Research Output 1983 2017

2017

A dynamical approach to phytoplankton blooms

Jones, C. K. R. T. & Maultsby, B. Feb 1 2017 In : Discrete and Continuous Dynamical Systems- Series A. 37, 2, p. 859-878 20 p.

Research output: Contribution to journalArticle

Algae
Phytoplankton
Advection-diffusion
Existence and Uniqueness Results
Advection
2 Citations

Counting spectrum via the Maslov index for one dimensional θ−periodic schrÖdinger operators

Jones, C. K. R. T., Latushkin, Y. & Sukhtaiev, S. 2017 In : Proceedings of the American Mathematical Society. 145, 1, p. 363-377 15 p.

Research output: Contribution to journalArticle

Maslov Index
Schrödinger Operator
Mathematical operators
Counting
Boundary conditions
2016
1 Citations

Geometric phase in the Hopf bundle and the stability of non-linear waves

Grudzien, C. J., Bridges, T. J. & Jones, C. K. R. T. Nov 1 2016 In : Physica D: Nonlinear Phenomena. 334, p. 4-18 15 p.

Research output: Contribution to journalArticle

bundles
eigenvalues
traveling waves
dynamical systems
linear operators
4 Citations

Mixed-mode oscillations of El Niño-Southern Oscillation

Roberts, A., Guckenheimer, J., Widiasih, E., Timmermann, A. & Jones, C. K. R. T. Apr 1 2016 In : Journal of the Atmospheric Sciences. 73, 4, p. 1755-1766 12 p.

Research output: Contribution to journalArticle

El Nino-Southern Oscillation
oscillation
El Nino
climate modeling
climate

On the spectral and modulational stability of periodic wavetrains for nonlinear Klein-Gordon equations

Jones, C. K. R. T., Marangell, R., Miller, P. D. & Plaza, R. G. Jun 1 2016 In : Bulletin of the Brazilian Mathematical Society. 47, 2, p. 417-429 13 p.

Research output: Contribution to journalArticle

Nonlinear Klein-Gordon Equation
Modulational Instability
Spectral Analysis
Stability Analysis
Modulation
3 Citations

The Morse and Maslov indices for multidimensional Schrödinger operators with matrix-valued potentials

Cox, G., Jones, C. K. R. T., Latushkin, Y. & Sukhtayev, A. Jan 1 2016 In : Transactions of the American Mathematical Society. 368, 11, p. 8145-8207 63 p.

Research output: Contribution to journalArticle

Maslov Index
Morse Index
Schrödinger Operator
Boundary conditions
Eigenvalue
2015
2 Citations

A bimodality trap in model projections

Santitissadeekorn, N. & Jones, C. Mar 23 2015 In : Chaos. 25, 3, 1.4915090

Research output: Contribution to journalArticle

Bimodality
Trap
projection
traps
Projection
5 Citations

A Morse Index Theorem for Elliptic Operators on Bounded Domains

Cox, G., Jones, C. K. R. T. & Marzuola, J. L. Aug 3 2015 In : Communications in Partial Differential Equations. 40, 8, p. 1467-1497 31 p.

Research output: Contribution to journalArticle

Morse Index
Index Theorem
Elliptic Operator
Boundary value problems
Stars
1 Citations

Approximation of Random Slow Manifolds and Settling of Inertial Particles Under Uncertainty

Ren, J., Duan, J. & Jones, C. K. R. T. Dec 1 2015 In : Journal of Dynamics and Differential Equations. 27, 3-4, p. 961-979 19 p.

Research output: Contribution to journalArticle

Slow Manifold
Stochastic Dynamical Systems
Uncertainty
Stable Manifold
Dimension Reduction
9 Citations

Mixed mode oscillations in a conceptual climate model

Roberts, A., Widiasih, E., Wechselberger, M. & Jones, C. K. R. T. Feb 1 2015 In : Physica D: Nonlinear Phenomena. 292-293, p. 70-83 14 p.

Research output: Contribution to journalArticle

climate models
oscillations
climate
carbon
funnels
Climate

Preface to the series

Jones, C. K. R. T., Sandstede, B. & Young, L. S. Aug 8 2015 Dynamics of Partial Differential Equations. Springer International Publishing, p. v-vi

Research output: Chapter in Book/Report/Conference proceedingForeword/postscript

Series
8 Citations

Two-stage filtering for joint state-parameter estimation

Santitissadeekorn, N. & Jones, C. 2015 In : Monthly Weather Review. 143, 6, p. 2028-2042 15 p.

Research output: Contribution to journalArticle

parameter estimation
parameter
Kalman filter
data assimilation
climate modeling
2014

Observing System Simulation Experiments of cross-layer Lagrangian data assimilation

Santitissadeekorn, N., Spiller, E. T., Jones, C., Rutarindwa, R., Liu, L. & Ide, K. Jan 1 2014 In : Dynamics of Atmospheres and Oceans. 66, p. 77-93 17 p.

Research output: Contribution to journalArticle

data assimilation
Vortex flow
simulation
experiment
Experiments
8 Citations

Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation

Jones, C. K. R. T., Marangell, R., Miller, P. D. & Plaza, R. G. Jan 1 2014 In : Journal of Differential Equations. 257, 12, p. 4632-4703 72 p.

Research output: Contribution to journalArticle

Nonlinear Klein-Gordon Equation
Spectral Stability
Spectral Analysis
Modulation
Periodic Travelling Wave Solution
2013
13 Citations

On the stability analysis of periodic sine-Gordon traveling waves

Jones, C. K. R. T., Marangell, R., Miller, P. D. & Plaza, R. G. May 15 2013 In : Physica D: Nonlinear Phenomena. 251, p. 63-74 12 p.

Research output: Contribution to journalArticle

traveling waves
propagation velocity
wave equations
3 Citations

The impact of nonlinearity in Lagrangian data assimilation

Apte, A. & Jones, C. K. R. T. 2013 In : Nonlinear Processes in Geophysics. 20, 3, p. 329-341 13 p.

Research output: Contribution to journalArticle

assimilation
data assimilation
Kalman filters
nonlinearity
Kalman filter
2012
1 Citations

On the existence of high Lewis number combustion fronts

Ghazaryan, A. & Jones, C. Feb 1 2012 In : Mathematics and Computers in Simulation. 82, 6, p. 1133-1141 9 p.

Research output: Contribution to journalArticle

Combustion
Geometric Singular Perturbation Theory
Reaction rates
Ignition
Reaction Rate
4 Citations

The spectrum of travelling wave solutions to the sine-Gordon equation

Jones, C. K. R. T. & Marangell, R. Oct 2012 In : Discrete and Continuous Dynamical Systems - Series S. 5, 5, p. 925-937 13 p.

Research output: Contribution to journalArticle

sine-Gordon equation
Sine-Gordon Equation
Traveling Wave Solutions
Point Spectrum
Essential Spectrum
7 Citations

Unstable gap solitons in inhomogeneous nonlinear Schrödinger equations

Marangell, R., Susanto, H. & Jones, C. K. R. T. Aug 15 2012 In : Journal of Differential Equations. 253, 4, p. 1191-1205 15 p.

Research output: Contribution to journalArticle

Nonlinear Schrödinger Equation
Solitons
Unstable
Phase Portrait
Inhomogeneity
2011
6 Citations

Capturing eddy shedding in the Gulf of Mexico from Lagrangian observations

Vernieres, G., Jones, C. K. R. T. & Ide, K. Jan 15 2011 In : Physica D: Nonlinear Phenomena. 240, 2, p. 166-179 14 p.

Research output: Contribution to journalArticle

Gulf of Mexico
assimilation
vortices
detachment
stations
15 Citations

Multi-dimensional Morse index theorems and a symplectic view of elliptic boundary value problems

Deng, J. & Jones, C. Mar 2011 In : Transactions of the American Mathematical Society. 363, 3, p. 1487-1508 22 p.

Research output: Contribution to journalArticle

Morse Index
Index Theorem
Elliptic Boundary Value Problems
Boundary value problems
Boundary conditions

Will climate change mathematics (?)

Jones, C. K. R. T. Jun 2011 In : IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications). 76, 3, p. 353-370 18 p.

Research output: Contribution to journalArticle

Climate Change
Climate change
Climate
Earth (planet)
Mathematical models
2010
12 Citations

Localized standing waves in inhomogeneous Schrödinger equations

Marangell, R., Jones, C. K. R. T. & Susanto, H. Sep 1 2010 In : Nonlinearity. 23, 9, p. 2059-2080 22 p.

Research output: Contribution to journalArticle

Standing Wave
standing waves
Schrödinger Equation
Excited States
defocusing
2009
12 Citations

Capturing deviation from ergodicity at different scales

Scott, S. E., Redd, T. C., Kuznetsov, L., Mezić, I. & Jones, C. K. R. T. Aug 1 2009 In : Physica D: Nonlinear Phenomena. 238, 16, p. 1668-1679 12 p.

Research output: Contribution to journalArticle

deviation
defects
dynamical systems
harmonic analysis
dyadics
7 Citations

Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations

Manukian, V., Costanzino, N., Jones, C. K. R. T. & Sandstede, B. Dec 2009 In : Journal of Dynamics and Differential Equations. 21, 4, p. 607-622 16 p.

Research output: Contribution to journalArticle

Ostrovsky Equation
Short Pulse
Flip
Orbit
Lyapunov-Schmidt Reduction
10 Citations

Generalized exchange lemmas and orbits heteroclinic to invariant manifolds

Jones, C. K. R. T. & Tin, S. K. Dec 2009 In : Discrete and Continuous Dynamical Systems - Series S. 2, 4, p. 967-1023 57 p.

Research output: Contribution to journalReview article

Heteroclinic Orbit
Invariant Manifolds
Lemma
Phase Space
Orbits
6 Citations

On the stability of high Lewis number combustion fronts

Ghazaryan, A. & Jones, C. K. R. T. Jul 2009 In : Discrete and Continuous Dynamical Systems. 24, 3, p. 809-826 18 p.

Research output: Contribution to journalArticle

Combustion
Spectral Stability
Wavefronts
Wave Front
Geometric Singular Perturbation Theory
18 Citations

Solitary waves of the regularized short pulse and ostrovsky equations

Costanzino, N., Manukian, V. & Jones, C. K. R. T. 2009 In : SIAM Journal on Mathematical Analysis. 41, 5, p. 2088-2106 19 p.

Research output: Contribution to journalArticle

Ostrovsky Equation
Short Pulse
Solitary Waves
Solitons
Regularization
2008
21 Citations

A Bayesian approach to Lagrangian data assimilation

Apte, A., Jones, C. K. R. T. & Stuart, A. M. Mar 2008 In : Tellus, Series A: Dynamic Meteorology and Oceanography. 60 A, 2, p. 336-347 12 p.

Research output: Contribution to journalArticle

data assimilation
Markov chain
Kalman filter
sampling
smoothing
33 Citations

Data assimilation: Mathematical and statistical perspectives

Apte, A., Jones, C. K. R. T., Stuart, A. M. & Voss, J. Mar 20 2008 In : International Journal for Numerical Methods in Fluids. 56, 8, p. 1033-1046 14 p.

Research output: Contribution to journalArticle

Data Assimilation
Probability distributions
Kalman filters
Optimal Solution
Dynamical systems
13 Citations

Electrical waves in a one-dimensional model of cardiac tissue

Beck, M., Jones, C. K. R. T., Schaeffer, D. & Wechselberger, M. 2008 In : SIAM Journal on Applied Dynamical Systems. 7, 4, p. 1558-1581 24 p.

Research output: Contribution to journalArticle

One-dimensional Model
Cardiac
Tissue
Essential Spectrum
Impulse
21 Citations

Modified particle filter methods for assimilating Lagrangian data into a point-vortex model

Spiller, E. T., Budhiraja, A., Ide, K. & Jones, C. K. R. T. Jul 15 2008 In : Physica D: Nonlinear Phenomena. 237, 10-12, p. 1498-1506 9 p.

Research output: Contribution to journalArticle

Point Vortex
Filter Method
Particle Method
Extended Kalman filters
Particle Filter
1 Citations

The suppression of four-wave mixing by random dispersion

Horne, R. L., Jones, C. K. R. T. & Schäfer, T. 2008 In : SIAM Journal on Applied Mathematics. 69, 3, p. 690-703 14 p.

Research output: Contribution to journalArticle

Four-wave Mixing
Four wave mixing
Optical Communication
Probability Distribution Function
White noise
22 Citations

Using flow geometry for drifter deployment in Lagrangian data assimilation

Salman, H., Ide, K. & Jones, C. K. R. T. Mar 1 2008 In : Tellus, Series A: Dynamic Meteorology and Oceanography. 60 A, 2, p. 321-335 15 p.

Research output: Contribution to journalArticle

drifter
data assimilation
geometry
targeting
vortex
2007
2 Citations

Preface

Ide, K. & Jones, C. K. R. T. Jun 1 2007 In : Physica D: Nonlinear Phenomena. 230, 1-2

Research output: Contribution to journalEditorial

35 Citations

Solitary waves under the competition of linear and nonlinear periodic potentials

Rapti, Z., Kevrekidis, P. G., Konotop, V. V. & Jones, C. K. R. T. Nov 23 2007 In : Journal of Physics A: Mathematical and Theoretical. 40, 47, p. 14151-14163 13 p.

Research output: Contribution to journalArticle

Nonlinear Lattice
Periodic Potential
Solitary Waves
Solitons
solitary waves
5 Citations

Traveling waves in porous media combustion: Uniqueness of waves for small thermal diffusivity

Ghazaryan, A., Gordon, P. & Jones, C. K. R. T. Dec 2007 In : Journal of Dynamics and Differential Equations. 19, 4, p. 951-966 16 p.

Research output: Contribution to journalArticle

Thermal Diffusivity
Combustion
Traveling Wave
Porous Media
Uniqueness
2006
50 Citations

A method for assimilating Lagrangian data into a shallow-water-equation ocean model

Salman, H., Kuznetsov, L., Jones, C. K. R. T. & Ide, K. Apr 1 2006 In : Monthly Weather Review. 134, 4, p. 1081-1101 21 p.

Research output: Contribution to journalArticle

shallow-water equation
ocean
Kalman filter
drifter
gyre
2005
8 Citations

Soliton broadening under random dispersion fluctuations: Importance sampling based on low-dimensional reductions

Moore, R. O., Schäfer, T. & Jones, C. K. R. T. Dec 15 2005 In : Optics Communications. 256, 4-6, p. 439-450 12 p.

Research output: Contribution to journalArticle

Importance sampling
Solitons
solitary waves
sampling
probability distribution functions
3 Citations

The effects of weak randomness on pulse interactions and four-wave mixing products

Horne, R. L., Jones, C. K. R. T. & Schäfer, T. Jun 1 2005 In : Physica D: Nonlinear Phenomena. 205, 1-4, p. 70-79 10 p.

Research output: Contribution to journalArticle

Four-wave Mixing
Four wave mixing
four-wave mixing
Randomness
products
87 Citations

Ultra-short pulses in linear and nonlinear media

Chung, Y., Jones, C. K. R. T., Schäfer, T. & Wayne, C. E. 2005 In : Nonlinearity. 18, 3, p. 1351-1374 24 p.

Research output: Contribution to journalArticle

Ultrashort Pulse
Maxwell equations
Ultrashort pulses
Short Pulse
Wave equations
6 Citations

Viscous perturbations of marginally stable Euler flow and finite-time Melnikov theory

Grenier, E., Jones, C. K. R. T., Rousset, F. & Sandstede, B. Mar 2005 In : Nonlinearity. 18, 2, p. 465-483 19 p.

Research output: Contribution to journalArticle

Vorticity
base flow
Euler
Viscous Dissipation
Perturbation
2004
5 Citations

Assessing coherent feature kinematics in ocean models

Kuznetsov, L., Jones, C. K. R. T., Toner, M. & Kirwan, A. D. Apr 15 2004 In : Physica D: Nonlinear Phenomena. 191, 1-2, p. 81-105 25 p.

Research output: Contribution to journalArticle

ocean models
Ocean
Kinematics
kinematics
Forcing
15 Citations

Cross-jet Lagrangian transport and mixing in a 2 1/2-layer model

Yuan, G. C., Pratt, L. J. & Jones, C. K. R. T. Sep 2004 In : Journal of Physical Oceanography. 34, 9, p. 1991-2005 15 p.

Research output: Contribution to journalArticle

active layer
potential vorticity
barotropic instability
baroclinic instability
meander
8 Citations

Dispersion-managed solitons via an averaged variational principle

Jackson, R. K., Jones, C. K. R. T. & Zharnitsky, V. Mar 15 2004 In : Physica D: Nonlinear Phenomena. 190, 1-2, p. 63-77 15 p.

Research output: Contribution to journalArticle

variational principles
Solitons
Variational Principle
solitary waves
Constrained Minimization
7 Citations

Estimating the predictability of an oceanic time series using linear and nonlinear methods

Yuan, G. C., Lozier, M. S., Pratt, L. J., Jones, C. K. R. T. & Helfrich, K. R. Aug 15 2004 In : Journal of Geophysical Research C: Oceans. 109, 8

Research output: Contribution to journalArticle

Time series
time series analysis
estimating
time series
shelves
4 Citations

Stable pulse solutions for the nonlinear Schrödinger equation with higher order dispersion management

Moesert, J. T., Jones, C. K. R. T. & Zharnitsky, V. 2004 In : SIAM Journal on Mathematical Analysis. 35, 6, p. 1486-1511 26 p.

Research output: Contribution to journalArticle

Dispersion Management
Nonlinear equations
Nonlinear Schrödinger Equation
Communication Systems
Fiber Optics Communications
2003
73 Citations

A method for assimilation of Lagrangian data

Kuznetsov, L., Ide, K. & Jones, C. K. R. T. Oct 1 2003 In : Monthly Weather Review. 131, 10, p. 2247-2260 14 p.

Research output: Contribution to journalArticle

tracer
drifter
vortex flow
flow structure
Kalman filter
60 Citations

Chlorophyll dispersal by eddy-eddy interactions in the Gulf of Mexico

Toner, M., Kirwan, J. D., Poje, A. C., Kantha, L. H., Müller-Karger, F. E. & Jones, C. K. R. T. Apr 15 2003 In : Journal of Geophysical Research C: Oceans. 108, 4, p. 2-1 2 p.

Research output: Contribution to journalArticle

Gulf of Mexico
ocean color
chlorophylls
Chlorophyll
shelves