Publications and Technical Reports

Research Publications

Negrón-Marrero, P. V. and Sivaloganathan, J., The repulsion property in nonlinear elasticity and a numerical scheme to circumvent it, submitted, SIAM J. Appl. Math., June 2023 (arXiv:2304.07390, April 2023).
Negrón-Marrero, P. V. and Sivaloganathan, J., Cavitation of a spherical body under mechanical and self gravitational forces, accepted for publication, Proceedings A of the Royal Society of Edinburgh, December 2023 (arXiv:2012.05755, December 2020).
Negrón-Marrero, P. V. and Sivaloganathan, J., Infinite energy cavitating solutions: a variational approach, SIAM J. Appl. Math., Vol. 82, No. 3, pp. 849--871, 2022 (arXiv:2112.10631, December 2021).
Negrón-Marrero, P. V., Chaotic dynamics of a three particle array under Lennard-Jones type forces and a fixed area constraint, arXiv:2009.02246, September 2020.
Negrón-Marrero, P. V. and Sivaloganathan, J., On the convergence of a regularization scheme for approximating cavitation solutions with prescribed cavity volume, SIAM J. Appl. Math., 80(1), 119-141, January 2020.
Negrón-Marrero, P. V. and López-Serrano, M., Minimal energy configurations of finite molecular arrays, Symmetry, 11, 158, 2019; (doi:10.3390/sym11020158), and in Symmetry in Applied Mathematics, Sorana D. Bolboaca and Lorentz Jantschi (Eds.), January 2021, ISBN 978-3-03943-791-7.
Negrón-Marrero, P. V. and Sivaloganathan, J., A characterisation of the boundary displacements which induce cavitation in an elastic body, Journal of Elasticity, Vol. 109, Issue 1, pp 1-33, 2012 (DOI 10.1007/s10659-011-9366-x).
Negrón-Marrero, P. V. and Campo, E., A nonlinear model of an actuator, Proceedings of the SPIE Optics+Photonics Conference, San Diego, California, August, 2011.
Negrón-Marrero, P. V. and Sivaloganathan, J., The radial volume derivative and the critical boundary displacement for cavitation, SIAM Journal of Applied Mathematics, Vol. 71, No.6, pp. 2185-2204, 2011.
Negrón-Marrero, P.V. and Montes-Pizarro, E., Violation of the Complementing Condition and Local Bifurcation in Nonlinear Elasticity, Journal of Elasticity, 107:151-178, 2012, (DOI) 10.1007/s10659-011-9349-y.
Negrón-Marrero, P.V. and Montes-Pizarro, E., The Complementing Condition and its role on a global bifurcation theory applicable to nonlinear elasticity, New York Journal of Mathematics, 17a (2011) 245-265.
Negrón-Marrero, P. V. and Sivaloganathan, J., The Numerical Computation of the Critical Boundary Displacement for Radial Cavitation, Mathematics and Mechanics of Solids, 14: 696–726, 2009.
Montes-Pizarro, E. and Negrón-Marrero, P. V., Local Bifurcation analysis of a Second Gradient Model for Deformations of a Rectangular Slab, Journal of Elasticity, Vol. 86, No. 2, 173-204, 2006.
Negrón-Marrero, P.V., The Hanging Rope of Minimum Elongation for a Nonlinear Stress-Strain Relation, Journal of Elasticity, 71: 133--155, 2003.
Negrón-Marrero, P.V. and Montes-Pizarro, E., Axisymmetric Deformations of Buckling and Barreling Type for Cylinders Under Lateral Compression-The Linear Problem, Journal of Elasticity, 65: 61-86, 2001.
Negrón-Marrero, P.V., A Genetic Algorithm for Computing Singular Minimizers of the Calculus of Variations, Proceedings of the XV Interuniversity Mathematical Research Seminar (XV SIDIM), February 2000.
Negrón-Marrero, P.V., An Analysis of the Linearized Equations for Axisymmetric Deformations of Hyperelastic Cylinders, Journal of Mathematics and Mechanics of Solids, 4: 109-133, 1999.
Negrón-Marrero, P.V., An Algebraic Criterion for Cavitation, Journal of Mathematical Modeling and Scientific Computing, Proceedings of the 10th International Conference on Mathematical Modeling and Computer Modeling and Scientific Computing, Boston, July 1995; X.J.R. Avula and Anil Nerode, Editors, Vol. 6, 1996.
Negrón-Marrero, P.V. and Betancourt, O., The Numerical Computation of Singular Minimizers in Two Dimensional Elasticity, Journal of Computational Physics, Vol. 113, No. 2, pp. 291-303, August 1994.
Negrón-Marrero, P.V. and Betancourt, O., A Pre-Conditioned Spectral Collocation Method for two Dimensional Nonlinear Elasticity, Journal of Mathematical Modeling and Scientific Computing, Proceedings of the 9th International Conference on Mathematical Modeling and Computer Modeling and Scientific Computing, Berkeley, July 1993, X.J.R. Avula, Editor, Vol. 4, 1994.
Negrón-Marrero, P.V. and Santiago-Figueroa, B., Novel Stability Patterns for the Necking of Plates in Tension: A Numerical Study, Applied Numerical Mathematics, Vol. 13, 491-512, 1994.
Marcano-Velázquez, M. and Negrón-Marrero, P.V., The Numerical Solution of the von Karman Equations using Multigrid Methods, Congressus Numerantium, 94, 17-28, 1993.
Negrón-Marrero, P.V., Shear Instabilities for the Buckling of Nonlinearly Elastic Plates, Quarterly of Applied Mathematics, Vol. XLIX, No. 3, 477-493, 1991.
Negrón-Marrero, P.V., A Numerical Method for Detecting Singular Minimizers of Multidimensional Problems in Nonlinear Elasticity, Numerische Mathematik, 58, 135-144, 1990.
Negrón-Marrero, P.V. and Antman, S.S., Singular Bifurcation Problems for the Buckling of Anisotropic Plates, Proc. Roy. Soc. London A 427, 95-137, 1990.
Negrón Marrero, P.V., Necked States of Nonlinearly Elastic Plates, Proceedings of The Royal Society of Edinburgh, 112A, 277-291, 1989.
Negrón Marrero, P.V. and Carbonera, C., The Numerical Computation of Compressed States for Nonlinearly Elastic Anisotropic Plates, Numerische Mathematik, 56, 93-107, 1989.
Antman, S.S. and Negrón-Marrero, P.V., The Remarkable Nature of Radially Symmetric Equilibrium States of Nonlinearly Elastic Bodies, Journal of Elasticity, 131-164, 1987.

Books

Negrón Marrero, Pablo V., Fundamentos del Análisis Computacional, Editorial MATE-UPRH, 2021.
Negrón Marrero, Pablo V., Cálculo de Varias Variables, Editorial MATE-UPRH, 2021.
Negrón Marrero, Pablo V., Ecuaciones Diferenciales Ordinarias, Editorial MATE-UPRH, 2021.
Negrón Marrero, Pablo V., Algebra Lineal, Editorial MATE-UPRH, 2020.

Publications with students

A. De Jesús Espinosa and P. V. Negrón-Marrero, On the determination of photo-actuation effects for a polymer/MWCNT composite fiber based cantilever, Proceedings of the National Conferences on Undergraduate Research (NCUR), La Crosse, Wisconsin, April 2013.
Greichaly Cabrera and P. V. Negrón-Marrero, Pursuit Problems: Generalizations and Numerical Simulations, Proceedings of the National Conferences on Undergraduate Research (NCUR), Ithaca, NY, April 2011.
Abner Ortiz, Greichaly Cabrera, and Negrón-Marrero, P. V., Finite Element Method Simulations of Composite Materials, Proceedings of The National Conference on Undergraduate Research, University of Montana, Missoula, April 2010.
Yesenia Cruz and Negrón-Marrero, P. V., A Mathematical Model for Detecting Diabetes, Proceedings of the National Conferences on Undergraduate Research, University of Wisconsin La-Crosse, La-Crosse, Wisconsin, April 2009
Abner Ortiz, Greichaly Cabrera, and Negrón-Marrero, P. V., The Non-Linear Cantilever: A Graphical User Interface, Proceedings of Proceedings of the National Conferences on Undergraduate Research, University of Wisconsin La-Crosse, La-Crosse, Wisconsin, April 2009.
Jessica Flores and Negrón-Marrero, P. V., The numerical computation of the critical boundary displacement for radial cavitation for composite materials, Proceedings of the National Conferences on Undergraduate Research, Salisbury, Maryland, April 2008.
Jessica Flores and Negrón-Marrero, P. V., The brachistochrone problem on a vertical plane and over surfaces, Proceedings of the National Conferences on Undergraduate Research, San Rafael, California, April 2007.

Technical Reports

Negrón-Marrero, P. V. and Jiménez-González, J., Nonplanar reflector arrays for capturing sun light , Technical Report, May 2022.
Negrón-Marrero, P. V., The brachistochrone problem over surfaces , Technical Report, April 2022.
Negrón-Marrero, P. V., A note on the Radon-Riesz property , Technical Report, March 2021.

Computer Simulations of Wavefronts in Drosophila Embryos

Negrón-Marrero, P. V., What is the value of $\lim_{x\rightarrow0^\circ}\frac{\sin x}{x}$ ?, Technical Report, March 2013.
Negrón-Marrero, P. V., Montes-Pizarro, E., Velázquez, J., Arreglos de espejos no planares para la recolección de luz solar, Informe Técnico, Febrero 2013.
Negrón-Marrero, P. V., The Random Homotopy Method for Signal Tracking and Global Positioning Systems (GPS), Technical Report, February 2007.
Flores-Rosado, J. and Negrón-Marrero, P. V., A Graphical User Interface to Explore the Brachistochrone Problem, Technical Report, May 2006.
Negrón-Marrero, P. V. and Avenancio, C., A model for the dynamics of a kite with an arbitrary lift coefficient, Technical Report, February 2006
Negrón-Marrero, P. V., Differentiating trigonometric functions of angles measured in degrees, submitted to Mathematics Teacher, January 2006.
Negrón-Marrero, P. V., The Brachistochrone Problem Revisited, Technical Report, April 2005.
Negrón-Marrero, P. V. and Bárbara L. Santiago-Figueroa, The Nonlinear Brachistochrone Problem with Friction, Technical Report, July 2005.
Negrón-Marrero, P. V. and Bárbara L. Santiago-Figueroa, An inverse problem for the rope of minimum elongation, Technical Report, Department of Mathematics, University of Puerto Rico, Humacao, May 2003.
Negrón-Marrero, P. V., Nonlinear Problems Depending on a Parameter: Continuation Methods, Limit Points, Simple Bifurcation, Technical Report, Department of Mathematics, University of Puerto Rico, Humacao, May 1999.
Negrón-Marrero, P. V., Muñoz-Alicea R., and Marcano-Velázquez, M., A Mathematical Model for Macrophage, T Cell, and Mycobacterium Tuberculosis Interactions, Technical Report, Department of Mathematics, University of Puerto Rico, Humacao, July 1999.

Master Theses Directed

David Torres, Estudio comparativo de métodos de pre-acondicionamiento para la solucion de ecuaciones elípticas, Master Thesis, University of Puerto Rico, August 1996.
Claudia Talavera, Computación numérica de mínimos singulares en el contexto de elasticidad no lineal para el caso de dos dimensiones: generalizaciones y resultados adicionales, Master Thesis, University of Puerto Rico, August 1996.
René Alvarado, Un método de pre-acondicionamiento para el computo de mínimos singulares del calculo de variaciones en una dimensión, Master Thesis, University of Puerto Rico, March 1995.
Javier Rodríguez, Métodos de direcciones alternantes en optimización nolineal, Master Thesis, University of Puerto Rico, March 1995.
Virgen Serrano, La solución de sistemas polinomiales usando métodos homotópicos, Master Thesis, University of Puerto Rico, October 1994.
José Benabe, Un método multi-mallas para la solución de problemas de optimización de gran escala, Master Thesis, University of Puerto Rico, May 1993.
Julio Díaz, Solución de la ecuación de los estados comprimidos de placas circulares mediante métodos de continuación multi-mallas, Master Thesis, University of Puerto Rico, December 1992.
Bárbara Santiago, On the numerical stability of necked states of circular plates in tension, Master Thesis, University of Puerto Rico, December 1991.
Mariano Marcano, Soluciones numéricas para las ecuaciones de von Kárman usando metodos multi-mallas, Master Thesis, University of Puerto Rico, December 1990.