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@article{luskin79, author="Mitchell Luskin", title="An approximation procedure for nonsymmetric, nonlinear hyperbolic systems with nonlinear boundary conditions", journal="SIAM J. Numer. Anal.", volume=16, year=1979, pages="145--164"} @article{luskin79a, author="Mitchell Luskin", title="A {G}alerkin method for nonlinear parabolic equations with nonlinear boundary conditions", journal="Math. Comput.", volume=33, year=1979, pages="493--519"} @article{luskin79b, author="Mitchell Luskin", title="Convergence of a finite element method for the approximation of normal modes of the oceans", journal="Math. Comput.", volume=33, year=1979, pages="493--519"} @article{luskinnagylaki79, author="Mitchell Luskin and Tom Nagylaki", title="Numerical analysis of weak random drift in a cline", journal="Genetics", volume=92, year=1979, pages="297--303"} @article{luskin80, author="Mitchell Luskin", title="A finite element method for first order hyperbolic systems", journal="Math. Comput.", volume=35, year=1980, pages="1093--1112"} @article{desclouxluskin81, author="Jean Descoux and Mitchell Luskin and Jacques Rappaz", title="Approximation of the spectrum of closed operators: the determination of normal modes of a rotating basin", journal="Math. Comput.", volume=36, year=1981, pages="137--154"} @article{luskinrannacher81, author="Mitchell Luskin and Rolf Rannacher", title="On the smoothing property of the {G}alerkin method for parabolic equations", journal="SIAM J. Numer. Anal.", volume=19, year=1981, pages="93--113"} @article{luskin81, author="Mitchell Luskin", title="On the existence of global smooth solutions for a model equation for fluid flow in a pipe", journal="J. Math. Anal. Appl.", volume=84, year=1981, pages="614--630"} @inproceedings{babuskaluskin81, author="Ivo Bab{\v u}ska and Mitchell Luskin", title="An adaptive time discretization procedure for parabolic problems", booktitle="Proceedings of the Fourth IMACS International Symposium on Computer Methods for Partial Differential Equations", year=1981} @inproceedings{luskintemple81, author="Mitchell Luskin and Blake Temple", title="Stability and error bonds for a fractional step scheme to compute weak solutions of the nonlinear waterhammer problem", booktitle="Lectures on the Numerical Solution of Partial Differential Equations", publisher="Department of Mathematics, University of Maryland", volume=20, year=1981, pages="270--289"} @article{luskintemple82, author="Mitchell Luskin and Blake Temple", title="The existence of a global weak solution to the nonlinear waterhammer problem", journal="Comm. Pure Appl. Math.", volume=35, year=1982, pages="697--735"} @article{desclouxluskin82, author="Jean Descloux and Mitchell Luskin", title="On a finite element method to solve the criticality eigenvalue problem for the transport equation", journal="SIAM J. Numer. Anal.", volume=19, year=1982, pages="1208--1218"} @article{luskinrannacher82, author="Mitchell Luskin and Rolf Rannacher", title="On the smoothing property of the {C}rank-{N}icolson scheme", journal="Applicable Analysis", volume=14, year=1982, pages="117--135"} @inproceedings{kheshgiluskin83, author="Haroon Kheshgi and Mitchell Luskin", title="On the variable sign penalty approximation of the {N}avier-{S}tokes equation", booktitle="Nonlinear Partial Differential Equations", series="Contemporary Mathematics", volume=17, editor="Joel Smoller", publisher="American Mathematical Society", address="Providence", year=1983} @inproceedings{kheshgiluskin84, author="Haroon Kheshgi and Mitchell Luskin", title="Improved flux calculations for viscous incompressible flow by the variable penalty method", booktitle="Lectures in Applied Mathematics", publisher="American Mathematical Society", address="Providence", volume=22, year=1984} @article{luskin84, author="Mitchell Luskin", title="On the classification of the equations of viscoelasticity", journal="Journal of Non-Newtonian Fluid Mechanics", volume=16, year=1984, pages="3--11"} @article{kheshgiluskin85, author="Haroon Kheshgi and Mitchell Luskin", title="Analysis of the finite element variable penalty method for {S}tokes equation", journal="Math. Comput.", volume=45, year=1985, pages="347--363"} @article{lorenceluskinmartin85, author="L. Lorence and Mitchell Luskin and William Martin", title="Analysis of a block {G}auss-{S}eidel iterative method for a finite element discretization of the neutron transport equation", journal="Transport Theory and Statistical Physics", volume=144, year=1985, pages="35--62"} @inproceedings{chipotluskin85, author="Michel Chipot and Stephen Kistler and Mitchell Luskin and David Perry", title="Elastohydrodynamical problems in magnetic recording", booktitle="Proceedings of the Congr\`es National d'Analyse Num\'erique", address="France", year=1985, pages="209--212"} @article{chipotluskin86, author="Michel Chipot and Mitchell Luskin", title="Existence and uniqueness of solutions to the compressible {R}eynolds lubrication equation", journal="SIAM Journal on Math. Analysis", volume=17, year=1986, pages="1390--1399"} @inproceedings{chipotluskin87, author="Michel Chipot and Mitchell Luskin", title="The compressible {R}eynolds lubrication equation", booktitle="Metastability and Incompletely Posed Problems", series="IMA Volumes in Mathematics and its Applications", volume=3, editor="S. Antman and J. Ericksen and D. Kinderlehrer and I. Muller", publisher="Springer-Verlag", address="New York", year=1987, pages="61--76"} @inproceedings{cohenhardtluskin87, author="Robert Cohen and Robert Hardt and David Kinderlehrer and San-Yih Lin and Mitchell Luskin", title="Minimum energy configurations for liquid crystals", booktitle="Theory and Applications of Liquid Crystals", series="IMA Volumes in Mathematics and its Applications", volume=5, editor="J. Ericksen and D. Kinderlehrer", publisher="Springer-Verlag", address="New York", year=1987, pages="99--121"} @inproceedings{hardtkinderlehrerluskin88, author="Robert Hardt and David Kinderlehrer and Mitchell Luskin", title="Remarks about the mathematical theory of liquid crystals", booktitle="Calculus of Variations and Partial Differential Equations", series="Lecture Notes in Mathematics", volume= 1340, editor="S. Hildebrandt and D. Kinderlehrer and M. Miranda", publisher=" Springer-Verlag", address="New York", year=1988, pages="123--138"} @article{linluskin89, author="San-Yih Lin and Mitchell Luskin", title="Relaxation methods for liquid crystal problems", journal="SIAM J. Numer. Anal.", volume=26, year=1989, pages="1310--1324"} @inproceedings{collinsluskin89, author="Charles Collins and Mitchell Luskin", title="The computation of the austenitic-martensitic phase transition", booktitle="Partial Differential Equations and Continuum Models of Phase Transitions", series="Lecture Notes in Physics", volume=344, editors="M. Rascle and D. Serre and M. Slemrod", publisher="Springer-Verlag", address="New York", year=1989, pages="34--50"} @article{luskinsell89, author="Mitchell Luskin and George Sell", title="Approximation theories for inertial manifolds", journal="Mathematical Modelling and Numerical Analysis", volume=23, year=1989, pages="445--461"} @article{cohenluskinlin89, author="Robert Cohen and San-Yih Lin and Mitchell Luskin", title="Relaxation and gradient methods for molecular orientation in liquid crystals", journal="Computer Physics Communications", volume=53, year=1989, pages="455--465"} @inproceedings{collinsluskin89a, author="Charles Collins and Mitchell Luskin", title="Computational results for phase transitions in shape memory materials", booktitle="Smart Materials, Structures, and Mathematical Issues", editor="C. Rogers", publisher="Technomic Publishing Co.", address="Lancaster, Pennsylvania", year=1989, pages="198--215"} @article{chipotluskin90, author="Michel Chipot and Mitchell Luskin", title="Existence of solutions to the elastohydrodynamical equations for magnetic recording systems", journal="SIAM Journal on Math Analysis", volume=21, year=1990, pages="1--17"} @inproceedings{collinsluskin90, author="Charles Collins and Mitchell Luskin", title="Numerical modeling of the microstructure of crystals with symmetry-related variants", booktitle="Proceedings of the US - Japan Workshop on Smart/Intelligent Materials and Systems", editor="I. Ahmad and A. Crowson and C. Rogers and M. Aizawa", publisher="Technomic Publishing Co.", address="Lancaster, Pennsylvania", year=1990, pages="309--318"} @article{fabesluskinsell91, author="Eugene Fabes and Mitchell Luskin and George Sell", title="Construction of inertial manifolds by elliptic regularization", journal="Journal of Differential Equations", volume=89, year=1991, pages="355--387"} @article{collinskinderlehrerluskin91, author="Charles Collins and David Kinderlehrer and Mitchell Luskin", title="Numerical approximation of the solution of a variational problem with a double well potential", journal="SIAM J. Numer. Anal.", volume=28, year=1991, pages="321--332"} @article{collinsluskin91, author="Charles Collins and Mitchell Luskin", title="Optimal order error estimates for the finite element approximation of the solution of a nonconvex variational problem", journal="Math. Comp.", year=1991, pages="621--637", volume=57} @inproceedings{luskin91, author="Mitchell Luskin", title="Numerical analysis of microstructure for crystals with a nonconvex energy density", booktitle="Progress in Partial Differential Eequations: the Metz Surveys", series="Pitman Research Notes in Mathematics Series", volume="249", editor="Michel Chipot and J. Saint Jean Paulin", publisher="Longman House", address="UK", pages="156--165", year=1991} @inproceedings{cohenluskin91, author="Robert Cohen and Mitchell Luskin", title="Field-induced instabilities in nematic liquid crystals", booktitle="Nematics: Mathematical and Physical Aspects", series="Nato ASI Series, Series C: Mathematical and Physical Sciences", volume=332, editors="J. M. Coron and F. Helein and J. M. Ghidaglia", publisher="Kluwer Academic Publishers", address="Dordrecht, Netherlands", pages="261--278", year=1991} @inproceedings{collinsluskinriordan91, author="C. Collins and M. Luskin and J. Riordan", title="Computational images of crystalline microstructure", booktitle="AMS Special Lectures in Mathematics and AMS Videotape Library", editor="J. Taylor", publisher="Amer. Math. Soc.", address="Providence", year=1991, pages="16--18"} @inproceedings{luskinpan91, author="Mitchell Luskin and T.-W. Pan", title="Shear flow instabilities in liquid crystals", booktitle="Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, Vol. 2", address="Trinity College, Dublin, Ireland", editor="R. Vichnevetsky and J.J.H. Miller", year=1991, pages="793--794"} @article{luskinma92, author="Mitchell Luskin and Ling Ma", year=1992, title="Analysis of the finite element approximation of microstructure in micromagnetics", journal="SIAM J. Numer. Anal.", volume=29, pages="320--331"} @article{luskinpan92, author="Mitchell Luskin and T.-W. Pan", title="Nonplanar shear flows for nonaligning nematic liquid crystals", journal="Journal of Non-Newtonian Fluid Mechanics", volume=42, pages="369--384", year="1992"} @inproceedings{collinsluskin93, author="Mitchell Luskin and Charles Collins", title="Computational results for martensitic twinning", editor="Perkins and Wayman", booktitle="Proceedings of the International Conference on Martensitic Transformations", publisher="Monterey Institute of Advanced Studies", address="Carmel, California", year=1993, pages="83--88"} @inproceedings{luskinma93, author="Mitchell Luskin and Ling Ma", title="Numerical optimization of the micromagnetics energy", booktitle="Mathematics in Smart Materials", organization="SPIE", notes="Vol. 1919", pages="19--29", year=1993} @inproceedings{collinsluskinriordan93, author="Charles Collins and Mitchell Luskin and James Riordan", year=1993, title="Computational results for a two-dimensional model of crystalline microstructure", booktitle="Microstructure and Phase Transitions", editor="J. Ericksen and R. James and D. Kinderlehrer and M. Luskin", note="IMA Volumes in Mathematics and Its Applications, vol. 54", publisher="Springer-Verlag", address="New York", pages="51--56"} @article{kloucekluskin94, author="Petr Klou\v{c}ek and Mitchell Luskin", title="The computation of the dynamics of the martensitic transformation", journal="Continuum Mech. Thermodyn.", pages="209--240", year=1994, volume=6} @article{kloucekluskin94b, author="Petr Klou\v{c}ek and Mitchell Luskin", title="Computational modeling of the martensitic transformation with surface energy", journal="Mathematical and Computer Modelling", volume=20, pages="101--121", year=1994} @article{kloucekliluskin, author="Petr Klou\v{c}ek and Bo Li and Mitchell Luskin", title="Analysis of a class of nonconforming finite elements for crystalline microstructures", journal="Math. Comput.", pages="1111-1135", year=1996, volume=65} @article{luskinacta, author="Mitchell Luskin", title="On the computation of crystalline microstructure", journal="Acta Numerica", pages="191--258", volume=5, year=1996} @article{luskiniciam96, author="Mitchell Luskin", title="Numerical analysis of a microstructure for a rotationally invariant, double well energy", journal="Zeitschrift f{\"u}r Angewandt Mathematik und Mechanik", year=1996, volume=76, pages="405--408"} @article{luskin95, author="Mitchell Luskin", title="Approximation of a laminated microstructure for a rotationally invariant, double well energy density", journal="Numer. Math.", year=1997, pages="205--221", volume=75} @article{liluskin96, author="Bo Li and Mitchell Luskin", title="Nonconforming finite element approximation of crystalline microstructure", journal="Math. Comp.", volume=67, pages="917--946", year="1998"} @article{liluskin97, author="Bo Li and Mitchell Luskin", title="Finite element analysis of microstructure for the cubic to tetragonal transformation", journal="SIAM J. Numer. Anal.", year="1998", volume=35, pages="376--392"} @inproceedings{enumath, author="Mitchell Luskin", booktitle="ENUMATH 97", title="The stability and numerical analysis of martensitic microstructure", year=1998, editor="H.~Bock and F.~Brezzi and R.~Glowinski and G.~Kanschat and Y.~Kuznetsov and J.~P{\'e}riaux and R.~Rannacher", pages="54--69" } @article{liluskin97b, author="Bo Li and Mitchell Luskin", title="Approximation of a laminate with varying volume fractions", journal="Mathematical Modelling and Numerical Analysis", volume=33, pages="67--87", year="1999"} @article{liluskin99, author="Bo Li and Mitchell Luskin", title="Theory and computation for the microstructure near the interface between twinned layers and a pure variant of martensite", journal="Materials Science \& Engineering A", year=1999, pages="237--240", volume=273} @article{bhattaliluskin98, author="Kaushik Bhattacharya and Bo Li and Mitchell Luskin", title="The simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation", journal="Archive for Rational Mechanics and Analysis", year="1999", volume=149, pages="123--154"} @inproceedings{luskin99, author="Mitchell Luskin", title="On the stability of microstructure for general martensitic transformations", booktitle="Lectures on Applied Mathematics", editor="H.-J. Bungartz and R. W. Hoppe and C. Zenger", publisher="Springer-Verlag", year=2000, pages="31--44"} @article{belikluskin99, author="Pavel B\v{e}l\'{\i}k and Mitchell Luskin", title="Stability of microstructure for tetragonal to monoclinic martensitic transformations", journal="Mathematical Modelling and Numerical Analysis", year="2000", pages="663--685", volume=34} @inproceedings{cockburnluskin, author="Bernardo Cockburn and Mitchell Luskin and Chi-Wang Shu and Endre S{\'u}li", title="Post-processing of {G}alerkin methods for hyperbolic problems", series="Lecture Notes in Computational Science and Engineering", booktitle="First International Symposium on Discontinuous Galerkin Methods", volume=33, publisher="Springer-Verlag", editor="Bernardo Cockburn and G. E. Karniadakis and Chi-Wang Shu", year=2000} @article{efendievluskin, author="Yalchin Efendiev and Mitchell Luskin", title="Stability of microstructures for some martensitic transformations", journal="Mathematical and Computer Modelling", year="2000", volume=34, pages="1289--1305"} @article{strutchupluskinzachariah, author="Henning Struchtrup and Mitchell Luskin and Michael Zachariah", title="A model for kinetically controlled internal phase segregation during aerosol coagulation", journal="J. Aerosol Science", volume=32, pages="1479--1504", year=2001} @article{belikbruleluskin, author="Pavel B\v{e}l\'{\i}k and Tim Brule and Mitchell Luskin", title="On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films", journal="Mathematical Modelling and Numerical Analysis", year="2001", pages="525--548", volume=35 } @article{belikluskin, author="Pavel B\v{e}l\'{\i}k and Mitchell Luskin", title="A total-variation surface energy model for thin films of martensitic crystals", journal="Interfaces and Free Boundaries", year="2002", volume=4, pages="71--88" } @article{efendievstrutchupluskinzachariah, author="Yalchin Efendiev and Henning Struchtrup and Mitchell Luskin and Michael Zachariah", title=" A hybrid sectional-moment model for coagulation and phase segregation in binary liquid nanodroplets", journal="J. Nanoparticle Research", year="2002", volume=4, pages="61--72" } @article{belikluskin2, author="Pavel B\v{e}l\'{\i}k and Mitchell Luskin", title="A computational model for the indentation and phase transformation of a martensitic thin film", journal="Journal of the Mechanics and Physics of Solids", year="2002", volume=50, pages="1789--1815"} @inproceedings{luskinicm, author="Mitchell Luskin", title="Computational modeling of microstructure", booktitle="Proceedings of the International Congress of Mathematicians, ICM 2002, Beijing", year=2002, volume="III", pages="707--716"} @INPROCEEDINGS{dundee, AUTHOR = "Pavel B\v{e}l\'{\i}k and Mitchell Luskin", TITLE = "Numerical Methods for Martensitic Phase Transformation and Microstructure", BOOKTITLE = "Proceedings of the 20th Biennial Conference on Numerical Analysis", YEAR = "2003", editor = "D F Griffiths and G A Watson", pages = "13--16", publisher = "University of Dundee", } @article{cockburnluskin2, author="Bernardo Cockburn and Mitchell Luskin and Chi-Wang Shu and Endre S{\'u}li", title="Enhanced accuracy by post-processing for finite element methods for hyperbolic equations", journal="Math. Comp.", volume=73, year=2003, pages="577--606" } @article{kruzikluskin, author="Martin Kru\v{z}\'{\i}k and Mitchell Luskin", title="The computation of martensitic microstructure with piecewise laminates", journal="Journal of Scientific Computing", volume=19, year=2003, pages="293--308" } @article{belikluskin03, author="Pavel B\v{e}l\'{\i}k and Mitchell Luskin", title="Approximation by piecewise constant functions in a BV metric", journal="Mathematical Models \& Methods in Applied Sciences", year=2003, volume=13, pages="373--393" } @article{belikluskin04, author="Pavel B\v{e}l\'{\i}k and Mitchell Luskin", title="A Computational Model For Martensitic Thin Films With Compositional Fluctuation", journal="Mathematical Models \& Methods in Applied Sciences", year=2004, volume=14, pages="1585--1598" } @article{belikluskin04b, author="Pavel B\v{e}l\'{\i}k and Mitchell Luskin", title="Computational modeling of softening in a structural phase transformation", journal="SIAM J. Multiscale Modeling \& Simulation", year=2005, volume=3, pages="764--781" } @article{rybkaluskin, author="Piotr Rybka and Mitchell Luskin", title="Existence of energy minimizers for magnetostrictive materials", journal="SIAM J. Math. Anal.", year="2005", pages="2004--2019", volume=36 } @article{belikluskin05, author="Pavel B\v{e}l\'{\i}k and Mitchell Luskin", title="The {$\Gamma$}-convergence of a sharp interface thin film model with non-convex elastic energy", journal="SIAM J. Math. Anal.", year=2006, volume=38, pages="414--433" } @article{liakhovaluskinzhang06, author="Julia Liakhova and Mitchell Luskin and Tianyu Zhang", title="Computational Modeling of Ferromagnetic Shape Memory Thin Films", journal="Ferroelectrics", volume=342, pages="73--82", year=2006 } @article{belikluskin06, author="Pavel B\v{e}l\'{\i}k and Mitchell Luskin", title="A Finite Element Model for Martensitic Thin Films", journal="Calcolo", volume=43, pages="197--215", year=2006 } @article{legollmoeckelluskin06, author="Fr\'ed\'eric Legoll and Mitchell Luskin and Richard Moeckel", title="Non-ergodicity of the {Nos\'e-Hoover} thermostatted harmonic oscillator", journal="Archive for Rational Mechanics and Analysis", year="2007", volume=184, pages="449--463" } @article{luskinzhang06, author="Mitchell Luskin and Tianyu Zhang", title="Numerical Analysis of a Model for Ferromagnetic Shape Memory Thin Films", journal="Computer Methods in Applied Mechanics and Engineering", year="2007", volume=196, pages="3759�-3770" } @article{arndtluskin07a, author="Marcel Arndt and Mitchell Luskin", title="Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation", journal="International Journal for Multiscale Computational Engineering", year="2007", volume=5, pages="407--415" } @article{dobsonccb07, author="M. Dobson and M. Luskin and R. S. Elliott and E. B. Tadmor", title="A Multilattice Quasicontinuum for Phase Transforming Materials: {Cascading Cauchy Born} Kinematics", journal="Journal of Computer-Aided Materials Design", year="2007", volume=14, pages="219--237" } @article{arndtluskin07b, author="Marcel Arndt and Mitchell Luskin", title="Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a {Frenkel-Kontorova} Model", journal="SIAM J. Multiscale Modeling \& Simulation", year="2008", volume=7, pages="147-170" } @article{dobsonluskin07, author="Matthew Dobson and Mitchell Luskin", title="Analysis of a force-based quasicontinuum approximation", journal="Mathematical Modelling and Numerical Analysis", year="2008", pages="113--139" } @Article{arndtluskin07c, author = {Marcel Arndt and Mitchell Luskin}, title = {Goal-Oriented Adaptive Mesh Refinement for the Quasicontinuum Approximation of a {Frenkel-Kontorova} Model}, journal={Computer Methods in Applied Mechanics and Engineering}, year = {2008}, volume=197, pages="4298--4306" } @article{dobsonluskin08, author="Matthew Dobson and Mitchell Luskin", title="Iterative solution of the quasicontinuum equilibrium equations with continuation", journal="Journal of Scientific Computing", year="2008", volume=37, pages="19--41" } @article{dobsonluskin09, author="Matthew Dobson and Mitchell Luskin", title="An Analysis of the Effect of Ghost Force Oscillation on Quasicontinuum Error", journal="Mathematical Modelling and Numerical Analysis", year="2009", volume=43, pages="591--604" } @article{dobsonluskin09b, author="Matthew Dobson and Mitchell Luskin", title="An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation", journal="SIAM. J. Numer. Anal.", volume=47, year="2009", pages="2455-2475" } @article{legollmoeckelluskin09, author="Fr\'ed\'eric Legoll and Mitchell Luskin and Richard Moeckel", title="Non-ergodicity of {Nos\'e-Hoover} dynamics", journal="Nonlinearity", year="2009", volume=22, pages="1673-1694" } @article{cluster09, author="Mitchell Luskin and Christoph Ortner", title="An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method", journal="SIAM. J. Numer. Anal.", year="2009", volume=47, pages="3070-3086" } @article{dobs-qcf2, author="Matthew Dobson and Mitchell Luskin and Christoph Ortner", title="Stability, Instability, and Error of the Force-Based Quasicontinuum Approximation", journal="Archive for Rational Mechanics and Analysis", year="2010", pages="179--202", volume="197", note="arXiv:0903.0610" } @article{doblusort:qcf.stab, author = {Dobson, M. and Luskin, M. and Ortner, C.}, title = {Sharp Stability Estimates for the Force-based Quasicontinuum Approximation of Homogeneous Tensile Deformation}, journal="SIAM J. Multiscale Modeling \& Simulation", year="2010", pages="782--802", volume=8, note="arXiv:0907.3861" } @article{doblusort:qce.stab, AUTHOR = {Matthew Dobson and Mitchell Luskin and Christoph Ortner}, TITLE = {Accuracy of Quasicontinuum Approximations Near Instabilities}, journal="Journal of the Mechanics and Physics of Solids", year="2010", pages="1741--1757", volume=58, NOTE={arXiv:0905.2914v2}, } @article{qcf.iterative, AUTHOR = {Matthew Dobson and Mitchell Luskin and Christoph Ortner}, TITLE = {Iterative Methods for the Force-based Quasicontinuum Approximation: Analysis of a 1D model problem}, note = {arXiv:0910.2013v3}, journal="Computer Methods in Applied Mechanics and Engineering", year="2011", pages="2697--2709", volume=200 } @article{eam.qc, AUTHOR = {Xingjie Helen Li and Mitchell Luskin}, TITLE = {An Analysis of the Quasi-Nonlocal Quasicontinuum Approximation of the Embedded Atom Model}, NOTE = {arXiv:1008.3628v4}, journal="International Journal for Multiscale Computational Engineering", year="2012", pages="33--49", volume=10 } @article{finite.range, AUTHOR = {Xingjie Helen Li and Mitchell Luskin}, TITLE = {A Generalized Quasi-Nonlocal Atomistic-to-Continuum Coupling Method with Finite Range Interaction}, NOTE = {arXiv:1007.2336v2, doi: 10.1093/imanum/drq049}, journal="IMA Journal of Numerical Analysis", year="2012", volume=32, pages="373--393" } @INCOLLECTION{luskin.iter.stat, AUTHOR = {Mitchell Luskin and Christoph Ortner}, TITLE = {Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation}, BOOKTITLE = {Numerical Analysis and Multiscale Computations}, series = {Lect. Notes Comput. Sci. Eng.}, PUBLISHER = {Springer Verlag}, volume=82, YEAR = {2012}, pages={331--368}, editor = {Bjorn Engquist and Olof Runborg and Richard Tsai}, note = {arXiv:1104.1774}, } @INCOLLECTION{luskin.durham, AUTHOR = {Brian Van Koten and Xingjie Helen Li and Mitchell Luskin and Christoph Ortner}, TITLE = {A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods}, series = {Lect. Notes Comput. Sci. Eng.}, BOOKTITLE = {Numerical Analysis of Multiscale Problems}, PUBLISHER = {Springer}, volume=83, pages="67--96", YEAR = {2012}, editor = {Ivan Graham and Tom Hou and Omar Lakkis and Rob Scheichl}, note = {arXiv:1012.6031}, } @article{oqc11, AUTHOR = {Pavel B\v{e}l\'{\i}k and Mitchell Luskin}, TITLE = {Analysis of the Quasi-nonlocal Approximation of Linear and Circular Chains in the Plane}, NOTE = {arXiv:1008.3716}, journal="SIAM J. Multiscale Modeling \& Simulation", year="2011", volume=9, pages="1495--1527" } @article{bqce11, author = {Brian {Van Koten} and Mitchell Luskin}, collaboration = {}, title = {Analysis of Energy-Based Blended Quasi-Continuum Approximations}, publisher = {SIAM}, year = {2011}, journal = {SIAM Journal on Numerical Analysis}, volume = {49}, number = {5}, pages = {2182-2209}, keywords = {quasi-continuum; error analysis; atomistic-to-continuum}, url = {http://link.aip.org/link/?SNA/49/2182/1}, doi = {10.1137/10081071X} } @INCOLLECTION{encyclopedia11, AUTHOR = {Mitchell Luskin and Christoph Ortner}, TITLE = {Atomistic-to-Continuum Coupling}, BOOKTITLE = {Encyclopedia of Applied and Computational Mathematics}, PUBLISHER = {Springer}, editor={Bjorn Engquist}, YEAR = {to appear, 2013}, } @article{parrep, AUTHOR = {Claude Le Bris and T. Leli{\`e}vre and Mitchell Luskin and Danny Perez}, TITLE = {A mathematical formalization of the parallel replica dynamics}, NOTE = {arXiv:1105.4636}, journal="Monte Carlo Methods Appl.", year="2012", volume=18, pages="119--146", } @article{eam2, AUTHOR = {Xingjie Helen Li and Mitchell Luskin}, TITLE = {Lattice Stability for Atomistic Chains Modeled by Local Approximations of the Embedded Atom Method}, NOTE = { arXiv:1108.4473}, journal="Computational Materials Science", year="to appear", } @article{bqcf, author="Xingjie Helen Li and Mitchell Luskin and Christoph Ortner", title="Positive-Definiteness of the Blended Force-Based Quasicontinuum Method", note={arXiv:1112.2528v1}, journal="SIAM J. Multiscale Modeling \& Simulation", year={to appear}, } @article{bqce12, author="Mitchell Luskin and Christoph Ortner and Brian {Van Koten}", title="Formulation and optimization of the energy-based blended quasicontinuum method", journal="Computer Methods in Applied Mechanics and Engineering", note={arXiv: 1112.2377}, year={to appear}, }