Books/Book-contributions

  1. A. Zisowsky, A. Arnold, M. Ehrhardt, T. Koprucki: Transient Simulation of \(k p\) - Schrödinger Systems using discrete transparent Boundary Conditions, Multi-Band Effective Mass Approximations, Advanced Mathematical Models and Numerical Techniques (2014) 247-272, M. Ehrhardt, T. Koprucki (Eds.), Springer (2014). [pdf] [www]
  2. A. Arnold, M. Ehrhardt, M. Schulte: Numerical Simulation of Quantum wave guides, VLSI and Computer Architecture (2009). ISBN: 978-1-60692-075-6, K. Watanabe (Ed.), Nova Publishers (2009). [pdf] [www]
  3. G. Allaire, A. Arnold, P. Degond, T. Y. Hou: Quantum Transport - Modelling, Analysis and Asymptotics, Lecture Notes in Mathematics 1946 (2008). ISBN: 978-3-540-79573-5, Springer (2008), Berlin. [pdf] [www]
  4. A. Arnold, A. Jüngel: Multi-scale modeling of quantum semiconductor devices, Analysis, Modeling and Simulation of Multiscale Problems (2006) 331-363, A. Mielke (Ed.), Springer (2006), Berlin-Heidelberg. [pdf] [www]
  5. N. Ben Abdallah, A. Arnold, P. Degond, I. M. Gamba, R. T. Glassey, C. D. Levermore, C. Ringhofer (eds.): Dispersive Transport Equations and Multiscale Models, IMA Volumes in Mathematics and its Applications 136 (2003), Springer (2003), New York. [pdf] [www]
  6. N. Ben Abdallah, A. Arnold, P. Degond, I. M. Gamba, R. T. Glassey, C. D. Levermore, C. Ringhofer (eds.): Transport in Transition Regimes, IMA Volumes in Mathematics and its Applications 135 (2003), Springer (2003), New York. [pdf] [www]

Publications in refereed journals

  1. A. Arnold, G. Toshpulatov: Trend to equilibrium and hypoelliptic regularity for the relativistic Fokker-Planck equation, to appear in SIAM J. Math. Analysis (2025). [pdf]
  2. A. Arnold, J. Körner: WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation, to appear in Advances in Computational Math. (2025). [pdf]
  3. A. Arnold, C. Klein, J. Körner, J. M. Melenk: Optimally truncated WKB approximation for the 1D stationary Schrödinger equation in the highly oscillatory regime, J. Computational and Applied Mathematics 457 (2025) 116240. [pdf]
  4. A. Arnold, A. Einav, T. Wöhrer: Sharp Decay of the Fisher Information for Degenerate Fokker-Planck Equations, Submitted (2023). [pdf]
  5. F. Achleitner, A. Arnold, V. Mehrmann, E. A. Nigsch: Hypocoercivity in Hilbert spaces, JFA 288 (2025) 110691. [pdf]
  6. A. Arnold, A. Einav, T. Wöhrer: Generalised Fisher Information Approach to Defective Fokker-Planck Equations, Submitted (2022). [pdf]
  7. A. Arnold, G. Toshpulatov: Exponential stability and hypoelliptic regularization for the kinetic Fokker-Planck equation with confining potential, J. Stat. Physics 191, 51 (2024). [pdf]
  8. A. Arnold, S. Geevers, I. Perugia, D. Ponomarev: On the limiting amplitude principle for the wave equation with variable coefficients, Comm. Partial Differential Equations 49, No. 4  (2024) 333-380. [pdf]
  9. A. Arnold, J. Erb: Sharp entropy decay for hypocoercive and non-symmetric Fokker-Planck equations with linear drift, Submitted (2020). [pdf]
  10. F. Achleitner, A. Arnold, V. Mehrmann: Hypocoercivity in algebraically constrained partial differential equations with application to Oseen equations, J. Dynam. Differential Equations (2023). [pdf]
  11. F. Achleitner, A. Arnold, V. Mehrmann: Hypocoercivity and controllability in linear semi-dissipative Hamiltonian ordinary differential equations and differential-algebraic equations, ZAMM 103 (2023). e202100171; 30pp. [pdf] [www]
  12. F. Achleitner, A. Arnold, E. A. Carlen: The Hypocoercivity Index for the short time behavior of linear time-invariant ODE systems, Journal of Differential Equations 371 (2023) 83-115. [pdf] [www]
  13. F. Achleitner, A. Arnold, V. Mehrmann: Hypocoercivity and hypocontractivity concepts for linear dynamical systems, Electron. J. Linear Algebra 39 (2023) 33-61. [pdf] [www]
  14. A. Arnold, B. Signorello: Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium, Kinetic and Related Models 15, No. 5 (2022) 753-773. [pdf] [www]
  15. A. Arnold, S. Geevers, I. Perugia, D. Ponomarev: On the exponential time-decay for the one-dimensional wave equation with variable coefficients, Comm. on Pure and Applied Analysis 21, No. 10 (2022) 3389-3405. [pdf] [www]
  16. A. Arnold, C. Schmeiser, B. Signorello: Propagator norm and sharp decay estimates for Fokker-Planck equations with linear drift, Comm. Math. Sc. 20, No. 4 (2022) 1047-1080. [pdf] [www]
  17. A. Arnold, C. Klein, B. Ujvari: WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment, BIT Numerical Mathematics 62 (2022) 1-22. [pdf] [www]
  18. A. Arnold, S. Geevers, I. Perugia, D. Ponomarev: An adaptive finite element method for high-frequency scattering problems with variable coefficients, Computers Math. Applic. 109 (2022) 1-14. [pdf] [www]
  19. J. Körner, A. Arnold, K. Döpfner: WKB-based scheme with adaptive step size control for the Schrödinger equation in the highly oscillatory regime, J. Comput. Appl. Math. 404 (2022) 113905, 18 pp. [pdf] [www]
  20. P. Amodio, A. Arnold, T. Levitina, G. Settanni, E. Weinmüller: On the Abramov approach for the numerical simulation of the whispering gallery modes in prolate spheroids, Appl. Math. Comput. 409, No. 125599 (2021) 1-14. [pdf] [www]
  21. A. Arnold, A. Einav, B. Signorello, T. Wöhrer: Large Time Convergence of the Non-homogeneous Goldstein-Taylor Equation, J. Stat. Phys. 182 (2021) 41. [pdf] [www]
  22. A. Arnold, K. Döpfner: Stationary Schrödinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point, Calcolo 57, No. 1, Paper no. 3 (2020) 44 pp. [pdf] [www]
  23. A. Arnold, S. Jin, T. Wöhrer: Sharp Decay Estimates in Local Sensitivity Analysis for Evolution Equations with Uncertainties: from ODEs to Linear Kinetic Equations, Journal of Differential Equations 268, No. 3 (2020) 1156-1204. [pdf] [www]
  24. D. Stürzer, A. Arnold, A. Kugi: Closed-loop Stability Analysis of a Gantry Crane with Heavy Chain, International Journal of Control 91, No. 8 (2018) 1931-1943. [pdf] [www]
  25. F. Achleitner, A. Arnold, E. A. Carlen: On multi-dimensional hypocoercive BGK models, Kinetic and Related Models 11, No. 4 (2018) 953-1009. [pdf] [www]
  26. A. Arnold, C. Negulescu: Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions, Numerische Mathematik 138, No. 2 (2018) 501-536. [pdf] [www]
  27. A. Arnold, A. Einav, T. Wöhrer: On The Rates of Decay to Equilibrium in Degenerate and Defective Fokker-Planck Equations, Journal of Differential Equations 264, No. 11 (2018) 6843-6872. [pdf] [www]
  28. L. Bian, G. Pang, S. Tang, A. Arnold: ALmost EXact boundary conditions for transient Schrödinger-Poisson system, J. Comput. Phys. 313 (2016) 233-246. [pdf] [www]
  29. M. Miletić, D. Stürzer, A. Arnold, A. Kugi: Stability of an Euler-Bernoulli beam with a nonlinear dynamic feedback system, IEEE Trans. Autom. Control 61, No. 10 (2016) 2782-2795. [pdf] [www]
  30. M. Miletić, A. Arnold: A piezoelectric Euler-Bernoulli beam with dynamic boundary control: Stability and dissipative FEM, Acta Applicandae Mathematicae 138, No. 1 (2015) 241-277. [pdf] [www]
  31. F. Achleitner, A. Arnold, D. Stürzer: Large-time behavior in non-symmetric Fokker-Planck equations, Rivista di Matematica della Università di Parma 6 (2015) 1-68. [pdf]
  32. M. Miletić, D. Stürzer, A. Arnold: An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip, Discrete Contin. Dyn. Sys. Ser. B 20, No. 9 (2015) 3029-3055. [pdf] [www]
  33. R. Hammer, W. Pötz, A. Arnold: Single-cone real-space finite difference scheme for the time-dependent Dirac equation, J. Comput. Phys. 265 (2014) 50-70.  [pdf] [www]  Erratum: Vol. 457 (2022), Paper No. 111118. [www]
  34. D. Stürzer, A. Arnold: Spectral Analysis and Long-Time Behaviour of a Fokker-Planck Equation with a Non-Local Perturbation, Rendiconti Lincei Cl. Sci. Fis. Mat. Natur. 25, No. 1 (2014) 53-89. Erratum: Vol. 27 (2016) 147-149. [pdf] [www]
  35. R. Hammer, W. Pötz, A. Arnold: A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equations in (1+1)D, J. Comput. Phys. 256 (2014) 728-747. [pdf] [www]
  36. L. Neumann, A. Arnold, W. Hochhauser: Zur Stabilität von geklebten und geklotzten Glasscheiben: Beurteilung der Dunkerley'schen Geraden zur Beulwertbestimmung, Bauingenieur 1 (2013) 14-21. [pdf]
  37. A. Arnold, J. Kim, X. Yao: Estimates for a class of oscillatory integrals and decay rates for wave-type equations, J. Math. Anal. Appl. 394, No. 1 (2012) 139-151. [pdf] [www]
  38. A. Arnold, M. Ehrhardt, M. Schulte, I. Sofronov: Discrete transparent boundary conditions for the Schrödinger equation on circular domains, Comm. Math. Sc. 10, No. 3 (2012) 889-916. [pdf]
  39. J. Kim, A. Arnold, X. Yao: Global estimates of fundamental solutions for higher-order Schrödinger equations, Monatshefte für Mathematik 168, No. 2 (2012) 253-266. [pdf] [www]
  40. A. Arnold, L. Desvillettes, C. Prévost: Existence of nontrivial steady states for populations structured with respect to space and a continuous trait, Comm. on Pure and Applied Analysis 11, No. 1 (2012) 83-96. [pdf] [www]
  41. A. Arnold, I. M. Gamba, M. P. Gualdani, S. Mischler, C. Mouhot, C. Sparber: The Wigner-Fokker-Planck equation: stationary states and large time behavior, Math. Models and Meth. in the Appl. Sc. 22, No. 11-1250034 (31 pages) (2012). [pdf] [www]
  42. A. Arnold, N. Ben Abdallah, C. Negulescu: WKB-based schemes for the oscillatory 1D Schrödinger equation in the semi-classical limit, SIAM J. Numer. Anal. 49, No. 4 (2011) 1436-1460. [pdf] [www]
  43. A. Arnold, J. A. Carrillo, C. Manzini: Refined long-time asymptotics for some polymeric fluid flow models, Comm. Math. Sc. 8, No. 3 (2010) 763-782. [pdf] [www]
  44. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt, A. Schädle: A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations, Commun. Comput. Phys. 4, No. 4 (2008) 729-796. [pdf] [www]
  45. A. Arnold, J. A. Carrillo, C. Klapproth: Improved entropy decay estimates for the heat equation, J. Math. Anal. Appl. 343, No. 1 (2008) 190-206. [pdf] [www]
  46. A. Arnold, E. A. Carlen, Q. Ju: Large-time behavior of non-symmetric Fokker-Planck type equations, Communications on Stochastic Analysis 2, No. 1 (2008) 153-175. [pdf] [www]
  47. M. Schulte, A. Arnold: Discrete transparent boundary conditions for the Schrödinger equation - a compact higher order scheme, Kinetic and Related Models 1, No. 1 (2008) 101-125. [pdf] [www]
  48. A. Arnold, E. Dhamo, C. Manzini: The Wigner-Poisson-Fokker-Planck system: global-in-time solutions and dispersive effects, Ann. Inst. H. Poincaré C, Anal. Non Linéaire 24, No. 4 (2007) 645-676. [pdf] [www]
  49. A. Arnold, J.-P. Bartier, J. Dolbeault: Interpolation between Logarithmic Sobolev and Poincaré Inequalities, Comm. Math. Sc. 5, No. 4 (2007) 971-979. [pdf] [www]
  50. A. Arnold, E. Dhamo, C. Manzini: Dispersive effects in quantum kinetic equations, Indiana Univ. Math. J. 56, No. 3 (2007) 1299-1331. [pdf] [www]
  51. A. Zisowsky, A. Arnold, M. Ehrhardt, T. Koprucki: Discrete Transparent Boundary Conditions for transient kp-Schrödinger Equations with Application to Quantum-Heterostructures, ZAMM 85, No. 11 (2005) 793-805. [pdf] [www]
  52. A. Arnold, J. Dolbeault: Refined Convex Sobolev Inequalities, J. Funct. Anal. 225, No. 2 (2005) 337-351. [pdf] [www]
  53. A. Arnold, J. A. Carrillo, L. Desvillettes, J. Dolbeault, A. Jüngel, C. Lederman, P. A. Markowich, G. Toscani, C. Villani: Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research, Monatshefte für Mathematik 142, No. 1-2 (2004) 35-43. [pdf] [www]
  54. A. Arnold, C. Sparber: Quantum dynamical semigroups for diffusion models with Hartree interaction, Comm. Math. Phys. 251, No. 1 (2004) 179-207. [pdf] [www]
  55. A. Arnold, R. Bosi: Global existence of the von Neumann equation for Hartree-Fock systems with Relaxation-Time, Submitted (2004). [pdf]
  56. A. Arnold, J. L. López, P. A. Markowich, J. Soler: An Analysis of Quantum Fokker-Planck Models: A Wigner Function Approach, Rev. Mat. Iberoam. 20, No. 3 (2004) 771-814. [pdf] [www]
  57. A. Arnold, M. Ehrhardt, I. Sofronov: Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability, Comm. Math. Sc. 1, No. 3 (2003) 501-556. [pdf] [www]
  58. A. Arnold, A. Unterreiter: Entropy Decay of Discretized Fokker-Planck Equations I - Temporal Semi-Discretization, Computers Math. Applic. 46, No. 10-11 (2003) 1683-1690. [pdf] [www]
  59. A. Arnold, J. A. Carrillo, E. Dhamo: On the periodic Wigner-Poisson-Fokker-Planck system, J. Math. Anal. Appl. 275 (2002) 263-276. [pdf] [www]
  60. A. Arnold, J. A. Carrillo, M. D. Tidriri: Large-time behavior of discrete kinetic equations with non-symmetric interactions, Math. Models and Meth. in the Appl. Sc. 12, No. 11 (2002) 1555-1564. [pdf] [www]
  61. A. Arnold: Mathematical concepts of open quantum boundary conditions, Transp. Theo. Stat. Phys. 30, No. 4-6 (2001) 561-584. [pdf] [www]
  62. M. Ehrhardt, A. Arnold: Discrete Transparent Boundary Conditions for the Schrödinger Equation, Rivista di Matematica della Università di Parma 6, No. 4 (2001) 57-108. [pdf]
  63. A. Arnold, J. A. Carrillo, I. M. Gamba, C.-W. Shu: Low and High Field Scaling Limits for the Vlasov- and Wigner-Poisson-Fokker-Planck Systems, Transp. Theo. Stat. Phys. 30, No. 2-3 (2001) 121-153. [pdf] [www]
  64. A. Arnold, P. A. Markowich, G. Toscani, A. Unterreiter: On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. PDE 26, No. 1-2 (2001) 43-100. [pdf] [www]
  65. A. Arnold, P. A. Markowich, G. Toscani: On large time asymptotics for drift-diffusion-Poisson systems, Transp. Theo. Stat. Phys. 29, No. 3-5 (2000) 571-581. [pdf] [www]
  66. A. Unterreiter, A. Arnold, P. A. Markowich, G. Toscani: On generalized Csiszár-Kullback inequalities, Monatshefte für Mathematik 131, No. 3 (2000) 235-253. [pdf] [www]
  67. A. Arnold, H. Lange, P. F. Zweifel: A discrete-velocity, stationary Wigner equation, J. Math. Phys. 41, No. 11 (2000) 7167-7180. [pdf] [www]
  68. A. Arnold: Numerically absorbing boundary conditions for quantum evolution equations, VLSI Design 6, No. 1-4 (1998) 313-319. [pdf] [www]
  69. A. Arnold, M. Ehrhardt: Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics, J. Comput. Phys. 145, No. 2 (1998) 611-638. [pdf] [www]
  70. A. Arnold, U. Giering: An Analysis of the Marshak Conditions for matching Boltzmann and Euler Equations, Math. Models and Meth. in the Appl. Sc. 7, No. 4 (1997) 557-577. [pdf] [www]
  71. A. Arnold, C. Ringhofer: An operator splitting method for the Wigner-Poisson problem, SIAM J. Numer. Anal. 33, No. 4 (1996) 1622-1643. [pdf] [www]
  72. A. Arnold, L. L. Bonilla, P. A. Markowich: Liapunov functionals and large-time asymptotics of mean-field nonlinear Fokker-Planck equations, Transp. Theo. Stat. Phys. 25, No. 7 (1996) 733-751. [pdf] [www]
  73. A. Arnold: Self-consistent relaxation-time models in quantum mechanics, Comm. PDE 21, No. 3&4 (1996) 473-506. [pdf] [www]
  74. A. Arnold, C. Ringhofer: Operator splitting methods applied to spectral discretizations of quantum transport equations, SIAM J. Numer. Anal. 32, No. 6 (1995) 1876-1894. [pdf] [www]
  75. A. Arnold: On absorbing boundary conditions for quantum transport equations, Math. Modell. Num. Anal. 28 (1994) 853-872. [pdf] [www]
  76. A. Arnold, F. Nier: Numerical analysis of the deterministic particle method applied to the Wigner equation, Math. of Comp. 58 (1992) 645-669. [pdf] [www]
  77. N. J. Mauser, A. Arnold, P. A. Markowich: The self-consistent Bloch-equation in one dimension, Computers Math. Applic. 21 (1991) 197-202. [pdf] [www]
  78. A. Arnold, F. Nier: The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case, Math. Meth. Appl. Sc. 14 (1991) 595-613. [pdf] [www]
  79. A. Arnold, P. A. Markowich, N. J. Mauser: The one-dimensional periodic Bloch-Poisson equation, Math. Models and Meth. in the Appl. Sc. 1 (1991) 83-112. [pdf] [www]
  80. A. Arnold, N. J. Mauser: An efficient method of bookkeeping next neighbours in molecular dynamics simulations, Comp. Phys. Comm. 59 (1990) 267-275. [pdf] [www]
  81. A. Arnold, P. A. Markowich: The periodic quantum Liouville-Poisson problem, Boll. U.M.I. 7 (1990) 449-484. [pdf]
  82. A. Arnold, N. J. Mauser, J. Hafner: A molecular dynamics study of the structure of liquid germanium, J. Phys., Cond. Matter 1 (1989) 965-980. [pdf] [www]
  83. A. Arnold, H. Steinrück: The 'electromagnetic' Wigner equation for an electron with spin, ZAMP 40, No. 6 (1989) 793-815. [pdf] [www]
  84. A. Arnold, P. Degond, P. A. Markowich, H. Steinrück: The Wigner-Poisson problem in a crystal, Appl. Math. Lett. 2, No. 2 (1989) 187-191. [pdf] [www]

Publications in conference proceedings

  1. F. Achleitner, A. Arnold, V. Mehrmann, E.A. Nigsch: Long- and short-time behavior of hypocoercive evolution equations via modal decompositions, submitted (2025). [pdf]
  2. F. Achleitner, A. Arnold, A. Jüngel: Hypocoercivity for Linear ODEs and Strong Stability for Runge—Kutta Methods, to appear in Proceedings of ICNAAM 2023, T.E. Simos (ed.), AIP Conf. Proc. 3315 (2025). [pdf]
  3. J. Körner, A. Arnold, C. Klein, J. M. Melenk: Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation, to appear in Proceedings of ICNAAM 2023, T.E. Simos (ed.), AIP Conf. Proc. 3315 (2025). [pdf]
  4. A. Arnold, J. Körner: High-order WKB-based method for the 1D stationary Schrödinger equation in the semi-classical limit, Proceedings of ICNAAM 2022, T.E. Simos (ed.), AIP Conf. Proc. 3094, 220002 (2024). [pdf]
  5. F. Achleitner, A. Arnold, A. Jüngel: Necessary and sufficient conditions for strong stability of explicit Runge-Kutta methods, Proceedings of "Particle Systems and Partial Differential Equations X" (2022), Eric Carlen, Patrícia Goncalves, Ana Jacinta Soares (eds.), Springer Nature (2024) 1-21. [pdf]
  6. A. Arnold, J. Dolbeault, C. Schmeiser, T. Wöhrer: Sharpening of decay rates in Fourier based hypocoercivity methods, Recent Advances in Kinetic Equations and Applications, Proceedings of INdAM-workshop, Rome, Nov. 2019, No. 48 (2021) 1-50, F. Salvarani (ed.), Springer INdAM Series. [pdf] [www]
  7. K. Döpfner, A. Arnold: On the stationary Schrödinger equation in the semi-classical limit: Asymptotic blow-up at a turning point, PAMM 19, No. 1 (2019). 90th GAMM Annual Meeting, Wiley. [pdf] [www]
  8. F. Achleitner, A. Arnold, B. Signorello: On optimal decay estimates for ODEs and PDEs with modal decomposition, Stochastic Dynamics out of Equilibrium, Springer Proceedings in Mathematics & Statistics 282 (2019) 241-264, G. Giacomin et al. (eds.), Springer. [pdf] [www]
  9. F. Achleitner, A. Arnold, E. A. Carlen: On linear hypocoercive BGK models, Proceedings of "Particle Systems and PDE's - III", Braga, Portugal, Dec. 2014 126 (2016) 1-37. [pdf] [www]
  10. A. Arnold, M. Ehrhardt: A Transparent Boundary Condition for an Elastic Bottom in Underwater Acoustics, Proceedings of the "6th Conference on Finite Difference Methods: Theory and Applications," Lozenetz, Bulgaria, June 2014; in Lectures Notes in Computer Science 9045 "Finite Difference Methods, Theory and Applications" (2015) 15-24, I. Dimov, I. Faragó, L. Vulkov (eds.), Springer. [pdf] [www]
  11. A. Arnold, L. Neumann, W. Hochhauser: Stability of glued and embedded Glass Panes: Dunkerley straight Line as a conservative Estimate of superimposed buckling Coefficients, IFAC-PapersOnLine (2013) 124-129. Proceedings of the "7th Vienna International Conference on Mathematical Modelling" (I. Troch, F. Breitenecker, Ed.), Vienna 2012. [pdf] [www]
  12. J. Geier, A. Arnold: WKB-based schemes for two-band Schrödinger equations in the highly oscillatory regime, Nanosystems: Physics, Chemistry, Mathematics 2, No. 3 (2011) 7-28. [pdf]
  13. M. Miletić, A. Arnold: Euler-Bernoulli Beam with Boundary Control: Stability and FEM, PAMM 11, No. 1 (2011) 681-682. [pdf] [www]
  14. A. Arnold, J. Geier: Asymptotically correct finite difference schemes for highly oscillatory ODEs, AIP Conference Proceedings 1281 (2010) 206-209. International Conference of Numerical Analysis and Applied Mathematics 2010, T. E. Simos (ed.). [pdf] [www]
  15. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt, A. Schädle: A Review of artificial boundary conditions for the Schrödinger equation, PAMM 7, No. 1 (2008) 1023201-1023202. [pdf] [www]
  16. A. Arnold, F. Fagnola, L. Neumann: Quantum Fokker-Planck models: the Lindblad and Wigner approaches, Quantum Probability and related Topics - Proceedings of the 28th Conference (Series: QP-PQ: Quantum Probability and White Noise Analysis - Vol. 23), J.C. García, R. Quezada, S.B. Sontz (Eds.), World Scientific (2008). [pdf] [www]
  17. A. Arnold, M. Schulte: Transparent boundary conditions for quantum-waveguide simulations, Proceedings of MATHMOD 2006, Vienna, Austria, Mathematics and Computers in Simulation 79 (2008) 898-905. [pdf] [www]
  18. A. Arnold, M. Schulte: Transparent boundary conditions for the 2D Schrödinger equation: efficient implementation, PAMM 7, No. 1 (2008) 1023203-1023204. [pdf] [www]
  19. A. Arnold, M. Ehrhardt, I. Sofronov: Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation, Domain Decomposition Methods in Science and Engineering (Series: Lecture Notes in Computational Science and Engineering) 40 (2004) 141-148, R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Widlund, J. Xu (eds.), Springer. [pdf] [www]
  20. M. Ehrhardt, A. Arnold: Discrete transparent boundary conditions for wide angle parabolic equations: Fast calculation and approximation, Proceedings of the "Seventh European Conference on Underwater Acoustics - ECUA 2004" - TU Delft, Netherlands, July 2004 (2004) 9-14, D. G. Simons (ed.). [pdf]
  21. A. Arnold, M. Ehrhardt, I. Sofronov: A Fast method to implement non-local discrete transparent boundary condition for the Schrödinger equation, PAMM 2, No. 1 (2003) 424-425. [pdf] [www]
  22. A. Arnold, E. A. Carlen: A generalized Bakry-Emery condition for non-symmetric diffusions, EQUADIFF 99, Proceedings of the "International Conference on Differential Equations", Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels (eds.), World Scientific Publishing (2000) 732-734. [pdf] [www]
  23. A. Arnold, M. Ehrhardt: Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics, in vol. II von "Proceedings of the Forth European Conference on Underwater Acoustics", Rom (1998), A. Alippi, G.B. Cannelli (eds.), CNR-Ist. di Acustica, Rome (1998) 769-774. [www]
  24. A. Arnold, M. Ehrhardt: A new discrete transparent boundary condition for standard and wide angle "parabolic" equations in underwater acoustics, Theoretical and Computational Acoustics '97, Y.-C. Teng et al. (ed.), Proceedings of the 3rd ICTCA, Newark, USA (1997) 623-635. [pdf] [www]
  25. A. Arnold: The relaxation-time von Neumann-Poisson equation, Proceedings of ICIAM 95, Hamburg (1995), Oskar Mahrenholtz, Reinhard Mennicken (eds.); ZAMM 76, No. S2 (1996) 293-296. [pdf]
  26. A. Arnold: The relaxation-time Wigner equation, Mathematical Problems in Semiconductor Physics, Proceedings of workshop in Rome, Italy (1993); Pitman Research Notes in Mathematics Series, Longman-London 340 (1995) 105-117, Marcati, Markowich, Natalini (eds.). [pdf]
  27. A. Arnold: A mixed spectral-collocation and operator splitting method for the Wigner- Poisson equation, Mathematics of Computation 1943-1993, Proceedings of symposium in Vancouver, Canada 1993, American Mathematical Society (1994) 249-253, W. Gautschi (ed.). [pdf]
  28. A. Arnold, C. Ringhofer: Operator splitting methods for the Wigner-Poisson equation, Proceedings of the International Workshop on Computational Electronics, Urbana-Champaign, USA (1992). [pdf] [www]
  29. A. Arnold: Quantum transport in semiconductors: numerical methods, Proceedings of Numsim '91, Berlin, ZIB, Technical Report 91, No. 8 (1991) 51-56, Gajewski, Deuflhard, Markowich (eds.). [pdf]
  30. A. Arnold, P. A. Markowich: Quantum transport models for semiconductors, Applied and Industrial Mathematics (1991) 301-307, R. Spigler (ed.), Kluwer Acad. Publ. [pdf] [www]

Conference Posters

  1. R. Hammer, C. Ertler, W. Pötz, A. Arnold: Dynamics of Dirac Fermions in Topological Insulators, Internat. Symposium on Advanced Nanodevices and Nanotechnology 2011, Maui, USA (2011). [pdf]

Lecture Notes

  1. A. Arnold: Entropy method and the large-time behavior of parabolic equations, Summer School in Ravello, Italy (2002) 1-37. [pdf]