Publications
In press
46. On flexible tubes conducting fluid: geometric nonlinear theory, stability and dynamics, with V. Putkaradze, to appear in J. Nonlin. Sci.
45. Lagrangian reductions and integrable systems in condensed matter, with M. Monastyrsky and T.~S. Ratiu, to appear in Comm. Math. Phys.
44. Dynamics of elastic strands with rolling contact, with V. Putkaradze, to appear in Physica D.
43. Dynamics and geometric control of flexible solar updraft towers, with M. Chi, V. Putkaradze, and P. Vorobieff, to appear in Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.
42. A dual pair for free boundary fluids, with C. Vizman, to appear in International Journal of Geometric Methods in Modern Physics.
41. Dirac reduction for nonholonomic mechanical systems on semidirect products, with H. Yoshimura, to appear in Advances in Applied Mathematics.
40. Multisymplectic variational integrators and space/time symplecticity, with F. Demoures and T. S. Ratiu, to appear in Analysis and Applications.
39. Discrete variational Lie group discretization of geometrically exact beam dynamics, with F. Demoures, S. Leyendecker, S. Ober-Blobaum, T. S. Ratiu, and Y. Weinand, to appear in Numerische Mathematiks, DOI 10.1007/s00211-014-0659-4.
2014
38. A geometric theory of selective decay with applications in MHD, with D. D. Holm [2014], Nonlinearity, 27, 1747-1777.
37. Principal bundles of embeddings and nonlinear Grassmannians, with C. Vizman [2014], J. Global Analysis and Geometry, 46, 293-312.
36. Multisymplectic Lie group variational integrators for a geometrically exact beam in R3, with F. Demoures, M. Kobilarov, and T. S. Ratiu [2014], Commun. Nonlin. Sci. Numer. Simulat., 19 (10), 3492-3512.
35. Exact geometric theory for flexible, fluid-conducting tubes, with V. Putkaradze [2014], C. R. Mécanique, 342, 79-84.
34. Integrable G-strands on semisimple Lie groups, with D. D. Holm and T. S. Ratiu [2014], J. Phys. A: Math. Theor., 47, 075201.
33. Dual pairs for nonabelian fluids, with C. Vizman [2014], to appear in Fields Institute Communications series, special volume in memory of Jerrold E. Marsden.
32. Variational discretization for rotating stratified fluids, with M. Desbrun, E. Gawlik, and V. Zeitlin [2014], Disc. Cont. Dyn. Syst. Series A 34(2), 479-511.
2013
31. Equivalent theories of liquid crystal dynamics, with T. S. Ratiu and C. Tronci [2013], Archive for Rational Mechanics and Analysis, 210 (3), 773–811.
30. Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphim groups, with C. Tronci and C. Vizman [2013], J. Geom. Mech. 5(1), 39-84.
29. Clebsch variational principles in field theories and singular solutions of covariant EPDiff equations [2013], Rep. Math. Phys. 71(2), 231-277.
28. Selective decay by Casimir dissipation in inviscid fluids, with D. D. Holm [2013], Nonlinearity 26, 495-524.
2012
27. Dynamics of elastic rods in perfect friction contact, with V. Putkaradze [2013], Phys. Rev. Lett., 109(24), 244303.
26. Reduced variational formulation in free boundary continuum mechanics, with J. E. Marsden and T. S. Ratiu [2012], J. Nonlin. Sci., 22(4), 463-497.
25. Vlasov moment flows and geodesics on the Jacobi group, with C. Tronci [2012], J. Math. Phys., 53, 123502.
24. Geometric dynamics of optimization, with D. D. Holm and T. S. Ratiu [2012], Comm. Math. Sci., 11(1), 163-231.
23. Invariant higher-order variational problems II, with D. D. Holm, D. Meier, T. S. Ratiu and F.-X. Vialard [2012], J. Nonlin. Sci., 22(4), 553-597.
22. Euler-Poincaré approaches to nematodynamics, with T. S. Ratiu and C. Tronci [2012], Act. Appl. Math., 120, 127-151.
21. Exact geometric theory of dendronized polymer dynamics, with D. D. Holm, V. Putkaradze, and T. S. Ratiu [2011], Adv. Appl. Math., 48, 535-574.
20. Invariant higher-order variational problems, with D. D. Holm, D. M. Meier, T. S. Ratiu, F.-X. Vialard [2011], Comm. Math. Phys., 309(2), 413-458.
2011
19. Un-reduction, with M. Bruveris, D. Ellis, D. D. Holm, [2011], Journal of Geometric Mechanics, 3(4), 363-387.
18. Lagrange-Poincaré field equations, with D. Ellis, D. D. Holm, and T. S. Ratiu, [2011], Journal of Geometry and Physics, 61(11), 2120-2146.
17. Geometry of nonabelian charged fluids, with T. S. Ratiu, [2011], Dynamics of PDEs, 8(1), 5-19.
16. Clebsch optimal control formulation in mechanics, with T. S. Ratiu, [2011], Journal of Geometric Mechanics, 3(1), 47-79.
15. Dual pairs in fluid dynamics, with C. Vizman, [2011], Annals of Global Analysis and Geometry, 41(1), 1-24.
14. Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions, with D. D. Holm, and T. S. Ratiu [2011], J. Brazilian Math. Soc., 42(4), 579-606.
13. The momentum map representation of images, with M. Bruveris, D. D. Holm, and T. S. Ratiu [2011], J. Nonlin. Sci., 21, 115–150.
2010
12. The helicity and vorticity of liquid-crystal flows, with C. Tronci [2010], Proc. R. Soc. A, Math. Phys. Eng. Sci., 467(2128), 1197-1213.
11. Reduction theory for symmetry breaking with applications to nematic systems, with C. Tronci [2010], Phys. D, 239(20-22), 1929–1947.
10. Symmetry reduced dynamics of charged molecular strands, with D. Ellis, D. D. Holm, V. Putkaradze, and T. S. Ratiu, [2010], Archive for Rational Mechanics and Analysis, 197 (2), 811–902.
9. A new Lagrangian dynamic reduction in field theory, with T. S. Ratiu, [2010], Annales de l’Institut Fourier, 16 (3), 1125–1160.
2009
8. Variational principles for spin systems and the Kirchhoff rod, with D. D. Holm, and T. S. Ratiu, [2009], Journal of Geometric Mechanics 1 (4)417–444.
7. On the classification of coadjoint orbits of the Sobolev Bott-Virasoro group, [2009], Journal of Functional Analysis, 256(9) 2815–2841.
6. The geometric structure of complex fluids, with T. S. Ratiu, [2009], Adv. Appl. Math., 42(2) 176–275.
2008
5. Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids, with T. S. Ratiu, [2008], Journal of Symplectic Geometry, 6(2) 189–237.
4. Affine Lie-Poisson reduction, Yang-Mills magnetohydrodynamics, and superfluids, with T. S. Ratiu, [2008], J. Phys. A: Math. Theor., 41 344007.
3. Poisson reduction and the Hamiltonian structure of the Euler-Yang-Mills equations, with T. S. Ratiu, [2008], Cont. Math., Weinstein vol. 450, 113–126.
2007
2. Group actions on chains of Banach manifolds and application to fluid dynamics, with T. S. Ratiu, [2007], Annals of Global Analysis and Geometry, 31(3), 287–328.
2005
1. The Lie-Poisson structure of the averaged Euler equations, with T. S. Ratiu[2005], Dynamics of Partial Differential Equations, 2(1),25–57.
Submitted papers
3. Understanding memristors and memcapacitors in engneering mechanics and applications, with J.-S. Pei, J. P. Wright, M. D. Todd, and S. F. Masri.
2. Weil-Petersson geodesics on the universal Techüller space, with T. S. Ratiu.
1. The geometry of Teichmüller Space and the Euler-Weil-Petersson equations, with J. E. Marsden and T. S. Ratiu.
Conference Proceedings
5. Asynchronous variational Lie group integration for geometrically exact beam dynamics, with F. Demoures, T. Leitz, S. Leyendecker, S. Ober-Blöbaum, and T. S. Ratiu [2013], Multibody Dynamics, ECCOMAS, Zagreb, Croatia, 01-04 July 2013.
4. Asynchronous variational Lie group integration for geometrically exact beam dynamics, with F. Demoures, T. Leitz, S. Leyendecker, S. Ober-Blöbaum, and T. S. Ratiu [2013], GAMM Annual Meeting, Novi Sad, Serbia, 18-22 March 2013.
3. Hamilton-Pontryagin principle for incompressible ideal fluids, with H. Yoshimura, [2011], Proceeding of the Sixth International Conference on Fluid Mechanics, Guangzhou, China.
2. Flexible beam in R3 under large overall motions and asynchronous variational integrators, with F. Demoures, J. Nembrini, T. S. Ratiu, and Y. Weinand [2011], IABSE-IASS Symposium, London.
1. Well-Posedness of higher dimensional Camassa-Holm equations, [2008], Bulletin of the Transilvania University of Brasov 15(50) Series B - 2008.
