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Our group:

Here is a list of our members and a short description of their main research interests.

For more information on a particular member please go to their personal webpage by clicking the desired name.

Prospective students and collaborators: If you want to get involved with our group please feel free to contact us.

[Members] - [Associate Members] - [Postdocs] - [Visitors] - [Research Students]


Phase engineering for a vortex pair:
Initial phase for a flat background Bose-Einstein condensate producing a vortex pair. To see the film click on the image


Peter Blomgren - Numerical analysis, image processing, partial differential equations.
My current research focuses on time reversal and imaging in complex (random) media. Imaging, time reversal, and communications in noisy environments require entirely different considerations from the usual ones in homogeneous, known environments. For example, super-resolution is the remarkable enhancement of refocusing of space-time fields when they are time-reversed by active transducer arrays in a random, unknown medium. I am also interested on image restoration. Given a measured image, the goal is to produce a more useful image according to some criteria, e.g. increase the smoothness as measured by a functional, subject to constraints imposed by estimates of the degradation of the image. In the past I reviewed some renormalization techniques, concerning period doubling bifurcations, chaos, and universality for logistic-type families.

Ricardo Carretero - Applied mathematics, nonlinear lattices, nonlinear waves.
My main research interests lie in Dynamical Systems and Computation applied to spatio-temporal systems. These include spatio-temporal nonlinear time series reconstruction, discrete breathers, solitons, nonlinear wave propagation, blowup and metastability in reaction-diffusion systems, adaptive mesh methods for solving Partial Differential Equations. I am particularly interested in the dynamics of chains of optical (fiber optics) or quantum matter (Bose-Einstein condensates) solitons. Of particular interest is the construction of extended and localized vibrational states. I also study the effects of introducing impurities leading to erratic motion of these localized vibrations.

Christopher Curtis - Applied mathematics, nonlinear waves, integrable systems.
My work focuses on the study of dynamics in nonlinear wave equations. These equations arise in a large number of physical problems, and they represent an important and active branch of applied mathematics. Thus my work sits at the intersection of mathematics and real world modeling. The techniques that I employ range from rigorous analysis to asymptotic methods and numerical approximation. I have applied these tools to provide insights into several different areas of physics and mathematical biology.

Jérôme Gilles - Harmonic/functional analysis, wavelets, signal/image processing.
My main research interests are in harmonic analysis and its application for signal/image analysis or restoration purposes. I recently started to develop a new kind of wavelets (called Empirical Wavelets) which are adaptive wavelets, i.e the filter bank depends on the spectrum information of the analyzed signal/image. We are currently working on developing a mathematical theory of empirical wavelets, as well as exploring their applications. For instance, these wavelets outperform classic wavelets for texture segmentation task (we apply them to analyze Scanning Tunneling Microscopy images), to extract and study the dynamics of deep brain signals. I am also leading some research on algorithms for imaging through atmospheric turbulence. We explore different path to reach high level of restoration and we also develop algorithms to perform reliable moving target detection through the turbulence.

Joe Mahaffy - Mathematical biology, delay differential equations
My primary research interests center on Mathematical Biology and Delay Differential Equations. One area of research examines mathematical models for cellular control systems. I have developed dynamical models for growing cultures of Escherichia coli, which help explain the complicated controls governing the initiation of replication of DNA or the beginning of the bacterial cell cycle. A second area or research in Mathematical Biology is on models of hematopoiesis. Age-structured models for erythrocytes and platelets have been analyzed with results that provide insight into some of the cyclical diseases of the blood. Both of these modeling efforts have required analysis of delay differential equations.

Antonio Palacios - Applied mathematics, bifurcations, symmetries
My research interests are in Applied Mathematics with emphasis in Nonlinear Dynamical Systems and Bifurcation Theory in Systems with Symmetry. I am particularly interested in the application of these areas to study scientific and engineering problems in mathematical biology and mathematical physics. Following these interests, in recent years I have been working on two primary projects. One project pertains modeling and understanding the spatio-temporal complexity of two-phase flow interactions, heat transfer and chemical reactions in fluidized beds. The second project involves using a dynamical system approach to unravel the complexity of the interplay between heart interneurons and heart motoneurons which leads to the heartbeat of leeches.

Associate Members:

Chris Rasmussen - Mathematics Education, Department of Mathematics, SDSU
Differential equations and Dynamical Systems in Mathematics Education:
My interests focus on the learning and teaching of undergraduate mathematics, using differential equations and dynamical systems as a prototype to investigate how approaches that have been successful at promoting student learning in earlier grade levels can be adapted to the university setting. I am interested in analyzing the instructional theory of Realistic Mathematics Education and empirical and theoretical elaborations of the role and function of argumentation, symbol-use, and tool use in learning of differential equations and effective means by which teachers can support student learning.

Arlette Baljon - Department of Physics, SDSU
Plasticity and Memory of Soft Materials
My group employs large-scale computer simulations to study soft materials, such as nanometer thin polymeric films. When these films are subjected to moderate shear, classical chaotic behavior has been observed in both simulations and experiments. However, if the amplitude of oscillatory shear passes a critical threshold, they start to behave differently. For instance, under repeated cycling, viscosity slowly rises. Most likely the film reorganizes itself into heterogeneous clusters, which slowly adapt themselves to the applied stress. Thus the film possesses "memory": its properties depend on the shear history. No explanation of how such memory is exactly stored in the micro structure is available yet. Modern complexity theory might provide new insights. Experiments on reinforced plastics show very similar rich kinetic behavior- which we likewise plan to study.

Calvin Johnson - Department of Physics, SDSU
Theoretical and Computational Nuclear Structure and Nuclear Astrophysics
I am interested in modeling nuclear deformations by solitons moving on the surface of a liquid drop, both in classical and quantum treatments. Surprisingly, even a purely classical approach seems to follow the pattern of deformation seen in purely quantum many-body nuclear models, such as the SU(3) group model. I am also interested in the transition between quasi-periodic and chaotic motion in strange attractors, which may be related to pole reversals in astrophysical dynamos that generate magnetic fields: the Sun's dynamo is periodic while the Earth's, it seems, is not.


[2015-2016] Jocirei Ferreira - Federal University of Mato Grosso, Brazil.
Complex patterns of oscillations in networks of crystal oscillators.

[2012-2014] Bernard S. Chan - University of Western Ontario, Canada.
Bifurcations in coupled Hamiltonian systems with symmetry.

[2007-2008] Manjun Ma - Nanhua University, Hunan, China
Nonlinear waves and Dynamical Systems:
The project involves studying the stability of dark soliton stripes (DSSs) in the context of the Nonlinear Schrödinger equation. The aim is to characterize possible ways to stabilize the inherent modulational instability of DSSs by means of external potentials.

Long term visitors:

[01/14-03/14] Al Sievers - Dept. of Physics, Cornell University
Solitons in micro- and macro-mechanical arrays of oscillators:
Prof. Sievers' research focusses on the exploration of energy localization in discrete nonlinear lattices, both classical and quantum mechanical.

[04/07] Alexandru Nicolin - Niels Bohr Institute
Faraday Waves in BECs:
Our collaboration focusses on the formation of Faraday waves in Bose-Einstein condensates. In particular, when periodically varying the trapping potential holding the BEC it is possible to produce Faraday (surface) waves on the condensate.

[08/07-11/07] Máximo Agüero Granados - Universidad Autónoma del Estado de México
Non-classical solitons:
The collaboration deals with the existence and stability of non-classical solitons. In particular, we are interested in compactons and peakons in continuum approximations for DNA lattices.

[07/07-10/07] Faustino Palmero Acebedo - Grupo de Física No Lineal (GFNL), Universidad de Sevilla, Spain
Nonlinear Physics, localization, discrete breathers, chaos in nonlinear oscillators:
My current research interests lie in the study of problems related to localization of energy by nonlinearity in classical and quantum lattices. I am specially interested in localization in crystals, in problems related to the connection of some families of discrete breathers to Anderson modes, in some DNA models, in the interplay between geometry and nonlinearity and the interaction of moving breathers with impurities, in quantum localization phenomenom in Hubbard models and, recently, in systems described by the Discrete Nonlinear Schrödinger equation, as nonlinear optical waveguides and Bose-Einstein condensates.

[2005-2006] Alvaro Salas-Brito - Laboratorio de Sistemas Dinamicos, UAM, Azcapotzalco, Mexico
Dynamical Systems, Hamiltonian and Quantum Chaos:
My research interests lie in Dynamical Systems and Computation applied to the transition to chaos in dissipative and Hamiltonian systems and in the study of ratchets and the effects of chaos on their dynamics. I also have interest in integrable systems and in other topics of mathematical physics.

[2005-2006] Hilda-Noemi Núñez-Yépez - Physics Department, UAM, Iztapalapa, Mexico
Dynamical Systems, Astronomy and Astrophysics:
My research interests lie in Dynamical Systems and in the study of chaotic dynamics in cosmological models. I am interested also in other topics of mathematical physics particularly in pursuing the study of conditions for chaotic behavior in models of stellar dynamics or globular cluster formation under the influence of effective galactic potentials.

Research Students:

  • Misha Kutzman, Ph.D. Fa17 - Present : Time-frequency representations for signal processing in neuroscience
  • Yuan Huang, Ph.D. Fa16 - Fa17 (visiting student from China): empirical wavelet texture analysis
  • Kevin Joiner, Ph.D. Sp14 - Present : Modelling the transport of bateriophage viruses
  • Vinnie Berardi, Ph.D. Fa13 - Present : Behavioral models and second hand smoke exposure.
  • Trevor Hawkins, Ph.D. Fa13 - Present : Computational Fluid Dynamics
  • Julia Rossi, Ph.D. Fa13 - Present : Coherent structures in polariton condensates
  • Marty Kandes, Ph.D. Fa10 - Fa15 : Effects of non-inertial frames in BECs
  • Carlos Prieto, Ph.D. Fa08 - Present : Vortex nucleation in dipolar condensates
  • Daniel Lyons, Ph.D. Fa12 - F14 : Nonlinear channelizer
  • James Turtle, Ph.D. Fa12 - Present : Bifurcations and dynamics of spin-torque nano-oscillators arrays for microwave signal generation
  • Susan Berggren, Ph.D. Sp07 - 2013 : Arrays of Superconducting Quantum Interference Devices
  • Eunsil Baik, Ph.D. Fa08 - 2012 : Vortex interactions in binary condensates
  • Ron Caplan, Ph.D. Fa07 - 2012 : Dynamics and interactions of vortex rings using GPU computing
  • Rafael Navarro, Ph.D. Sp07 - 2012 : Vortex interaction in Bose-Eintein condensates
  • Huy Vu, Ph.D. Sp07 - 2011 : Ring of Vibratory Gyroscopes
  • Joan Martinez, Ph.D. Sp07 - 2010 : Flame dynamics/patterns
  • John Aven, Ph.D. Sp06 - 2010 : Coupled quantum magnetic devices
  • Carlos Bazan, Ph.D. Fa06 - 2009 : Image reconstruction of mitochondria tomographyg
  • Beltran Rodriguez, Ph.D. Fa04 - 2009 : phage and bacterial biodiversity
  • Scott Gasner, Ph.D. Fa04 - 2006 : Flame dynamics
  • Bing Zhu, Ph.D. Sp04 - 2008 : Bubble dynamics
  • Patrick Longhini, Ph.D. Sp03 - 2005 : Nonlinear dynamics of coupled fluxgate magnetometers.

  • Jouie Aymes, M.Sc. Sp18 - Present : Detection of harmonic mode supports of arbitrary shape in 2D Fourier spectra.
  • Kyle Woolsey, M.Sc. Sp18 - Present : Development of a pseudo-spherical Fourier transform.
  • Lourdes Coria, M.Sc. Sp18 - Present : Collective behavior of networks of Colpitts Oscillators.
  • Nicholas Ferrante, M.Sc. - Fa17 - Present : Modeling and Image restoration within atmospheric turbulence.
  • Ludwig Siegert, M.Sc. Fa17 - Present : Sparsity methods in image super-resolution.
  • Zach Maches, M.Sc. Fa17 - Present: Von Kármán vortex streets.
  • Joshua Borjon, M.Sc. Fa17 - Present: Vortex dynamics in BECs
  • Jouie Ames, M.Sc. Fa17 - Present: scale-space 2D modes detection
  • Ericka Negroni, M.Sc. Sp17 - Present: tracking of moving target through atmospheric turbulence
  • Jake Talley, Ph.D. Fa14 - Sp17 : Vortex ring dynamics and GPU computing
  • Tony Silveti Falls, M.Sc. Fa16 - Sp17 : Empirical Gabor frames
  • Susan Deeb, M.Sc. - Fa16 - Present: Deep brain signal analysis
  • Francis Alvarez, M.Sc. - Sp16 - Sp17 : Lucky imaging.
  • Loni Olender, M.Sc. Sp16 - Fa17 : Hopfield neural networks.
  • Greg Behm, M.Sc. Sp16 - Sp17 : Effects of noise and delay in networks of crystal oscillators
  • Eunji Yoo, M.Sc. Sp16 - Fa17 : Nonlinear waves in density stratified fluids over underwater topography.
  • William Markuske, M.Sc. Fa14 - Present : Dynamics of vortices under free surface waves.
  • Matthew Richards, M.Sc. Fa14 - Sp17 : Superfluid vortex nucleation around an inpurity
  • Aileen Nguyen, M.Sc. Fa14 : Modeling the spread of Lyme disease in Connecticut
  • Martin Rodriguez Jr., M.Sc. Fa14 - Sp17 : Interactions Between Dispersive Shock Waves and Quantum Vortices
  • Jordyn Moscoso, M.Sc. Fa14 - Sp16 : Periodic solutions to nonlinear wave equations using pseudo-spectral based continuation schemes
  • Steven Reeves, M.Sc. Fa14 - Sp16 : Networks of coupled crystal oscillators for precision timing
  • Robert Demonte, M.Sc. Sp14 - Present : Periodic Solutions and Their Stability in Honeycomb Lattices
  • Adam Dorrego, M.Sc. Fa14 - Present : Stochastic control in economics/finance models
  • Joshua Taylor, M.Sc. Sp14 - Sp17 : Compressed Sensing
  • Anibal Cruz, M.Sc. Sp14 - Sp17 : Computational Fluid Dynamcis
  • Tyler Levasseur, M.Sc. Sp14 - Sp17 : Feedforward networks tuned near a Hopf bifurcation
  • Nicholas Fisher, M.Sc. Fa13 - Fa14 : Image Processing for Cancer Classification
  • Hung Viet Nguyen, M.Sc. Sp13 : Image Processing of Cardiomyocyte Contractility
  • James Mullinix, M.Sc. Fa12 - Fa15 : Vibrational modes of turbine blades
  • Kevin Joiner, M.Sc. Fa10 - 2013 : Vibrating membranes for material transport
  • Joseph Horton, M.Sc. Fa11 - Fa13 : Classifying Capsid Proteins
  • Adam Oberlander, M.Sc. Fa10 - Fa13 : Optimization of Michell Truss Systems
  • David New, M.Sc. Sp10 - 2012 : Climate modeling
  • Vinnie Berardi, M.Sc. Fa10 - 2013 : Nonlinear waves in granular chains
  • William Henry, M.Sc. Fa09 - 2013 : Matter wave ratchets
  • Sara Wang, M.Sc. Fa10 - 2013 : Control of growth in E. coli
  • Trevor Hawkins, M.Sc. Fa10 - Present : Shape and Deformation of Cardiocytes
  • Erin Daly, M.Sc. Fa10 - Sp12 : Multiphase Levelset methods
  • Joseph Marcucilli, M.Sc. Fa10 : Inverse Scale Space Methods
  • Richard Shaffer, M.Sc. Fa10 - 2013 : Spintronics
  • Katie Beauvais, M.Sc. Fa10 - 2013 : Spintronics
  • Carlos Prieto, M.Sc. Fa08 - 2012 : Dark soliton nucleation in dipolar condensates
  • Kelly Kaldenberg, M.Sc. Sp07 - Present : Inverse Scale Space Methods for Image Reconstruction
  • Tim Busken, M.Sc. Fa10 - 2012 : Stability in delay differential equations
  • Ryan Humphrey, M.Sc. Sp09 : Inpainting Using Anisotropic Diffusion
  • Michelle Miller, M.Sc. Sp08 : Level Set Methods for Biomedical Imaging
  • Eugenia Chen, M.Sc. Sp08 : Optimizing a Coral Nerve Net
  • Nathan Davies, M.Sc. Sp07 - 2011 : Ring of Vibratory Gyroscopes
  • Aaron Donahue, M.Sc. Fa08 - 2010 : Water waves under forcing
  • Jeremy Banning, M.Sc. Fa08 - 2011 : Dynamics of Rings of Almost-Identical Oscillators
  • Daniel Lyons, M.Sc. Fa08 - 2010 : Effects of Delay on Coupled Sensor Systems
  • Max Rietmann, M.Sc. Fa07 - 2009 : Matter wave ratchets
  • Scott Strachan, M.Sc. Sp09 : Climate modeling
  • Hervé Nganguia, M.Sc. Fa06 - 2007 : mathematical biology: cyrcadian rythms
  • Mayra Hernandez, M.Sc. Fa06 - 2007 : magnetic sensors
  • John Everts, M.Sc. Fa06 - 2008 : scattering in discrete nonlinear lattices
  • Ron Caplan, M.Sc. Fa07 - 2008 : Modulation instabilities in nonlinear media
  • Suchitra Jagdish, M.Sc. Fa05 - 2009 : Component separation in binary BECs
  • Christopher Silva, M.Sc. Fa05 - 2006 : chaos and fractals in the magnetic pendulum
  • Michael Davis, M.Sc. Sp05 - 2006 : Manipulation of matter waves
  • Christopher Chong, M.Sc. Fa04 - Sp06 : Dynamics and mobility of solitons in discrete media
  • John Aven, M.Sc. Fa05 - Sp06 : Coupled quantum magnetic devices
  • Norbert Renz, M.Sc. Sp04 - 2004 : Multi-frequency for beam steering
  • Scott Gasner, M.Sc. Fa04 - 2004 : Flame dynamics
  • Christopher Luedders, M.Sc. Sp04 : Localized oscillations in nonlinear lattices.
  • Rafael Navarro, M.Sc. Fa04 : Bose-Einstein condensates in periodic traps.
  • Misael Camarena, M.Sc. Fa03 - 2005 : Biometric finger identification.
  • Alberto Rodriguez, Open University, Fa03: Biometric finger identification.
  • Patrick Longhini, M.Sc. Fa02: Complex interactions in arrays of coupled neurons.
  • Kichol Lee, M.Sc. Fa00 : Modeling and simulation of two-phase flows interactions.

  • Steven Cozine, B.Sc. Sp18 : Turbulence mitigation algorithms.
  • Zachary Comejo, B.Sc. Sp18 : Early seizure detection algorithms.
  • Victor Arjona, B.Sc. - Summer 17: Comparison of super-resolution algorithms
  • Evan Bartley, B.Sc. Sp16 : Existence of stationary vortex configurations using generating functions.
  • Nicholas Ferrante, B.Sc. - Fa15 - Sp16: acquisition of the Open Turbulent Image Set (OTIS dataset)
  • Thomas Dean, B.Sc. Sp16 : Existence and stability of periodic vortex choreographies.
  • Rodrigo Carbajal, B.Sc. Fa15 : Reduced vortex dynamics on Bose-Einstein condensates.
  • Theresa Morrison, B.Sc. Fa15 : Shear flows and the interactions of vortices with free surface waves.
  • Zach Maches, B.Sc. Fa14 - Sp17: Von Kármán vortex streets.
  • Alexis Romero, B.Sc. Sp14 : Von Kármán vortex streets.
  • Kenny Sokolowski, B.Sc. Fa11 : Interaction dynamics of BEC vortices.
  • Andrew Miller, B.Sc. Sp11 - Fa13 : Dynamics of a bouncing car.
  • Artem Mavrin, B.Sc. Sp11 - 2012 : Scattering of discrete breathers.
  • Dan Lanier, B.Sc. Sp07 : Helicopter Stability and Control.
  • Scott Hazen, B.Sc. Sp06 : Reduction dynamics for vortex interactions in BECs.
  • Brian Chapler, B.Sc. Sp06 : Chaos an autoparametric resonance in Hamiltonian systems.
  • Troy Mestler, B.Sc. Fa05 : Effects of tidal forces on planetary orbits.
  • Bryan Sheddy, B.Sc. Fa05 : Newton method for periodic orbits in higher dim systems.
  • Franz Rueckert, B.Sc. Fa03 : Bubble dynamics.
  • Habib Juarez, B.Sc. Sp02 : Dynamical systems applied to cryptography.
  • Reine Raheb, B.Sc. Sp02 : Transition to chaos in an extensible pendulum
  • Andrew Bernardi, B.Sc. Fa01 : Fractals from topographical data of the Baja California gulf.
  • Chris Eisele, B.Sc. Fa00 : Symmetry-breaking pattern formation in the Kuramoto-Sivashinsky equation.

This page has been accessed * times since February 2002.

Maintained by Ricardo Carretero
Ricardo Carretero Gonzalez Antonio Palacios Peter Blomgren Joe Mahaffy Diana Verzi San Diego San Diego State University SDSU California West coast MS master masters PhD doctorate doctoral graduate undergraduate concentration emphasis applied mathematics chaos chaotic fractal fractals dynamics dynamical systems nonlinear nonlinear dynamical systems nonlinear dynamics NLDS model modeling modelling publication publications research preprints analysis adaptivity aggregation bifurcation bifurcations bioloby blowup blow up blow-up bose bose-einstein breather breathers CML CMLs condensates coupled map lattices delay differential determinism deterministic differential einstein embedding equation equations fluidization fluidized GPE heteroclinic homoclinic ILM ILMs image restoration intrinsic localized modes lattices manifold map maps math mathematical bioloby metastability moving mesh NLS nonlinear waves numerics numerical ODE ODEs orbit orbits pattern patterns PDE PDEs POD prediction proper orthogonal decomposition reconstruction soliton solitons spatio temporal stable stochastic studies study systems tangle temporal time series unstable