### SCIENCE SUB-PAGES

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# PUBLICATIONS

### Journal Articles

The Open Flux Problem.

J.A. Linker, R.M. Caplan, C. Downs, P. Riley, Z. Mikic, R. Lionello, C. J. Henney, C. N. Arge, Y. Liu, M. L. Derosa, A. Yeates, and M. J. Owens.

Submitted to*The Astrophysical Journal*. arXiv:1708.02342. PDF.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.