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: Research - peer-reviewArticle

Algae
Phytoplankton
Advection-diffusion
Existence and Uniqueness Results
Diffusion Model
1 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: Research - peer-reviewArticle

Maslov Index
Schrödinger Operator
Counting
Eigenvalue
Mathematical operators
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: Research - peer-reviewArticle

bundles
eigenvalues
traveling waves
dynamical systems
linear operators
3 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: Research - peer-reviewArticle

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: Research - peer-reviewArticle

Nonlinear Klein-Gordon Equation
Modulational Instability
Spectral Analysis
Stability Analysis
Modulation
2 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: Research - peer-reviewArticle

Maslov Index
Morse Index
Schrödinger Operator
Eigenvalue
Path
2015
2 Citations

A bimodality trap in model projections

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

Research output: Research - peer-reviewArticle

Bimodality
Trap
Projection
Model
projection
4 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: Research - peer-reviewArticle

Morse Index
Index Theorem
Elliptic Operator
Bounded Domain
Boundary value problems
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: Research - peer-reviewArticle

Slow Manifold
Uncertainty
Approximation
Stochastic Dynamical Systems
Stable Manifold
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: Research - peer-reviewArticle

climate models
oscillations
carbon
climate
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: ResearchForeword/postscript

Series
7 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: Research - peer-reviewArticle

parameter estimation
parameter
method
Kalman filter
data assimilation
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: Research - peer-reviewArticle

data assimilation
simulation
experiment
Vortex flow
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: Research - peer-reviewArticle

Nonlinear Klein-Gordon Equation
Spectral Stability
Spectral Analysis
Modulation
Periodic Travelling Wave Solution
2013
12 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: Research - peer-reviewArticle

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: Research - peer-reviewArticle

data assimilation
nonlinearity
effect
assimilation
Kalman filters
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: Research - peer-reviewArticle

Combustion
Model
Reaction rates
Ignition
Mathematical models
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: Research - peer-reviewArticle

Sine-Gordon Equation
Traveling Wave Solutions
Operator
sine-Gordon equation
Point Spectrum
6 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: Research - peer-reviewArticle

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: Research - peer-reviewArticle

Gulf of Mexico
vortices
assimilation
detachment
stations
14 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: Research - peer-reviewArticle

Morse Index
Index Theorem
Elliptic Boundary Value Problems
Oscillation
Boundary value problems
Climate Change
Climate
Climate change
Earth (planet)
Mathematical models
2010
12 Citations

Localized standing waves in inhomogeneous Schrödinger equations

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

Research output: Research - peer-reviewArticle

Standing Wave
Schrödinger Equation
standing waves
Excited States
Norm
2009
11 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: Research - peer-reviewArticle

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: Research - peer-reviewArticle

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: Research - peer-reviewReview article

Heteroclinic Orbit
Invariant Manifolds
Lemma
Phase Space
Orbit
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: Research - peer-reviewArticle

Combustion
Wavefronts
Spectral Stability
Wave Front
Model
16 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: Research - peer-reviewArticle

Ostrovsky Equation
Short Pulse
Solitary Waves
Regularization
Term
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: Research - peer-reviewArticle

data assimilation
distribution
method
Markov chain
Kalman filter
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: Research - peer-reviewArticle

Data Assimilation
Probability distributions
Optimal Solution
Kalman filters
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: Research - peer-reviewArticle

One-dimensional Model
Cardiac
Tissue
Essential Spectrum
Impulse
20 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: Research - peer-reviewArticle

Point Vortex
Filter Method
Particle Method
Particle Filter
Model
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: Research - peer-reviewArticle

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 2008 In : Tellus, Series A: Dynamic Meteorology and Oceanography. 60 A, 2, p. 321-335 15 p.

Research output: Research - peer-reviewArticle

drifter
data assimilation
geometry
method
targeting
2007
2 Citations

Preface

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

Research output: Research - peer-reviewEditorial

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: Research - peer-reviewArticle

Nonlinear Lattice
Periodic Potential
Solitary Waves
solitary waves
Solitons
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: Research - peer-reviewArticle

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 2006 In : Monthly Weather Review. 134, 4, p. 1081-1101 21 p.

Research output: Research - peer-reviewArticle

shallow-water equation
ocean
method
assimilation
Kalman filter
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: Research - peer-reviewArticle

solitary waves
sampling
Importance sampling
Solitons
simulation
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: Research - peer-reviewArticle

Four-wave Mixing
Randomness
Interaction
four-wave mixing
products
85 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: Research - peer-reviewArticle

Ultrashort Pulse
Maxwell equations
Ultrashort pulses
pulses
Short Pulse
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: Research - peer-reviewArticle

Vorticity
Euler
Perturbation
perturbation
Viscous Dissipation
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: Research - peer-reviewArticle

Ocean
Kinematics
Model
ocean models
kinematics
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: Research - peer-reviewArticle

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: Research - peer-reviewArticle

Variational Principle
Solitons
variational principles
solitary waves
pulses
6 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: Research - peer-reviewArticle

estimating
time series
method
time series analysis
methodology
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: Research - peer-reviewArticle

Dispersion Management
Nonlinear Schrödinger Equation
Communication Systems
Higher Order
Nonlinear equations
2003
73 Citations

A method for assimilation of Lagrangian data

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

Research output: Research - peer-reviewArticle

tracer
method
assimilation
drifter
vortex flow
56 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: Research - peer-reviewArticle

Gulf of Mexico
chlorophylls
shelves
vortices
interactions