**Publications**

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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**2016**

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.

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* 71(11):2218-2230. DOI: 10.1016/j.camwa.2015.12.006.

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.

Sigurdsson JK and P Atzberger. 2015. “Hydrodynamic Coupling of Particle Inclusions Embedded in Curved Lipid Bilayer Membranes.” *Soft Matter*, Online First June 27, 2016. DOI: 10.1039/C6SM00194G.

Sun Y, P Sun, B Zheng, and G Lin. 2016. “Error analysis of finite element method for Poissonâ€“Nernstâ€“Planck equations.” *Journal of Computational and Applied Mathematics* 301:28-43. DOI: 10.1016/j.cam.2016.01.028.

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.

**2015**

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.

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/j.jcp.2014.09.020.

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.

Li J and P Stinis. 2015. “Mesh refinement for uncertainty quantification through model reduction.” *Journal of Computational Physics* 280:164-183. DOI: 10.1016/j.jcp.2014.09.021.

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/j.jcp.2015.03.047.

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.

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.

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/j.cam.2014.06.024.

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.

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.

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.

**2014**

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/j.jcp.2014.03.050.

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/j.jcp.2013.11.016.

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.

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/j.jcp.2013.11.019.

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*, Accepted Manuscript, Published Online September 08, 2014. 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/j.jcp.2014.02.003.

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/j.jcp.2014.07.001.

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.

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/j.jcp.2013.12.014.

*Related Highlight*: Surpassing Boundaries in Fluid Dyamics

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/j.jcp.2014.07.051.

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 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/j.jcp.2013.09.039.

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.

**2013**

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.

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.

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/j.jcp.2013.06.031.