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## Schmidt, Bernd

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 Author ID: schmidt.bernd Published as: Schmidt, B.; Schmidt, Bernd Homepage: http://www.math.uni-augsburg.de/de/prof/ana/arbeitsgruppe/schmidt/
 Documents Indexed: 39 Publications since 2000, including 1 Book
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#### Co-Authors

 11 single-authored 6 Ortiz, Michael 4 Friedrich, Manuel 3 Stefanelli, Ulisse 2 Braun, Julian 2 Fraternali, Fernando 2 Friesecke, Gero 2 González, M. I. 2 Jesenko, Martin 2 Mainini, Edoardo 2 Theil, Florian 1 Au Yeung, Yuen 1 Bompadre, Agustín 1 Braides, Andrea 1 Huisinga, Wilhelm 1 Jansen, Sabine 1 König, Wolfgang Dieter 1 Kreutz, Leonard C. 1 Leyendecker, Sigrid 1 Piovano, Paolo 1 Schlömerkemper, Anja
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#### Serials

 5 Archive for Rational Mechanics and Analysis 4 Calculus of Variations and Partial Differential Equations 3 Multiscale Modeling & Simulation 3 Networks and Heterogeneous Media 2 Journal of Statistical Physics 2 International Journal for Numerical Methods in Engineering 2 Journal of Nonlinear Science 1 Communications in Mathematical Physics 1 Journal of the Mechanics and Physics of Solids 1 Nonlinearity 1 SIAM Journal on Numerical Analysis 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 Continuum Mechanics and Thermodynamics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Oberwolfach Reports
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#### Fields

 21 Mechanics of deformable solids (74-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 8 Statistical mechanics, structure of matter (82-XX) 5 Mechanics of particles and systems (70-XX) 4 Numerical analysis (65-XX) 3 Partial differential equations (35-XX) 3 Quantum theory (81-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

32 Publications have been cited 265 times in 191 Documents Cited by Year
Plate theory for stressed heterogeneous multilayers of finite bending energy. Zbl 1116.74034
Schmidt, Bernd
2007
Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape. Zbl 1379.74002
Au Yeung, Yuen; Friesecke, Gero; Schmidt, Bernd
2012
Eigenfracture: an eigendeformation approach to variational fracture. Zbl 1173.74040
Schmidt, Bernd; Fraternali, Fernando; Ortiz, Michael
2009
Linear $$\Gamma$$-limits of multiwell energies in nonlinear elasticity theory. Zbl 1160.74321
Schmidt, Bernd
2008
Ground states of the 2D sticky disc model: fine properties and $$N^{3/4}$$ law for the deviation from the asymptotic Wulff shape. Zbl 1292.82027
Schmidt, Bernd
2013
On the derivation of linear elasticity from atomistic models. Zbl 1183.74020
Schmidt, Bernd
2009
On the passage from atomic to continuum theory for thin films. Zbl 1156.74028
Schmidt, Bernd
2008
A derivation of continuum nonlinear plate theory from atomistic models. Zbl 1117.49018
Schmidt, Bernd
2006
Metastability and dominant eigenvalues of transfer operators. Zbl 1207.82021
Huisinga, Wilhelm; Schmidt, Bernd
2006
On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth. Zbl 1283.49013
Braun, Julian; Schmidt, Bernd
2013
Convergence analysis of meshfree approximation schemes. Zbl 1416.65469
Bompadre, A.; Schmidt, B.; Ortiz, M.
2012
An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem. Zbl 1302.74144
Friedrich, Manuel; Schmidt, Bernd
2014
Energy-stepping integrators in Lagrangian mechanics. Zbl 1188.70002
Gonzalez, M.; Schmidt, B.; Ortiz, M.
2010
Minimal energy configurations of strained multi-layers. Zbl 1129.49045
Schmidt, Bernd
2007
$$\Gamma$$-convergence of variational integrators for constrained systems. Zbl 1179.37112
Schmidt, Bernd; Leyendecker, Sigrid; Ortiz, Michael
2009
An analysis of crystal cleavage in the passage from atomistic models to continuum theory. Zbl 1329.82025
Friedrich, Manuel; Schmidt, Bernd
2015
$$N^{3/4}$$ law in the cubic lattice. Zbl 1426.82065
Mainini, Edoardo; Piovano, Paolo; Schmidt, Bernd; Stefanelli, Ulisse
2019
On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime. Zbl 1332.74044
Friedrich, Manuel; Schmidt, Bernd
2015
Universal formulae for the limiting elastic energy of membrane networks. Zbl 1244.74080
Schmidt, Bernd; Fraternali, Fernando
2012
Discrete-to-continuum limit of magnetic forces: Dependence on the distance between bodies. Zbl 1185.78006
Schlömerkemper, Anja; Schmidt, Bernd
2009
Effective theories for thin elastic films. Discrete-to-continuum limits for membranes and plates and minimal energy configurations of strained multi-layers. Zbl 1126.74002
Schmidt, Bernd
2006
Closure and commutability results for $$\Gamma$$-limits and the geometric linearization and homogenization of multiwell energy functionals. Zbl 1301.49032
Jesenko, Martin; Schmidt, Bernd
2014
Force-stepping integrators in Lagrangian mechanics. Zbl 1202.70006
Gonzalez, M.; Schmidt, B.; Ortiz, M.
2010
Time-independent gravitational fields. Zbl 0974.83012
Beig, Robert; Schmidt, Bernd
2000
A variational approach to Navier-Stokes. Zbl 1406.35237
Ortiz, Michael; Schmidt, Bernd; Stefanelli, Ulisse
2018
Homogenization and the limit of vanishing hardening in Hencky plasticity with non-convex potentials. Zbl 1387.49016
Jesenko, Martin; Schmidt, Bernd
2018
Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory. Zbl 1356.35239
Braun, Julian; Schmidt, Bernd
2016
Existence of families of spacetimes with a Newtonian limit. Zbl 1177.83060
Oliynyk, Todd Andrew; Schmidt, Bernd
2009
Qualitative properties of a continuum theory for thin films. Zbl 1142.74026
Schmidt, Bernd
2008
Surface energy and boundary layers for a chain of atoms at low temperature. Zbl 1456.82666
Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, Florian
2021
Maximal fluctuations around the Wulff shape for edge-isoperimetric sets in $${\mathbb{Z}}^d$$: a sharp scaling law. Zbl 1454.05121
Mainini, Edoardo; Schmidt, Bernd
2020
On the infinite particle limit in Lagrangian dynamics and convergence of optimal transportation meshfree methods. Zbl 1370.37121
Schmidt, Bernd
2014
Surface energy and boundary layers for a chain of atoms at low temperature. Zbl 1456.82666
Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, Florian
2021
Maximal fluctuations around the Wulff shape for edge-isoperimetric sets in $${\mathbb{Z}}^d$$: a sharp scaling law. Zbl 1454.05121
Mainini, Edoardo; Schmidt, Bernd
2020
$$N^{3/4}$$ law in the cubic lattice. Zbl 1426.82065
Mainini, Edoardo; Piovano, Paolo; Schmidt, Bernd; Stefanelli, Ulisse
2019
A variational approach to Navier-Stokes. Zbl 1406.35237
Ortiz, Michael; Schmidt, Bernd; Stefanelli, Ulisse
2018
Homogenization and the limit of vanishing hardening in Hencky plasticity with non-convex potentials. Zbl 1387.49016
Jesenko, Martin; Schmidt, Bernd
2018
Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory. Zbl 1356.35239
Braun, Julian; Schmidt, Bernd
2016
An analysis of crystal cleavage in the passage from atomistic models to continuum theory. Zbl 1329.82025
Friedrich, Manuel; Schmidt, Bernd
2015
On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime. Zbl 1332.74044
Friedrich, Manuel; Schmidt, Bernd
2015
An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem. Zbl 1302.74144
Friedrich, Manuel; Schmidt, Bernd
2014
Closure and commutability results for $$\Gamma$$-limits and the geometric linearization and homogenization of multiwell energy functionals. Zbl 1301.49032
Jesenko, Martin; Schmidt, Bernd
2014
On the infinite particle limit in Lagrangian dynamics and convergence of optimal transportation meshfree methods. Zbl 1370.37121
Schmidt, Bernd
2014
Ground states of the 2D sticky disc model: fine properties and $$N^{3/4}$$ law for the deviation from the asymptotic Wulff shape. Zbl 1292.82027
Schmidt, Bernd
2013
On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth. Zbl 1283.49013
Braun, Julian; Schmidt, Bernd
2013
Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape. Zbl 1379.74002
Au Yeung, Yuen; Friesecke, Gero; Schmidt, Bernd
2012
Convergence analysis of meshfree approximation schemes. Zbl 1416.65469
Bompadre, A.; Schmidt, B.; Ortiz, M.
2012
Universal formulae for the limiting elastic energy of membrane networks. Zbl 1244.74080
Schmidt, Bernd; Fraternali, Fernando
2012
Energy-stepping integrators in Lagrangian mechanics. Zbl 1188.70002
Gonzalez, M.; Schmidt, B.; Ortiz, M.
2010
Force-stepping integrators in Lagrangian mechanics. Zbl 1202.70006
Gonzalez, M.; Schmidt, B.; Ortiz, M.
2010
Eigenfracture: an eigendeformation approach to variational fracture. Zbl 1173.74040
Schmidt, Bernd; Fraternali, Fernando; Ortiz, Michael
2009
On the derivation of linear elasticity from atomistic models. Zbl 1183.74020
Schmidt, Bernd
2009
$$\Gamma$$-convergence of variational integrators for constrained systems. Zbl 1179.37112
Schmidt, Bernd; Leyendecker, Sigrid; Ortiz, Michael
2009
Discrete-to-continuum limit of magnetic forces: Dependence on the distance between bodies. Zbl 1185.78006
Schlömerkemper, Anja; Schmidt, Bernd
2009
Existence of families of spacetimes with a Newtonian limit. Zbl 1177.83060
Oliynyk, Todd Andrew; Schmidt, Bernd
2009
Linear $$\Gamma$$-limits of multiwell energies in nonlinear elasticity theory. Zbl 1160.74321
Schmidt, Bernd
2008
On the passage from atomic to continuum theory for thin films. Zbl 1156.74028
Schmidt, Bernd
2008
Qualitative properties of a continuum theory for thin films. Zbl 1142.74026
Schmidt, Bernd
2008
Plate theory for stressed heterogeneous multilayers of finite bending energy. Zbl 1116.74034
Schmidt, Bernd
2007
Minimal energy configurations of strained multi-layers. Zbl 1129.49045
Schmidt, Bernd
2007
A derivation of continuum nonlinear plate theory from atomistic models. Zbl 1117.49018
Schmidt, Bernd
2006
Metastability and dominant eigenvalues of transfer operators. Zbl 1207.82021
Huisinga, Wilhelm; Schmidt, Bernd
2006
Effective theories for thin elastic films. Discrete-to-continuum limits for membranes and plates and minimal energy configurations of strained multi-layers. Zbl 1126.74002
Schmidt, Bernd
2006
Time-independent gravitational fields. Zbl 0974.83012
Beig, Robert; Schmidt, Bernd
2000
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#### Cited by 271 Authors

 17 Schmidt, Bernd 13 Friedrich, Manuel 10 Ortiz, Michael 9 Stefanelli, Ulisse 8 Agostiniani, Virginia 8 Cicalese, Marco 8 Hornung, Peter 6 DeSimone, Antonio 6 Velčić, Igor 5 Alicandro, Roberto 5 Kreutz, Leonard C. 5 Mainini, Edoardo 5 Neukamm, Stefan 5 Piovano, Paolo 5 Schlömerkemper, Anja 4 Braides, Andrea 4 Davoli, Elisa 4 De Luca, Lucia 4 Lazzaroni, Giuliano 4 Palombaro, Mariapia 4 Ruf, Matthias 4 Schäffner, Mathias 4 Weinberg, Kerstin 3 Bartels, Sören 3 Fraternali, Fernando 3 König, Wolfgang Dieter 3 Lew, Adrian J. 3 Lewicka, Marta 3 Leyendecker, Sigrid 3 Lipton, Robert P. 3 Raoult, Annie 3 Schütte, Christof 3 Sun, WaiChing 3 Weber, Marcus 2 Amendola, Ada 2 Bétermin, Laurent 2 Bonito, Andrea 2 Braun, Julian 2 Carrillo de la Plata, José Antonio 2 Dal Maso, Gianni 2 Desmet, Wim 2 Djurdjevac Conrad, Natasa 2 Focardi, Matteo 2 Friesecke, Gero 2 Grandi, Diego 2 Greco, Francesco 2 Jansen, Sabine C. 2 Jiang, Hao 2 Johnson, Gwen 2 Junge, Oliver 2 Koumatos, Konstantinos 2 Krause, Rolf H. 2 Kružík, Martin 2 Kumar, Siddhant 2 Li, Bentian 2 Li, Bo 2 Lu, Jian 2 Lucantonio, Alessandro 2 Lučić, Danka 2 Mielke, Alexander 2 Mora, Maria Giovanna 2 Natário, José 2 Negri, Matteo 2 Nochetto, Ricardo Horacio 2 Paroni, Roberto 2 Ponsiglione, Marcello 2 Rabczuk, Timon 2 Scardia, Lucia 2 Shen, Yongxing 2 Solombrino, Francesco 2 Theil, Florian 2 Tomassetti, Giuseppe 2 Zanini, Chiara 1 Alben, Silas D. 1 Allaire, Grégoire 1 Andrianov, Igor V. 1 Anitescu, Cosmin 1 Arroyo, María José 1 Arroyo, Marino 1 Awrejcewicz, Jan 1 Bach, Annika 1 Bauer, Robert Otto 1 Benešová, Barbora 1 Bian, Xin 1 Bilgen, Carola 1 Bittracher, Andreas 1 Blanc, Xavier 1 Blass, T. J. 1 Böhlke, Thomas 1 Bourdin, Blaise 1 Bourne, David P. 1 Bruckner, Sharon 1 Bryant, Eric C. 1 Buchert, Thomas 1 Bufford, Laura 1 Cañizo, José Alfredo 1 Carpentieri, Gerardo 1 Chen, Xian 1 Chiaramonte, Maurizio M. 1 Chipot, Michel ...and 171 more Authors
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#### Cited in 65 Serials

 18 Archive for Rational Mechanics and Analysis 15 Computer Methods in Applied Mechanics and Engineering 15 International Journal for Numerical Methods in Engineering 11 Calculus of Variations and Partial Differential Equations 10 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 9 SIAM Journal on Mathematical Analysis 8 Journal of Elasticity 7 Journal of Nonlinear Science 6 Journal of Statistical Physics 5 Communications in Mathematical Physics 5 Journal of the Mechanics and Physics of Solids 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Meccanica 4 Continuum Mechanics and Thermodynamics 3 General Relativity and Gravitation 3 Journal of Computational Physics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Networks and Heterogeneous Media 2 Journal of Mathematical Physics 2 Nonlinearity 2 Journal of Differential Equations 2 Multiscale Modeling & Simulation 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Computational Dynamics 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 Rocky Mountain Journal of Mathematics 1 Theoretical and Mathematical Physics 1 Journal of Geometry and Physics 1 Journal of Optimization Theory and Applications 1 Transactions of the American Mathematical Society 1 Physica D 1 The Annals of Applied Probability 1 Communications in Partial Differential Equations 1 Linear Algebra and its Applications 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Review 1 Stochastic Processes and their Applications 1 Numerical Linear Algebra with Applications 1 NoDEA. Nonlinear Differential Equations and Applications 1 Mathematical Problems in Engineering 1 Mathematics and Mechanics of Solids 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Brazilian Journal of Probability and Statistics 1 Archives of Computational Methods in Engineering 1 Communications on Pure and Applied Analysis 1 Milan Journal of Mathematics 1 SIAM Journal on Applied Dynamical Systems 1 International Journal of Computational Methods 1 International Journal of Fracture 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Communications in Mathematical Analysis 1 Nonlinear Analysis. Hybrid Systems 1 Advances in Calculus of Variations 1 Analysis & PDE 1 ISRN Applied Mathematics 1 East Asian Journal on Applied Mathematics 1 EMS Surveys in Mathematical Sciences 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Bollettino dell’Unione Matematica Italiana 1 Mathematics in Engineering
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#### Cited in 28 Fields

 127 Mechanics of deformable solids (74-XX) 56 Calculus of variations and optimal control; optimization (49-XX) 43 Statistical mechanics, structure of matter (82-XX) 35 Partial differential equations (35-XX) 24 Numerical analysis (65-XX) 14 Mechanics of particles and systems (70-XX) 13 Differential geometry (53-XX) 11 Fluid mechanics (76-XX) 10 Probability theory and stochastic processes (60-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Quantum theory (81-XX) 5 Relativity and gravitational theory (83-XX) 4 Convex and discrete geometry (52-XX) 3 Combinatorics (05-XX) 3 Real functions (26-XX) 3 Ordinary differential equations (34-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX)