Edit Profile (opens in new tab) Arnold, Anton Compute Distance To: Compute Author ID: arnold.anton Published as: Arnold, Anton; Arnold, A. Documents Indexed: 83 Publications since 1989 8 Contributions as Editor Co-Authors: 77 Co-Authors with 83 Joint Publications 2,123 Co-Co-Authors all top 5 Co-Authors 7 single-authored 11 Markowich, Peter Alexander 10 Ehrhardt, Matthias 7 Carlen, Eric Anders 6 Carrillo de la Plata, José Antonio 6 Desvillettes, Laurent 6 Stürzer, Dominik 5 Toscani, Giuseppe 4 Achleitner, Franz 4 Martínez Gamba, Irene 4 Ringhofer, Christian A. 3 Ben Abdallah, Naoufel 3 Degond, Pierre 3 Dhamo, Elidon 3 Dolbeault, Jean 3 Hammer, René 3 Manzini, Chiara 3 Miletić, Maja 3 Pötz, Walter 3 Schulte, Maike 3 Signorello, Beatrice 3 Unterreiter, Andreas 3 Wöhrer, Tobias 2 Döpfner, Kirian 2 Einav, Amit 2 Glassey, Robert T. 2 Jüngel, Ansgar 2 Kim, Jinmyong 2 Koprucki, Thomas 2 Kugi, Andreas 2 Levermore, C. David 2 Mauser, Norbert Julius 2 Negulescu, Claudia 2 Nier, Francis 2 Sparber, Christof 2 Steinrück, Herbert 2 Yao, Xiaohua 2 Zisowsky, Andrea 1 Amodio, Pierluigi 1 Antoine, Xavier 1 Bartier, Jean-Philippe 1 Besse, Christophe 1 Bian, Lei 1 Bonilla, Luis Lopez 1 Cercignani, Carlo 1 Drmota, Michael 1 Fagnola, Franco 1 Geevers, Sjoerd 1 Geier, J. 1 Giering, Ulrich 1 Gualdani, Maria Pia 1 Ju, Qiangchang 1 Kanta, M. 1 Klapproth, Corinna 1 Klein, Christian 1 Körner, Jannis 1 Krob, Daniel 1 Lange, Horst 1 Lederman, Claudia B. 1 Levitina, Tatiana V. 1 López, José Luis 1 Mischler, Stéphane 1 Mouhot, Clément 1 Pang, Gang 1 Perugia, Ilaria 1 Pietra, Paola 1 Prévost, Céline 1 Schädle, Achim 1 Schmeiser, Christian 1 Schmock, Uwe 1 Settanni, Giuseppina 1 Shu, Chi-Wang 1 Soler, Juan S. 1 Tang, Shaoqiang 1 Tidriri, Moulay D. 1 Ujvari, Bernhard 1 Viertl, Reinhard Karl Wolfgang 1 Villani, Cédric 1 Weinmüller, Ewa B. 1 Zweifel, Paul F. all top 5 Serials 5 Journal of Computational Physics 5 Communications in Mathematical Sciences 4 Transport Theory and Statistical Physics 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Oberwolfach Reports 3 Computers & Mathematics with Applications 3 Journal of Mathematical Analysis and Applications 3 Monatshefte für Mathematik 3 SIAM Journal on Numerical Analysis 3 Kinetic and Related Models 2 Journal of Differential Equations 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Communications in Partial Differential Equations 2 The IMA Volumes in Mathematics and its Applications 1 Communications in Mathematical Physics 1 International Journal of Control 1 Information Processing Letters 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics of Computation 1 Applied Mathematics and Computation 1 BIT 1 Calcolo 1 IEEE Transactions on Automatic Control 1 Indiana University Mathematics Journal 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Revista Matemática Iberoamericana 1 Internationale Mathematische Nachrichten 1 Applied Mathematics Letters 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Rivista di Matematica della Università di Parma. Serie 6 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Communications in Computational Physics 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Communications on Stochastic Analysis 1 Rivista di Matematica della Università di Parma. New Series 1 Nanosistemy: Fizika, Khimiya, Matematika all top 5 Fields 61 Partial differential equations (35-XX) 31 Statistical mechanics, structure of matter (82-XX) 30 Numerical analysis (65-XX) 26 Quantum theory (81-XX) 10 Ordinary differential equations (34-XX) 9 Operator theory (47-XX) 7 General and overarching topics; collections (00-XX) 7 Fluid mechanics (76-XX) 6 Integral equations (45-XX) 4 Mechanics of deformable solids (74-XX) 3 Real functions (26-XX) 3 Systems theory; control (93-XX) 2 History and biography (01-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Probability theory and stochastic processes (60-XX) 2 Optics, electromagnetic theory (78-XX) 1 Measure and integration (28-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 67 Publications have been cited 956 times in 646 Documents Cited by ▼ Year ▼ On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Zbl 0982.35113Arnold, Anton; Markowich, Peter; Toscani, Giuseppe; Unterreiter, Andreas 165 2001 A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Zbl 1364.65178Antoine, Xavier; Arnold, Anton; Besse, Christophe; Ehrhardt, Matthias; Schadle, Achim 106 2008 Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability. Zbl 1085.65513Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan 72 2003 Discrete transparent boundary conditions for the Schrödinger equation. Zbl 0993.65097Ehrhardt, M.; Arnold, A. 39 2001 On generalized Csiszár-Kullback inequalities. Zbl 1015.94003Unterreiter, Andreas; Arnold, Anton; Markowich, Peter; Toscani, Giuseppe 32 2000 Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C. 30 2004 Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics. Zbl 0915.76081Arnold, Anton; Ehrhardt, Matthias 29 1998 Self-consistent relaxation-time models in quantum mechanics. Zbl 0849.35113Arnold, Anton 29 1996 An analysis of quantum Fokker-Planck models: a Wigner function approach. Zbl 1062.35097Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan 28 2004 Existence of nontrivial steady states for populations structured with respect to space and a continuous trait. Zbl 1303.92091Arnold, Anton; Desvillettes, Laurent; Prévost, Céline 25 2012 Mathematical concepts of open quantum boundary conditions. Zbl 1019.81010Arnold, Anton 24 2001 On large time asymptotics for drift-diffusion-Poisson systems. Zbl 1017.82041Arnold, Anton; Markowich, Peter; Toscani, Giuseppe 23 2000 Large-time behavior in non-symmetric Fokker-Planck equations. Zbl 1342.35394Achleitner, Franz; Arnold, Anton; Stürzer, Dominik 19 2015 A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in \((1+1)\)D. Zbl 1349.81085Hammer, René; Pötz, Walter; Arnold, Anton 17 2014 Interpolation between logarithmic Sobolev and Poincaré inequalities. Zbl 1146.60063Arnold, Anton; Bartier, Jean-Philippe; Dolbeault, Jean 17 2007 An operator splitting method for the Wigner-Poisson problem. Zbl 0860.65143Arnold, Anton; Ringhofer, Christian 16 1996 Refined convex Sobolev inequalities. Zbl 1087.35018Arnold, Anton; Dolbeault, Jean 15 2005 Low and high field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck systems. Zbl 1106.82381Arnold, A.; Carrillo, J. A.; Gamba, I.; Shu, C.-W. 14 2001 Large-time behavior of non-symmetric Fokker-Planck type equations. Zbl 1331.82042Arnold, Anton; Carlen, Eric; Ju, Qiangchang 14 2008 The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. Zbl 0742.35078Arnold, Anton; Nier, Francis 13 1991 Global estimates of fundamental solutions for higher-order Schrödinger equations. Zbl 1256.35106Kim, JinMyong; Arnold, Anton; Yao, Xiaohua 12 2012 Refined long-time asymptotics for some polymeric fluid flow models. Zbl 1213.35094Arnold, A.; Carrillo, J. A.; Manzini, C. 11 2010 Discrete transparent boundary conditions for the Schrödinger equation – a compact higher order scheme. Zbl 1145.65058Schulte, Maike; Arnold, Anton 11 2008 Mathematical properties of quantum evolution equations. Zbl 1170.82372Arnold, Anton 11 2008 The “electromagnetic” Wigner equation for an electron with spin. Zbl 0701.35130Arnold, Anton; Steinrück, Herbert 10 1989 WKB-based schemes for the oscillatory 1D Schrödinger equation in the semiclassical limit. Zbl 1230.65078Arnold, Anton; Ben Abdallah, Naoufel; Negulescu, Claudia 10 2011 The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects. Zbl 1121.82031Arnold, Anton; Dhamo, Elidon; Manzini, Chiara 10 2007 A discrete-velocity, stationary Wigner equation. Zbl 1019.82020Arnold, Anton; Lange, Horst; Zweifel, Paul F. 9 2000 Quantum dynamical semigroups for diffusion models with Hartree interaction. Zbl 1085.82004Arnold, A.; Sparber, C. 9 2004 On linear hypocoercive BGK models. Zbl 1353.35113Achleitner, Franz; Arnold, Anton; Carlen, Eric A. 9 2016 Single-cone real-space finite difference scheme for the time-dependent Dirac equation. Zbl 1349.65301Hammer, René; Pötz, Walter; Arnold, Anton 8 2014 Discrete transparent boundary conditions for the Schrödinger equation on circular domains. Zbl 1256.35103Arnold, Anton; Ehrhardt, Matthias; Schulte, Maike; Sofronov, Ivan 8 2012 On absorbing boundary conditions for quantum transport equations. Zbl 0821.45002Arnold, Anton 7 1994 On multi-dimensional hypocoercive BGK models. Zbl 1405.82023Achleitner, Franz; Arnold, Anton; Carlen, Eric A. 7 2018 The Wigner-Fokker-Planck equation: stationary states and large time behavior. Zbl 1253.82065Arnold, Anton; Gamba, Irene M.; Gualdani, Maria Pia; Mischler, Stéphane; Mouhot, Clement; Sparber, Christof 7 2012 Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system. Zbl 1359.93399Miletić, Maja; Stürzer, Dominik; Arnold, Anton; Kugi, Andreas 7 2016 Dispersive effects in quantum kinetic equations. Zbl 1161.35040Arnold, Anton; Dhamo, Elidon; Manzini, Chiara 6 2007 Operator splitting methods applied to spectral discretizations of quantum transport equations. Zbl 0847.65074Arnold, Anton; Ringhofer, Christian 5 1995 Quantum Fokker-Planck models: the Lindblad and Wigner approaches. Zbl 1180.81089Arnold, A.; Fagnola, F.; Neumann, L. 5 2008 Discrete transparent boundary conditions for transient \(kp\)-Schrödinger equations with application to quantum heterostructures. Zbl 1080.65080Zisowsky, Andrea; Arnold, Anton; Ehrhardt, Matthias; Koprucki, Thomas 5 2005 On the periodic Wigner–Poisson–Fokker–Planck system. Zbl 1014.35084Arnold, Anton; Carrillo, Jose A.; Dhamo, Elidon 5 2002 On the rates of decay to equilibrium in degenerate and defective Fokker-Planck equations. Zbl 1387.35579Arnold, Anton; Einav, Amit; Wöhrer, Tobias 4 2018 The one-dimensional periodic Bloch-Poisson equation. Zbl 0828.34073Arnold, Anton; Markowich, Peter A.; Mauser, Norbert 4 1991 Entropy decay of discretized Fokker-Planck equations. I: Temporal semidiscretization. Zbl 1053.82025Arnold, A.; Unterreiter, A. 4 2003 Transparent boundary conditions for quantum-waveguide simulations. Zbl 1159.82326Arnold, Anton; Schulte, Maike 3 2008 Estimates for a class of oscillatory integrals and decay rates for wave-type equations. Zbl 1248.35032Arnold, Anton; Kim, JinMyong; Yao, Xiaohua 3 2012 On optimal decay estimates for ODEs and PDEs with modal decomposition. Zbl 1442.82028Achleitner, Franz; Arnold, Anton; Signorello, Beatrice 3 2019 Improved entropy decay estimates for the heat equation. Zbl 1139.35012Arnold, A.; Carrillo, J. A.; Klapproth, C. 3 2008 A piezoelectric Euler-Bernoulli beam with dynamic boundary control: stability and dissipative FEM. Zbl 1326.35034Miletić, Maja; Arnold, Anton 3 2015 Multi-scale modeling of quantum semiconductor devices. Zbl 1366.82062Arnold, Anton; Jüngel, Ansgar 3 2006 The Wigner-Poisson problem in a crystal. Zbl 0822.58070Arnold, A.; Degond, P.; Markowich, P. A.; Steinrück, Herbert 2 1989 A generalized Bakry-Emery condition for non-symmetric diffusions. Zbl 0967.35057Arnold, Anton; Carlen, Eric 2 2000 The relaxation-time Wigner equation. Zbl 0870.35085Arnold, Anton 2 1995 An analysis of the Marshak conditions for matching Boltzmann and Euler equations. Zbl 0882.76078Arnold, Anton; Giering, Ulrich 2 1997 Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions. Zbl 1421.65020Arnold, Anton; Negulescu, Claudia 2 2018 Stationary Schrödinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point. Zbl 1439.34078Arnold, Anton; Döpfner, Kirian 2 2020 Sharp decay estimates in local sensitivity analysis for evolution equations with uncertainties: from ODEs to linear kinetic equations. Zbl 1428.35036Arnold, Anton; Jin, Shi; Wöhrer, Tobias 2 2020 Large-time behavior of discrete kinetic equations with non-symmetric interactions. Zbl 1033.35072Arnold, Anton; Carrillo, Jose A.; Tidriri, Moulay D. 2 2002 Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation. Zbl 1066.65081Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan 2 2005 An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip. Zbl 1329.35065Miletić, Maja; Stürzer, Dominik; Arnold, Anton 2 2015 Numerical analysis of the deterministic particle method applied to the Wigner equation. Zbl 0763.65092Arnold, Anton; Nier, Francis 1 1992 Spectral analysis and long-time behaviour of a Fokker-Planck equation with a non-local perturbation. Zbl 1291.35406Stürzer, Dominik; Arnold, Anton 1 2014 The periodic quantum Liouville-Poisson problem. Zbl 0727.35113Arnold, Anton; Markowich, Peter A. 1 1990 Almost exact boundary conditions for transient Schrödinger-Poisson system. Zbl 1349.65267Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton 1 2016 Closed-loop stability analysis of a gantry crane with heavy chain and payload. Zbl 1397.93181Stürzer, Dominik; Arnold, Anton; Kugi, Andreas 1 2018 Recognizable subsets of the two letter plactic monoid. Zbl 1337.68172Arnold, A.; Kanta, M.; Krob, D. 1 1997 Large time convergence of the non-homogeneous Goldstein-Taylor equation. Zbl 1459.82259Arnold, Anton; Einav, Amit; Signorello, Beatrice; Wöhrer, Tobias 1 2021 Large time convergence of the non-homogeneous Goldstein-Taylor equation. Zbl 1459.82259Arnold, Anton; Einav, Amit; Signorello, Beatrice; Wöhrer, Tobias 1 2021 Stationary Schrödinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point. Zbl 1439.34078Arnold, Anton; Döpfner, Kirian 2 2020 Sharp decay estimates in local sensitivity analysis for evolution equations with uncertainties: from ODEs to linear kinetic equations. Zbl 1428.35036Arnold, Anton; Jin, Shi; Wöhrer, Tobias 2 2020 On optimal decay estimates for ODEs and PDEs with modal decomposition. Zbl 1442.82028Achleitner, Franz; Arnold, Anton; Signorello, Beatrice 3 2019 On multi-dimensional hypocoercive BGK models. Zbl 1405.82023Achleitner, Franz; Arnold, Anton; Carlen, Eric A. 7 2018 On the rates of decay to equilibrium in degenerate and defective Fokker-Planck equations. Zbl 1387.35579Arnold, Anton; Einav, Amit; Wöhrer, Tobias 4 2018 Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions. Zbl 1421.65020Arnold, Anton; Negulescu, Claudia 2 2018 Closed-loop stability analysis of a gantry crane with heavy chain and payload. Zbl 1397.93181Stürzer, Dominik; Arnold, Anton; Kugi, Andreas 1 2018 On linear hypocoercive BGK models. Zbl 1353.35113Achleitner, Franz; Arnold, Anton; Carlen, Eric A. 9 2016 Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system. Zbl 1359.93399Miletić, Maja; Stürzer, Dominik; Arnold, Anton; Kugi, Andreas 7 2016 Almost exact boundary conditions for transient Schrödinger-Poisson system. Zbl 1349.65267Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton 1 2016 Large-time behavior in non-symmetric Fokker-Planck equations. Zbl 1342.35394Achleitner, Franz; Arnold, Anton; Stürzer, Dominik 19 2015 A piezoelectric Euler-Bernoulli beam with dynamic boundary control: stability and dissipative FEM. Zbl 1326.35034Miletić, Maja; Arnold, Anton 3 2015 An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip. Zbl 1329.35065Miletić, Maja; Stürzer, Dominik; Arnold, Anton 2 2015 A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in \((1+1)\)D. Zbl 1349.81085Hammer, René; Pötz, Walter; Arnold, Anton 17 2014 Single-cone real-space finite difference scheme for the time-dependent Dirac equation. Zbl 1349.65301Hammer, René; Pötz, Walter; Arnold, Anton 8 2014 Spectral analysis and long-time behaviour of a Fokker-Planck equation with a non-local perturbation. Zbl 1291.35406Stürzer, Dominik; Arnold, Anton 1 2014 Existence of nontrivial steady states for populations structured with respect to space and a continuous trait. Zbl 1303.92091Arnold, Anton; Desvillettes, Laurent; Prévost, Céline 25 2012 Global estimates of fundamental solutions for higher-order Schrödinger equations. Zbl 1256.35106Kim, JinMyong; Arnold, Anton; Yao, Xiaohua 12 2012 Discrete transparent boundary conditions for the Schrödinger equation on circular domains. Zbl 1256.35103Arnold, Anton; Ehrhardt, Matthias; Schulte, Maike; Sofronov, Ivan 8 2012 The Wigner-Fokker-Planck equation: stationary states and large time behavior. Zbl 1253.82065Arnold, Anton; Gamba, Irene M.; Gualdani, Maria Pia; Mischler, Stéphane; Mouhot, Clement; Sparber, Christof 7 2012 Estimates for a class of oscillatory integrals and decay rates for wave-type equations. Zbl 1248.35032Arnold, Anton; Kim, JinMyong; Yao, Xiaohua 3 2012 WKB-based schemes for the oscillatory 1D Schrödinger equation in the semiclassical limit. Zbl 1230.65078Arnold, Anton; Ben Abdallah, Naoufel; Negulescu, Claudia 10 2011 Refined long-time asymptotics for some polymeric fluid flow models. Zbl 1213.35094Arnold, A.; Carrillo, J. A.; Manzini, C. 11 2010 A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Zbl 1364.65178Antoine, Xavier; Arnold, Anton; Besse, Christophe; Ehrhardt, Matthias; Schadle, Achim 106 2008 Large-time behavior of non-symmetric Fokker-Planck type equations. Zbl 1331.82042Arnold, Anton; Carlen, Eric; Ju, Qiangchang 14 2008 Discrete transparent boundary conditions for the Schrödinger equation – a compact higher order scheme. Zbl 1145.65058Schulte, Maike; Arnold, Anton 11 2008 Mathematical properties of quantum evolution equations. Zbl 1170.82372Arnold, Anton 11 2008 Quantum Fokker-Planck models: the Lindblad and Wigner approaches. Zbl 1180.81089Arnold, A.; Fagnola, F.; Neumann, L. 5 2008 Transparent boundary conditions for quantum-waveguide simulations. Zbl 1159.82326Arnold, Anton; Schulte, Maike 3 2008 Improved entropy decay estimates for the heat equation. Zbl 1139.35012Arnold, A.; Carrillo, J. A.; Klapproth, C. 3 2008 Interpolation between logarithmic Sobolev and Poincaré inequalities. Zbl 1146.60063Arnold, Anton; Bartier, Jean-Philippe; Dolbeault, Jean 17 2007 The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects. Zbl 1121.82031Arnold, Anton; Dhamo, Elidon; Manzini, Chiara 10 2007 Dispersive effects in quantum kinetic equations. Zbl 1161.35040Arnold, Anton; Dhamo, Elidon; Manzini, Chiara 6 2007 Multi-scale modeling of quantum semiconductor devices. Zbl 1366.82062Arnold, Anton; Jüngel, Ansgar 3 2006 Refined convex Sobolev inequalities. Zbl 1087.35018Arnold, Anton; Dolbeault, Jean 15 2005 Discrete transparent boundary conditions for transient \(kp\)-Schrödinger equations with application to quantum heterostructures. Zbl 1080.65080Zisowsky, Andrea; Arnold, Anton; Ehrhardt, Matthias; Koprucki, Thomas 5 2005 Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation. Zbl 1066.65081Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan 2 2005 Entropies and equilibria of many-particle systems: an essay on recent research. Zbl 1063.35109Arnold, A.; Carrillo, J. A.; Desvillettes, L.; Dolbeault, J.; Jüngel, A.; Lederman, C.; Markowich, P. A.; Toscani, G.; Villani, C. 30 2004 An analysis of quantum Fokker-Planck models: a Wigner function approach. Zbl 1062.35097Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan 28 2004 Quantum dynamical semigroups for diffusion models with Hartree interaction. Zbl 1085.82004Arnold, A.; Sparber, C. 9 2004 Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability. Zbl 1085.65513Arnold, Anton; Ehrhardt, Matthias; Sofronov, Ivan 72 2003 Entropy decay of discretized Fokker-Planck equations. I: Temporal semidiscretization. Zbl 1053.82025Arnold, A.; Unterreiter, A. 4 2003 On the periodic Wigner–Poisson–Fokker–Planck system. Zbl 1014.35084Arnold, Anton; Carrillo, Jose A.; Dhamo, Elidon 5 2002 Large-time behavior of discrete kinetic equations with non-symmetric interactions. Zbl 1033.35072Arnold, Anton; Carrillo, Jose A.; Tidriri, Moulay D. 2 2002 On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Zbl 0982.35113Arnold, Anton; Markowich, Peter; Toscani, Giuseppe; Unterreiter, Andreas 165 2001 Discrete transparent boundary conditions for the Schrödinger equation. Zbl 0993.65097Ehrhardt, M.; Arnold, A. 39 2001 Mathematical concepts of open quantum boundary conditions. Zbl 1019.81010Arnold, Anton 24 2001 Low and high field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck systems. Zbl 1106.82381Arnold, A.; Carrillo, J. A.; Gamba, I.; Shu, C.-W. 14 2001 On generalized Csiszár-Kullback inequalities. Zbl 1015.94003Unterreiter, Andreas; Arnold, Anton; Markowich, Peter; Toscani, Giuseppe 32 2000 On large time asymptotics for drift-diffusion-Poisson systems. Zbl 1017.82041Arnold, Anton; Markowich, Peter; Toscani, Giuseppe 23 2000 A discrete-velocity, stationary Wigner equation. Zbl 1019.82020Arnold, Anton; Lange, Horst; Zweifel, Paul F. 9 2000 A generalized Bakry-Emery condition for non-symmetric diffusions. Zbl 0967.35057Arnold, Anton; Carlen, Eric 2 2000 Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics. Zbl 0915.76081Arnold, Anton; Ehrhardt, Matthias 29 1998 An analysis of the Marshak conditions for matching Boltzmann and Euler equations. Zbl 0882.76078Arnold, Anton; Giering, Ulrich 2 1997 Recognizable subsets of the two letter plactic monoid. Zbl 1337.68172Arnold, A.; Kanta, M.; Krob, D. 1 1997 Self-consistent relaxation-time models in quantum mechanics. Zbl 0849.35113Arnold, Anton 29 1996 An operator splitting method for the Wigner-Poisson problem. Zbl 0860.65143Arnold, Anton; Ringhofer, Christian 16 1996 Operator splitting methods applied to spectral discretizations of quantum transport equations. Zbl 0847.65074Arnold, Anton; Ringhofer, Christian 5 1995 The relaxation-time Wigner equation. Zbl 0870.35085Arnold, Anton 2 1995 On absorbing boundary conditions for quantum transport equations. Zbl 0821.45002Arnold, Anton 7 1994 Numerical analysis of the deterministic particle method applied to the Wigner equation. Zbl 0763.65092Arnold, Anton; Nier, Francis 1 1992 The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. Zbl 0742.35078Arnold, Anton; Nier, Francis 13 1991 The one-dimensional periodic Bloch-Poisson equation. Zbl 0828.34073Arnold, Anton; Markowich, Peter A.; Mauser, Norbert 4 1991 The periodic quantum Liouville-Poisson problem. Zbl 0727.35113Arnold, Anton; Markowich, Peter A. 1 1990 The “electromagnetic” Wigner equation for an electron with spin. Zbl 0701.35130Arnold, Anton; Steinrück, Herbert 10 1989 The Wigner-Poisson problem in a crystal. Zbl 0822.58070Arnold, A.; Degond, P.; Markowich, P. A.; Steinrück, Herbert 2 1989 all cited Publications top 5 cited Publications all top 5 Cited by 833 Authors 31 Arnold, Anton 28 Dolbeault, Jean 22 Antoine, Xavier 17 Jüngel, Ansgar 15 Carrillo de la Plata, José Antonio 15 Zheng, Chunxiong 14 Toscani, Giuseppe 14 Zhang, Jiwei 13 Markowich, Peter Alexander 12 López, José Luis 11 Ehrhardt, Matthias 11 Lorin, Emmanuel 11 Méhats, Florian 10 Besse, Christophe 9 Tang, Shaoqiang 8 Degond, Pierre 8 Zlotnik, Alexander A. 7 Barletti, Luigi 7 Fellner, Klemens 7 Goudon, Thierry 7 Pang, Gang 7 Perthame, Benoît 7 Pinaud, Olivier 7 Wu, Xiaonan 6 Bao, Weizhu 6 Esteban, Maria J. 6 Frosali, Giovanni 6 Han, Houde 6 Lelièvre, Tony 6 Mirrahimi, Sepideh 5 Cai, Yongyong 5 Calvez, Vincent 5 Cañizo, José Alfredo 5 Chainais-Hillairet, Claire 5 Čiegis, Raimondas 5 Henderson, Christopher 5 Li, Jiyong 5 Manzini, Chiara 5 Montejo-Gámez, Jesús 5 Nieto, Juanjo 5 Petrov, Pavel S. 5 Soler, Juan S. 5 Tang, Qinglin 5 Yin, Jia 5 Zisowsky, Andrea 4 Barrett, John W. 4 Ben Abdallah, Naoufel 4 Bouin, Emeric 4 Carlen, Eric Anders 4 Desvillettes, Laurent 4 Di Francesco, Marco 4 Du, Qiang 4 Gentil, Ivan 4 Girardin, Léo 4 Huang, Zhongyi 4 Kowalczyk, Michał 4 Li, Bin 4 Liu, Hailiang 4 Lorenzi, Tommaso 4 Loss, Michael 4 Lu, Tiao 4 Mielke, Alexander 4 Noble, Pascal 4 Pavliotis, Grigorios A. 4 Pötz, Walter 4 Ringhofer, Christian A. 4 Saanouni, Tarek 4 Sparber, Christof 4 Stoltz, Gabriel 4 Süli, Endre E. 4 Tang, Bao Quoc 4 Vaibhav, Vishal 4 Vazquez, Juan Luis 4 Wang, Shu 4 Yang, Xu 3 Abounouh, Mostafa 3 Achleitner, Franz 3 Al Moatassime, Hassan 3 Bartier, Jean-Philippe 3 Bolley, François 3 Burger, Martin 3 Cancès, Clément 3 Carles, Rémi 3 Coulombel, Jean-François 3 Dang Quang A 3 Del Pino, Manuel A. 3 Dreher, Michael 3 Faraj, Ali 3 Friese, Tilmann 3 Furioli, Giulia 3 Gerasimenko, Viktor Ivanovich 3 Geuzaine, Christophe A. 3 Gualdani, Maria Pia 3 Guillin, Arnaud 3 Haskovec, Jan 3 Herda, Maxime 3 Ji, Songsong 3 Jia, Xiaowei 3 Jiang, Haiyan 3 Jiang, Shidong ...and 733 more Authors all top 5 Cited in 181 Serials 55 Journal of Computational Physics 28 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 19 Journal of Statistical Physics 19 Journal of Scientific Computing 18 Journal of Differential Equations 18 Journal of Functional Analysis 15 Journal of Computational and Applied Mathematics 15 Kinetic and Related Models 14 Numerische Mathematik 14 Applied Numerical Mathematics 13 Journal of Mathematical Analysis and Applications 12 Journal of Mathematical Physics 11 Transport Theory and Statistical Physics 11 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Archive for Rational Mechanics and Analysis 10 Communications in Partial Differential Equations 10 SIAM Journal on Mathematical Analysis 9 Applied Mathematics Letters 8 SIAM Journal on Numerical Analysis 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 Computers & Mathematics with Applications 7 Communications in Mathematical Physics 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Discrete and Continuous Dynamical Systems 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 SIAM Journal on Scientific Computing 5 Nonlinearity 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Mathematics and Computers in Simulation 5 Numerical Methods for Partial Differential Equations 5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 5 Doklady Mathematics 5 Multiscale Modeling & Simulation 5 Communications in Computational Physics 4 Applicable Analysis 4 International Journal of Control 4 Mathematical Methods in the Applied Sciences 4 Wave Motion 4 Mathematics of Computation 4 Chinese Annals of Mathematics. Series B 4 Mathematical and Computer Modelling 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Discrete and Continuous Dynamical Systems. Series B 3 Communications on Pure and Applied Mathematics 3 Bulletin of Mathematical Biology 3 The Annals of Probability 3 Applied Mathematics and Computation 3 Automatica 3 Monatshefte für Mathematik 3 Acta Applicandae Mathematicae 3 Physica D 3 Revista Matemática Iberoamericana 3 The Annals of Applied Probability 3 Numerical Algorithms 3 Journal of Nonlinear Science 3 Calculus of Variations and Partial Differential Equations 3 Annales Henri Poincaré 3 Frontiers of Mathematics in China 3 Science China. Mathematics 3 East Asian Journal on Applied Mathematics 3 Annales Henri Lebesgue 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Mathematical Biology 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Quarterly of Applied Mathematics 2 Transactions of the American Mathematical Society 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Computational Mechanics 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 International Journal of Computer Mathematics 2 SIAM Journal on Applied Mathematics 2 Potential Analysis 2 Journal of Mathematical Sciences (New York) 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Interfaces and Free Boundaries 2 Nonlinear Analysis. Real World Applications 2 Mathematical Modelling and Analysis 2 Advanced Nonlinear Studies 2 International Journal of Computational Methods 2 Journal of Computational Acoustics 2 Boundary Value Problems 2 Research in the Mathematical Sciences 1 Modern Physics Letters B 1 Astrophysics and Space Science 1 Bulletin of the Australian Mathematical Society 1 Computer Physics Communications 1 General Relativity and Gravitation 1 Inverse Problems 1 Physica A 1 Physics Letters. A 1 Reports on Mathematical Physics 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Reviews in Mathematical Physics 1 Journal of Geometry and Physics 1 Theory of Probability and its Applications 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 BIT ...and 81 more Serials all top 5 Cited in 43 Fields 462 Partial differential equations (35-XX) 225 Numerical analysis (65-XX) 174 Statistical mechanics, structure of matter (82-XX) 102 Quantum theory (81-XX) 87 Fluid mechanics (76-XX) 58 Biology and other natural sciences (92-XX) 51 Probability theory and stochastic processes (60-XX) 40 Operator theory (47-XX) 30 Functional analysis (46-XX) 29 Integral equations (45-XX) 24 Real functions (26-XX) 24 Optics, electromagnetic theory (78-XX) 22 Dynamical systems and ergodic theory (37-XX) 19 Ordinary differential equations (34-XX) 18 Mechanics of deformable solids (74-XX) 17 Global analysis, analysis on manifolds (58-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Information and communication theory, circuits (94-XX) 11 Systems theory; control (93-XX) 9 Classical thermodynamics, heat transfer (80-XX) 7 Differential geometry (53-XX) 6 Difference and functional equations (39-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Integral transforms, operational calculus (44-XX) 6 Geophysics (86-XX) 5 Approximations and expansions (41-XX) 5 Mechanics of particles and systems (70-XX) 5 Astronomy and astrophysics (85-XX) 4 Statistics (62-XX) 4 Relativity and gravitational theory (83-XX) 3 Special functions (33-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Convex and discrete geometry (52-XX) 2 Computer science (68-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) Citations by Year