Electrically charged fluids

renSelf-similar solution of PME

Droplets microinterferogram

shock waves
Convergent shock waves


Santiago Ignacio Betelu


    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



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 Non-Uniqueness 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 1-4, 15 pp. 28-35 (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. 51-58 (2005)

6- S. I. Betelu and M. A. Fontelos,
''Capillarity driven spreading of circular drops of shear thinning fluid'',
Mathematical and computer modelling, 40 (7-8), 729-734  (2004).

7- Niethammer M, Betelu S, Sapiro G, et al.
'Area based medial axis of planar curves',
International Journal of Computer Vision, 60 (3), 203-224 (2004).

8-  S. I. Betelu and J. R. King,
``Explicit solutions of a two-dimensional fourth order non-linear diffusion equation'',
Mathematical and Computer Modelling, 37 (3-4), 395-403. (2003).

9- S. I. Betelu and M. A. Fontelos,
''Capillarity driven spreading of power-law fluids'',
Applied Mathematics Letters 16 (8), 1315-1320 (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, 46 167-178 (2002)

11- S. I. Betelu, D. G. Aronson,
''Focusing of non-circular self-similar 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.228-252 (2001). 

13- S. I. Betelu, D. G. Aronson and S. B. Angenent
''Renormalization study of two-dimensional convergent solutions of the porous medium equation'',
Physica D, 138, p. 344-359, (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. 943-952 (2000).

15-  S. I. Betelu, G. Sapiro, A. Tannenbaum and P. Giblin,
''Noise-resistant affine skeletons of planar curves'',
 Lect Notes Comput Sc 1842, pp. 742-754, (2000).

16- J. Y. Wang, S. Betelu, and B. M. Law
 'Line tension approaching a first-order 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 two-dimensional corner solution for a nonlinear diffusion equation'
Applied Math. Letters, 13, pp. 119-123 (2000). 

19- J. Wang, S. Betelu and B. Law,
'Line tension effects near first-order wetting transitions'
Physical Review Letters, 83, number 18 pp. 3677-3680 (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,
''Non-circular focussing flow in viscous gravity currents'',
Phys. Rev. E 58 p. 6182-6187 (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. 407-421 (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, 137-149 (1998) 

24- S. Betelu, J. Diez and R. Gratton,
''Cusped ripples at the plane surface of a viscous liquid'',
Arch. Appl. Mech. 69 p.36-46 (1998)

25- S. Betelu , J. Diez, L. Thomas, R. Gratton, B. Marino,
''A boundary-elements 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 non-linear 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,
''Quasi-self-similarity 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) 


1) 1989-1994: 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) 1994-1997: Ph.D. in Physics at UNCPBA, Argentina.
Thesis: Plane Stokes Flows near singular points of the free surface.


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 ultra-thin 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 self-similarity in fluid mechanics. Gasdynamics and porous medium flows. Thin films and lubrication approximation. Micromagnetism and Landau-Lifshitz equations. Development of numerical techniques.

Assistant (2002-2008) and associate (2008-2011) 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.

5- Parallel computing of solutions of PDEs

6- Modeling biological neural networks


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 (1998-2000). 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 problem-solving sessions (1992-1997).

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 non-oscillatory methods), Riemann solvers for gasdynamics, numerical renormalization and fast marching algorithms, octrees for N-body computations as Barnes-Hut 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.
8- Construction of inexpensive, passively cooled GPU systems for physical simulations and education.
9- High Performance Computing with Infiniband, Data Vortex and GPUs.

Fortran, C, C++, Opencl, MPI, Matlab, Mathematica. I have experience working with supercomputers
at the Supercomputing Institute of the UMN, at the UNT and UT. I programmed mainly codes for numerical simulations in fluid dynamics, biology, quantum mechanics and signal processing.

LANGUAGES: English and Spanish

With PDE-solving rig.