Physics 640: Scientific Computation and Visualization

Prof. Tomas Materdey

http://www.faculty.umb.edu/tomas_materdey/640

Fall ’011 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)

Notes 1

 

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 Time-Domain (FDTD) and the numerical solution of wave equations in 1D

-Finite-Difference in the Time-Domain (FDTD) and the numerical solution of Maxwell’s equations in 2D

-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

Notes 2

 

Bilbiography:

1.- A.  Taflove  and  S.  C.  Hagness,  Computational  Electrodynamics:  The  Finite-Difference  Time-Domain  Method,  3rd  ed.   Norwood,  MAArtech  House,  2005.

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.)    Dordrecht,  Netherlands:  Kluwer  (1998).

 

Week 5 & 6:

-Absorbing Boundary Conditions in FDTD

Example Program FDTD2D

 

Project 3:

a)      1)Run and visualize results from the FDTD2D programs for some input file; 2) Implement FDTD1D with 2 and 3 media with ABC    AND

b)      Feed a correct mode for two parallel dielectric waveguides, observe wave coupling  OR

c)      Write a FDTD 2D code for wave propagation in Fortran 77 as extension of Project 2, with absorbing boundary conditions

 

Notes 3

Notes 4

Notes 5

 

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

 

Notes 5

Notes 6

 

 

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; wavelets; and fractals

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

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

 

Notes 7

 

 

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 Time-Frequency Signal Analysis, IEEE Trans. Acoust., Speech, Sig. Proc., vol. 36, pp.1518-1521, 1988

[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, Boston, 2002

[14]      Rumelhart, D.E. and McCleland, J.L., eds., Parallel Distributed Processing: Learning Internal Representations by Error Propagations, Cambridge, MA, MIT Press, 1986

[15]  Sejnowski, T.J., and Rosenberg, C.R., NETalk: A Parallel Network that Learns to Read Aloud, Dept. of Electrical Engineering and Computer Science, John Hopkins University, 1986

[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 Time Delay Neural Networks, IEEE Trans. Acoustics, Speech, Signal Proc., ASSP-37, pp. 328-339, 1989.

 

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

 

Bibliography:

1.- Richard E. Crandall, Projects in Scientific Computation, Springer-Verlag (1994).

2.- Bhalla, U. S. (2003). "Understanding complex signaling networks through models and metaphors." Prog Biophys Mol Biol 81(1): 45-65.

3.- Wiechert, W. (2002). "Modeling and simulation: tools for metabolic engineering." J Biotechnol 94(1): 37-63.

4.- Trelease, R. B. (2002). "Anatomical informatics: Millennial perspectives on a newer frontier." Anat Rec 269(5): 224-35.

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." Comput Methods Programs Biomed 67(2): 85-103.

7.- Sardari, S. and D. Sardari (2002). "Applications of artificial neural network in AIDS research and therapy." Curr Pharm Des 8(8): 659-70.

8.- Saiz, L. and M. L. Klein (2002). "Computer simulation studies of model biological membranes." Acc Chem Res 35(6): 482-9.

9.- Blake, J. F. (2000). "Chemoinformatics - predicting the physicochemical properties of 'drug-like' molecules." Curr Opin Biotechnol 11(1): 104-7.

10.- Lemmen, C. and T. Lengauer (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 understanding small-large molecules interactions." Farmaco 57(2): 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). "Why model malaria?" Parasitol Today 16(12): 511-6.

14.- Neptune, R. R. (2000). "Computer modeling and simulation of human movement. Applications in sport and rehabilitation." Phys Med Rehabil Clin N Am 11(2): 417-34, viii.

15.- Pandy, M. G. (2001). "Computer modeling and simulation of human movement." Annu Rev Biomed Eng 3: 245-73.

16.- Weiss, J. A. and J. C. Gardiner (2001). "Computational modeling of ligament mechanics." Crit Rev Biomed Eng 29(3): 303-71.

17.- Yoganandan, N., S. Kumaresan, et al. (2001). "Biomechanics of the cervical spine Part 2. Cervical spine soft tissue responses and biomechanical modeling." Clin Biomech (Bristol, Avon) 16(1): 1-27.

18.- Azar, F. S., D. N. Metaxas, et al. (2002). "Methods for modeling and predicting mechanical deformations of the breast under external perturbations." Med Image Anal 6(1): 1-27.

19.- Tenti, G., J. M. Drake, et al. (2000). "Brain biomechanics: mathematical modeling of hydrocephalus." Neurol Res 22(1): 19-24.

20.- Bornholdt, S. (2001). "Modeling genetic networks and their evolution: a complex dynamical systems perspective." Biol Chem 382(9): 1289-99.

21.- Klonowski, W. (2001). "Non-equilibrium proteins." Comput Chem 25(4): 349-68.

22.- Loew, L. M. and J. C. Schaff (2001). "The Virtual Cell: a software environment for computational cell biology." Trends Biotechnol 19(10): 401-6.

23.- Novosel'tsev, V. N., A. Novosel'tseva Zh, et al. (2001). "[Mathematical modeling and simulation of life history and tradeoffs]." Adv Gerontol 7: 52-64.

24.- Demarco, J. J., I. J. Chetty, et al. (2002). "A Monte Carlo tutorial and the application for radiotherapy treatment planning." Med Dosim 27(1): 43-50.

25.- Morgan, J. A. and D. Rhodes (2002). "Mathematical modeling of plant metabolic pathways." Metab Eng 4(1): 80-9.

26.- Neves, S. R. and R. Iyengar (2002). "Modeling of signaling networks." Bioessays 24(12): 1110-7.