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author | bnewbold <bnewbold@eta.mit.edu> | 2009-01-16 04:29:16 -0500 |
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committer | bnewbold <bnewbold@eta.mit.edu> | 2009-01-16 04:29:16 -0500 |
commit | df1d1038048c1db7e1f7c2436993c3017de2542a (patch) | |
tree | f402fa51f4480437585e3363ff862f9c08bb7946 /proposal | |
download | 8thesis-df1d1038048c1db7e1f7c2436993c3017de2542a.tar.gz 8thesis-df1d1038048c1db7e1f7c2436993c3017de2542a.zip |
initial import of existing content
Diffstat (limited to 'proposal')
-rw-r--r-- | proposal/bnewbold_8thesis_proposal.lyx | 146 | ||||
-rw-r--r-- | proposal/bnewbold_8thesis_proposal.pdf | bin | 0 -> 45946 bytes | |||
-rw-r--r-- | proposal/bnewbold_8thesis_proposal.skel.pdf | bin | 0 -> 42278 bytes |
3 files changed, 146 insertions, 0 deletions
diff --git a/proposal/bnewbold_8thesis_proposal.lyx b/proposal/bnewbold_8thesis_proposal.lyx new file mode 100644 index 0000000..708b44d --- /dev/null +++ b/proposal/bnewbold_8thesis_proposal.lyx @@ -0,0 +1,146 @@ +#LyX 1.5.2 created this file. For more info see http://www.lyx.org/ +\lyxformat 276 +\begin_document +\begin_header +\textclass article +\language english +\inputencoding auto +\font_roman default +\font_sans default +\font_typewriter default +\font_default_family default +\font_sc false +\font_osf false +\font_sf_scale 100 +\font_tt_scale 100 +\graphics default +\paperfontsize default +\papersize default +\use_geometry false +\use_amsmath 1 +\use_esint 1 +\cite_engine basic +\use_bibtopic false +\paperorientation portrait +\secnumdepth 3 +\tocdepth 3 +\paragraph_separation indent +\defskip medskip +\quotes_language english +\papercolumns 1 +\papersides 1 +\paperpagestyle default +\tracking_changes false +\output_changes false +\author "" +\author "" +\end_header + +\begin_body + +\begin_layout Title +A Computational Elucidation of Curved Spacetime +\end_layout + +\begin_layout Date +\begin_inset Formula $\today$ +\end_inset + + +\end_layout + +\begin_layout Author +Bryan Newbold +\end_layout + +\begin_layout Quotation +Advisor: Prof. + Gerald J. + Sussman, EECS +\end_layout + +\begin_layout Standard +I propose to implement a geometric formulation of curved space time in a + functional computer programming language, and to explore the space of simulatio +ns and manipulations made possible by such a formulation. + A primary motivation is to state the foundations of General Relativity + in a non-ambiguous manner. + +\end_layout + +\begin_layout Standard +This work follows several attempts to formulate curved spacetime on computers + for the purpose of numerical calculations and algebraic manipulation. + Most of these packages are specially designed for the tasks of tensor analysis + and/or efficient numerical calculation, as is appropriate for use in calculatio +ns. + A crucial difference of this proposed work will be to carefully build up + the geometric and analytical tools in a general purpose functional programing + language (mit-scheme). + As a learning and reference tool, this will allow users to explore the + inner workings and structure of the system, which I believe is essential + to understanding the system as a whole. + +\end_layout + +\begin_layout Standard +The frame field representation will be used to emphasize the geometric propertie +s of curved space time, as opposed to the more traditional coordinate heavy + tensor analysis approach. +\end_layout + +\begin_layout Standard +The resulting work will include a full implementation with source code and + documentation, as well as example problems and qualitative comparisons + with existing packages and software systems. +\end_layout + +\begin_layout Bibliography +\begin_inset LatexCommand bibitem +key "key-1" + +\end_inset + +Functional Differential Geometry, G. + Sussman and J. + Wisdom (2005) +\end_layout + +\begin_layout Bibliography +\begin_inset LatexCommand bibitem +key "key-2" + +\end_inset + +Structure and Interpretation of Classical Mechanics, G. + Sussman and J. + Wisdom (2001) +\end_layout + +\begin_layout Bibliography +\begin_inset LatexCommand bibitem +key "key-1" + +\end_inset + +"Algebraic Computing in General Relativity", Ray d'Inverno (from General + Relativity, G. + Hall and J. + Pulham) +\end_layout + +\begin_layout Bibliography +\begin_inset LatexCommand bibitem +key "key-2" + +\end_inset + +"The Use of Algebraic Computing in General Relativity", H. + I. + Cohen, A. + Leringe and Y. + Sundblad +\end_layout + +\end_body +\end_document diff --git a/proposal/bnewbold_8thesis_proposal.pdf b/proposal/bnewbold_8thesis_proposal.pdf Binary files differnew file mode 100644 index 0000000..095e7ce --- /dev/null +++ b/proposal/bnewbold_8thesis_proposal.pdf diff --git a/proposal/bnewbold_8thesis_proposal.skel.pdf b/proposal/bnewbold_8thesis_proposal.skel.pdf Binary files differnew file mode 100644 index 0000000..b9d2632 --- /dev/null +++ b/proposal/bnewbold_8thesis_proposal.skel.pdf |