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Computational Sciences & Mathematics


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The CM4 team measures its success, in part, on its fundamental contributions to the scientific literature, focusing primarily on mathematics and materials science, as well as the generation and dissemination of algorithms and open-source software.

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Wang X, P Gao, Y Yang, H Guo, and D Wu. 2018. “Dynamic and programmable morphology and size evolution via a living hierarchical self-assembly strategy.” Nature Communications. 9(1):2772. DOI: 10.1038/s41467-018-05142-3.


Chen LP, B Zheng, G Lin, and N Voulgarakis. 2017. “A Two-level Stochastic Collocation Method for Semilinear Elliptic Equations with Random Coefficients.” Journal of Computational and Applied Mathematics 315:195-207. DOI: 10.1016/ OSTI Link.

Cheung J, AL Frischknecht, M Perego, and P Bochev. 2017. “A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale.” Journal of Computational Physics 348:364–384. DOI: 10.1016/ OSTI Link.

Deng M, W Pan, and GE Karniadakis. 2017. “Anisotropic single-particle dissipative particle dynamics model.” Journal of Computational Physics 336:481-491. DOI: 10.1016/ OSTI Link.

Hao ZP, WR Cao, and G Lin. 2017. “A Second-order Difference Scheme for the Time Fractional Substantial Diffusion Equation.” Journal of Computational and Applied Mathematics 313:54-69. DOI: 10.1016/ OSTI Link.

Hu KB, Y Ma, and J Xu. 2017. “Stable Finite Element Methods Preserving ▽⋅B=0 Exactly MHD Models.” Numberische Mathematik 135(2):371-396. DOI: 10.1007/s00211-016-0803-4.

Karagiannis G, BA Konomi, G Lin, and F Liang. 2017. “Parallel and interacting stochastic approximation annealing algorithms for global optimisation.” Statistics and Computing 27(4):927-945. DOI: 10.1007/s11222-016-9663-0.

Lei H, X Yang, Z Li, and GE Karniadakis. 2017. “Systematic parameter inference in stochastic mesoscopic modeling.” Journal of Computational Physics 330:571-593. DOI: 10.1016/ OSTI Link.

Li Z, HS Lee, E Darve, and GE Karniadakis. 2017. “Computing the Non-Markovian Coarse-grained Interactions Derived from the Mori-Zwanzig Formalism in Molecular Systems: Application to Polymer Melts.” Journal of Chemical Physics 146(1):014104 DOI: 10.1063/1.4973347. OSTI Link.

Maxey MR. 2017. “Simulation Methods for Particulate Flows and Concentrated Suspensions.” Annual Review of Fluid Mechanics 49:171-193 DOI: 10.1146/annurev-fluid-122414-034408.

Pan W, K Kim, M Perego, AM Tartakovsky, and ML Parks. 2017. “Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics.” Journal of Computational Physics 334:125-144. DOI: 10.1016/ OSTI Link.

Trask N, M Perego, and P Bochev. 2017. “A High-Order Staggered Meshless Method for Elliptic Problems.” SIAM Journal on Scientific Computing 39(2):A479-A502. DOI: 10.1137/16M1055992. OSTI Link.

Wallace B and PJ Atzberger. 2017. “Förster resonance energy transfer: Role of diffusion of fluorophore orientation and separation in observed shifts of FRET efficiency.” PLoS ONE 12(5):e0177122. DOI: 10.1371/journal.pone.0177122. OSTI Link.


Bian X, M Deng, Y-H Tang, and GE Karniadakis. 2016. “Analysis of hydrodynamic fluctuations in heterogeneous adjacent multidomains in shear flow.” Physical Review E 93(3):033312. DOI: 10.1103/PhysRevE.93.033312.

Bochev P and D Ridzal. 2016. “Optimization-based additive decomposition of weakly coercive problems with applications.” Computers & Mathematics with Applications, Proceedings of the conference on Advances in Scientific Computing and Applied Mathematics. A special issue in honor of Max Gunzburger’s 70th birthday 71(11):2140-2154. DOI: 10.1016/j.camwa.2015.12.032.

D'Elia M, M Perego, P Bochev, and D Littlewood. 2016. “A Coupling Strategy for Nonlocal and Local Diffusion Models with Mixed Volume Constraints and Boundary Conditions.” Computers & Mathematics with Applications, Proceedings of the conference on Advances in Scientific Computing and Applied Mathematics. A special issue in honor of Max Gunzburger’s 70th birthday 71(11):2218-2230. DOI: 10.1016/j.camwa.2015.12.006.

Deng M, Z Li, O Borodin, and GE Karniadakis. 2016. “cDPD: A new dissipative particle dynamics method for modeling electrokinetic phenomena at the mesoscale.” The Journal of Chemical Physics 145(14):144109. DOI: 10.1063/1.4964628. OSTI Link.

Ginting V, G Lin, and J Liu. 2016. “On Application of the Weak Galerkin Finite Element Method to a Two-Phase Model for Subsurface Flow.” Journal of Scientific Computing 66(1):225-239. DOI: 10.1007/s10915-015-0021-8.

Konomi BA, G Karagiannis, K Lai, and G Lin. 2016. “Bayesian Treed Calibration: an application to carbon capture with AX sorbent.” Journal of the American Statistical Association. Online First, June 09, 2016. DOI: 10.1080/01621459.2016.1190279.

Lei H, NA Baker, and X Li. 2016. “Data-driven parameterization of the generalized Langevin equation.” Proceedings of the National Academy of Sciences of the United States of America 113(50):14183-14188. DOI: 10.1073/pnas.1609587113. OSTI Link.

Lei H, NA Baker, L Wu, GK Schenter, CJ Mundy, and AM Tartakovsky. 2016. “Smoothed dissipative particle dynamics model for mesoscopic multiphase flows in the presence of thermal fluctuations.” Physical Review E 94(2):023304. DOI: 10.1103/PhysRevE.94.023304. OSTI Link.

Li J. and P. Stinis. 2016. “A unified framework for mesh refinement in random and physical space.” Journal of Computational Physics 323:243-264. DOI: 10.1016/ OSTI Link.

Li Z, X Bian, X Yang, and GE Karniadakis. 2016. “A comparative study of coarse-graining methods for polymeric fluids: Mori-Zwanzig vs. iterative Boltzmann inversion vs. stochastic parametric optimization.” The Journal of Chemical Physics 145(4):044102. DOI: 10.1063/1.4959121. OSTI Link.

Metti MS, J Xu, and C Liu. 2016. “Energetically stable discretizations for charge transport and electrokinetic models.” Journal of Computational Physics 306:1-18. DOI: 10.1016/

Olson D, AV Shapeev, PB Bochev, and M Luskin. 2016. “Analysis of an optimization-based atomistic-to-continuum coupling method for point defects.” ESAIM: Mathematical Modeling and Numerical Analysis 50(1):1-41. DOI: 10.1051/m2an/2015023. OSTI Link.

*Sigurdsson JK and P Atzberger. 2016. “Hydrodynamic Coupling of Particle Inclusions Embedded in Curved Lipid Bilayer Membranes.” Soft Matter 12(32):6685-6707. DOI: 10.1039/C6SM00194G. *COVER (click to view)

Sun Y, P Sun, B Zheng, and G Lin. 2016. “Error analysis of finite element method for Poisson–Nernst–Planck equations.” Journal of Computational and Applied Mathematics 301:28-43. DOI: 10.1016/ OSTI Link.

Tang Y-H, Z Li, X Li, M Deng, and GE Karniadakis. 2016. “Non-Equilibrium Dynamics of Vesicles and Micelles by Self-Assembly of Block Copolymers with Double Thermoresponsivity.” Macromolecules 49(7):2895-2903. DOI: 10.1021/acs.macromol.6b00365.

Trask N, M Maxey, and X Hu. 2016. “Compact moving least squares: an optimization framework for generating high-order compact meshless discretizations.” Journal of Computational Physics 326:596-611. DOI: 10.1016/

Xu J and S Zhang. 2016. “Optimal finite element methods for interface problems.” Chapter in Domain Decomposition Methods in Science and Engineering XXII, Volume 104 of Lecture Notes in Computational Science and Engineering, eds. T. Dickopf, MJ Gander, L Halpern, R Krause, and LF Pavarino, pp 77-91. Springer International Publishing, Switzerland. DOI: 10.1007/978-3-319-18827-0_7.

Yang K, H Lei, NA Baker, and G Lin. 2016. “Enhancing sparsity of Hermite polynomial expansions by iterative rotations.” Journal of Computational Physics 307:94-109. DOI: 10.1016/ OSTI Link.

Yang K, Y Mehmani, WA Perkins, A Pasquali, M Schönherr, K Kim, M Perego, ML Parks, N Trask, MT Balhoff, MC Richmond, M Geier, M Krafczyk, L-S Luo, AM Tartakovsky, and TD Scheibe. 2016. “Intercomparison of 3D pore-scale flow and solute transport simulation methods.” Advances in Water Resources 95:176-189. DOI: 10.1016/j.advwatres.2015.09.015. OSTI Link.

Yang K, P Sun, L Wang, J Xu, and L Zhang. 2016. “Modeling and simulations for fluid and rotating structure interactions.” Computer Methods in Applied Mechanics and Engineering 311:788-814. DOI: 10.1016/j.cma.2016.09.020. OSTI Link.


Bao J, W Xu, P Bhattacharya, M Stewart, J-G Zhang, and W Pan. 2015. “Discharge Performance of Li–O2 Batteries Using a Multiscale Modeling Approach.” The Journal of Physical Chemistry C 119(27):14851-14860. DOI: 10.1021/acs.jpcc.5b01441.

Bian X, Z Li, M Deng, and GE Karniadakis. 2015. “Fluctuating hydrodynamics in periodic domains and heterogeneous adjacent multidomains: Thermal equilibrium.” Physical Review E 92(5):053302. DOI: 10.1103/PhysRevE.92.053302.

Bian X, Z Li, and GE Karniadakis. 2015. “Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition.” Journal of Computational Physics 297:132-155. DOI: 10.1016/ OSTI Link.

Hao Z, G Lin, and Z Sun. 2015. “A high-order difference scheme for the fractional sub-diffusion equation.” International Journal of Computer Mathematics, 1-22. DOI: 10.1080/00207160.2015.1109642.

Hao W, Z Xu, C Liu, and G Lin. 2015. “A Fictitious Domain Method with a Hybrid Cell Model for Simulating Motion of Cells in Fluid Flow.” Journal of Computational Physics 280:345-362. DOI: 10.1016/ OSTI Link.

Herschlag GJ, S Mitran, and G Lin. 2015. “A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.” Journal of Chemical Physics 142(23):234703. DOI: 10.1063/1.4922515.

Karagiannis G, BA Konomi, and G Lin. 2015. “A Bayesian mixed shrinkage prior procedure for spatial–stochastic basis selection and evaluation of gPC expansions: Applications to elliptic SPDEs.” Journal of Computational Physics 284:528-546. DOI: 10.1016/ OSTI Link.

Konomi B, G Karagiannis, and G Lin. 2015. “On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization.” Journal of Statistical Planning and Inference 157-158:1-15. DOI: 10.1016/j.jspi.2014.08.010. OSTI Link.

Konomi BA and G Lin. 2015. “Low-Cost Multi-Dimensional Gaussian Process with Application to Uncertainty Quantification.” International Journal for Uncertainty Quantification 5(4):375-392. DOI: 10.1615/Int.J.UncertaintyQuantification.2015007941.

Lee HS, S-H Ahn, and EF Darve. 2015. “Building a Coarse-Grained Model Based on the Mori-Zwanzig Formalism.” MRS Proceedings 1753. DOI: 10.1557/opl.2015.185.

Lei H, CJ Mundy, GK Schenter, and NK Voulgarakis. 2015. “Modeling nanoscale hydrodynamics by smoothed dissipative particle dynamics.” The Journal of Chemical Physics 142(19):194504. DOI: 10.1063/1.4921222. OSTI Link.

Lei H, X Yang, B Zheng, G Lin, and NA Baker. 2015. “Constructing Surrogate Models of Complex Systems with Enhanced Sparsity: Quantifying the Influence of Conformational Uncertainty in Biomolecular Solvation.” Multiscale Modeling & Simulation 13(4):1327-1353. DOI: 10.1137/140981587. OSTI Link.

Li J, G Lin, and X Yang. 2015. “A Frozen Gaussian Approximation-based Multi-level Particle Swarm Optimization for Seismic Inversion.” Journal of Computational Physics 296:58-71. DOI: 10.1016/

Li J and P Stinis. 2015. “Mesh refinement for uncertainty quantification through model reduction.” Journal of Computational Physics 280:164-183. DOI: 10.1016/ OSTI Link.

Li W and G Lin. 2015. “An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions.” Journal of Computational Physics 294:173-190. DOI: 10.1016/ OSTI Link.

Li Z, X Bian, X Li, and GE Karniadakis. 2015. “Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism.” The Journal of Chemical Physics 143(24):243128. DOI: 10.1063/1.4935490. OSTI Link.

Li Z, Y-H Tang, X Li, and GE Karniadakis. 2015. “Mesoscale modeling of phase transition dynamics of thermoresponsive polymers.” Chemical Communications 51(55):11038-11040. DOI: 10.1039/C5CC01684C.

Li Z, A Yazdani, A Tartakovsky, and GE Karniadakis. 2015. “Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems.” The Journal of Chemical Physics 143(1):014101. DOI: 10.1063/1.4923254. OSTI Link.

Lin G and GE Karniadakis. 2015. “Stochastic Systems.” Invited Chapter in Encyclopedia of Applied and Computational Mathematics, Vol. 1, ed. B Engquist, pp. 1404-1409. Springer-Verlag Berlin Heidelberg.

Lin G, J Liu, and F Sadre-Marandi. 2015. “A comparative study of the weak Galerkin, discontinuous Galerkin, and mixed finite element methods.” Journal of Computational and Applied Mathematics 273:346-362. DOI: 10.1016/ OSTI Link.

Meng D, B Zheng, G Lin, and ML Sushko. 2015. “Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment.” Communications in Computational Physics 16(5):1298-1322. DOI: 10.4208/cicp.040913.120514a.

Pan W, M Daily, and NA Baker. 2015. “Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics.” BMC Biophysics 8:7. DOI: 10.1186/s13628-015-0021-y. OSTI Link.

Sousa EM, G Lin, and U Shumlak. 2015. “Uncertainty Quantification of the GEM Challenge Magnetic Reconnection Problem using the Multilevel Monte Carlo Method.” International Journal for Uncertainty Quantification 5(4):327-339. DOI: 10.1615/Int.J.UncertaintyQuantification.2015006492.

Stinis P. 2015. “Renormalized Mori–Zwanzig-reduced models for systems without scale separation.” Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences 471(2176):20140446. DOI: 10.1098/rspa.2014.0446.

Tabak G and PJ Atzberger. 2015. “Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations.” SIAM Journal on Applied Mathematics 75(4):1884-1914. DOI: 10.1137/15M1019088.

Tang Y-H, S Kudo, X Bian, Z Li, and GE Karniadakis. 2015. “Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers.” Journal of Computational Physics 297:13-31. DOI: 10.1016/ OSTI Link.

Tartakovsky AM, N Trask, K Pan, B Jones, W Pan, and JR Williams. 2015. “Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media.” Computational Geosciences, pp. 1-28. DOI: 10.1007/s10596-015-9468-9.

Trask N, M Maxey, K Kim, M Perego, ML Parks, K Yang, and J Xu. 2015. “A scalable consistent second-order SPH solver for unsteady low Reynolds number flows.” Computer Methods in Applied Mechanics and Engineering 289:155-178. DOI: 10.1016/j.cma.2014.12.027. OSTI Link.

Wu CH, TG Fai, PJ Atzberger, and CS Peskin. “Simulation of Osmotic Swelling by the Stochastic Immersed Boundary Method.” SIAM Journal on Scientific Computing 37(4):B660-B688. DOI: 10.1137/14098404X.

Xu J and K Yang. 2015. “Well-posedness and robust preconditioners for the discretized fluid-structure interaction systems.” Computer Methods in Applied Mechanics and Engineering 292:69-91. DOI: 10.1016/j.cma.2014.09.034.

Zhang B, BA Konomi, H Sang, G Karagiannis, and G Lin. 2015. “Full scale multi-output Gaussian process emulator with nonseparable auto-covariance functions.” Journal of Computational Physics 300:623-642. DOI: 10.1016/ OSTI Link.

Zheng M, X Wan, and GE Karniadakis. 2015. “Adaptive multi-element polynomial chaos with discrete measure: Algorithms and application to SPDEs.” Applied Numerical Mathematics 90:91-110. DOI: 10.1016/j.apnum.2014.11.006.


Choi M, TP Sapsis, and GE Karniadakis. 2014. “On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations.” Journal of Computational Physics 270:1-20. DOI: 10.1016/

Del Razo MJ, W Pan, H Qian, and G Lin. 2014. “Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion.” The Journal of Physical Chemistry B 118(25):7037-7046. DOI: 10.1021/jp5030125.

Deng M and GE Karniadakis. 2014. “Electrostatic correlations near charged planar surfaces.” The Journal of Chemical Physics 141(9):094703. DOI: 10.1063/1.4894053.

Deng M and GE Karniadakis. 2014. “Coarse-Grained Modeling of Protein Unfolding Dynamics.” Multiscale Modeling & Simulation 12(1):109-118. DOI: 10.1137/130921519.

Fedosov DA, M Dao, GE Karniadakis, and S Suresh. 2014. “Computational Biorheology of Human Blood Flow in Health and Disease.” Annals of Biomedical Engineering 42(2):368-387. DOI: 10.1007/s10439-013-0922-3.

Grinberg L, M Deng, GE Karniadakis, and A Yakhot. 2014. “Window proper orthogonal decomposition: Application to continuum and atomistic data.” Chapter 10 in Reduced Order Methods for Modeling and Computational Reduction, MS&A-Modeling, Simulation and Applications Vol 9, eds. A Quarteroni and G Rozza, pp. 275-303. Springer International Publishing, Switzerland. DOI: 10.1007/978-3-319-02090-7_10.

Karagiannis G and G Lin. 2014 “Selection of Polynomial Chaos Bases via Bayesian Model Uncertainty Methods with Applications to Sparse Approximation of PDEs with Stochastic Inputs.” Journal of Computational Physics 259:114-134. DOI: 10.1016/

Kim C and GE Karniadakis. 2014. “Brownian Motion of a Rayleigh Particle Confined in a Channel: A Generalized Langevin Equation Approach.” Journal of Statistical Physics, pp. 1-26. DOI: 10.1007/s10955-014-1160-2.

Kim C and GE Karniadakis. 2014. “Time Correlation Functions of Brownian Motion and Evaluation of Friction Coefficient in the Near-Brownian-Limit Regime.” Multiscale Modeling & Simulation 12(1):225-248. DOI: 10.1137/130929916.

Konomi B, G Karagiannis, A Sarkar, X Sun, and G Lin. 2014. “Bayesian Treed Multivariate Gaussian Process with Adaptive Design: Application to a Carbon Capture Unit.” Technometrics 56(2):145-158. DOI: 10.1080/00401706.2013.879078.

Kordilla J, W Pan, and AM Tartakovsky. 2014. “Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations.” Journal of Chemical Physics 141(22):224112. DOI: 10.1063/1.4902238. OSTI Link.

Liang F, Y Cheng, and G Lin. 2014. “Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule.” Journal of the American Statistical Association 109(506):847-863. DOI: 10.1080/01621459.2013.872993.

Li W, G Lin, and D Zhang. 2014. “An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling.” Journal of Computational Physics 258:752-772. DOI: 10.1016/

Li Z, X Bian, B Caswell, and GE Karniadakis. 2014. “Construction of dissipative particle dynamics models for complex fluids via the Mori-Zwanzig formulation.” Soft Matter 10(43):8659-8672. DOI: 10.1039/C4SM01387E.

Li Z, Y-H Tang, H Lei, B Caswell, and GE Karniadakis. 2014. “Energy-conserving dissipative particle dynamics with temperature-dependent properties.” Journal of Computational Physics 265:113-127. DOI: 10.1016/

Lin G, J Bao, and Z Xu. 2014. “A three-dimensional phase field model coupled with a lattice kinetics solver for modeling crystal growth in furnaces with accelerated crucible rotation and traveling magnetic field.” Computers & Fluids 103:204-214. DOI: 10.1016/j.compfluid.2014.07.027.

Lin G, J Bao, Z Xu, AM Tartakovsky, and CH Henager Jr. 2014. “A Phase-Field Model Coupled with Lattice Kinetics Solver for Modeling Crystal Growth in Furnaces.” Communications in Computational Physics 15(1):76-92. DOI: 10.4208/cicp.300612.210313a.

Lin G, J Liu, L Mu, and X Ye. 2014. “Weak Galerkin Finite Element Methods for Darcy Flow: Anisotropy and Heterogeneity.” Journal of Computational Physics 276:422-437, 2014. DOI: 10.1016/

Mauro AJ, JK Sigurdsson, J Shrake, PJ Atzberger, and SA Isaacson. 2014. “A First-Passage Kinetic Monte Carlo method for reaction–drift–diffusion processes.” Journal of Computational Physics 259:536-567. DOI: 10.1016/

Meng D, Q Zhang, X Gao, S Wu, and G Lin. 2014. “LipidMiner: a software for automated identification and quantification of lipids from multiple liquid chromatography-mass spectrometry data files.” Rapid Communications in Mass Spectrometry 28(8):981-985. DOI: 10.1002/rcm.6865.

Olson D, P Bochev, M Luskin and AV Shapeev. 2014. “Development of an Optimization-Based Atomistic-to-Continuum Coupling Method.” Chapter 3 in Lecture Notes in Computer Science, eds. I Lirkov, S Margenov, and J Wasniewski, pp. 33-44. Springer Berlin Heidelberg, Germany. DOI: 10.1007/978-3-662-43880-0_3.

Olson D, PB Bochev, M Luskin, and AV Shapeev. 2014. “An Optimization-based Atomistic-to-Continuum Coupling Method.” SIAM Journal on Numerical Analysis 52(4):2183-2204. DOI: 10.1137/13091734X. OSTI Link.

Pan W, J Bao, and AM Tartakovsky. 2014. “Smoothed Particle Hydrodynamics Continuous Boundary Force Method for Navier-Stokes Equations Subject to a Robin Boundary Condition.” Journal of Computational Physics 259:242-259. DOI: 10.1016/

Perdikaris P and GE Karniadakis. 2014. “Fractional-order Viscoelasticity in One-dimensional Blood Flow Models.” Annals of Biomedical Engineering 42(5):1012-1023. DOI: 10.1007/s10439-014-0970-3.

Plunkett P, J Hu, C Siefert, and PJ Atzberger. 2014. “Spatially adaptive stochastic methods for fluid-structure interactions subject to thermal fluctuations in domains with complex geometries.” Journal of Computational Physics 277:121-137. DOI: 10.1016/

Quemeneur F, JK Sigurdsson, M Renner, PJ Atzberger, P Bassereau, and D Lacoste. 2014. “Shape matters in protein mobility within membranes.” Proceedings of the National Academy of Sciences of the United States of America 111(14):5083-5087. DOI: 10.1073/pnas.1321054111.

Samanta A, ME Tuckerman, T-Q Yu, and W E. 2014. “Microscopic mechanisms of equilibrium melting of a solid.” Science 346(6210):729-732. DOI: 10.1126/science.1253810.

Shao S, N Abdolrahim, DF Bahr, G Lin, and HM Zbib. 2014. “Stochastic Effects in Plasticity in Small Volumes.” International Journal of Plasticity 52:117-132. DOI: 10.1016/j.ijplas.2013.09.005.

Shi X and G Lin. 2014. “Modeling the Sedimentation of Red Blood Cells in Flow under Strong External Magnetic Body Force Using a Lattice Boltzmann Fictitious Domain Method.” Numerical Mathematics: Theory, Methods and Applications 7(4):512-523.

Tang Y-H and GE Karniadakis. 2014. “Accelerating dissipative particle dynamics simulations on GPUs: Algorithms, numerics and applications.” Computer Physics Communications 185(11):2809-2822. DOI: 10.1016/j.cpc.2014.06.015.

Venturi D and GE Karniadakis. 2014. “Convolutionless Nakajima-Zwanzig Equations for Stochastic Analysis in Nonlinear Dynamical Systems.” Proceedings of the Royal Society A 470(2166):20130754. DOI: 10.1098/rspa.2013.0754.

Wei J, G Lin, L Jiang, and Y Efendiev. 2014. “Analysis of Variance-based Mixed Multiscale Finite Element Method and Applications in Stochastic Two-phase Flows.” International Journal for Uncertainty Quantification 4(6):455-477. DOI: 10.1615/Int.J.UncertaintyQuantification.2014006135.

Xu G, G Lin, and J Liu. 2014. “Rare Event Simulation for Stochastic Korteweg-de Vries Equation.” SIAM/ASA Journal on Uncertainty Quantification 2(1):698-716. DOI: 10.1137/130944473.

Zayernouri M, W Cao, Z Zhang, and GE Karniadakis. 2014. “Spectral and Discontinuous Spectral Element Methods for Fractional Delay Equations.” Computational Methods in Science and Engineering. SIAM Journal on Scientific Computing 36(6):B904-B929. DOI: 10.1137/130935884.

Zayernouri M and GE Karniadakis. 2014. “Discontinuous Spectral Element Methods for Time- and Space-Fractional Advection Equations.” SIAM Journal on Scientific Computing 36(4):B684-B707. DOI: 10.1137/130940967.

Zayernouri M and GE Karniadakis. 2014. “Exponentially accurate spectral and spectral element methods for fractional ODEs.” Journal of Computational Physics 257(Part A):460-480. DOI: 10.1016/

Zayernouri M and GE Karniadakis. 2014. “Fractional Spectral Collocation Method.” SIAM Journal on Scientific Computing 36(1):A40-A62. DOI: 10.1137/130933216.

Zhang Z, MV Tretyakov, B Rozovskii, and GE Karniadakis. 2014. “A Recursive Sparse Grid Collocation Method for Differential Equations with White Noise.” SIAM Journal on Scientific Computing 36(4):A1652-A1677. DOI: 10.1137/130938906.

Zhang ZW, X Hu, TY Hou, G Lin, and M. Yan. 2014. “An adaptive ANOVA-based data-driven stochastic method for elliptic PDE with random coefficients.” Communications in Computational Physics 16(3):571-598.

Zhou Y. 2014. “Legendre Functions, Spherical Rotations, and Multiple Elliptic Integrals.” The Ramanujan Journal 34(3):373-428. DOI: 10.1007/s11139-013-9502-2.

Zhou Y. 2014. “On Some Integrals Over the Product of Three Legendre Functions.” The Ramanujan Journal 35(2):311-326. DOI: 10.1007/s11139-013-9504-0.


Atzberger PJ. 2013. “Incorporating Shear into Stochastic Eulerian-Lagrangian Methods for Rheological Studies of Complex Fluids and Soft Materials.” Physica D: Nonlinear Phenomena 265:57–70. DOI: 10.1016/j.physd.2013.09.002.

E W and H Shen. 2013. “Exact Renormalization Group Analysis of the Model For Turbulent Transport by the Shear Flow.” Journal of Statistical Physics 153(4):553-571. DOI: 10.1007/s10955-013-0854-1.

Fedosov D, M Dao, GE Karniadakis, and S Suresh. 2013. “Computational Biorheology of Human Blood Flow in Health and Disease.” Annals of Biomedical Engineering, Special Issue: Frontiers in Bioengineering. Published Online, Oct. 12, 2013. DOI: 10.1007/s10439-013-0922-3.

Kim C and GE Karniadakis. 2013. “Microscopic theory of Brownian motion revisited: The Rayleigh Model.” Physical Review E 87(3):032129. DOI: 10.1103/PhysRevE.87.032129.

Lei H and GE Karniadakis. 2013. “Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations.” Proceedings of the National Academy of Sciences (PNAS) 110(28):11326-11330. DOI: 10.1073/pnas.1221297110.

Pan W and AM Tartakovsky. 2013. “Dissipative particle dynamics model for colloid transport in porous media.” Advances in Water Resources 58:41-48. DOI: 10.1016/j.advwatres.2013.04.004.

Peng Z, X Li, I Pivkin, M Dao, GE Karniadakis, and S Suresh. 2013. “Lipid-bilayer and cytoskeletal interactions in a red blood cell.” Proceedings of the National Academy of Sciences (PNAS) 110(33):13356-13361. DOI: 10.1073/pnas.1311827110.

*Plunkett P, BA Camley, KL Weirich, J Israelachvili, and PJ Atzberger. 2013. “Simulation of Edge Facilitated Adsorption and Critical Concentration Induced Rupture of Vesicles at a Surface.” Soft Matter 9(35):8420.8427. DOI: 10.1039/C3SM50443C. *COVER (click to view)

Rolfe BA, J Chun, and YL Joo. 2013. “Dynamics of Micelle-Nanoparticle Systems Undergoing Shear: A Coarse-Grained Molecular Dynamics Approach.” Soft Matter, 9(43):10294-10305. DOI: 10.1039/C3SM52194J.

Sigurdsson JK, FLH Brown, and PJ Atzberger. 2013. “Hybrid continuum-particle method for fluctuating lipid bilayer membranes with diffusing protein inclusions.” Journal of Computational Physics 252:65-85. DOI: 10.1016/

Stinis P. 2013. “Renormalized reduced models for singular PDEs.” Communications in Applied Mathematics and Computational Science 8(1):39-66. DOI: 10.2140/camcos.2013.8.39.

Wang Y, JK Sigurdsson, E Brandt, and PJ Atzberger. 2013. “Dynamic implicit-solvent coarse-grained models of lipid bilayer membranes: Fluctuating hydrodynamics thermostat.” Physical Review E 88(2):023301. DOI: 10.1103/PhysRevE.88.023301.

Zayernouri M and GE Karniadakis. 2013. “Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation.” Journal of Computational Physics 252(1):495-517. DOI: 10.1016/

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