25,868 research outputs found
Pascalâs wager: tracking an intended reader in the structure of the argument
Pascalâs wager is the name of an argument in favor of belief in God presented by Blaise Pascal in §233 of Thoughts. Ian Hacking (1972) pointed out that Pascalâs text involves three different versions of the argument. This paper proceeds from this identification, but it concerns an examination of the rhetorical strategy realized by Pascalâs argumentation. The final form of Pascalâs argument is considered as a product that could be established only through a specific process of persuasion led with respect to an intended reader with a particular set of initial beliefs. The text uses insights from the pragmaâdialectical approach to argumentation, especially the concept of rhetorical effectiveness of particular choices from the topical potential. The argumentation structure of Pascalâs wager is considered to be a reflection of the anticipated course of dialogue with the reader critically testing the sustainability of Pascalâs standpoint âYou should believe in Godâ. Based on the argumentation reconstruction of three versions of the argument, Pascalâs idea of opponent/audience is identified. A rhetorical analysis of the effects of his argumentative strategy is proposed. The analysis is based on two perspectives on Pascalâs argument: it examines the strategy implemented consistently by all arguments and the strategy of a formulation of different versions of the wager
Towards a cross-correlation approach to strong-field dynamics in Black Hole spacetimes
The qualitative and quantitative understanding of near-horizon gravitational
dynamics in the strong-field regime represents a challenge both at a
fundamental level and in astrophysical applications. Recent advances in
numerical relativity and in the geometric characterization of black hole
horizons open new conceptual and technical avenues into the problem. We discuss
here a research methodology in which spacetime dynamics is probed through the
cross-correlation of geometric quantities constructed on the black hole horizon
and on null infinity. These two hypersurfaces respond to evolving gravitational
fields in the bulk, providing canonical "test screens" in a "scattering"-like
perspective onto spacetime dynamics. More specifically, we adopt a 3+1 Initial
Value Problem approach to the construction of generic spacetimes and discuss
the role and properties of dynamical trapping horizons as canonical inner
"screens" in this context. We apply these ideas and techniques to the study of
the recoil dynamics in post-merger binary black holes, an important issue in
supermassive galactic black hole mergers.Comment: 16 pages, 5 figures, contribution to the proceedings volume of the
Spanish Relativity Meeting ERE2011: "Towards new paradigms", Madrid, Spain,
29 Aug-2 Sep 201
Cylindrically symmetric Greenâs function approach for modeling the crystal growth morphology of ice
We describe a front-tracking Greenâs function approach to modeling cylindrically symmetric crystal growth. This method is simple to implement, and with little computer power can adequately model a wide range of physical situations. We apply the method to modeling the hexagonal prism growth of ice crystals, which is governed primarily by diffusion along with anisotropic surface kinetic processes. From ice crystal growth observations in air, we derive measurements of the kinetic growth coefficients for the basal and prism faces as a function of temperature, for supersaturations near the water saturation level. These measurements are interpreted in the context of a model for the nucleation and growth of ice, in which the growth dynamics are dominated by the structure of a disordered layer on the ice surfaces
A Dynamic Game Model of Collective Choice in Multi-Agent Systems
Inspired by successful biological collective decision mechanisms such as
honey bees searching for a new colony or the collective navigation of fish
schools, we consider a mean field games (MFG)-like scenario where a large
number of agents have to make a choice among a set of different potential
target destinations. Each individual both influences and is influenced by the
group's decision, as well as the mean trajectory of all the agents. The model
can be interpreted as a stylized version of opinion crystallization in an
election for example. The agents' biases are dictated first by their initial
spatial position and, in a subsequent generalization of the model, by a
combination of initial position and a priori individual preference. The agents
have linear dynamics and are coupled through a modified form of quadratic cost.
Fixed point based finite population equilibrium conditions are identified and
associated existence conditions are established. In general multiple equilibria
may exist and the agents need to know all initial conditions to compute them
precisely. However, as the number of agents increases sufficiently, we show
that 1) the computed fixed point equilibria qualify as epsilon Nash equilibria,
2) agents no longer require all initial conditions to compute the equilibria
but rather can do so based on a representative probability distribution of
these conditions now viewed as random variables. Numerical results are
reported
Solving Einstein's Equations With Dual Coordinate Frames
A method is introduced for solving Einstein's equations using two distinct
coordinate systems. The coordinate basis vectors associated with one system are
used to project out components of the metric and other fields, in analogy with
the way fields are projected onto an orthonormal tetrad basis. These field
components are then determined as functions of a second independent coordinate
system. The transformation to the second coordinate system can be thought of as
a mapping from the original ``inertial'' coordinate system to the computational
domain. This dual-coordinate method is used to perform stable numerical
evolutions of a black-hole spacetime using the generalized harmonic form of
Einstein's equations in coordinates that rotate with respect to the inertial
frame at infinity; such evolutions are found to be generically unstable using a
single rotating coordinate frame. The dual-coordinate method is also used here
to evolve binary black-hole spacetimes for several orbits. The great
flexibility of this method allows comoving coordinates to be adjusted with a
feedback control system that keeps the excision boundaries of the holes within
their respective apparent horizons.Comment: Updated to agree with published versio
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