Moongyu Park's Publications:

29. (M. Park and D. Sheen) Rectangular noncomforming finite element method for Poisson-Nernst-Planck equations, preprint.

28. (M.J. Mueterthies, M. Park and J.H. Cushman) Mathematical modeling and simulation for water-bromine battery with hydrogen and supercapacitors, preprint.

27. (H. Zhaopeng, M. Park, Z. Cai and G. Lin) Finite element method for two-sided fractional elliptic differential equations with variable coefficient, submitted.

26. (M. Park and J.H. Cushman) Homogenization of Carbon-Nanotube brush Electrodes, submitted.

25. (M. Park and J.H. Cushman) Upscaling interpretation of nonlocal fields, gradients and divergences, SIAM Multiscale Modeling and Simulation Vol. 13, No. 4, 1136 -- 1145 (2015).

24. (M. Park) Stability analysis and error estimate of flowfield-dependent variation method for first order linear hyperbolic equations, Journal of Computational and Applied Mathematics, Vol. 285, 125 -- 131 (2015).

23. (M. Park, J.H. Cushman and D. O'Malley) fBm run with a multi-scaling clock mimics diffusion of spherical colloids in microstructural fluids, Langmuir, vol. 30, No. 38, 11263 - 11266 (2014)

22. (M. Park, D. O'Malley and J.H. Cushman) Generalized Similarity/Renormalization Groups and Nonlinear Clocks for Multiscaling, Physical Review E, Vol 89, 042104 (2014).

21. (M. Park) Upscaling Levy motions in Porous media with long range correlations, Journal of Math Physics, Vol 54, 083302 (2013); doi: 10.1063/1.4818264

20. (J.H. Cushman, D. O'Malley and M. Park) Anomalous Diffusion, Renormalization Groups, Scaling Laws and Classification: A Reflection on Recent Efforts, Advances in Water Resources, Vol 62, 207 - 214 (2013)

19. (M. Park) Upscaling Microbial Motility in Porous Media, a book chapter in "Medical Physics", Edited by Marcin Balcerzyk, (ISBN-10: 1622575903, ISBN-13: 978-1622575909) Nova Science Publishers, Inc. (2012)

18. (O.A. Toutonji, S. Yoo and M. Park) "Stability Analysis of VEISV Propagation Modeling for Network Worm Attach", Applied Mathematical Modelling, vol 36, 2751 - 2761 (2012).

17. (J.H. Cushman, M. Park and D. O'Malley) Anomalous Diffusion in Confined Nano-films Revisited, Advances in Water Resources, Vol 34, 490 - 494 (2011).

16. (M. Park and J.H. Cushman) "The Complexity of Brownian Processes run with Nonlinear Clocks, Modern Physics Letters B, Vol 25 No. 1, 1 - 10 (2011).

15. (J. Cushman, M. Park, M. Moroni, N. Kleinfelter-Domelle and D. O'Malley) A Universal Field Equation for Dispersive Processes in Geophysics, Stochastic Environmental Research and Risk Assessment, Vol. 25, 1 - 10 (2011).

14. (O.A. Toutonji, S. Yoo and M.Park) "Analyzing the Propagation of Network Multi-Malwares Worm attack considering security countermeasure", Cyber Security and Information Intelligence Research Workshop, Oak Ridge, (2010).

13. (J.H. Cushman, M. Park and D. O'Malley) The Chaotic Dynamics of Super-Diffusion Revisited, Geophysical Research Letters, Vol. 36, L08812 (2009).

12. (J. Cushman, D. O'Malley and M. Park) Anomalous Diffusion as Modeled by a Nonstationary Extension of Brownian Motion, Physical Review E, Vol. 79, 032101 (2009).

11. (M. Park and J. Cushman) Operator-stable Levy motions and renormalizing the chaotic dynamics of microbes in anisotropic porous media, -- J. Stat. Mech. Vol. 2009, No 2, P02039, (Feb 2009): Impact Factor = 2.4.

10. (N. Kleinfelter, M. Park and J. Cushman) Mixture Theory and Unsaturated Flow in Swelling Soils: Where We Are -- Transport in Porous Media, Vol 68, No 1, 69--89, (2007).

9. (M. Park and J. Cushman) On Upscaling Operator-Stable Levy motions in fractal porous media -- Journal of Computational Physics 217, 159--165, (2006): Impact Factor = 5.29

8. (M. Park, N. Kleinfelter and J. Cushman) Renormalizing Chaotic Dynamics in Fractal Porous Media with Application to Microbe Motility -- Geophys. Res. Lett., 33, L01401, (2006): Impact Factor = 2.3.

7. (J.H. Cushman, M. Park, N. Kleinfelter and M. Moroni) Super-Diffusion via Levy Lagrangian Velocity Processes -- Geophysical Research Letters, Vol. 32, no. 19, L19816, (2005).

6. (M. Park, N. Kleinfelter and J. Cushman) Scaling Laws and Dispersion Equations for L\'{e}vy Particles in One dimensional Fractal Porous Media -- Physical Review E 72, 056305, (2005): Impact Factor = 2.352.

5. (M. Park, N. Kleinfelter and J. Cushman) Upscaling of Levy motions in One dimensional Porous media via Central Limit Theorems: -- SIAM Multiscale Modeling and Simulation Vol 4, No. 4, pp 1233-1244, (2005) : Impact Factor = 1.135.

4. (N. Kleinfelter, M. Park and J. Cushman) Micromorphic fluid in an elastic porous body: blood flow in tissues with microcirculation. -- Int. J. Multiscale Comp. Eng., Vol. 3, no. 1, 71--84, (2005).

3. (Z. Cai, J. Douglas, Jr.M. Park) Development and Analysis of Higher Order Finite Volume Methods over Rectangles for Elliptic Equations. -- Adv. Comp. Math. Vol 19, (2003) issue 1-3, pp 3 -- 33, 2003 : I.F.=0.926.

2. (S. K. Chung and M. Park) Spectral Analysis for Hyperbolic Integro-differential equations with a Weakly Singular Kernel -- J. Korea SIAM Vol. 2, no.2, 31--40, 1998.

1. (S. K. Chung, A. K. Pani and M. Park) Convergence of finite difference method for the generalized solutions of Sobolev equations -- J. Korean Math. Soc. vol. 34, no. 3, 515--531, 1997.

Thesis (advisors: Jim Douglas, Jr. and Z. Cai, Purdue University):

Development and Analysis of Higher Order Finite Volume methods for Elliptic Equations.


2. (M. Park) On developing and analyzing mixed finite element methods for the valuation of options on assets with stochastic volatilities -- the final report to Mini-grant of UA Huntsville (2010)

1. (M. Park and J. Douglas, Jr.) MDT tool in a Slanted Wellbore -- report to Schlumberger (2003).