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

Publications in refereed journals:

  1. F. Achleitner, A. Arnold, and E.A. Carlen: On multi-dimensional hypocoercive BGK models, submitted 2017.
  2. A. Arnold, A. Einav and T. Wöhrer: On the rates of decay to equilibrium in degenerate and defective Fokker-Planck equations, submitted 2017.
  3. D. Stürzer, A. Arnold, and A. Kugi: Closed-loop stability analysis of a gantry crane with heavy chain, to appear in International Journal of Control, 2017.
  4. A. Arnold, C. Negulescu: Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions, to appear in Numerische Mathematik, 2017.
  5. L. Bian, G. Pang, S. Tang, A. Arnold: ALmost EXact boundary conditions for transient Schrödinger-Poisson system, J. Comput. Phys. 313 (2016), 233-246.
  6. F. Achleitner, A. Arnold and D. Stürzer: Large-time behavior in non-symmetric Fokker-Planck equations, Rivista di Matematica della Università 6 (2015) 1-68.
  7. M. Miletic, D. Stürzer, A. Arnold, A. Kugi: Stability of an Euler-Bernouilli beam with nonlinear dynamic feedback system, IEEE Transactions on Automatic Control 61, No.10 (2016) 2782-2795.
  8. M. Miletic, D. Stürzer and A. Arnold: An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip, Discrete and Continuous Dynamical Systems-B 20, No.9 (2015) 3029-3055.
  9. A.Arnold and J. Erb: Sharp entropy decay for hypocoercive and non-symmetric Fokker-Planck equations with linear drift, submitted 2014.
  10. R. Hammer, W. Pötz, and A. Arnold: Single-cone real-space finite difference scheme for the time-dependent Dirac equation, J. Comput. Phys. 265(2014) 50-70.
  11. M. Miletic, A. Arnold: A piezoelectric Euler-Bernoulli beam with dynamic boundary control: Stability and dissipative FEM, Acta Applicandae Mathematicae 138, No.1 (2015) 241-277.
  12. 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. Phy. 256 (2014) 728-747.
  13. D. Stürzer, A. Arnold: Spectral Analysis and Long-Time Behaviour of a Fokker-Planck Equation with a Non-Local Perturbation, Rendiconti Lincei Matematica e Applicazioni 25, No. 1 (2014) 53-89. Erratum: 27, No.1 (2016) 147-149.
  14. A. Arnold, M. Ehrhardt, M. Schulte, I. Sofronov: Discrete transparent boundary conditions for the Schrödinger equation on circular domains, Commun. Mathematical Sciences 10, No. 3 (2012) 889-916..
  15. JinMyong Kim, Anton Arnold and Xiaohua Yao: Global estimates of fundamental solutions for higher-order Schrödinger equations , Monatshefte für Mathematik 168, No.2, (2012) 253-266.
  16. 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.
  17. L. Neumann, A. Arnold and W. Hochhauser: Zur Stabilität von geklebten und geklotzten Glasscheiben: Beurteilung der Dunkerley´schen Geraden zur Beulwertbestimmung, Bauingenieur 1-2013, 14-21.
  18. A. Arnold, JinMyong Kim, Xiaohua Yao: Estimates for a class of oscillatory integrals and decay rates for wave-type equations, J. of Math. Analysis and Applications 394, No. 1 (2012) 139-151.
  19. A. Arnold, I. Gamba, M.P. Gualdani, S. Mischler, C. Mouhot, C. Sparber: The Wigner-Fokker-Planck equation: stationary states and large time behavior, Math. Mod. Methods Appl. Sc. 22, No. 11 (2012)1250034 (31 pages).
  20. 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.
  21. 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.
  22. A. Arnold, E. Carlen, Q. Ju: Large-time behavior of non-symmetric Fokker-Planck type equations
    Communications in Stochastic Analysis 2, Nr. 1 (2008) 153-175.
  23. 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, Nr. 4 (2008) 729-796.
  24. 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.
  25. 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.
  26. A. Arnold, E. Dhamo, Ch. Manzini: Dispersive effects in quantum kinetic equations,
    Indiana Univ. Math. J. 56, Nr. 3 (2007) 1299-1331.
  27. A. Arnold, J.-P. Bartier, J. Dolbeault: Interpolation between Logarithmic Sobolev and Poincaré Inequalities ,
    Comm. Math. Sc. 5, No. 4 (2007) 971-979.
  28. A. Arnold, E. Dhamo, C. Manzini: The Wigner-Poisson-Fokker-Planck system: global-in-time solutions and dispersive effects , Annales de l'IHP (C) - Analyse non lineaire 24, Nr.4 (2007) 645-676.
  29. A. Zisowsky, A. Arnold, M. Ehrhardt, T. Koprucki: Discrete Transparent Boundary Conditions for transient kp-Schrödinger Equations with Application to Quantum-Heterostructures, ZAMM 85, Nr. 11 (2005) 793-805.
  30. A. Arnold, J. Dolbeault: Refined Convex Sobolev Inequalities, J. Funct. Anal. 225, No.2 (2005) 337-351.
  31. A. Arnold, R. Bosi: Global existence of the von Neumann equation for Hartree-Fock systems with Relaxation-Time , Preprint 2004.
  32. A. Arnold, J.L. Lopez, 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.
  33. 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.
  34. A. Arnold, C. Sparber: Quantum dynamical semigroups for diffusion models with Hartree interaction, Comm. Math. Phys. 251, no.1 (2004) 179-207.
  35. A. Arnold, M. Ehrhardt, I. Sofronov: Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability , Commun. Mathematical Sciences vol. 1, no. 3 (2003) 501-556.
  36. A. Arnold, A. Unterreiter Entropy Decay of Discretized Fokker-Planck Equations I - Temporal Semi-Discretization , Comp. Math. Appl. 46, No. 10-11 (2003) 1683-1690.
  37. A. Arnold, J. Carrillo, E. Dhamo On the periodic Wigner-Poisson-Fokker-Planck system , J. Math. Anal. Appl. 275 (2002) 263-276.
  38. A. Arnold, J. Carrillo, M. Tidriri: Large time behavior of discrete kinetic equations with non-symmetric interactions , Math. Mod. Methods Appl. Sc. vol. 12, no. 11 (2002) 1555-1564.
  39. M. Ehrhardt, A. Arnold: Discrete Transparent Boundary Conditions for the Schrödinger Equation , Revista di Matematica della Universita di Parma 6/4 (2001) 57-108
  40. A. Arnold: Mathematical concepts of open quantum boundary conditions , Transp. Theory Stat. Phys., 30/4-6 (2001) 561-584.
  41. A. Arnold, J.A. Carrillo, I. Gamba, C.W. Shu: Low and High Field Scaling Limits for the Vlasov- and Wigner-Poisson-Fokker-Planck Systems , Transp. Theory Stat. Phys. 30/2-3 (2001).
  42. A. Arnold, P. Markowich, G. Toscani, A. Unterreiter: On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations , Comm. PDE 26/1-2 (2001) 43-100.
  43. A. Unterreiter, A. Arnold, P. Markowich, G. Toscani: On generalized Csiszar-Kullback inequalities , Monatshefte für Mathematik vol. 131 (2000) 235-253.
  44. A. Arnold, H. Lange, P.F. Zweifel: A discrete-velocity, stationary Wigner equation , J. Math. Phys. vol. 41-11 (2000) 7167-7180.
  45. A. Arnold, P. Markowich, G. Toscani: On large time asymptotics for drift-diffusion-Poisson systems , Transp. Theory Stat. Phys. vol. 29/3-5 (2000) 571-581.
  46. A. Arnold, M. Ehrhardt: Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics , J. Comput. Physics vol. 145-2 (1998) 611-638.
  47. A. Arnold: Numerically absorbing boundary conditions for quantum evolution equations , VLSI Design 6 No. 1-4 (1998) 313-319. Abbildungen.
  48. A. Arnold, U. Giering: An Analysis of the Marshak Conditions for matching Boltzmann and Euler Equations , Math. Models and Meth. in the Appl. Sc. vol. 7-4 (1997) 557-577; Abb.1 , Abb.2.
  49. A. Arnold, L. L. Bonilla, P. A. Markowich: Liapunov functionals and large-time asymptotics of mean-field Fokker-Planck equations , Transp. Theo. Stat. Phys. vol. 25-7 (1996) 733-751.
  50. A. Arnold: Self-consistent relaxation-time models in quantum mechanics , Comm. PDE vol. 21-3&4 (1996) 473-506.
  51. A. Arnold, C. Ringhofer: An operator splitting method for the Wigner-Poisson problem , SIAM J. of Num. Anal., vol. 33-4 (1996) 1622-1643.
  52. A. Arnold, C. Ringhofer: Operator splitting methods applied to spectral discretizations of quantum transport equations , SIAM J. of Num. Anal., vol. 32-6 (1995) 1876-1894.
  53. A. Arnold: On absorbing boundary conditions for quantum transport equations , Math. Modell. Num. Anal. 28 (1994) 853-872.
  54. A. Arnold, F. Nier: Numerical analysis of the deterministic particle method applied to the Wigner equation , Math. of Comp. 58 (1992) 645-669.
  55. A. Arnold, P. A. Markowich, N. Mauser: The one-dimensional periodic Bloch-Poisson equation , Math. Models and Meth. in the Appl. Sc. 1 (1991) 83-112.
  56. 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.
  57. N. Mauser, A. Arnold, P. A. Markowich: The self-consistent Bloch-equation in one dimension , Computers Math. Applic. 21 (1991) 197-202.
  58. A. Arnold, P. A. Markowich: The periodic quantum Liouville-Poisson problem , Boll. U.M.I. 7 (1990) 449-484.
  59. A. Arnold, N. Mauser: An efficient method of bookkeeping next neighbours in molecular dynamics simulation , Comp. Phys. Comm. 59 (1990) 267-275.
  60. A. Arnold, H. Steinrück: The `electromagnetic' Wigner equation for an electron with spin, ZAMP 40, No. 6 (1989) 793-815.
  61. 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.
  62. A. Arnold, N. Mauser, J. Hafner: A molecular dynamics study of the structure of liquid germanium , J. Phys., Cond. Matter 1 (1989) 965-980.

Publications in conference proceedings:

  1. F. Achleitner, A. Arnold, E.A. Carlen: On linear hypocoercive BGK models , in Proceedings of "Particle Systems and PDE's - III", Braga, Portugal, Dec. 2014;
    in Springer Proceedings in Mathematics & Statistics, vol. 126, 2016; p. 1-37.
  2. 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", (I. Dimov, I. Faragó, L. Vulkov, Eds.), Springer (2015); p.15-24
  3. 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:Proceedings of the "7th Vienna International Conference on Mathematical Modelling" (I. Troch, F. Breitenecker, Ed.), Vienna 2012; p.124-129 (2013)
  4. 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.
  5. M. Miletic, A. Arnold: Euler-Bernoulli Beam with Boundary Control: Stability and FEM ,
    Proceedings in Applied Mathematics and Mechanics 11, Issue 1 (2011), 681-682.
  6. A. Arnold, J. Geier: Asymptotically correct finite difference schemes for highly oscillatory ODEs ,
    AIP Conference Proceedings 1281 I (T.E. Simos, Ed.) "International Conference of Numerical Analysis and Applied Mathematics 2010", Rhodes, Greece 2010; p. 206-209.
  7. 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.
  8. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt, A. Schädle A Review of artificial boundary conditions for the Schrödinger equation , Proceedings in Applied Mathematics and Mechanics 7, No. 1 (2008), Pages 1023201 - 1023202.
  9. A. Arnold, M. Schulte: Transparent boundary conditions for the 2D Schrödinger equation: efficient implementation, Proceedings in Applied Mathematics and Mechanics 7, No. 1 (2008) 1023203-1023204.
  10. A. Arnold, M. Schulte: Transparent boundary conditions for quantum-waveguide simulations,
    Mathematics and Computers in Simulation 79 (2008), 898-905; Proceedings of MATHMOD 2006, Vienna, Austria.
  11. M. Ehrhardt and A. Arnold: Discrete transparent boundary conditions for wide angle parabolic equations: Fast calculation and approximation, in: "Proceedings of the Seventh European Conference on Underwater Acoustics - ECUA 2004", D.G. Simons (Ed.), TU Delft, Netherlands, July 2004, pp 9-14.
  12. A. Arnold, M. Ehrhardt, I. Sofronov: Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation , in: Domain Decomposition Methods in Science and Engineering (Series: Lecture Notes in Computational Science and Engineering), Vol. 40, R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Widlund, J. Xu (Eds.) Springer 2004, pp 141-148.
  13. A. Arnold, M. Ehrhardt, I. Sofronov: A Fast method to implement non-local discrete transparent boundary condition for the Schrödinger equation., Proceedings in Applied Mathematics and Mechanics, vol. 2/1 (2003) 424-425.
  14. A. Arnold, E. Carlen: A generalized Bakry-Emery condition for non-symmetric diffusions , in 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.
  15. A. Arnold, M. Ehrhardt: A new discrete transparent boundary condition for standard and wide angle "parabolic" equations in underwater acoustics , in Thoeretical and Computational Acoustics '97, Y.-C. Teng et al. (ed.), Proceedings of the 3rd ICTCA, Newark, USA (1997) 623-635.
  16. A. Arnold: The relaxation-time von Neumann-Poisson equation , Proceedings of ICIAM 95, Hamburg (1995), Oskar Mahrenholtz, Reinhard Mennicken (eds.); ZAMM 76 S2 (1996) 293-296.
  17. A. Arnold: The relaxation-time Wigner equation , in Mathematical Problems in Semiconductor Physics , Marcati, Markowich, Natalini (ed.), Proceedings of workshop in Rome, Italy (1993); Pitman Research Notes in Mathematics Series, vol. 340, Longman-London (1995) 105-117.
  18. A. Arnold: A mixed spectral-collocation and operator splitting method for the Wigner- Poisson equation , in Mathematics of Computation 1943-1993 , W. Gautschi (ed.) Proceedings of symposium in Vancouver, Canada 1993, American Mathematical Society (1994) 249-253.
  19. A. Arnold, C. Ringhofer: Operator splitting methods for the Wigner-Poisson equation , Proceedings of the International Workshop on Computational Electronics, Urbana-Champaign, USA (1992).
  20. A. Arnold: Quantum transport in semiconductors: numerical methods, Proceedings of Numsim '91, Berlin (ed. Gajewski, Deuflhard, Markowich); Technical Report 91-8, ZIB (1991) 51-56.
  21. A. Arnold, P.A. Markowich: Quantum transport models for semiconductors , in Applied and Industrial Mathematics, R. Spigler (ed.), Kluwer Acad. Publ. (1991) 301-307.

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.

Lecture Notes:

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