Measuring Resident Attitudes towards Voluntourism: an Analysis of the Social Exchange Theory (SET)

The purpose of this study is to introduce the concept of “voluntourism” and its applicability as an alternative form of tourism due to its ability to combine recreational activities with service and learning. The location and proximity of a local community to tourism practices affect the way in which the community perceives the effects of voluntourism as a whole, which is why importance is placed on the residents’ perceptions and attitudes towards voluntourism through an analysis incorporating the Social Exchange Theory (SET). This study will focus on the perceptions of residents living on Andaman Island in Thailand, an area that was significantly affected by the 2004 Indian Ocean Tsunami

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.Comment: 16 pages, 5 figure

Black hole-neutron star mergers: effects of the orientation of the black hole spin

The spin of black holes in black hole-neutron star (BHNS) binaries can have a strong influence on the merger dynamics and the postmerger state; a wide variety of spin magnitudes and orientations are expected to occur in nature. In this paper, we report the first simulations in full general relativity of BHNS mergers with misaligned black hole spin. We vary the spin magnitude from a/m=0 to a/m=0.9 for aligned cases, and we vary the misalignment angle from 0 to 80 degrees for a/m=0.5. We restrict our study to 3:1 mass ratio systems and use a simple Gamma-law equation of state. We find that the misalignment angle has a strong effect on the mass of the postmerger accretion disk, but only for angles greater than ~ 40 degrees. Although the disk mass varies significantly with spin magnitude and misalignment angle, we find that all disks have very similar lifetimes ~ 100ms. Their thermal and rotational profiles are also very similar. For a misaligned merger, the disk is tilted with respect to the final black hole's spin axis. This will cause the disk to precess, but on a timescale longer than the accretion time. In all cases, we find promising setups for gamma-ray burst production: the disks are hot, thick, and hyperaccreting, and a baryon-clear region exists above the black hole.Comment: 15 pages, 13 figure

Black hole evolution by spectral methods

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast to finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.Comment: 20 pages, 17 figures, submitted to PR

Marching Along : Army Song

https://digitalcommons.library.umaine.edu/mmb-ps/1287/thumbnail.jp

Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit

The increasing sophistication and accuracy of numerical simulations of compact binaries (especially binary black holes) presents the opportunity to test the regime in which post-Newtonian (PN) predictions for the emitted gravitational waves are accurate. In order to confront numerical results with those of post-Newtonian theory, it is convenient to compare multipolar decompositions of the two waveforms. It is pointed out here that the individual modes can be computed to higher post-Newtonian order by examining the radiative multipole moments of the system, rather than by decomposing the 2.5PN polarization waveforms. In particular, the dominant (l = 2, m = 2) mode can be computed to 3PN order. Individual modes are computed to as high a post-Newtonian order as possible given previous post-Newtonian results.Comment: 15 page

Constraints from rocks in the Taiwan orogen on crustal stress levels and rheology

Taiwan's Hsüehshan range experienced penetrative coaxial deformation within and near the brittle-plastic transition between ∼6.5 and 3 Ma. This recent and short-lasting deformation in an active, well-studied orogen makes it an ideal natural laboratory for studying crustal rheology. Recrystallized grain size piezometry in quartz and Ti-in-quartz thermobarometry yield peak differential stresses of ∼200 MPa at 250–300°C that taper off to ∼80 MPa at ∼350°C and ∼14 MPa at ∼400–500°C. Stress results do not vary with lithology: recrystallized quartz veins in slates and metasiltstones yield equivalent stresses as recrystallized grains in quartzites. A minimum strain rate of 2.9 × 10^(−15) s^(−1) associated with this deformation is calculated by dividing a strain measurement (axial strain ∼0.3) in a strongly deformed quartzite by the available 3.5 m.y. deformation interval. We estimate a maximum strain rate of 7.0 × 10^(−14) s^(−1) by distributing the geodetic convergence rate throughout a region homogeneously deformed under horizontal compression. These stress, strain rate and temperature estimates are consistent with the predictions of widely applied dislocation creep flow laws for quartzite. The samples record stress levels at the brittle-plastic transition, indicating a coefficient of friction (μ) of 0.37 in the upper crust consistent with results based on critical taper. Integrated crustal strength of the Hsüehshan range amounts to 1.7 × 10^(12) N/m based on our analysis, consistent with potential energy constraints based on topography. Other strength profiles are considered, however high crustal stresses (>300 MPa) conflict with our analysis. The study supports the use of the recrystallized grain size piezometer in quartz as a quick and inexpensive method for resolving stress histories in greenschist facies rocks. For consistency with the independent constraints presented here, we find it accurate to within +20%/−40%, significantly better than previously recognized

Einstein boundary conditions for the 3+1 Einstein equations

In the 3+1 framework of the Einstein equations for the case of vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space-derivatives of the intrinsic metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields.Comment: Revtex 4, 6 pages, text and references added, typos corrected, to appear in Phys. Rev.

Ruling Out Chaos in Compact Binary Systems

We investigate the orbits of compact binary systems during the final inspiral period before coalescence by integrating numerically the second-order post-Newtonian equations of motion. We include spin-orbit and spin-spin coupling terms, which, according to a recent study by Levin [J. Levin, Phys. Rev. Lett. 84, 3515 (2000)], may cause the orbits to become chaotic. To examine this claim, we study the divergence of initially nearby phase-space trajectories and attempt to measure the Lyapunov exponent gamma. Even for systems with maximally spinning objects and large spin-orbit misalignment angles, we find no chaotic behavior. For all the systems we consider, we can place a strict lower limit on the divergence time t_L=1/gamma that is many times greater than the typical inspiral time, suggesting that chaos should not adversely affect the detection of inspiral events by upcoming gravitational-wave detectors.Comment: 8 pages, 4 figures, submitted to Phys. Rev. Let

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review