Research

Publications:

2018:

“A probabiliistic forecast using a Lagrangian sea-ice model: appliction to search and rescue operations,” To appear in The Cryosphere (2018) (with Matthias Rabatel, Alberto Carrassi, Pierre Rampal and Laurent Bertino)

“The Maslov Index and instability of pulses in gradient reaction-diffusion systems,” To appear in Phil. Trans. Roy. Soc. A (with Margaret Beck, Graham Cox, Yuri Latushkin, Kelly McQuighan, and Alim Sukhtayev)

“On the Existence and Stability of Fast Traveling Waves in a Doubly-Diffusive FitzHughNagumo System.” arXiv preprint arXiv:1709.09132 (2017). To appear in SIAM Journal on Applied Dynamical Systems (2018) (with Paul Cornwell)

2017:

“A dynamical approach to phytoplankton blooms,” Discrete & Continuous Dynamical Systems-A 37, no. 2 (2017): 859-878. (with Bevin Maultsby)

“Rank deficiency of Kalman error covariance matrices in linear perfect model,” SIAM Journal on Control and Optimization 55, no. 2 (2017): 741-759. (with Karthik S. Gurumoorthy, Colin Grudzien, Amit Apte, and Alberto Carrassi)

“Degenerate Kalman filter error covariances and their convergence onto the unstable subspace.” SIAM/ASA Journal on Uncertainty Quantification 5, no. 1 (2017): 304333. (with Marc Bocquet, Karthik Gurumoorthy, Amit Apte, Alberto Carrassi, and Colin Grudzien)

“A coherent structure approach for parameter estimation in Lagrangian Data Assimilation.” Physica D 360, 36-45 (2017). (with John Maclean and Naratip Santitissadeekorn)

“Counting spectrum via the Maslov index for one dimensional -periodic Schroedinger operators.” Proceedings of the American Mathematical Society 145, no. 1 (2017): 363-377 (with Yuri Latushkin and Selim Sukhtaiev)

2016:

“The Maslov and Morse indices for multidimensional Schroedinger operators with matrix valued potentials,” Transactions of the American Mathematical Society 368, 11 (2016): 8145-8207. (with Graham Cox, Yuri Latushkin, and Alim Sukhtayev)

“Manifold decompositions and indices of Schroedinger operators,” Indiana Univ. Math. J. 66 5 (2017), 15731602 (with Graham Cox and Jeremy Marzuola)

“Mixed mode oscillations of the El-Nin˜o-Southern Oscillation,” Journal of the Atmospheric Sciences 73, no. 4 (2016): 1755-1766. (with Andrew Roberts, Esther Widiasih, Axel Timmermann and John Guckenheimer)

2015:

“Approximation of random slow manifolds and inertial particles under uncertainty,” Journal of Dynamics and Differential Equations 27 (2015), 961-979 (with Jinqiao Duan and Jian Ren)

“Mixed-mode oscillations in a conceptual climate model,” Physica D 292 (2015) 7083(with Andrew Roberts, Esther Widiasih and Martin Wechselberger)

“A Morse index theorem for elliptic operators on bounded domains,” Comm. PDE 40 (2015) 1467-1497 (with Graham Cox and Jeremy Marzuola)

“Two-stage filtering for joint state-parameter estimation,” Monthly Weather Review 143 (2015) 20282042 (with Naratip Santitissadeekorn)

“A Bimodality Trap in Model Projections,” Chaos: An Interdisciplinary Journal of Nonlinear Science 25 (2015) 036412 (2015); (with Naratip Santitissadeekorn)

2014:

“Observing System Simulation Experiments of Cross-Layer Lagrangian Data Assimilation,” Dynamics of Atmospheres and Oceans, 66 (2014) 77-93 (with Naratip Santitissadeekorn, Elaine T. Spiller, Regis Rutarindwa, Liyan Liu, and Kayo Ide)

“Spectral and Modulational Stability of Periodic Wavetrains for the Nonlinear Klein-Gordon Equation,” Journal of Differential Equations 257 (2014), 4632-4703 (with Robert Marangell, Peter Miller and Ram´on Plaza)

2013:

“The Morse and Maslov indices for matrix Hill’s Equations,” Proceedings of Symposia in Pure Mathematics, 87 (2013) (with Y.Latushkin and R.Marangell)

“On the stability analysis of periodic sineGordon traveling waves,” Physica D, 251 (2013) (with Robert Marangell, Peter Miller and Ram´on Plaza)

“The impact of nonlinearity in Lagrangian data assimilation,” Nonlin. Processes Geophys., 20 (2013) (with Amit Apte)

“Assimilating en-route Lagrangian observations,” Tellus A 65 (2013) (with Elaine Spiller and Amit Apte)

2012:

“Stability of Traveling Wave Solutions to the Sine-Gordon Equation” Discrete and Continuous Dynamical Systems -Series S 5 (2012) (with R.Marangell)

“Unstable gap solitons in inhomogeneous nonlinear Schr¨odinger equations,” Journal of Differential Equations, 253 (2012) (with Hadi Susanto and Robert Marangell)

“On the existence of high Lewis number combustion fronts,” Mathematics and Computers in Simulation, 82 (2012) (with A.Ghazaryan)

2011:

“Capturing eddy shedding in the Gulf of Mexico from Lagrangian observations” Physica D 240 (2011) (with G.Vernier`es and K.Ide)

“Multi-dimensional Morse index theorems and a symplectic view of elliptic boundary value problems” Transactions AMS 363 (2011) (with J.Deng)

2010:

“Solitary waves of the regularized short pulse and Ostrovsky equations” SIAM Journal of Mathematical Analysis 41 (2010) (with N.Costanzino and V. Manukian)

“Localized standing waves in inhomogeneous Schr¨odinger equations” Nonlinearity 23 (2010) (with R. Marangell and H. Susanto)

2009:

“On the stability of high Lewis number combustion fronts” Discrete and Continuous Dynamical Systems 24 (2009) (with A.Ghazaryan)

“Generalized exchange lemmas and orbits heteroclinic to invariant manifolds” Discrete and Continuous Dynamical Systems 2 (2009) (with S.-K.Tin)

“Capturing deviation from ergodicity at different scales” Physica D 238 (2009) (with S.Scott, T.C.Redd, L.Kuznetsov, and I.Mezi´c)

“Existence of multi-pulse solutions of the regularized short pulse and Ostrovsky equations” JDDE 21 (2009) (with V.Manukian, N.Costanzino and B. Sandstede)

2008:

“Using flow geometry for drifter deployment in Lagrangian data assimilation” Tellus A 60 (2008) 321-335 (with H.Salman and K.Ide)

“Modified particle filter methods for assimilating Lagrangian data into a point-vortex model” Physica D 237 (2008) 1498-1506 (with E.T. Spiller, A. Budhiraja, and K. Ide)

“A Bayesian approach to Lagrangian data assimilation” Tellus A 60 (2008) 336-347 (with A.Apte and A.Stuart)

“Data assimilation: mathematical and statistical perspectives” Int. J. Num. Meth. Fluids 56 (2008) 1033-1046 (with A.Apte, A.M.Stuart and J.Voss)

“Electrical waves in a one-dimensional model of cardiac tissue” SIAM Journal of Applied Dynamical Systems 7 (2008) 1558-1581 (with M.Beck, D.Schaefer and M.Wechselberger)

“The suppression of four-wave mixing by random dispersion” to appear in SIAM Journal of Applied Mathematics 69 (2008) (with R.Horne and T. Sch¨afer)