Physics 640:
Scientific Computation and Visualization
Prof.
http://www.faculty.umb.edu/tomas_materdey/640
Fall ’08 Syllabus
Week 1 & 2:
-Introduction
to Matlab and the Fast Fourier Transform (FFT)
*Matlab, FFT, noise elimination in
signal processing
*Discrete-time Fourier Transform in Fortran
Project 1:
a) Write a code
to look at the real and imaginary parts of the FFT of a sum signal of two
sinusoids of different frequencies; eliminate the high frequency portion of the
spectrum, then show plots of the inverse transforms (IFFT) of the real parts
and the imaginary parts. Explain what was the difference
versus doing the inverse transform on the direct transform without separating
the real and imaginary parts.
b) Use a
low-pass filter on the spectrum of a signal with white noise added (SNR=2,
ratio of amplitudes) to recover the original signal without noise. Repeat for
SNR=1. Show with plots what did you obtain; is it important to have a minimum
number of points of the signal?
c) Write a Fortran code to do the discrete-time Fourier Transform of a
sum of two sinusoids of different frequencies. Get the output file from the
UNIX machine and show the plots using Matlab.
Links: Fortran Standard; Example of a fortran code (FDTD2D)
Bibliography:
1.- Duhamel, P.; Vetterli, M.:
"Fast Fourier transforms: a tutorial review and a state of the art",
Signal Process. 19 (1990), no. 4, 259--299.
MR91a:94004
2.- Oppenheim and Willsky, Signals
and Systems 2ed, Prentice Hall; ISBN: 0-13-814757-4, Chapters 3-5
3.- Kamen and Heck, Fundamentals of
Signals and Systems, Prentice Hall, chapters 4 and 7
http://users.ece.gatech.edu/~bonnie/book/
4.- Wavelet Online: http://www.wavelet.org
5.- H.D. Knoble, Fortran Resources,
http://www.personal.psu.edu/faculty/h/d/hdk/fortran.html
6.- Open Directory Project, Fortran
Source Codes and More: http://www.dmoz.org/Computers/Programming/Languages/Fortran
Week 3 & 4
-Introduction
to numerical algorithms
-Finite-Difference
in the
-Finite-Difference
in the
-Implementation
of a FDTD code in Fortran:
Project 2:
a)
Develop
a Fortran code to propagate a sinusoid or a Gaussian pulse in 1D, save outputs
into a file
b)
Show
the animations using Matlab
Bilbiography:
1.-
A. Taflove and S. C.
Hagness, Computational
Electrodynamics: The Finite-Difference Time-Domain
Method, 3rd ed.
2.- D.M. Sullivan, Electromagnetic
Simulation Using the FDTD Method , IEEE Press
3.- K. S. Yee, ``Numerical solution of
initial boundary value problems involving Maxwell's equations in isotropic
media,'' IEEE Trans. Antennas Propagat., vol. AP-14, no. 4, pp.
302--307, 1966.
4.- A. Taflove
and M. E. Brodwin, "Numerical
solution of steady-state electromagnetic
scattering problems using the time-dependent
Maxwell's equations," IEEE Trans. Microwave Theory and Techniques, vol.
23, pp. 623-630,
Aug. 1975. (Download Paper2.pdf )
5.- A. Taflove
and K. R. Umashankar, "Solution
of Complex Electromagnetic Penetration and
Scattering Problems in Unbounded Regions," pp.
83-113 in Computational Methods for Infinite Domain
Media-Structure Interactions, American Society of
Mechanical Engineers, AMD vol. 46 (1981).
6.-V. Sathiaseelan,
B. B. Mittal, A.
J. Fenn, and A. Taflove, "Recent Advances in
External Electromagnetic Hyperthermia," Chap. 10 in Advances in Radiation
Therapy, B. B. Mittal, J.
A. Purdy, and K. K. Ang, eds. (Cancer Treatment and
Research, S. T. Rosen,
series ed.)
Week 5 & 6:
-Absorbing
Boundary Conditions in FDTD
Example Program
FDTD2D
Project 3:
a)
Run
and visualize results from the FDTD2D programs AND
b)
Feed
a correct mode for two parallel dielectric waveguides, observe wave
coupling OR
c)
FDTD1D for EM waves
with ABC and implement a two and three media, should see reflection(s) and
transmission(s) (FDTD can handle any number of media we may have). Implement a
“perfectly absorbing layer”.
Bibliography:
1.-D. Marcuse, Theory
of Dielectric Optical Waveguides
2.-B. Engquist and A. Majda, ``Absorbing boundary conditions
for the numerical simulation of waves,'' Math. Comp., vol. 31, pp. 629--651, 1977.
3.-E. L. Lindman, ````Free-space'' boundary conditions for
the time dependent wave equation,'' J. Comput. Phys., vol. 18, pp. 67--78, 1975.
4.-G. Mur, ``Absorbing boundary conditions for the
finite-difference approximation of the time-domain electromagnetic-field
equations,'' IEEE Trans. Electromagn. Compat., vol. EMC-23, no. 4, pp.
377--382, 1981.
5.-R. L. Higdon, ``Absorbing boundary conditions for
difference approximations to the multi-dimensional wave equations,'' Math. Comput., vol.
47, no. 176, pp. 437--459, 1986.
6.-R. L. Higdon, ``Numerical absorbing boundary conditions
for the wave equation,'' Math. Comput., vol. 49, no. 179, pp. 65--90, 1987.
Week 7 & 8:
-Introduction
to Molecular Dynamics/Metropolis Algorithm/Monte Carlo
Project 4:
a)
Molecular
interactions, execute the Example Program MolDyn for
several particles with different initial conditions, is there low or high
sensitivity on these conditions? Use output files to visualize animations of
particle motions using Matlab.
b)
Execute
an example program based on the Metropolis
algorithm, varying on or two parameters, present results using Matlab
Bibliography:
1.-F. Ercolessi, A Molecular Dynamics
Primer, http://www.fisica.uniud.it/~ercolessi/
2.-M. Field, A Practical Introduction to the Simulation of Molecular Systems
3.-N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H.
Teller and E. Teller, (1953) J. Chem. Phys. 21, 1087-1092.
4.-Z.Q. Li and H.A. Scheraga, (1987) Proc. Natl. Acad.
Sci. USA 84, 6611-6615.
5.-Rasmussen, J. L. (1984). A Fortran
program for statistical evaluation of pseudorandom number generators. Behavior
Research Methods and Instrumentation, 16, 63-64.
6.-The Basics of Monte Carlo Simulations:
http://www.cs.cornell.edu/jwoller/samples/montecarlo/default.html
Week 9 & 10:
-Introduction
to time-frequency analysis: Wigner function and wavelets
Project 5:
a)
Develop
a Matlab code that allows you to recognize a vowel from a recording (wav file) using the
Wigner transform.
b)
Write
a Matlab code to demonstrate the advantage of using wavelet transform versus
Fourier transform in signal recovery
Matlab code to
calculate the Wigner
function; and wavelet
subroutines will be available
c)
Modify
a Fortran code for the Mandelbrot fractals, visualize the self-similarity
effect using Matlab
Matlab code to
calculate the Wigner
function; and wavelet
subroutines will be available
Bibliography:
[1] Rabiner and Juang, Fundamentals of Speech Recognition,
Prentice Hall, 1993
[2] Rabiner, L.R., and Levinson, S.E., Isolated and Connected Word Recognition
–Theory and Selected Applications, IEEE Trans. Communications, COM-29 (5),
pp. 621-659, May 1981
[3] Rabiner and
Schafer, Digital Processing of Speech
Signals, Prentice Hall, 1978
[4] Atal, B.S., and Hanauer, S.L., Speech Analysis and Synthesis by Linear
Prediction of the Speech Wave, J. Acoust. Soc. Am., 50 (2), pp. 637-655,
August 1971.
[5] Meeklenbrauker and
Hlawatsch, The Wigner Distribution,
Elsevier, 1997
[6] Wigner, E.P., Phys.
Rev. 40, pp.749-759, 1932
[7] Cohen, L., Time-Frequency Analysis, Prentice Hall,
1995
[8] Allen, J.B., Application of Short-Time Fourier Transform
to Speech Processing and Spectral Analysis, IEEE Int. Conf. On Acoustics,
Speech and Sig. Proc., pp 1012-1015, Paris, France, May 1982
[9] Boashash,B., Note on the Use of the Wigner Distribution for
[10] Bouachache,B., and
Rodriguez, F., Recognition of
Time-Varying Signals in the Time-Frequency Domain by Means of the Wigner
Function, IEEE Int. Conf. On Acoustics, Speech, and Sig. Proc., pp. 2251-2254,
San Diego, CA, 1984
[11] Materdey, T. and
Seyler, C., Int. J. Modern Physics B, vol. 17, no. 25, 4555
(2003)
[12] Materdey, T. and
Seyler, C., Int. J. Modern Physics B, vol. 17, no. 26, 4683
(2003)
[13] Materdey, T. The Wigner Function as a
Voice Identification Tool, Interactive Demo, IEEE Vis 2002,
[14] Rumelhart, D.E. and McCleland, J.L., eds., Parallel Distributed Processing: Learning
Internal Representations by Error Propagations,
[15] Sejnowski, T.J., and
[16]
Mitchell, P., Fortran-77 Neural
Network Simulator (F77NNS) User Guide, Cosmic program #MSC-21638, National
Aeronautics and Space Administration, 1987
[17]
Lippmann, R., An Introduction to
Computing with Neural Nets, IEEE ASSP Mag., 4 (2), pp. 4-22, April 1987.
[18]
Weibel, A., Hanazawa, T., Hinton, G., Shikano, K., Lang, K.J., Phoneme Recognition Using
Week 11-14:
Numerical
Projects in Biology/Chemistry/Physics/Engineering
-Week 11: Topic selection and background information
research
-Week 12-13: Project performance
-Week 14: Result visualizations, presentations, and
conclusions
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Springer-Verlag (1994).
2.-
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Biotechnol 94(1): 37-63.
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5.- Tesfatsion, L. (2002).
"Agent-based computational economics: growing economies from the bottom
up." Artif Life 8(1): 55-82.
6.- Sun, W. and P. Lal (2002).
"Recent development on computer aided tissue engineering--a review."
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7.- Sardari, S. and D. Sardari
(2002). "Applications of artificial neural network in
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of 'drug-like' molecules." Curr Opin Biotechnol 11(1): 104-7.
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(2000). "Computational methods for the structural
alignment of molecules." J Comput Aided Mol Des 14(3): 215-32.
11.- Botta, M., F. Corelli, et al.
(2002). "Molecular modeling as a powerful technique for
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153-65.
12.- Noble, D. (2002). "Modeling the heart--from genes to cells to the whole
organ." Science 295(5560): 1678-82.
13.- McKenzie, F. E. (2000).
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14.- Neptune, R. R. (2000). "Computer modeling and simulation of human movement. Applications in sport and rehabilitation." Phys Med
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15.- Pandy, M. G. (2001). "Computer modeling and simulation of human movement."
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16.- Weiss, J. A. and J. C.
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(2000). "Brain biomechanics: mathematical modeling of hydrocephalus."
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20.- Bornholdt, S. (2001). "Modeling genetic networks and their evolution: a complex
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21.- Klonowski, W. (2001). "Non-equilibrium proteins." Comput Chem 25(4):
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22.- Loew, L. M. and J. C. Schaff
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25.- Morgan, J. A. and D. Rhodes
(2002). "Mathematical modeling of plant metabolic
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26.- Neves, S. R. and R. Iyengar
(2002). "Modeling of signaling networks."
Bioessays 24(12): 1110-7.