Andrea Dziubek

Teaching

• Spring 2019: MAT 460, MAT 560 Numerical Differential Equations (2 sections, Utica and Albany)
  
• Advanced Certificate Computational Mathematical Modeling (CMM)

  Education and training for students with a BS in mathematics, physics, engineering, or a comparable program for careers in science and industry as well as for further graduate study in the area of physically based computational mathematical modeling and data analysis. It stresses fundamentals and applications equally. Students will learn how to model, analyze and solve problems from science and engineering using advanced methods from linear algebra, differential equations, and computational mathematics.

Research Interests

• Modeling and Simulation of Problems in Ophthalmology (Biomedical Applications)
• Continuum Mechanics (Elasticity/Shells, Fluids, Materials), Exterior Calculus, Asymptotic Analysis
• Structure Preserving Numerical Methods, Discrete Exterior Calculus, Finite Element Methods

Selected Publications

• Tensor Analysis, Heinz Schade, Klaus Neemann, Translated by Andrea Dziubek, Edmond Rusjan, De Gruyter, 2018, ISBN 978-3-11-040426-5. (i) Publisher Web Page, (ii) from Amazon, (iii) German version with German reviews, (iv) among the top five goodreads on Tensor Analysis.
  Tensor calculus is a prerequisite for many tasks in physics and engineering. This book introduces the symbolic and the index notation side by side and offers easy access to techniques in the field by focusing on algorithms in index notation. It explains the required algebraic tools and contains numerous exercises with answers, making it suitable for self study for students and researchers in areas such as solid mechanics, fluid mechanics, and electrodynamics.
  Contents: Algebraic Tools, Tensor Analysis in Symbolic Notation and in Cartesian Coordinates, Algebra of Second Order Tensors, Tensor Analysis in Curvilinear Coordinates, Representation of Tensor Functions. Appendices: Solutions to the Problems; Cylindrical Coordinates and Spherical Coordinates.

• Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model. A. Dziubek, G. Guidoboni, A. Harris, A.H. Hirani, E. Rusjan, W. Thistleton. Biomechanics and Modeling in Mechanobiology. pp 1-15, Springer, DOI: 10.1007/s10237-015- 0731-8. 2015 (abstract,pdf)
  
• Using Generalized Dimensional Analysis to Obtain Reduced Effective Model Equations for Condensation in Slender Tubes with Rotational Symmetry. ASME Journal of Heat Transfer 135(5), 051501, 2013
  arxiv.org/abs/1101.5718
• Equations for Two-Phase Flows: A Primer. Meccanica, Vol 47(8), pp 1819-1836, 2012
  arxiv.org/abs/1101.5732
• Modeling, Analysis and Numerical Simulation of a Moving Boundary Problem with Phase Change and Surface Tension, Thesis, Berlin University of Technology, Germany, 12/2006
• Lecture Notes: Bilanzgleichungen (Introduction to Continuum Mechanics Script, German)

Recent Activites

Some Work in Progress

• Ocular Blood Flow Modeling: Together with external collaborators, Giovanna Guidoboni, (Mathematics, Indiana University Purdue University Indianapolis and University of Strasbourg, France) and Anil Hirani, (Mathematics, University of Illinois), we developed a computational model to theoretically investigate retinal perfusion, i.e., hemodynamics in the microvasculature nourishing the retinal tissue. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size, (iii) defined on a two-dimensional curved surface embedded in the three-dimensional space. The model predictions support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics.
• Geometric Mechanics and Structure Preserving Numerical Methods: We aim to model relevant problems from fluids, elasticity, and relativity in exterior calculus language and solve these problems using discrete exterior calculus based methods. The aim is to demonstrate the potential of these new methods for modeling complex materials and other applications in engineering and science. We started the project started at our GSMCM workshop (see below) in collaboration with other participants,

Undergraduate Research Activities

• SUNY SURP18, Summer Undergraduate Research Program June - August 2018
• Slocum Dickson Research Award Scholarship, August 2015 - May 2016
• SUNY STEM15 Research Passport Program, June - August 2015
• 2014 STEM Undergraduate Research Program, May - August 2014
• Hudson River Undergraduate Mathematics Conference, 2012, 2013, 2015

Recent Presentations

• CMS - Winter meeting, Advances and Applications in Geometric and Structure-Preserving Discretizations Session, Vancouver, Canada, 12/07-12/10/2018
  Literature Review of Structure Preserving Discretizations for Shell Models
• IMA - Institute for Mathematics and its Applications, Special Workshop Mathematics and Mechanics in the 22nd Century: Seven Decades and Counting..., Eugene, OR, 10/23-25/2015
  Poster: Effect of ocular shape and vascular geometry on retinal hemodynamics, A. Dziubek (presenter), joint work with G. Guidoboni, A. Harris, A. N. Hirani, E. Rusjan, W. Thistleton
• SEI - 7th Annual SUNY Eye Institute Meeting, SUNY POLY, CNSE, Albany, NY, 9/26/2015
  Poster: Recent Progress in the EYE DEC Retinal Perfusion Model - Changes in Ocular Shape play a role in Retinal Blood Perfusion, A. Dziubek, A. Harris, A.N. Hirani, E. Rusjan, W. Thistleton.
• IMA - Institute for Mathematics and its Applications, Special Workshop Structure-Preserving Discretizations of Partial Differential Equations, University of Minnesota, MN, 10/22-24/2014
  Poster: DEC - A Software Environment to Model Blood Flow in the Eye, A. Dziubek, E. Rusjan
• SEI - 6th Annual SUNY Eye Institute Meeting, Upstate Medical University Syracuse, NY, 9/27/2014
  How to Validate a Mathematical Model of the Eye, Joint work with A. Benavente-Perez (SUNY College of Optometry, NYC), E. Rusjan, B. Thistleton
• MAA Math Fest, Portland, Oregon, Invited Paper Session, The Eyes Have It: Mathematical Modeling of the Retina, 8/9/2014
  New Paradigms in Retinal Blood Flow Simulation (Invited by E. Camacho)
• WCCM XI, ECCM V, ECFD VI, 11th. World Congress on Computational Mechanics, Barcelona, Spain, Minisymposium Computational Modeling of Multiphysics/Multiscale Coupled Processes in Biological and Nanotechnological Systems, 7/25/2015
  Retinal blood flow changes and vascular parameters and structure, A. Dziubek (speaker), E. Rusjan and W. Thistleton. (Invited by R. Sacco, POLIMI, Italy, G. Guidoboni, IUPUI, R. Melnik, WLU, Canada)
• COPDE - Conference on Partial Differential Equations, Novacella, Italy, 5/30/2014
  Retinal blood flow changes and vascular parameters and structure, A. Dziubek, E. Rusjan (speaker), W. Thistleton. (Invited talk)
• SEI - 5th Annual SUNY Eye Institute Meeting, Downstate Medical Center, Brooklyn, NY, 10/19-20/2013
  Presented the ARVO and FMD posters
• FMD - Proceedings of the ASME/FDA 2013, 1st Annual Frontiers in Medical Devices, Washington DC, 12 September 2013
  Poster: Challenges in Blood Flow Simulation: Numerical Methods and Image Processing Tools, A. Dziubek, E. Rusjan, W. Thistleton
  
• AMMCS - Applied Mathematics, Modeling and Computational Science, Waterloo, August 28, 2013
  Modeling Oxygen Dynamics of the Retina - Using Discrete Exterior Calculus, A. Dziubek, G. Guidoboni, A. Hirani, E. Rusjan (speaker)
  
• 8th Conference on Applied Mathematics and Scientific Computing, Sibenik, Croatia, June 12, 2013
  A Discrete Exterior Calculus Model of Blood Flow in the Retina, A. Dziubek, G. Guidoboni, A. Hirani, E. Rusjan (speaker)
  
• ARVO - The Association for Research in Vision and Ophthalmology, Seattle, 6 May 2013
  Poster: Effect of ocular curvature and myopia on retinal blood flow: a theoretical study, A Dziubek, G. Guidoboni, A. Hirani, A. Harris
  
• AMS Sectional Meeting, Rochester Institute of Technology, NY, September 22-23, 2012, Special Session on Applied and Computational Mathematics (Ludwig Kohaupt)
  Modeling the oxygen dynamics of the retina of the eye with discrete exterior calculus, A. Dziubek, G. Guidoboni, A. Hirani, E. Rusjan
  Optimizing Discrete Exterior Calculus, E. Rusjan, A. Dziubek
• Focus Program on Geometry, Mechanics and Dynamics, the Legacy of Jerry Marsden, Fields Institute, Toronto, CA, July 2012 (D.E. Chang, D. Holm, G.W. Patrick, T. Ratiu)
  A Model for the Retina Including Blood Flow and Deformation, A. Dziubek, E. Rusjan
• 11th USNCCM, Minneapolis, MN, July 28, 2011, Minisymposium Geometric and Exterior Calculus Methods in Computational Mechanics (Robert Haber, Douglas Arnold)
  Discrete Exterior Calculus for Biomedical Applications, A. Dziubek, G. Guidoboni
• Workshop on Moving Frames in Geometry, Centre de recherches mathematiques (CRM) Universite de Montreal, CA, June 17, 2011 (N. Kamran, A. Smith)
  Modeling Biomembranes using Calculus of Variations and Exterior Calculus
• Discrete Differential Geometry and Applications, 2010 Barrett Memorial Lectures, The Universiy of Tennessee, TN, May 17-21 2010 (Ken Stephenson, Alexander Bobenko)
  Poster: Discrete Differential Geometry for Closed Elastic Biomembranes

Previous Applied Math Seminars, External Speakers, Events, SUNY Poly

• Wenfeng Chen (SUNYPoly, Mathematics), Introduction to Differential Operator Method for Solving Linear Nonhomogeneous Differential Equations with Constant Coefficients, September 9, 2016, noon, in DON 2159
• Souhayl Sadik, Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta A Geometric Theory of Nonlinear Morphoelastic Shells 15 April 2016, 2pm, DON 2159
• Kaushik Kalyanaraman, Computer Science and Applied Mathematics, SCoReC at Rensaler Polytechnic Institute, Troy, NY, Donuts, pretzels, fluid flow, and ranking sports teams: a short tour of discretizing Laplacians on meshes and graphs. 25 March 2106, 2pm, DON 2159
• Wenfeng Chen (SUNYPoly, Mathematics), An Attempt to discretize Witten's Deformation using concepts from Discrete Exterior Calculus, March 20, 2015, 2pm, in DON 2159
• Tanzid Sultan (SUNYPoly Math Major), Mercury's orbit around the Sun, March 5, 2015, noon, DON 2159
• Robert Lowry, SUNY Suffolk, Gauged Poisson Structures and Compressible Free Boundary Fluids, , April 25, 2014, noon, DON 2159
• Alexandra Benavente, SUNY College of Optometry, NYC, Modeling ocular blood flow to help prevent blindness, March 28, 2014, noon, Student Center Theater (Provost Lecture series)
• Michael Karow, University of Technology Berlin, Germany, Pseudospectra for structured matrix perturbations, May 30, 2013, 1pm, DON G152
• Holger Heumann, Visiting Scholar at Rutgers University, NJ, Lagrangian and Eulerian Methods for Generalized Advection-Diffusion, April 19, 2013, 12pm, DON G152
• Applied Mathematics Seminar
  • STEMUR Summer 2014: Ocular Blood Flow Modeling and Retinal Image Processing, Poster Presentations
    Saw Franco, Zach Harvey, James Huchital, Paul Lastowicka, Joe Pasqualetti, Daniel Yaciuk
    (Students from Applied Mathematics, Engineering, and Computer Science)
    29 August, 2014, DON 2159
  • Mathematical Modeling of retinal vascular structure, Multiscale Methods, Image Segmentation (Spring 2014)
  • SPNM & Image Processsing Tools for ODEs & PDEs with Applications in Medical Science, Data Analysis, and Engineering (Fall 2013)
  • Structure Preserving Numerical Methods for ODEs and PDEs (Spring 2013)
  • Geometry and Symmetry Based Numerical Methods (Fall 2012)
  • Discrete Exterior Calculus (Spring 2012)
  • Exterior Calculus and Discrete Exterior Calculus (Fall 2011)

Conferences/Workshops attended

• BIRS 5-day workshop: Connections in Geometric Numerical Integration and Structure-Preserving Discretization, International Research Station for Mathematical Innovation and Discovery, Alberta, CA, June 11-16, 2017
• 4th Biennial Int. Symposium on Age Macular Degeneration (AMD), Harward Medical School, Department of Opthalmology, Boston, October 20-22, 2016, (P. A'Amore)
• CMS Winter Meeting, Session on on Recent Advances in Structure-Preserving Discretizations, Niagara Falls, Canada, December 2-5, 2016 (A. Bihlo, A. Wan)
• NYU-Oxford Workshop on Mathematical Models of Defects and Patterns, PIRE event, Courant Institute, NYU, NYC, January 5-8, 2016 (R. V. Kohn, J. M. Ball, G. Leoni, P. Palffy-Muhoray)
• IGAschool2014, Isogeometric Analysis, Fundamentals and Applications, ECCAM, Barcelona, Spain, July 27, 2014 (E.H. van Brummelen, T.J.R. Hughes, T. Kvamsdal, A. Reali, Sunday only)
• From the Clinic to Partial Differential Equations and Back: Emerging challenges for Cardiovascular Mathematics, ICERM, Brown University, Providence, RI, January 20-24, 2014 (L Grinberg, AM Robertson, PJ Blanco, A Veneziani, JN Oshinski, WR Taylor)
• AMS Fall Central Sectional Meeting, University of Akron, Akron, OH, October 20-21, 2012, Special Sessions on Applied Topology
• NSF/CBMS Conference: Finite Element Exterior Calculus (FEEC), ICERM, Brown University, Provience, RI, June 11-15, 2012 (A. Demlow, J. Guzman, D. Leykekhman)
• DDG@SoCG (Geometry Processing and Physical Simulations), 28th ACM Symposium on Computational Geometry, Chapel Hill, NA, June 18-20, 2012 (A. Hirani, M. Desbrun)

Seminars and Workshop at IUPUI (previous)

• Applied Math Seminar (Fall 2010)
• Workshop Discrete Differential Geometry for Multiphase Flow Problems
  (April 2010, Organizer, with G. Guidoboni)
• Red Blood Cell Seminar (Spring 2010)
• Modelling Red Blood Cells using Differential Forms (Fall 2009)
  Text: Differential Forms with Applications to the Physical Sciences, Harley Flanders, Dover, 1989
  The Geometry of Physics, Theodore Frankel, Cambridge, 2004
• Modelling Red Blood Cells using Shell Theory (Summer 2008)
  Text: Cosserat Theories, Shells, Rods and Points, M.B. Rubin, Kluwer, 2000

Previous Teaching SUNY Poly (SUNY IT), IUPUI, RHIT

• MAT 280 Linear Algebra (Fall 2017, 2018)
• MAT 260 Ordinary Differential Equations & Series Solutions
• MAT 152 Calculus II (Fall 2013, Spring/Fall 2014)
• MAT 253 Calculus III (2012 - 2017)
• MAT 460 Numerical Differential Equations Spring 2015, Spring 2016, Spring 2017)
• MAT 423 Vector and Tensor Calculus (Fall 2014 Flyer, Fall 2016 Flyer)
• MAT 460 Numerical Differential Equations (Fall 2012, Spring 2016) Flyer
• MAT 112 Elements of Calculus (Fall 2011, 2 sections. Spring 2012)
• Vector Calculus (second part of Spring semester 2011, maternity cover), IUPUI
  Text: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, Hubbard and Hubbard
• Multidimensional Mathematics (Spring 2011), Multivariate Calculus (Fall 2010), Analytic Geometry and Calculus II (Spring 2010, Fall 2009), IUPUI
  Text: Calculus, Sixth Edition, by James Stewart and Notes
• Calculus II, Differential Equations, Matrix Algebra and Systems of Differential equations, Vector Calculus, RHIT

Employment

• current: Associate Professor, Department of Mathematics and Physics, SUNY Polytechnic Institute (Former State University of New York Institute of Technology), NY
• 2011-2018: Assistant Professor, Department of Mathematics and Physics, SUNY Polytechnic Institute (Former State University of New York Institute of Technology), NY
• 2009-2011: Research Associate, Department of Mathematical Sciences, Indiana University Purdue University Indianapolis (IUPUI), IN
• 2007-2008: Visiting Assistant Professor, Department of Mathematics, Rose-Hulman Institute of Technology (RHIT), IN
• 2004-2006: Part Time Lecturer, Project Group Applied Mathematics, Institute of Mathematics, Berlin University of Technology (TUB), Germany
• 1998-2004: One of two heads of the Project Group Applied Mathematics, Institute of Mathematics, TUB, Germany