Santiago Ignacio Betelu
Teaching
Currently teaching
3410 and 3420.
Research projects:
Singularities
in charged droplets
Spreading of charged
fluids
Molecular simulation of
interface cusps formation
Summary of other projects
PUBLICATIONS IN REFEREED JOURNALS
1 SI Betelu, J Iaia,
'Solutions of the porous medium equation with degenerate interfaces',
European Journal of Applied Mathematics (2013)
2 S. I. Betelu, M. A. Fontelos, U. Kindelan and O. Vantzos,
''Singularities on charged viscous droplets,
Physics of Fluids, 18, 051706 (2006)
3 S. I. Betelu, N. D. Alikakos and X. Chen,
'Explicit Stationary Solutions in Multiple Well Dynamics and NonUniqueness
of interfacial energy densities',
European Journal of Applied Mathematics (2006)
4 S. I. Betelu and M. A. Fontelos,
'Spreading of a charged microdroplet'
Physica D Nonlinear Phenomena, 209, Issues 14, 15
pp. 2835 (2005)
5 S. I. Betelu, M. A. Fontelos and U. Kindelan,
''The shape of charged drops: Symmetry breaking bifurcations and numerical
results'',
Progress in Nonlinear Differential Equations and their Applications, 63, pp.
5158 (2005)
6 S. I. Betelu and M. A. Fontelos,
''Capillarity driven spreading of circular drops of shear thinning fluid'',
Mathematical and computer modelling, 40 (78), 729734 (2004).
7 Niethammer M, Betelu S, Sapiro G, et al.
'Area based medial axis of planar curves',
International Journal of Computer Vision, 60 (3), 203224 (2004).
8 S. I. Betelu and J. R. King,
``Explicit solutions of a twodimensional fourth order nonlinear diffusion
equation'',
Mathematical and Computer Modelling, 37 (34), 395403. (2003).
9 S. I. Betelu and M. A. Fontelos,
''Capillarity driven spreading of powerlaw fluids'',
Applied Mathematics Letters 16 (8), 13151320 (2003).
10 S. Betelu, R. Gulliver and W. Littman,
"Boundary control of PDEs via curvature flows: the view from the
boundary, II"
Applied Mathematics and Optimization, 46 167178 (2002)
11 S. I. Betelu, D. G. Aronson,
''Focusing of noncircular selfsimilar shock waves'',
Physical Review Letters, Vol. 87 No. 7 (2001).
12 S. B. Angenent, D. G. Aronson, S.
I. Betelu and J. S. Lowengrub,
''Focusing of an elongated hole in porous medium flow'',
Physica D, Vol. 151, pp.228252 (2001).
13 S. I. Betelu, D. G. Aronson and S. B. Angenent
''Renormalization study of twodimensional convergent solutions of the porous
medium equation'',
Physica D, 138, p. 344359, (2000).
14 S. I. Betelu, G. Sapiro and A. Tannenbaum,
''On the computation of Affine Skeletons of Plane Curves and the Detection of
Skew Symmetries'',
Pattern Recognition, Vol 34 pp. 943952 (2000).
15 S. I. Betelu, G. Sapiro, A. Tannenbaum and P. Giblin,
''Noiseresistant affine skeletons of planar curves'',
Lect Notes Comput Sc 1842, pp. 742754, (2000).
16 J. Y. Wang, S. Betelu, and B. M. Law
'Line tension approaching a firstorder wetting transition:
Experimental results from contact angle measurements'
Physical Review E, Vol 63 (2000).
17 S. Betelu, J. Diez,
'A two dimensional similarity solution for capillary driven flows',
Physica D 126, p.136 (1999).
18 S. Betelu,
'A twodimensional corner solution for a nonlinear diffusion equation'
Applied Math. Letters, 13, pp. 119123 (2000).
19 J. Wang, S. Betelu and B. Law,
'Line tension effects near firstorder wetting transitions'
Physical Review Letters, 83, number 18 pp. 36773680 (1999)
20 S. Betelu, Law B. M. and Huang C. C.,
'Spreading dynamics of terraced droplets',
Phys. Rev. E, 59 p. 6699 (1999) ONLINE
21 J. Diez, L. P. Thomas, S. Betelu, R. Gratton, B. Marino, J. Gratton,
D. G. Aronson and S. B. Angenent,
''Noncircular focussing flow in viscous gravity
currents'',
Phys. Rev. E 58 p. 61826187 (1998)
22 J. Diez, S. Betelu and R. Gratton,
''The crumbling of a viscous prism with an inclined free surface'',
Arch. Appl. Mech. 68 p. 407421 (1998)
23 S. Betelu, R. Gratton and J. Diez,
''Observation of cusps during the levelling of free surfaces in viscous
flows'',
J. Fluid Mech. 377, 137149 (1998)
24 S. Betelu, J. Diez and R. Gratton,
''Cusped ripples at the plane surface of a viscous liquid'',
Arch. Appl. Mech. 69 p.3646 (1998)
25 S. Betelu , J. Diez, L. Thomas, R. Gratton, B. Marino,
''A boundaryelements method for viscous gravity currents '',
Int. J. for Numerical Methods in Fluids 25, 1, (1997).
26 B. Marino, L. Thomas, R. Gratton, J. Diez, S. Betelu,
''Waiting time solutions of a nonlinear diffusion Equation: Experimental
study of a creeping flow near a waiting front'',
Phys. Rev. E. 54, (1996)
27 R. Gratton, J. Diez,
L. Thomas, B. Marino, S. Betelu,
''Quasiselfsimilarity for wetting drops '',
Phys. Rev. E 53,.3563 (1996).
28 L. Thomas, R. Gratton, B. Marino, S. Betelu ,
J. Diez,
''Measurement of the slope of a liquid free surface along a line by a schlieren system with anamorphic elements '',
Measurements Science and Technology 7, 1 (1996)
29 S. Betelu , J. Diez, L. Thomas, R. Gratton, B. Marino,
''Instantaneous viscous flow in a corner bounded by free surfaces '',
Phys. Fluids 8, 2269 (1996)
____________________________________________________________________________
EDUCATION
1) 19891994: BS in Physics at UNCPBA, Argentina (Universidad Nacional del Centro de la Provincia
de Buenos Aires).
Thesis: Columnar to Equiaxed Transicion
in Aluminum base Alloys.
2) 19941997: Ph.D. in Physics at UNCPBA, Argentina.
Thesis: Plane Stokes Flows near singular points of the free surface.
RESEARCH EXPERIENCE:
Research during my Ph.D in Argentina from
May 1994 to November 1997:
1 Theoretical Fluid Mechanics: simulation of the spreading of viscous
liquids on plane substrates. Computations with boundary elements methods,
finite differences and construccion of explicit
solutions to the Stokes equations.
2 Experimental Fluid Mechanics: design and implementation of optical
diagnostics based on interferometry, schlieren and shadowgraphy for the measurement on viscous flows.
Experiments in spreadings and cusps formation in
flows of small Reynolds number.
Postdoctoral Position at Kansas State University from November 1997
to November 1998,
as a Research Associate at the Physics Department:
1 Experimental ellipsometry for the measurement of
ultrathin films of fluids on silicon substrates. Developped
software for analysis of ellipsometric data.
Preparation and cleaning of silicon surfaces and theoretical modeling of
liquid crystals spreading.
2 Design of optical measurements and experiments for the measurement of line
tension including fabrication of silane monolayers,
and design of an interferometric microscope.
Visiting Assistant Professor at the Mathematics Department of the
University of Minnesota from November 1998 to July 2000:
1 Modelling of porous medium flows with 2D finite differences, numerical
renormalization and ENO discretizations, and construction
of exact and approximate 2D selfsimilar solutions
for thin film flows of viscous liquids on plane surfaces.
2 In collaboration with the Electrical and Computer Engineering Department,
I did research on skeletonization of planar shapes,
symmetry detection in digital images, image enhancement and processing of 3D
data.
Postdoctoral position at the Institute of Mathematics and its
Applications from July 2000 to July 2002
1 Image processing, smoothing of 3D textured surfaces, Mathematics in Multimedia.
2 Scaling and selfsimilarity in fluid mechanics. Gasdynamics
and porous medium flows. Thin films and lubrication approximation. Micromagnetism and LandauLifshitz
equations. Development of numerical techniques.
Assistant
(20022008) and associate (20082011) Professor at the Mathematics Department
of the University of North Texas
1 Applied fluid dynamics. Lubrication theory, spreading of liquids on solid
substrates, partial differential equations of nonlinear degenerate diffusion.
2 Numerical analysis of the Allen Cahn equations applied to the curvature
flow of curves with triple joints: finite differences methods and boundary
value problems.
3 Electrically charged fluids with free surfaces: lubrication theory,
boundary elements methods and asymptotic analysis.
4 Variational methods for image interpolation.
5 Study of the dynamics of electrically charged fluids.
Current research:
1 Design of algorithms for image processing based on partial differential
equations.
2 Fractal patterns in fluid flow.
3 Study of the shape of the free surface of charged anisotropic and
multiphase materials.
4 Investigation on automatic PDE solvers.
TEACHING EXPERIENCE
Assistant Professor at the UNT: I teach courses of Calculus,
Differential Equations, Probabilities, Statistics, Numerical Analysis. I also
directed the thesis of Orestis Vantzos entitled
"Mathematical modeling of charged liquid droplets: numerical simulation
and stability analysis". I also created a new course on numerical
analysis (contents here).
Visiting Assistant professor at the Mathematics Department of the
University of Minnesota.
I taught courses in Partial Differential Equations with Applications, an
introductory course of Precalculus, and College
Algebra and Probability. I was responsible for the lectures, organizing the
teaching assistants, and preparing the exams (19982000). This last year I
was the coordinator of the course.
Teaching Assistant at the Universidad Nacional
del Centro (UNCPBA), Tandil, Argentina.
I taught courses of Electricity and Magnetism, Fluid Mechanics and
Elasticity. I was
responsible for laboratory and problemsolving sessions (19921997).
TECHNICAL SKILLS
1 Design of optical measurements with interferometry, schlieren
and ellipsometry.
2 Digital image acquisition and processing. Data analysis.
3 Preparation of silicon substrates and fabrication of silane
monolayers.
4 Design of experiments in fluid mechanics.
5 Numerical simulation in fluid mechanics with finite differences, boundary
elements methods, FFT methods, ENO (essencially
nonoscillatory methods), Riemann solvers for gasdynamics,
numerical renormalization and fast marching algorithms, octrees
for Nbody computations as BarnesHut and modifications. Numerical methods
applied to image processing.
6 Construction of new explicit solutions for partial differential equations
in fluid mechanics.
7 Design of algorithms for image processing.
PROGRAMMING SKILLS
Fortran, C, C++, Matlab and Mathematica.
I have experience working with supercomputers
at the Supercomputing Institute of the UMN and at the UNT. I programmed
mainly codes for data processing, image enhancement and numerical simulations
in fluid dynamics.
LANGUAGES: English and Spanish
