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

