It is safe to say that almost every practicing
scientist today uses a computer. Many use
the computer to develop models, even among
experimentalists. How many program such models
efficiently? What does it mean to program
efficiently, from a scientific point-of-view?
How many are simply patching old code that
has become somewhat worn out?
In a recent survey
[2][3] most respondents claimed to spend
about 15 hours a week developing software
and 20 hours a week using it; accounting
for about 70% of their time. Almost half
claim that they spend more time developing
software now than they did five years ago,
and 70% claim that they spend much more time
using it. More than half reported developing
their own software, while 35% reported working
in groups of up to five people. The primary
hardware are desktop machines and small clusters
running small codes (usually less than 5000
lines of code) and most time is spent on
coding and debugging. The biggest complaint
is poor documentation. The biggest worry
is that people are not sure how to verify
their code, and second is that they do not
know how to produce the most efficient code.
The vast majority of scientists have little
or no formal training in software design,
nor do they feel that they have the time
to acquire it; they take an informal, self-study
approach to the problem.
The bottom line of
all of this is that most scientists use computers
at a fundamentally primitive level. This
impedes what work can be done through self-limitation
in the scope of work believed possible, in
the choice of methods to attack problems,
and in the tools to implement those methods.
What is needed is
a way to produce top-quality research in
the methods of scientific computation, ways
to implement these methods that are as close
to platform independent as possible, the
application of such implementation to problems
of scientific interest, the dissemination
of these ideas to the scientific clients
of such work, and the education of existing
and future scientists in them.
The purpose of a scientific computation institute
is to bring together experts in software
design, mathematical and computational methods,
and application fields into one place where
they can discuss their respective issues,
apply their respective talents, and solve
problems of mutual interest. The emphasis
is on solving scientific problems through
computational means. Some of the participants
should be from industry, some from government,
some from academe, and some from the public
at large. A non-profit organization is ideally
suited for the task of merging these disparate
populations.
The goal of such
an institute should be the development of
research in both applications and methods,
and the development of educational and operational
resources for the individual scientist. This
will result in a set of deliverables. Some
deliverables will be research and review
papers. Some will be tutorials in the effective
use of software, hardware, specific computational
methods, specific mathematical methods, and
specific methods that are applied to specific
problems. All of these will be available
on the Internet through a dedicated web site.
The institute will also provide several services:
Courses, both in-person and over the web, to teach basic and advanced techniques in Mathematica, heuristics, algorithm development, software development, research methodology, computational techniques for specific types of problems, and mathematical/scientific principles relevant to specific types of problems.
A Summer School to teach effective programming, heuristics, methodology, and research. To go to the Summer School web site, click here.
Summer Internships to bring in students from among high school seniors, undergraduate and graduate intuitions of higher learning (both foreign and domestic) to teach them to operate and develop software effectively, and to provide them with solid research experience. This will include frequent meetings for discussing research problems.
Year-long internships for members of the general public (Citizen Scientists, as they are called), recent graduates and post-docs, and professional scientists, mathematicians, and engineers, to provide more substantial research opportunities.
Madison Area Science and Technology (MAST) is a not-for-profit scientific research and education organization that was established in 1999. During the last eleven years we have worked with government (the National Weather Service and local emergency management agencies), industry, and academic institutions. The senior personnel of MAST have extensive computational experience in a wide range of applications and methods. All senior personnel have years of programming experience in Mathematica.
MAST has chosen to use Mathematica, produced by Wolfram Research, as its primary software development system.
While the list of interesting problems that can be addressed by such a group as the MAST-ISC is almost endless, there are some problems that are of particular interest to our staff. The problems we can address are also chosen as those that can be explored effectively with desktop work stations, small clusters, and GPU-equipped systems; we are not in competition with supercomputer centers.
Compact objects are white dwarf stars, neutron stars, and black holes. They are interesting because of the incredible states of compression of the matter that form them. White dwarfs experience electron degeneracy, neutron stars experience neutron degeneracy and the possibility of quark matter phase transitions at their cores, and black holes experience a compression that holds out the possibility of the matter within them being crushed out of physical existence through an artifact called a singularity. There are several good texts on compact objects that we use [7][8][9][10] [11][12][13][14]. Here are some specific problems of interest:
The equation of state for neutron star matter and neutron star structure [15], [16].
Neutron star propulsion.
The process of neutron star formation [17].
Black hole formation [18].
The fate of matter falling into a black hole [19].
Scattering of waves by black holes [20].
Whether in diffuse matter in the interstellar medium, a blast wave in a fluid, or a compression wave in a dense solid, shock waves are a discontinuity that propagates through the medium within which they travel. There are several good texts on shock waves that we use [21][22][23][24]. Here are some specific problems of interest:
Shock wave dynamics in condensed and diffuse matter [25].
Detonation dynamics [26].
Shock waves in curved spacetimes [27].
Fluids account for as much as three quarters of the states of matter in the universe. If we include exotic states such a superfluid vortices, quantum gauge hydrodynamics, and treating the matter in the early universe as a hot-dense plasma, fluid models are finding wide application. There are several good texts on fluid dynamics that we use [28][29][30][31][32][33][34][35][36]. Here are some specific problems of interest:
Specialized hydrocodes for various purposes [4].
Thunderstorm modeling [37].
Tornado modeling [38].
Accretion disk modeling [39][40][41][42].
Asteroid impact dynamics [43].
Underwater oil leakage plume dynamics [43].
Pyroclastic flow dynamics [43].
Dynamical systems are systems that exhibit change with respect to a parameter, such as time. Chaotic dynamical systems exhibit chaotic change, that is they have a positive Lyapunov exponent, or they have a strange attractor. There are several good texts on dynamical systems and chaos theory that we use [44][45][46][47][48][49][50][51][52][53]. Here are some specific problems of interest:
Calculating Lyapunov exponents form first principles [54].
Differential equations and analysis on fractals [55][56].
The interaction between objects, on whatever scale, comes down to scattering cross sections for impact and absorption. The applications of scattering theory are very important and range from CT scan data analysis, to sonar and radar theory, to collider theory. There are several good texts on scattering theory that we use [57][58][59][60][61][62]. Here are some specific problems of interest:
The role of time delay in quantum scattering [63].
Scattering theory and unitary operators, orthogonal polynomials, and CMV matrices [64][65][66][67].
Casimir theory using scattering amplitudes [68].
Compton scattering in the astrophysical context [69].
Application of scattering theory to mesoscopic circuit dynamics [70].
Inverse scattering through the Lippmann-Schwinger equation [71][72][73].
Quantum computers hold a great deal of promise due to quantum effects, such as the superposition of states, should the problems of quantum algorithm design be overcome. There are several good texts on quantum computing that we use [74][75][76][77][78]. Here is a specific problem of interest:
Developing a quantum computer simulator [75][79][80].
Bioinformatics is the application of mathematical and computational tools to problems in molecular biology. One area of development is the incorporation of statistical mechanical ideas into bioinformatics, specifically the idea of entropy of information channels. Biophysics is the application of existing physics to biological systems and the invention of new physics based on biological systems. There are several good texts on bioinformatics and biophysics that we use [81][82][83][84][85]. Here are some specific problems of interest:
Computational modeling of HIV-therapy schemes [43].
Emergence of complexity [86].
Predicting the distribution of species [43].
Correlation of descent order genomic segments in viruses with their database accession date. [43].
Bayesian phylogenetic methods of cancer diagnosis given publicly available blood serum protein mass spectrometry data [43].
Bayesian neural network methods for diagnosing cancer based on micrographs [43].
Most of the application of mathematics to the sciences is in the form of differential equations. We intend to develop symbolic and numerical methods of solving, approximating solutions, and estimating solutions of ODEs and PDEs. There are several good texts on ODEs and PDEs that we use [87][88][89][90][91][92][93][94][05][96][97][98][99]. Here are some specific problems of interest:
Apply techniques arising from partial Fourier transforms [100].
Devise tests to determine solvability or non-solvability of operators [101][102][103][104][105].
Automation of integral estimation [106][107].
ODE solution methods [108][109].
Complete integrability [110][111][112][113][114].
Linearizability [115][116][117][118].
Geometry of ODEs [119][120].
Solution methods for PDEs [121].
Time series analysis of dinosaur extinction.
MAST expects to produce the following deliverables over the course of its first year:
Calculus tutorial for High School seniors and Citizen Scientists.
Mathematica tutorials, classes, and online videos for those not familiar with it.
Mathematical tutorials covering ODEs, linear algebra, PDEs, and numerical methods.
Proceedings of the Summer School.
These materials will be made available on the web and in hard copy through the Lulu print-on-demand publishing service. Development will not be limited to these, as all discussion sessions will be recorded and transcribed, and additional tutorials and writing will be developed as required.
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[2] Greg Wilson, (2009), "How Do Scientists Really Use Computers?", American Scientist, online at http://www.americanscientist.org/issues/pub/2009/5/how-do-scientists-really-use-computers/1.
[3] Jo Erskine Hannay, Carolyn MacLeod, Janice Singer, Hans Petter Langtangen, Dietmar Pfahl, Greg Wilson, "How do scientists develop and use scientific software?", Proceedings of the 2009 ICSE Workshop on Software Engineering for Computational Science and Engineering.
[4] George E. Hrabovsky, (2010), A Mathematica-Based Hydrodynamics Model, Proceedings of the 2010 International Conference on Scientific Computing, WorldComp 2010, Las Vegas, NV.
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[9] Norman K. Glendenning, (2007), Special and General Relativity With Applications to White Dwarfs, Neutron Stars, and Black Holes, Springer-Verlag, New York, Inc.
[10] Andreas Schmitt, (2010), Dense matter in compact stars—A pedagogical introduction—, arXiv:1001.3294v1 [astro-ph.SR].
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[17] Hans-Thomas Janka, (2004), "Neutron Star Formation and Birth Properties," Young Neutron Stars and Their Environments, IAU Symposium, Vol. 218, 2004, F. Camilo and B. M. Gaensler, eds.
[18] Yuichiro Sekiguchi, Masaru Shibata, (2010), "Formation of black hole and accretion disk in collapsar," arXiv:1009.5303v1 [astro-ph.HE].
[19] Shuang Nan Zhang, Yuan Liu, (2008), "Observe matter falling into a black hole," AIPConf. Proc.968:384-391, arXiv:0710.2443v1 [astro-ph].
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[38] D. C. Lewellen, W. S. Lewllen, (2007), "Near-Surface Intensification of Tornado Vortices", J. Atmos. Sci 64, 2176-2194.
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[43] Jack K. Horner, (2010), Private conversation.
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[45] John Guckenheimer, Philip Holmes, (1983), Nonlinear Oscilaltions, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, Inc.
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[48] Jun Kigami, (2001), Analysis on Fractals, Cambridge University Press.
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[50] Robert Herman, (1991), Geometric Structures in Nonlinear Physics, Math Sci Press.
[51] Tsutomu Kambe, (2004), Geometrical Theory of Dynamical Systems and Fluid Flows, World Scientific Publishing Pte. Ltd.
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[53] Robert Gilmore, Christophe Letellier, (2007), The Symmetry of Chaos, Oxford University Press, Inc.
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[55] Robert S. Strichartz, (2006), Differential Equations on Fractals A Tutorial, Princeton University Press.
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[58] Roy Pike, Pierre Sabatier, (2002), Scattering I, Academic Press, Inc.
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[60] Leung Tsang, Jin Au Kong, Kung-Hau Ding, (2000), Scattering of Electromagnetic Waves: Theories and Applications, John Wiley & Sons, Inc.
[61] Leung Tsang, Jin Au Kong, Kung-Hau Ding, Chi On Ao, (2001), Scattering of Electromagnetic Waves: Numerical Solutions, John Wiley & Sons, Inc.
[62] Leung Tsang, Jin Au Kong, (2001), Scattering of Electromagnetic Waves: Advanced Topics, John Wiley & Sons, Inc.
[63] S. Richard, R. Tiedra de Aldecoa, (2010), "Time delay is a common feature of quantum scattering theory," arXiv:1008.3433v1 [math-ph].
[64] M. J. Cantero, L. Moral, L. Velazquez, (2004), "Minimal representations of unitary operators and orthogonal polynomials on the unit circle," arXiv:math/0405246v1 [math.CA].
[65] Irina Nenciu, (2006), "CMV matrices in random matrix theory and integrable systems: a survey,"J. Phys. A: Math. Gen. 39 (2006), 8811--8822.
[66] Barry Simon, (2006), "CMV matrices: Five years after,"arXiv:math/0603093v1 [math.SP].
[67] L. Golinskii, A. Kheifets, F. Peherstorfer, P. Yuditskii, (2010), "Scattering theory for CMV matrices: uniqueness, Helson--Szegö and Strong Szegö theorems," arXiv:1008.3284v1 [math.SP].
[68] Sahand Jamal Rahi, Thorsten Emig, Robert L. Jaffe, (2010), "Geometry and material effects in Casimir physics - Scattering theory," arXiv:1007.4355v1 [quant-ph]
[69] Juri Poutanen, Indrek Vurm, (2010), "Theory of Compton scattering by anisotropic electrons," Astrophys. J. Suppl. Ser.,189:286-308, 2010.
[70] Vered Ben-Moshe, Dhurba Rai, Spiros S. Skourtis, Abraham Nitzan, (2010), "Steady state current transfer and scattering theory." arXiv:1002.2775v1 [cond-mat.mes-hall].
[71] Christopher J. Winfield, (2005), "A study of resolvent and spectra for some unbounded quantum potentials," Rocky Mountain Journal of Mathematics vol. 35 (4).
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[123] Douglas Poole, Willy Hereman, (2010), "Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions," arXiv:1007.5119v1 [nlin.SI].
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