Juan Lopez
Professor,
School of Mathematical and Statistical Sciences
-
Phone: 480-965-8843
-
-
GWC 640 TEMPE, AZ 85287-1804
-
Mail code: 1804Campus: Tempe
-
Long Bio
Juan Lopez conducts research in two broad areas:
Rotation and buoyancy dominated flows, addressing the transitions from laminar to turbulence, resolving in detail the complex bifurcational processes involved. These are of fundamental interest and have applications in geophysics, aerodynamics and industrial processes. The tools used include direct numerical simulations of the Navier-Stokes equations and the extensive use of dynamical systems theory to unravel the spatio-temporal complexity involved. These lines of research have been consistently supported by National Science Foundation (CBET and DMS).
Interfacial hydrodynamics, addressing the influence of surfactants, such as lung surfactants, and more recently proteins which have a tendency to form amyloid fibrils at sheared interfaces. These are of interest due to their prevalence in neurodegenerative diseases, including Alzheimer’s and Parkinson’s. These lines of research have been consistently supported by National Science Foundation (CBET and DMS) and NASA (Biophys.).
Education
Ph.D. Monash University, Australia 1985
Research Website URL
Publications
- Albrecht T, Blackburn HM, Lopez JM, Manasseh R & Meunier P. Triadic resonances in precessing rapidly rotating cylinder flows. Journal of Fluid mechanics (2015).
- Gutierrez-Castillo P & Lopez JM. Instabilities of the sidewall boundary layer in a rapidly rotating split cylinder. European J. Mechanics B: Fluids (2015).
- Lopez JM & Hirsa AH. Coupling of the interfacial and bulk flow in knife-edge viscometers. Physics of Fluids (2015).
- Marques F & Lopez JM. Precession of a rapidly rotating cylinder flow: traverse through resonance. Journal of Fluid Mechanics (2015).
- Raghunandan A, Lopez JM & Hirsa AH. Bulk flow driven by a viscous monolayer. Journal of Fluid Mechanics (2015).
- Young JE, Posada D, Lopez JM & Hirsa AH. Flow-induced 2D protein crystallization: Characterization of the coupled interfacial and bulk flows. Soft Matter (2015).
- Curbelo J, Lopez JM, Mancho AM & Marques F. Large Prandtl number confined rotating convection: Centrifugal effects on wall modes. Phys. Rev. E (2014).
- Curbelo, J, Lopez, JM, Mancho, AM and Marques, F. Confined rotating convection with large Prandtl number: Centrifugal effects on wall modes. Physical Review E (2014).
- Lopez JM & Marques F. Rapidly rotating cylinder flow with an oscillating sidewall. Phys. Rev. E (2014).
- Lopez JM & Marques F. Three-dimensional instabilities in a discretely heated annular flow: Onset of spatio-temporal complexity via defect dynamics. Physics of Fluids (2014).
- Lopez JM and Marques F. Rapidly rotating cylinder flow with an oscillating sidewall. Physical Review E (2014).
- Marques F & Lopez JM. Spontaneous generation of a swirling plume in a stratified ambient. J. Fluid Mechanics (2014).
- Altmeyer S, Do Y and Lopez JM. Effect of elongational flow on ferrofuids under a magnetic field. Physical Review E (2013).
- Do, Y. and Lopez, J. M. Slow passage through multiple bifurcation points. Discrete and Continous Dynamical Systems B (2013).
- Lopez JM and Marques F. Instability of plumes driven by localized heating. Journal of Fluid Mechanics (2013).
- Marques F, Meseguer A, Lopez JM, Pacheco JR and Lopez JM. Bifurcations with imperfect SO(2) symmetry and pinning of rotating waves. Proceedings of the Royal Society A (2013).
- Sadoughi A, Lopez JM and Hirsa AH. Transition from Newtonian to non-Newtonian surface shear viscosity of phospholipid monolayers. Physics of Fluids (2013).
- Altmeyer, S., Do, Y. and Lopez, J. M. Influence of an inhomogeneous internal magnetic field on the flow dynamics of ferrofluid between differentially rotating cylinders,. Physical Review E (2012).
- Altmeyer, S., Do, Y., Marques, F. and Lopez, J. M. Symmetry-breaking Hopf bifurcations to 1-, 2-, and 3-tori in small-aspect-ratio counter-rotating Taylor-Couette. Physical Review E (2012).
- Brady, P. T., Herrmann, M. and Lopez, J. M. Addendum to ``Two-fluid confined flow in a cylinder driven by a rotating endwall'. Physical Review E (2012).
- Brady, P. T., Herrmann, M. and Lopez, J. M. Code verification for finite volume muMltiphase scalar equations using the method of manufactured solutions. Journal of Computational Physics (2012).
- Brady, P. T., Herrmann, M. and Lopez, J. M. Two-fluid confined flow in a cylinder driven by a rotating endwall. Physical Review E (2012).
- Lopez, J. M. Three-dimensional swirling flows in a tall cylinder driven by a rotating endwall. Physics of Fluids (2012).
- Lopez, J. M., Sankar, M. and Do, Y. Constant-flux discrete heating in a unit aspect-ratio annulus. Fluid Dynamics Research (2012).
- Nunez, J., Ramos, E. and Lopez, J. M. Mixed Fourier-Galerkin--finite-volume method to solve the fluid dynamics equations in cylindrical geometries. Fluid Dynamic Research (2012).
- Sankar, M., Kim, B., Lopez, J. M. and Do, Y. Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus. International Journal of Heat and Mass Transfer (2012).
- Sankar, M., Park, Y., Lopez, J. M. and Do, Y. Double-diffusive convection from a discrete heat and solute source in a vertical porous annulus. Transport in Porous Media (2012).
- Blackburn, H. M. and Lopez, J. M. Modulated waves in a periodically driven annular cavity. Journal of Fluid Mechanics (2011).
- Brady, P. T., Herrmann, M. and Lopez, J. M. Confined thermocapillary motion of a three-dimensional deformable drop. Physics of Fluids (2011).
- Lopez, J. M. and Marques, F. Instabilities and inertial waves generated in a librating cylinder. Journal of Fluid Mechanics (2011).
- Pacheco, J. R., Lopez, J. M. and Marques, F. Pinning of rotating waves to defects in finite Taylor-Couette flow. Journal of Fluid Mechanics (2011).
- Panades, C., Marques, F. and Lopez, J. M. Transitions to three-dimensional flows in a cylinder driven by oscillations of the sidewall. Journal of Fluid Mechanics (2011).
- Park, Y., Do, Y. and Lopez, J. M. Slow passage through resonance. Physical Review E (2011).
- Sankar, M., Park, Y., Lopez, J. M. and Do, Y. Numerical study of natural convection in a vertical porous annulus with discrete heating. International Journal of Heat and Mass transfer (2011).
- Do, Y., Lopez, J. M. and Marques, F. Optimal harmonic response in a confined crossflow boundary layer flow. Physical Review E (2010).
- Lopez, J. M. and Marques, F. Sidewall boundary layer instabilities in a rapidly rotating cylinder driven by a differentially co-rotating lid. Physics of Fluids (2010).
- Rubio, A., Lopez, J. M. and Marques, F. Onset of Kuppers-Lortz-like dynamics in finite rotating thermal convection. Journal of Fluid Mechanics (2010).
- Cui, Y. D., Lopez, J. M., Lim, T. T. and Marques, F. Harmonically forced enclosed swirling flow. Physics of Fluids (2009).
- Lopez, J. M. and Marques, F. Centrifugal effects in rotating convection: nonlinear dynamics. Journal of Fluid Mechanics (2009).
- Lopez, J. M., Marques, F., Rubio, A. M. and Avila, M. Crossflow instability of finite Bodewadt flows: transients and spiral waves. Physics of Fluids (2009).
- Rubio, A., Lopez, J. M. and Marques, F. Interacting oscillatory boundary layers and wall modes in modulated rotating convection. Journal of Fluid Mechanics (2009).
- Abshagen. Lopez, Marques and Pfister. Bursting dynamics due to a homoclinic cascade in Taylor-Couette flow. Journal of Fluid Mechanics (2008).
- Avila, Grimes, Lopez and Marques. Global endwall effects on centrifugally stable flows. Physics of Fluids (2008).
- Azadani, Lopez and Hirsa. Coupling between protein-laden films and a shearing bulk flow. Journal of Colloids and Interface Science (2008).
- F. Marques, Juan Lopez. Influence of wall modes on the onset of bulk convection in a rotating cylinder. Physics of Fluids (2008).
- Juan Lopez, Y. Cui, F. Marques, T. Lim. Quenching of vortex breakdown oscillations via harmonic modulation. Journal of Fluid Mechanics (2008).
- Juan Lopez, Y. Cui, F. Marques, T. Lim. Quenching of vortex breakdown oscillations via harmonic modulation. Journal of Fluid Mechanics (2008).
- M. Avila, M. Belisle, Juan Lopez, F. Marques, W. Saric. Mode competition in modulated Taylor-Couette flow. Journal of Fluid Mechanics (2008).
- Rubio, Lopez and Marques. Modulated rotating convection: radially travelling concentric rolls. Journal of Fluid Mechanics (2008).
- A. Azadani, Juan Lopez, A. Hirsa. Protein crystallization at the air/water interface induced by shearing bulk flow. Langmuir (2007).
- F. Marques, I. Mercader, , O. Batiste, , Juan Lopez. Centrifugal effects in rotating convection: Axisymmetric states and 3D instabilities. Journal of Fluid Mechanics (2007).
- J. Allen, Juan Lopez. Transition processes for junction vortex flow. Journal of Fluid Mechanics (2007).
- Juan Lopez, F. Marques, I. Mercader, O. Batiste. Onset of convection in a moderate aspect-ratio rotating cylinder: Eckhaus-Benjamin-Feir instability. Journal of Fluid Mechanics (2007).
- M. Avila, F. Marques, A. Meseguer, Juan Lopez. Stability control and catastrophic transition in a forced Taylor-Couette system. Journal of Fluid Mechanics (2007).
- A Hirsa, Juan Lopez, M Vogel, J Leung. Effects of shearing flow with inertia on monolayer mesoscale structure. Langmuir (2006).
- F Marques, Juan Lopez. Onset of three-dimensional unsteady states in small aspect-ratio Taylor-Couette flow. Journal of Fluid Mechanics (2006).
- Juan Lopez. Rotating and modulated rotating waves in transitions of an enclosed swirling flow. Journal of Fluid Mechanics (2006).
- Juan Lopez, A Rubio, F Marques. Traveling circular waves in axisymmetric rotating convection. Journal of Fluid Mechanics (2006).
- Juan Lopez, Y Cui, T Lim. An experimental and numerical investigation of the competition between axisymmetric time-periodic modes in an enclosed swirling flow. Physics of Fluids (2006).
- Avila, M, Marques, F, Lopez, Juan, Meseguer, A. Quasiperiodic flow in an axially forced Taylor-Couette system. (2006).
- Lopez, Juan, Marques, F, Mercader, I, Batiste, O. Rotating convection: Eckhaus-Benjamin-Feir instability. (2006).
- Marques, F, Lopez, Juan, Batiste, O, Mercader, I. Rotating convection: the influence of centrifugal buoyancy. (2006).
- Marques, F, Lopez, Juan, Batiste, O, Mercader, I. The influence of centrifugal buoyancy in rotating convection. (2006).
- Rubio, A, Lopez, Juan, Marques, F. Modulated rotating convection: Quenching wall modes. (2006).
- J Abshagen, Juan Lopez, F Marques, G Pfister. Mode competition of rotating waves in reflection-symmetric Taylor-Couette flow. Journal of Fluid Mechanics (2005).
- J Abshagen, Juan Lopez, F Marques, G Pfister. Symmetry breaking via global bifurcations of two tori in hydrodynamics. Physical Review Letters (2005).
- Leung, J, Hirsa, A, Lopez, Juan, Vogel, M. Monolayer phase coarsening using oscillatory flow. (2005).
- Lopez, Juan. Transitions in an enclosed swirling flow. (2005).
- Marques, F, Lopez, Juan, Abshagen, J, Pfister, G. Symmetry breaking via global bifurcations in Taylor-Couette flow. (2005).
- Rubio, A, Lopez, Juan, Marques, F. Traveling circular waves in rotating convection. (2005).
- Welfert, B, Lopez, Juan, Marques, F. Impact of noise on the onset of vortex breakdown. (2005).
- F Marques, Juan Lopez, H Blackburn. Bifurcations in systems with Z2 spatio-temporal and O(2) spatial symmetry. Physica D (2004).
- Juan Lopez, F Marques. Mode competition between rotating waves in a swirling flow with reflection symmetry. J. Fluid Mech (2004).
- Juan Lopez, F Marques, A Hirsa, R Miraghaie. Symmetry breaking in free-surface cylinder flows. J. Fluid Mech (2004).
- Juan Lopez, F Marques, J Shen. Complex dynamics in a short annular container with rotating bottom and inner cylinder. J. Fluid Mech (2004).
- Juan Lopez, M Vogel, A Hirsa. Influence of coexisting phases on the surface dilatational viscosity of Langmuir monolayers. Physical Review E (2004).
- M Vogel, R Miraghaie, Juan Lopez, A Hirsa. Flow-induced patterning of Langmuir monolayers. Langmuir (2004).
- V Iranzo, F Marques, Juan Lopez. From global to local bifurcations in a forced Taylor-Couette flow. Theoretical and Computational Fluid Dynamics (2004).
- F Marques, A Gelfgat, Juan Lopez. A tangent double Hopf bifurcation in a differentially rotating cylinder flow. Physical Review E (2003).
- F Marques, A Gelfgat, Juan Lopez. Tangent double Hopf bifurcation in a differentially rotating cylinder flow. Phys. Rev. E (2003).
- H Blackburn, Juan Lopez. On three-dimensional quasiperiodic Floquet instabilities of two-dimensional bluff body wakes. Phys. Fluids (2003).
- H Blackburn, Juan Lopez. The onset of three-dimensional standing and modulated travelling waves in a periodically-driven cavity flow. Journal of Fluid Mechanics (2003).
- Juan Lopez, F Marques. Short anulus Taylor-Couette flow: Onset of a very-low-frequency three-torus state. Physical Review E (2003).
- Juan Lopez, F Marques. Small aspect ratio Taylor-Couette flow: Onset of a very-low-frequency three-torus state. Phys. Rev. E (2003).
- R Miraghaie, Juan Lopez, A Hirsa. Flow induced patterning at the air/water interface. Physics of Fluids (2003).
- A Hirsa, Juan Lopez, R Miraghaie. Symmetry breaking to a rotating wave in a lid-driven cylinder with a free surface: Experimental observation. Physics of Fluids (2002).
- F Marques, Juan Lopez, J Shen. Mode interactions in an enclosed swirling flow: a double Hopf bifurcation between azimuthal wavenumbers 0 and 2. Journal of Fluid Mechanics (2002).
- F Marques, Juan Lopez, V Iranzo. Imperfect gluing bifurcation in a temporal glide-reflection symmetric Taylor-Couette flow. Physics of Fluids (2002).
- H Blackburn, Juan Lopez. Modulated rotating waves in an enclosed swirling flow. Journal of Fluid Mechanics (2002).
- J Sanchez, F Marques, Juan Lopez. A continuation and bifurcation technique for Navier-Stokes flows. Journal of Computational Physics (2002).
- Juan Lopez, A Hirsa. Non-Newtonian behavior of an insoluble monolayer: Effects of inertia. Journal of Colloid and Interface Science (2002).
- Juan Lopez, F Marques. Modulated Taylor-Couette flow: Onset of spiral modes. Theoretical and Computational Fluid Dynamics (2002).
- Juan Lopez, F Marques, J Shen. An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries II. Three dimensional cases. Journal of Computational Physics (2002).
- Juan Lopez, J Hart, F Marques, S Kittelman, J Shen. Instability and mode interactions in a differentially-driven rotating cylinder. Journal of Fluid Mechanics (2002).
- A Hirsa, Juan Lopez, R Miraghaie. Measurement and computation of hydrodynamic coupling at an air/water interface in the presence of an insoluble monolayer. Journal of Fluid Mechanics (2001).
- F Marques, Juan Lopez. Precessing vortex breakdown mode in an enclosed cylinder flow. Physics of Fluids (2001).
- F Marques, Juan Lopez, J Shen. A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances. Physica D (2001).
- Juan Lopez, A Hirsa. Oscillatory driven cavity with an air/water interface and an insoluble monolayer: Surface viscosity effects. Journal of Colloid and Interface Science (2001).
- A Hirsa, Juan Lopez, S Kim. Evolution of an initially columnar vortex terminating normal to a no-slip wall. Experiments in Fluids (2000).
- F Marques, Juan Lopez. Spatial and temporal resonances in a periodically forced extended system. Physica D (2000).
- G Talmage, J Walker, S Shyu, Juan Lopez. Inertial effects in the rotationally driven melt motion during the Czochralski growth of silicon crystals with a strong axial magnetic field. Journal of Applied Mathematics and Physics (ZAMP) (2000).
- H Blackburn, Juan Lopez. Symmetry breaking of the flow in a cylinder driven by a rotating endwall. Physics of Fluids (2000).
- Juan Lopez, A Hirsa. Surfactant influenced gas/liquid interfaces: Nonlinear equation of state and finite surface viscosities. Journal of Colloid and Interface Science (2000).
- Juan Lopez, F Marques. Determining the self-rotation number following a Naimark-Sacker bifurcation in the periodically forced Taylor-Couette flow. Journal of Applied Mathematics and Physics (ZAMP) (2000).
- Juan Lopez, F Marques. Dynamics of 3-tori in a periodically forced Navier-Stokes flow. Physical Review Letters (2000).
- Juan Lopez, F Marques, J Shen. Endwall effects in a periodically forced centrifugally unstable flow. Fluid Dynamics Research (2000).
- N Brummell, J Hart, Juan Lopez. On the flow induced by centrifugal buoyancy in a differentially-heated rotating cylinder. Theoretical and Computational Fluid Dynamics (2000).
- . Quasiperodic responses to parametric excitations. (2000).
Research Activity
- Lopez,Juan Manuel*. Catastrophic transition to turbulence in rotation-dominated flows. NSF-ENG-CBET(9/1/2013 - 8/31/2016).
- Lopez,Juan Manuel*. Amyloid fibrill formation in microgravity: Distinguishing interfacial flow effects. RPI(9/1/2013 - 8/31/2018).
- Lopez,Juan Manuel*. Collaborative Research Effects of interfacial viscosities on flow of lung surfactants. NSF-ENG(6/1/2011 - 8/31/2014).
- Mittelmann,Renate M*, Fernando,H J S, Herrmann,Marcus, Huang,Huei-Ping, Lopez,Juan Manuel, Mahalov,Alex, Tang,Wenbo. Plant Fund: SCREMS: Visualization of Complex Spatio-Temporal Multiscale Fluid Dynamic Phenomena. NSF-MPS-DMS(8/1/2009 - 7/31/2010).
- Lopez,Juan Manuel*, Herrmann,Marcus. Atomization of Liquids in Non-isothermal environments: Multi-scale Modeling and Simulations. NSF-MPS(7/1/2008 - 6/30/2012).
- Kostelich,Eric John*, Armbruster,Hans Dieter, Crook,Sharon Marie, Crook,Sharon Marie, Gardner,Carl L, Gelb,Anne, Jackiewicz,Zdzislaw, Jones,Donald, Lopez,Juan Manuel, Mahalov,Alex, Renaut,Rosemary Anne, Ringhofer,Christian, Welfert,Bruno Denis. CSUMS: Undergraduate research Experiences for Computational Math Science Majors at ASU. NSF-MPS-DMS(9/15/2007 - 8/31/2014).
- Lopez,Juan Manuel*, Welfert,Bruno Denis. Stochastic Parametric Forcing in Hydrodynamics. NSF-MPS(9/15/2005 - 8/31/2009).
- Lopez,Juan Manuel*. Collaborative Research: Multiphase Interfacial Hydrodynamics. NSF-MPS(6/1/2005 - 11/30/2008).
- Lopez,Juan Manuel*. COLLABORATIVE RESEARCH: THE ROLE OF MONOLAYER STRUCTURE ON INTERFACIAL HYDORDYNAMICS. NSF-ENG(7/1/2004 - 6/30/2007).
- Lopez,Juan Manuel*. EFFECTS OF BULK FLOW ON MONOLAYER FORMATION GAS/LIQUID INTERFACES. NSF-ENG(11/1/2001 - 10/31/2002).
- Lopez,Juan Manuel*, Saric,William S. SPATIAL & TEMPORAL RESONANCES IN HYDRODYNAMICS: A THEORETICAL, EXPERIMENTAL & NUMERICAL EXPLORATION. NSF-ENG(4/1/2000 - 3/31/2003).
- Lopez,Juan Manuel*. U.S.-SPAIN COOPERATIVE RESEARCH: DYNAMIC CONTROL AND PARAMETRIC RESONANCE IN HYDRODYNAMIC SYSTEMS. NSF-SBE(9/15/1998 - 8/31/2001).
- Lopez,Juan Manuel*. DYNAMIC CONTROL AND PARAMETRIC RESONANCE IN HYDRODYNAMIC SYSTEMS: A THEORETICAL, COMPUTATIONAL, AND EXPERIMENTAL INVESTIGATION. PENN STATE UNIV(6/1/1998 - 7/31/1999).
- Lopez,Juan Manuel*. DYNAMICS OF SURFACTANT - INGLUENCED GAS/LIQUID INTERFACES. NSF-ENG(5/15/1998 - 4/30/2002).
Teaching Website URL
Courses
2024 Fall
| Course Number | Course Title |
|---|---|
| MAT 462 | Applied Partial Diff Equations |
| APM 792 | Research |
| MAT 599 | Thesis |
2024 Summer
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| APM 792 | Research |
| APM 792 | Research |
2024 Spring
| Course Number | Course Title |
|---|---|
| MAT 492 | Honors Directed Study |
| MAT 493 | Honors Thesis |
| MAT 599 | Thesis |
| APM 792 | Research |
| APM 799 | Dissertation |
| MAT 343 | Applied Linear Algebra |
| MAT 343 | Applied Linear Algebra |
| MAT 495 | Undergraduate Research |
2023 Fall
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| MAT 599 | Thesis |
2023 Summer
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| APM 792 | Research |
| APM 792 | Research |
2023 Spring
| Course Number | Course Title |
|---|---|
| MAT 492 | Honors Directed Study |
| MAT 493 | Honors Thesis |
| MAT 599 | Thesis |
| APM 792 | Research |
| APM 799 | Dissertation |
| MAT 343 | Applied Linear Algebra |
| MAT 343 | Applied Linear Algebra |
| MAT 495 | Undergraduate Research |
2022 Fall
| Course Number | Course Title |
|---|---|
| MAT 462 | Applied Partial Diff Equations |
| APM 792 | Research |
| MAT 599 | Thesis |
2022 Summer
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| APM 792 | Research |
| APM 792 | Research |
2022 Spring
| Course Number | Course Title |
|---|---|
| MAT 492 | Honors Directed Study |
| MAT 493 | Honors Thesis |
| MAT 599 | Thesis |
| APM 792 | Research |
| APM 799 | Dissertation |
| MAT 343 | Applied Linear Algebra |
| MAT 343 | Applied Linear Algebra |
| MAT 495 | Undergraduate Research |
2021 Fall
| Course Number | Course Title |
|---|---|
| MAT 462 | Applied Partial Diff Equations |
| APM 792 | Research |
2021 Summer
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| APM 792 | Research |
| APM 792 | Research |
2021 Spring
| Course Number | Course Title |
|---|---|
| MAT 492 | Honors Directed Study |
| MAT 493 | Honors Thesis |
| MAT 599 | Thesis |
| APM 792 | Research |
| APM 799 | Dissertation |
| MAT 343 | Applied Linear Algebra |
| MAT 343 | Applied Linear Algebra |
| MAT 495 | Undergraduate Research |
2020 Fall
| Course Number | Course Title |
|---|---|
| MAT 462 | Applied Partial Diff Equations |
| APM 792 | Research |
2020 Summer
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| APM 792 | Research |
| APM 792 | Research |
2020 Spring
| Course Number | Course Title |
|---|---|
| MAT 492 | Honors Directed Study |
| MAT 493 | Honors Thesis |
| MAT 599 | Thesis |
| APM 792 | Research |
| APM 799 | Dissertation |
| MAT 343 | Applied Linear Algebra |
| MAT 343 | Applied Linear Algebra |
| MAT 495 | Undergraduate Research |
2019 Fall
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| MAT 343 | Applied Linear Algebra |
2019 Summer
| Course Number | Course Title |
|---|---|
| APM 792 | Research |
| APM 792 | Research |
| APM 792 | Research |