Tensor Analysis, Heinz Schade, Klaus Neemann, translated by Andrea Dziubek, Edmond Rusjan.
De Gruyter. 2018 ISBN 978-3-11-040426-5
(German version, goodreads).
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. The book 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. The German version is in its 3rd revised edition.
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:1101.5718
Equations for Two-Phase Flows: A Primer. Meccanica, Vol 47(8), pp 1819-1836. 2012 arxiv: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)
Research Projects
Geometric Mechanics and Structure Preserving Numerical Methods of (Cosserat) Shell Elasticity:
Many phenomena in physical, engineering, and biological systems are modeled by elastic shells. In contrast to classical continuum theory, where the smallest constitutive element of media is the point-particle, in Cosserat theory translations and rotations have a similar status. Cosserat shell models could be the key in understanding chain-complexes - and chain-complexes are fundamental for deriving structure preserving numerical methods. [International collaborators and workshops]
Exterior Calculus and Finite Element Exterior Calculus:
We model problems from science and engineering in exterior calculus language and solve them using the mixed methods of FEEC. We implement and analyze solution algorithms in NGSolve, a modern FE software package for partial differential equations on complex geometries. The goal is to demonstrate the potential of these methods for teaching and in applications. [Undergraduate research]
Combining Image Analysis and Blood Flow Simulation:
Geometric reconstruction of vascular tree networks is a critical step in the development of a physically based patient specific blood flow analysis framework. To accurately extract vascular networks from patient data, advanced image segmentation and classification approaches are necessary. Together with M. Reale and E. Rusjan (SUNY Poly) we combine image analysis and blood flow simulation in an end-to-end system to determine the resulting tree's feasibility. [SUNY POLY collaboration]
Ocular Blood Flow Modeling (previous):
Together with G. Guidoboni, (Electrical and Computer Engineering, University of Maine), A. Hirani, (Math, University of Illinois) and E. Rusjan (SUNY Poly), we developed a computational model to theoretically investigate retinal perfusion, i.e., hemodynamics in the microvasculature nourishing the retinal tissue. 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. [Previous work]
Research Activites, SUNY Poly
Utica Fall Workshop 2023
Geometric Mechanics and Structure Preserving Discretizations of Shell Elasticity
July 17 - July 28, 2023: A. Dziubek, M. Karow, M. Neunteufel, K. Hu
2 talks by Michael Neunteufel, Analysis and Scientific Computing, TU Wien, Austria,
co-developer of NGSolve
Utica Fall Workshop 2019
Geometric Mechanics and Structure Preserving Discretizations of Shell Elasticity
August 27 - September 2, 2019: A. Dziubek, M. Karow, R. Lowry, S. Sadik, C. Stoica, E. Rusjan
These two workshops are follow-up workshops to the 2015 Workshop
August 24 - August 30, 2015:
A. Dziubek, A. Hirani, A. Angoshtari, C. Cafaro, C. Stoica, E. Rusjan, F. Valiquette, H. Heumann, K. Kalyanaraman, M. Mohamed, M. Karow, R. Lowry, T. Schmah, T. Sadigov, W. Chen, W. Bauer, Z. Thomova, D. Yaciuk, M. Yermakov
Undergraduate Research Activities, SUNY Poly
FEEC - Independent Study (Fall 2023) and SUNY Undergraduate Research Program (Summer 2024) Student Poster Presentations (in addition to SUNY Poly Showcase Day Posters)
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.
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)
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
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
Lecture Series on 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
Lecture Series on Modelling Red Blood Cells using Shell Theory, Invited Speaker. (Summer 2008)
Text: Cosserat Theories, Shells, Rods and Points, M.B. Rubin, Kluwer, 2000
Classes taught, SUNY Poly (SUNY IT), IUPUI, RHIT
MAT 491 Independent Study, Finite Element Exterior Calculus and Mixed Methods for model problems, using NGSolve (Fall 2023)
MAT 112 Elements of Calculus (Fall 2011, 2 sections. Spring 2012)
MAT 151 Calculus I (Spring 2021)
MAT 152 Calculus II (Fall 2013, Spring/Fall 2014)
MAT 230 Ordinary Differential Equations (Fall 2019)
MAT 253 Calculus III (2012 -- 2017, Fall 2020, 2023)
MAT 260 Ordinary Differential Equations & Series Solutions
MAT 280 Linear Algebra (Fall 2017, 2018, 2019, 2021, 2022, Spring 2020, 2022, 2023)
MAT 423 Vector and Tensor Calculus (Fall 2016, 2021)
MAT 460 Numerical Differential Equations (Springs 2015 -- 2023)
MAT 480 Advanced Linear Algebra (undergraduate) (Spring/Fall 2021)
MAT 502 Linear Algebra (graduate), Advanced Certificate CMM (Fall 2020)
MAT 560 Numerical Differential Equations, Advanced Certificate CMM (Spring 2020)
IUPUI: Vector Calculus, Multidimensional Mathematics, Multivariate Calculus, Analytic Geometry and Calculus II
RHIT: Calculus II, Differential Equations, Matrix Algebra and Systems of Differential equations, Vector Calculus
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: Co-chair of the Project Group Applied Mathematics, Institute of Mathematics,
TUB, Germany