched asymptotics for degenerate Ricci flow neckpinchesNov 22 2010Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile ... More

Oscillatory approach to the singularity in vacuum $T^2$ symmetric spacetimesJan 14 2001Jan 16 2001A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.

Initial data engineeringMar 15 2004Jun 16 2005We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be constant near the ... More

Ricci flow neckpinches without rotational symmetryDec 10 2013Oct 21 2014We study "warped Berger" solutions $\big(\mc S^1\times\mc S^3,G(t)\big)$ of Ricci flow: generalized warped products with the metric induced on each fiber $\{s\}\times\mathrm{SU}(2)$ a left-invariant Berger metric. We prove that this structure is preserved ... More

Construction of N-body initial data sets in general relativityApr 08 2010Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains specified sub-regions ... More

Contracting asymptotics of the lapse-scalar field sub-system of the Einstein-scalar field equationsApr 05 2019We prove an asymptotic stability result for a linear coupled hyperbolic-elliptic system on a large class of singular background spacetimes in CMC gauge on the n-torus. At each spatial point these background spacetimes are perturbations of Kasner-like ... More

Quasi-linear symmetric hyperbolic Fuchsian systems in several space dimensionsMay 10 2012Sep 05 2012We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an extension of earlier ... More

Einstein Constraints on Asymptotically Euclidean ManifoldsJun 23 1999Jul 06 1999We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also ... More

A class of solutions to the Einstein equations with AVTD behavior in generalized wave gaugesFeb 09 2016Dec 29 2016We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the AVTD property, ... More

Effects of the Geometry of the Line-Forming Region on the Properties of Cyclotron Resonant Scattering LinesMar 11 1997We use a Monte Carlo radiative transfer code to examine the dependence of the properties of cyclotron resonant scattering lines on the spatial geometry and the optical depth of the line-forming region. We focus most of our attention on a line-forming ... More

Minimax Lower Bounds for Linear Independence TestingJan 23 2016Linear independence testing is a fundamental information-theoretic and statistical problem that can be posed as follows: given $n$ points $\{(X_i,Y_i)\}^n_{i=1}$ from a $p+q$ dimensional multivariate distribution where $X_i \in \mathbb{R}^p$ and $Y_i ... More

Analysis of Locally Coupled 3D Manipulation Mappings Based on Mobile Device MotionMar 24 2016Aug 01 2016We examine a class of techniques for 3D object manipulation on mobile devices, in which the device's physical motion is applied to 3D objects displayed on the device itself. Our work focuses specifically on the mapping between device motion and object ... More

Critical Phenomena in Nonlinear Sigma ModelsNov 13 1999Jun 01 2000We consider solutions to the nonlinear sigma model (wave maps) with target space S^3 and base space 3+1 Minkowski space, and we find critical behavior separating singular solutions from nonsingular solutions. For families of solutions with localized spatial ... More

Matters of Gravity, The Newsletter of the Topical Group in Gravitation of the American Physical Society, Volume 32, Fall 2008Sep 18 2008GGR News: - Remembering Wheeler, by Jim Isenberg; Research Briefs: - A Brief Summary of the WMAP5 Results, by Lyman Page; - Science with LIGO, by Maria Alessandra Papa; Conference Reports: - 7th LISA Symposium, by Edward K. Porter; - The Fourth Gulf Coast ... More

A Tangible Volume for Portable 3D InteractionMar 08 2016We present a new approach to achieve tangible object manipulation with a single, fully portable and self-contained device. Our solution is based on the concept of a "tangible volume". We turn a tangible object into a handheld fish-tank display. The tangible ... More

Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimesMay 09 2012Feb 03 2013We set up the singular initial value problem for quasilinear hyperbolic Fuchsian systems of first order and establish an existence and uniqueness theory for this problem with smooth data and smooth coefficients (and with even lower regularity). We apply ... More

Existence, uniqueness and other properties of the BCT (minimal strain lapse and shift) gaugeMar 31 2000Brady, Creighton and Thorne have proposed a choice of the lapse and shift for numerical evolutions in general relativity that extremizes a measure of the rate of change of the three-metric (BCT gauge). We investigate existence and uniqueness of this gauge, ... More

Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field TheoriesNov 09 2004With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical field theories. The canonical formluation works with fields ... More

Preference Between Allocentric and Egocentric 3D Manipulation in a Locally Coupled ConfigurationSep 28 2016We study user preference between allocentric and egocentric 3D manipulation on mobile devices, in a configuration where the motion of the device is applied to an object displayed on the device itself. We first evaluate this preference for translations ... More

Usability Comparison of Mouse, Touch and Tangible Inputs for 3D Data ManipulationMar 29 2016Apr 12 2016We evaluate the performance and usability of mouse-based, touch-based, and tangible interaction for manipulating objects in a 3D virtual environment. This comparison is a step toward a better understanding of the limitations and benefits of these existing ... More

Global Foliations of Vacuum Spacetimes with $T^2$ IsometryFeb 03 1997We prove a global existence theorem (with respect to a geometrically- defined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a $T^2$ isometry group with two-dimensional spacelike orbits, acting on $T^3$ spacelike ... More

Cyclotron Line Formation in a Radiation-driven OutflowJul 20 1997We calculate the properties of gamma-ray burst spectral lines formed by resonant cyclotron scattering in a radiation-driven outflow. Most previous models of line formation in gamma-ray bursts are appropriate at the polar cap of a neutron star located ... More

Cyclotron Line Formation in a Relativistic OutflowJan 09 1996There is mounting evidence that, if gamma-ray bursters are Galactic in origin, they are located in a Galactic corona at distances greater than 100 kpc. This has created a need to explore new models of cyclotron line formation. In most previous calculations ... More

A class of solutions to the Einstein equations with AVTD behavior in generalized wave gaugesFeb 09 2016We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the AVTD property, ... More

Momentum Maps and Classical Relativistic Fields. Part I: Covariant Field TheoryJan 16 1998Aug 19 2004This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge transformations ... More

Analysis of Locally Coupled 3D Manipulation Mappings Based on Mobile Device MotionMar 24 2016Jun 02 2017We examine a class of techniques for 3D object manipulation on mobile devices, in which the device's physical motion is applied to 3D objects displayed on the device itself. This "local coupling" between input and display creates specific challenges compared ... More

Non-CMC solutions of the Einstein constraint equations on asymptotically Euclidean manifoldsDec 02 2013In this note we prove two existence theorems for the Einstein constraint equations on asymptotically Euclidean manifolds. The first is for arbitrary mean curvature functions with restrictions on the size of the transverse-traceless data and the non-gravitational ... More

Deriving approximation tolerance constraints from verification runsApr 29 2016May 07 2016Approximate computing (AC) is an emerging paradigm for energy-efficient computation. The basic idea of AC is to sacrifice high precision for low energy by allowing for hardware which only carries out "approximately correct" calculations. For software ... More

On the constraint equations in Einstein-aether theories and the weak gravitational field limitJul 27 2012We discuss the set of constraints for Einstein-aether theories, comparing the flat background case with what is expected when the gravitational fields are dynamic. We note potential pathologies occurring in the weak gravitational field limit for some ... More

Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equationsOct 09 2009We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.