IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Paula Vasquez

  • Assistant Professor
  • Department of Mathematics
  • University of South Carolina


Education

Ph.D. Mathematical Sciences University of Delaware 2007
MBA Business Administration Goldey Beacom College 2002
B.S. Petroleum Engineering Universidad Nacional de Colombia 1998

Experience

2013 – Present Assistant Professor Department of Mathematics, University of South Carolina
2013 – 2010 Postdoctoral Fellow Department of Mathematics, University of North Carolina, Chapel Hill
2009 – 2007 Postdoctoral Fellow Department of Chemical Engineering, University of Delaware
2007 – 2004 Research Assistant Department of Mathematics, University of Delaware
2004 – 2002 Teaching Assistant / Instructor Department of Mathematics, University of Delaware

Research

Research Interests

Applied and computational mathematics

  • Multiscale modeling and simulation of viscoelastic fluid flows
    • Viscoelastic and diffusive transport processes in pulmonary mucus and mucus simulants
  • Computational and mathematical biology
    • Modeling the organization and distribution of chromosomes in yeast cells

Current Projects

  • Inverse characterization of complex fluids. In this project, we are developing computer simulations and constitutive models to describe the flow of mucus in cell cultures. This description involves the introduction of multiple time and length scales, as well as the use of constitutive equations that consider multiple species. This project is in collaboration with Greg Forest in the Math Department at UNC and David Hill in the Cystic Fibrosis Research Center at UNC.

  • Characterization of micro-heterogeneities in biological materials. Biological materials continuously adapt to changing conditions through coordinated mechanical and molecular responses. In many cases, this adaptation results in variations in the local viscous and elastic properties. Characterization of these micro-heterogeneities is important in the understanding of the underlying biological functions. This project is in collaboration with Greg Forest in the Math Department at UNC, David Hill in the Cystic Fibrosis Research Center at UNC, and Scott McKinley in the Math Department at UFL. The main objective of the project is to characterize (non-parametrically) spatial and temporal heterogeneities.

  • Modeling mitotic spindle in budding yeast cells. During cell division, once each pair of replicated chromosomes biorients, the linkage between the sister chromatids is broken and the spindle physically pulls the sisters to opposite poles. The small size of the yeast nucleus makes it difficult to visualize directly the steps involved in this chromosome segregation. Because of this, there is a need for the formulation of mathematical models capable of capturing the different biochemical, structural, and biophysical aspects that play a key role during cell division. This project is in collaboration with Greg Forest in the Math Department at UNC and Kerry Bloom in the Biology Department at UNC. The objective is to formulate, analyze, and simulate 3D models of cell division.

  • Bead-spring models of chromatin in budding yeast cells. It is hypothesized that the organization of chromosomes within the nucleus into territories dictates chromosome interactions. Understanding chromosome interactions plays a central role in the study of processes like DNA repair and gene expression. This project is in collaboration with Greg Forest in the Math Department at UNC and Kerry Bloom in the Biology Department at UNC. Our main objective is to formulate models capable of describing chromosome dynamics in vivo and use these models to gain insights into how chromosomes are organized and the mechanisms responsible for chromosome distribution during the life of a cell.


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Teaching Activities

Current Courses

  • MATH 728 - Selected Topics in Applied Mathematics
  • MATH 141 - Calculus I

Previous Courses

  • MATH 141 - Calculus I
  • MATH 520 - Ordinary Differential Equations
  • MATH 544 - Linear Algebra

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5 Selected Publications

  • P.A. Vasquez, J.A. Cribb, P. Moore, S. Norris, S. Shah, M.G. Forest and R. Superfine, "Nonlinear Signatures of Entangled Polymer Solutions in Active Microbead Rheology," Journal of Rheology. v 57 pp 1247-1264, 2013.
  • P.A. Vasquez, Y. Jin, K. Vuong, D.B. Hill and M.G. Forest. "A New Twist on Stokes' Second Problem: Partial Penetration of Nonlinearity in Sheared Viscoelastic Layers," J. Non-Newtonian Fluid Mech. v. 196, pp 36-50, 2013.
  • A.D. Stephens, R.A. Haggerty, P.A. Vasquez, L. Vicci, C.E. Snider, F. Shih, C. Quammen, C. Mullins, J. Haase, R.M. Taylor II, J.S. Verdaasdonk, M.R. Falvo, Y. Jin, M.G. Forest and K. Bloom. "Cohesin and Condensin form Loops of Pericentric Chromatin into a Non-linear Spring Network to Balance Microtubule-Based Force in Mitosis," The Journal of Cell Biology, 193(7), 1167-1180, 2013.
  • P.A. Vasquez, L.P. Cook and G.H. McKinley, "Wormlike Micellar Solutions: A Scission Model and Predictions," J. Non-Newtonian Fluid Mechanics. v. 144, no. 2-3, pp 122- 139, 2007.
  • J.W. Swan, P.A. Vasquez, P.A. Whitson, E.M. Fincke, K. Wakata, S.H. Magnus, F.D. Winne, M.R. Barratt, .H. Agui J, R.D. Green, N.R. Hall, D.Y. Bohman, C.T. Bunnell, A.P. Gast and E.M. Furst, "Multi-scale kinetics of a field-directed colloidal phase transition," PNAS v. 109, pp 16023-16028, 2012.

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IMI Preprints and Seminars

IMI Seminars



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Curriculum Vitae

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