Refereed Journal Publications

Submitted papers:

23. B. Akers, D.M. Ambrose, and J.D. Wright. Traveling waves from the arclength parameterization: Vortex sheets with surface tension. Submitted, 2012. [Preprint.]

Accepted papers:

22. D.M. Ambrose, M. Siegel, and S. Tlupova. A small-scale decomposition for 3D boundary integral computations with surface tension. J. Comp. Phys., Accepted, 2013. [Preprint.]
21. D.M. Ambrose, M. Kondrla, and M. Valle. Computing time-periodic solutions of a model for the vortex sheet with surface tension. Quart. Appl. Math., Accepted, 2013. [Preprint.]
20. D.M. Ambrose. The zero surface tension limit of two-dimensional interfacial Darcy flow. J. Math. Fluid Mech., Accepted, 2013. [Preprint.]
19. D.M. Ambrose and J.D. Wright. Dispersion vs. anti-diffusion: Well-posedness in variable coefficient and quasilinear equations of KdV-type. Indiana U. Math. J., Accepted, 2012. [Arxiv.]
18. D.M. Ambrose and J.D. Wright. Traveling waves and weak solutions for an equation with degenerate dispersion. Proc. Amer. Math. Soc., Accepted, 2012.

Published papers:

17. T. Milgrom and D.M. Ambrose. Temporal boundary value problems in interfacial fluid dynamics. Appl. Anal., 92:922-948, 2013.
16. D.M. Ambrose and S. Moskow. Scattering of electromagnetic waves by thin high contrast dielectrics: Effects of the object boundary. Comm. Math. Sci., 11: 293-314, 2013.
    
15. D.M. Ambrose, G. Simpson, J.D. Wright, and D.G. Yang. Ill-posedness of degenerate dispersive equations. Nonlinearity, 25: 2655-2680, 2012.
    
14. D.M. Ambrose and M. Siegel. A non-stiff boundary integral method for 3D porous media flow with surface tension. Math. Comput. Simulation, 82:968-983, 2012.
    
13. D.M. Ambrose, J.L. Bona, and D.P. Nicholls. Well-posedness of a model for water waves with viscosity. Discrete Contin. Dyn. Syst. Ser. B, 17:1113-1137, 2012.
    
12. D.M. Ambrose and J. Wilkening. Computation of time-periodic solutions of the Benjamin-Ono equation. J. Nonlinear Sci., 20:277-308, 2010.
    
11. D.M. Ambrose and J. Wilkening. Computation of symmetric, time-periodic solutions of the vortex sheet with surface tension. Proc. Natl. Acad. Sci. USA, 107:3361-3366, 2010.
    
10. D.M. Ambrose, M.C. Lopes Filho, H.J. Nussenzveig Lopes, and W.A. Strauss. Transport of interfaces with surface tension by 2D viscous flows. Interfaces Free Bound., 12:23-44, 2010.
    
9. D.M. Ambrose and J.D. Wright. Preservation of support and positivity for solutions of degenerate evolution equations. Nonlinearity, 23:607-620, 2010.
   
8. D.M. Ambrose and J. Wilkening. Global paths of time-periodic solutions of the Benjamin-Ono equation connecting pairs of traveling waves. Commun. Appl. Math. Comput. Sci., 4:177-215, 2009.
   
7. D.M. Ambrose. Singularity formation in a model for the vortex sheet with surface tension. Math. Comput. Simulation, 80:102-111, 2009.
   
6. D.M. Ambrose and N. Masmoudi. The zero surface tension limit of three-dimensional water waves. Indiana U. Math. J., 58:479-522, 2009.
   
5. D.M. Ambrose and N. Masmoudi. Well-posedness of 3D vortex sheets with surface tension. Comm. Math. Sci., 5:391-430, 2007.
   
4. D.M. Ambrose. Well-posedness of two-phase Darcy flow in 3D. Quart. Appl. Math., 65:189-203, 2007.
   
3. D.M. Ambrose and N. Masmoudi. The zero surface tension limit of two-dimensional water waves. Comm. Pure Appl. Math, 58:1287-1315, 2005.
   
2. D.M. Ambrose. Well-posedness of two-phase Hele-Shaw flow without surface tension. European J. Appl. Math., 15:597-607, 2004.
   
1. D.M. Ambrose. Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal., 35:211-244, 2003.
   

Refereed Conference Proceedings

Published papers:

4. D.M. Ambrose and J. Wilkening. Computation of time-periodic solutions of nonlinear systems of partial differential equations. Proceedings of Hyperbolic Problems: Theory, Numerics, and Applications. Beijing, China (2010). 2012, 273-280, Higher Education Press.
3. D.M. Ambrose. Short-time well-posedness of irrotational free-surface problems in 3D fluids. Proceedings of Hyperbolic Problems: Theory, Numerics, and Applications. Lyon, France (2006). 2008, 307-314, Springer-Verlag.
2. D.M. Ambrose. Regularization of the Kelvin-Helmholtz instability by surface tension. Phil. Trans. R. Soc. A. 365:2253-2266, 2007. Proceedings of the Semester on Wave Motion, Institute Mittag-Leffler (2005).
1. D.M. Ambrose. Short-time well-posedness of free-surface problems in 2D fluids. Proceedings of Hyperbolic Problems: Theory, Numerics, and Applications. Osaka, Japan (2004). 2006, 247-254, Yokohama Publishers.

External Funding

• PI for NSF Grant DMS-1016267, Collaborative Research: Efficient Surface-Based Numerical Methods for 3D Interfacial Flow with Surface Tension. $269,989. October 1, 2010 -- September 30, 2013. [This is a collaborative grant with Michael Siegel of NJIT.]
• PI for NSF Grant DMS-1008387, Dispersive PDE and Interfacial Fluid Dynamics. $159,000. September 15, 2010 -- August 31, 2013.
• PI for NSF grant DMS-0707807, Long-Time Behavior of Free-Surface Problems in Fluid Dynamics. $119,999. June 15, 2007 -- May 31, 2010. [Renumbered as DMS-0926378.]
• PI for NSF grant DMS-0406130, Analytical and Computational Approaches to Free-Surface Problems in Fluid Dynamics. $81,143. June 1, 2004 -- May 31, 2007. [Renumbered as DMS-0610898.]

Courses Taught at Drexel (Course webpages are available at learning.drexel.edu)

• Winter 2013: Math 123 (Calculus III), Math 210 (Differential Equations)
• Fall 2012: Math 110 (Precalculus), Math 210 (Differential Equations)
• Winter 2012: Math 210 (Differential Equations), Math 506 (Principles of Analysis II)
• Fall 2011: Math 210 (Differential Equations), Math 505 (Principles of Analysis I)
• Spring 2011: Math 499 (Independent Study/Differential Equations)
• Winter 2011: Math 210 (Differential Equations), Math 323 (Partial Differential Equations)
• Fall 2010: Math 121 (Calculus I), Math 680 (Special Topics: Fluid Dynamics)
• Winter 2010: Math 102 (Introduction to Analysis II), Math 210 (Differential Equations), Math 497 (Independent Study/Differential Equations II)
• Fall 2009: Math 121 (Calculus I), Math 210 (Differential Equations)
• Winter 2009: Math 210 (Differential Equations), Math 323 (Partial Differential Equations)
• Fall 2008: Math 121 (Calculus I), Math 210 (Differential Equations)