### SCIENCE SUB-PAGES

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# PUBLICATIONS

### Journal Articles

Synchronic coronal hole mapping using multi-instrument EUV images:

Data preparation and detection method.

R.M. Caplan, C. Downs, and J.A. Linker.

*The Astrophysical Journal*.**823**,1 (2016) 53. PDF.Properties of the Fast Forward Shock Driven by the July 23 2012 Extreme Coronal Mass Ejection.

P. Riley, R.M. Caplan, J. Giacalone, D. Lario, and Y. Liu.

*The Astrophysical Journal*.**819**,1 (2016) 57. PDF.Scattering and Leapfrogging of Vortex Rings in a Superfluid.

R.M. Caplan, J. D. Talley, R. Carretero-González, and P.G. Kevrekidis.

*Physics of Fluids*.**26**(2014) 097101. PDF.NLSEmagic: Nonlinear Schrödinger Equation Multidimensional Matlab-based GPU-accelerated Integrators using Compact High-order Schemes.

R.M. Caplan.

*Computer Physics Communications*.**184**,4 (2013) 1250-1271. PDF.A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and its Application to the Nonlinear Schrödinger Equation.

R.M. Caplan and R. Carretero-González.

*SIAM Journal on Scientific Computing*.**36**,1 (2014) A1-A19 PDF.A Two-Step High-Order Compact Scheme for the Laplacian Operator and its Implementation in an Explicit Method for Integrating the Nonlinear Schrödinger Equation.

R.M. Caplan and R. Carretero-González.

*Journal of Computational and Applied Mathematics*.**251**(2013) 33-46. PDF.Numerical Stability of Explicit Runge-Kutta Finite-Difference Schemes for the Nonlinear Schrödinger Equation.

R.M. Caplan and R. Carretero-González.

*Applied Numerical Mathematics*.**71**(2013) 24-40. PDF.

Awarded the 6th most successful IMACS paper published in 2013 in Applied Numerical Mathematics.Existence, Stability, and Scattering of Bright Vortices in the Cubic-Quintic Nonlinear Schrödinger Equation.

R.M. Caplan, R. Carretero-González, P.G. Kevrekidis, and B.A. Malomed.

*Mathematics and Computers in Simulation*.**82**,7 (2012) 1150-1171. PDF.Azimuthal Modulational Instability of Vortices in the Nonlinear Schrödinger Equation.

R.M. Caplan, Q.E. Hoq, R. Carretero-González, and P.G. Kevrekidis.

*Optics Communications*.**282**,7 (2009) 1399-1405. PDF.

### Conference Proceedings

Advancing parabolic operators in thermodynamic MHD models:

Explicit super time-stepping versus implicit schemes with Krylov solvers.

R. M. Caplan, Z. Mikic, J. A. Linker, and R. Lionello.

*Journal of Physics: Conference Series*. ASTRONUM 2016.**837**,1 (2017) 012016 PDF.MHD Simulation of the Bastille Day Event.

J.A. Linker, T. Torok, C. Downs, R. Lionello, V. Titov, R.M. Caplan, Z. Mikic, and P. Riley.

*AIP Conference Proceedings*, Solar Wind 14.**1720**, (2016) 020002. PDF.An Empirically Driven Time-Dependent Model of the Solar Wind.

J. A. Linker, R.M. Caplan, C. Downs, R. Lionello, P. Riley, Z. Mikic, C.J. Henney, C.N. Arge, T. Kim, and N. Pogorelov.

*Journal of Physics: Conference Series*. ASTRONUM 2015.**719**,1 (2016) 012012 PDF.Simulating the Nonlinear Schrödinger Equation using the Computational Capability of NVIDIA Graphics Cards

R.M. Caplan and R. Carretero-González.

*ACSESS Proceedings*.**ACSESS 2010**, (2010) AP10-04. PDF.Existence of Steady State Bright Vortex Solutions to the Cubic- Quintic Nonlinear Schrödinger Equation

R.M. Caplan and R. Carretero-González.

*ACSESS Proceedings*.**ACSESS 2009**, (2009) AP0903. PDF.

### Ph.D. Dissertation

**Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation utilizing GPU-Accelerated High-Order Compact Numerical Integrators**

Ph.D. Dissertation in Computational Science (2012).

Joint program with Claremont Graduate University and San Diego State University.

Committee Chair: Professor Ricardo Carretero.

Abstract▼. DOI: 10.5642/cguetd/52.

### Masters Thesis

**Azimuthal Modulational Instability of Vortex Solutions to the Two Dimensional Nonlinear Schrödinger Equation**

Masters Thesis in Computational Science (2008).

San Diego State University.

Thesis chair: Professor Ricardo Carretero.

Abstract▼ PDF.