Publications

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Selected recent publications and some frequently cited older publications of the Beamtheory and Dynamical Systems Group at Physics and Astronomy Department, Michigan State University

Books

Proceedings, Tenth Int. Conf. on P-Adic and Non-Archimedean Analysis, East Lansing, Michigan: M. Berz and K. Shamseddine (Eds.), American Mathematical Society, 2009, forthcoming
Proceedings, Fifteenth Int. Workshop on Beam Dynamics and Optimization, St. Petersburg, Florida: D. Ovsyannikov, M. Berz and P. Snopok (Eds.), World Scientific, 2009, forthcoming
Proceedings, Fifth Int. Workshop on Taylor Model Methods, Toronto, Canada: K. Jackson and M. Berz (Eds.), Communications of the Fields Institute, 2008, forthcoming
Proceedings, Eighth Int. Conf. on Computational Accelerator Physics, St. Petersburg, Russia: D. Ovsyannikov, M. Berz and K. Makino (Eds.), Elsevier, 2006, ISBN 0-168-9002558
An Introduction to the Physics of Beams: M. Berz, K. Makino and W. Wan, Taylor & Francis, forthcoming
Proceedings, Seventh Int. Conf. on Computational Accelerator Physics, East Lansing, Michigan: M. Berz and K. Makino (Eds.), Institute of Physics Publishing, 2004, ISBN 0-75-030939-3
Modern Map Methods in Particle Beam Physics: M. Berz, Academic Press, 1999, ISBN 0-12-014750-5
Computational Differentiation: Techniques, Applications, and Tools, Proc. AD1996, Santa Fe, New Mexico: M. Berz, C. Bischof, A. Griewank, G. Corliss (Eds.), SIAM, 1996, ISBN 0-89871-385-4
Proceedings, Int. Workshop on Nonlinear Effects in Accelerators, Berlin, Germany: M. Berz, S. Martin and K. Ziegler (Eds.), Institute of Physics Publishing, 1993, ISBN 0-7503-0238-0

Papers

Chaos, The Large Hadron Collider, and Michigan Taffy (Commencement Address Connected to Conferral of Honorary Doctorate): M. Berz, Saint Petersburg State University Newsletter 8 (3775) (2008) 19-20
On the Estimation of Topological Entropy on Surfaces: S. Newhouse, M. Berz, J. Grote and K. Makino, Contemporary Mathematics 469 (2008) 243-270
Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field: K. Shamseddine, M. Berz, Bulletin of the Belgian Mathematical Society 14 (2007) 1001-1015
Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: Long-term Stabilization by Preconditioning: K. Makino, M. Berz, International Journal of Differential Equations and Applications 10(4) (2005) 353-384
Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: Long-term Stabilization by Shrink Wrapping: M. Berz, K. Makino, International Journal of Differential Equations and Applications 10(4) (2005) 385-403
Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: The Single Step: K. Makino, M. Berz, International Journal of Pure and Applied Mathematics 36(2) (2006) 175-197
Long-Term Stability of Large Particle Accelerators: M. Berz, K. Makino, Y.-K. Kim, P. Snopok, in: ECMI Newsletter 39 (2006) (A. Frommer and B.Lang, Guest Editors)
Long-Term Stability of the Tevatron by Verified Global Optimization: M. Berz, K. Makino, Y.-K. Kim, Nuclear Instruments and Methods A558 (2005) 1-10
Simulation and Optimization of the Tevatron Accelerator: P. Snopok, C. Johnstone, M. Berz, in: Lecture Notes on Computational Science and Engineering 50 (2005) 199-209, Springer
Study and Optimal Correction of a Systematic Skew Quadrupole Field in the Tevatron: P. Snopok, C. Johnstone, M. Berz, D. Ovsyannikov, A. Ovsyannikov, Nuclear Instruments and Methods A558 (2005) 142-146
Exploring the bunching section of the Neutrino Factory: A.A. Poklonskiy, D.A. Ovsyannikov, A.D. Ovsyannikov, D. Neuffer, M. Berz, in: Proceedings, Physics and Control (2005) 272-277
Optimization of the Buncher and Phase Rotator for a Neutrino Factory: A. A. Poklonskiy, D. Neuffer, M. Berz, D. A. Ovsyannikov, A. D. Ovsyannikov in: Proceedings, Stability and Control Processes (2005) 282-291 (D. A. Ovsyannikov and L. A. Petrosyan, Editors)
Performance of Taylor Model Methods for Validated Integration of ODEs: M. Berz, K. Makino, Lecture Notes in Computer Science 3732 (2005) 65-74
Verified Global Optimization with Taylor Model-based Range Bounders: K. Makino, M. Berz, Transactions on Computers 11,4 (2005) 1611-1618
Taylor Models and Floating-Point Arithmetic: Proof that Arithmetic Operations are Validated in COSY: N. Revol, K. Makino, M. Berz, Journal of Logic and Algebraic Programming 64 (2005) 135-154 University of Lyon LIP Report RR 2003-11, MSU HEP report 30212
COSY INFINITY Version 9: K. Makino, M. Berz, Nuclear Instruments and Methods A558 (2005) 346-350
Staging Acceleration and Cooling in a Neutrino Factory: C. Johnstone, M. Berz, K. Makino, M. Berz, Nuclear Instruments and Methods A558,1 (2006) 282-291
Optimizing the Adiabatic Buncher and Phase Rotator: A. Poklonskiy, D. Neuffer, C. Johnstone, M. Berz, K. Makino, D. Ovsyannikov, A. Ovsyannikov, Nuclear Instruments and Methods A558 (2005) 135-141
Multipole Expansion Solution of the Laplace Equation using Surface Data: S. Manikonda, M. Berz, Nuclear Instruments and Methods A558,1 (2006) 175-183
High-Order Verified Solutions of the 3D Laplace Equation: S. Manikonda, M. Berz, K. Makino, Transactions on Computers 11,4 (2005) 1604-1610
An Accurate High-Order Method to Solve the Helmholtz Boundary Value Problem for the 3D Laplace Equation: S. Manikonda, M. Berz, International Journal of Pure and Applied Mathematics 23,3 (2005) 365-378
Generalized Power Series on a Non-Archimedean Field: K. Shamseddine, M. Berz, Indagationes Mathematicae 17,3 (2006) 457-477
Analytical Properties of Power Series on Levi-Civita Fields: K. Shamseddine, M. Berz, Annales Mathematiques Blaise Pascal 12 (2005) 309-329
High-Order DA Methods for the Determination of Poincaré Sections: J. Grote, M. Berz, K. Makino, Nuclear Instruments and Methods A558,1 (2006) 106-111
Verified Computation of High-Order Poincaré Maps: J. Grote, K. Makino, M. Berz, Transactions on Systems 11,4 (2005) 1986-1992
High-Order Representation of Poincaré Maps: J. Grote, M. Berz, K. Makino, in: Lecture Notes on Computational Science and Engineering 50 (2005) 59-66, Springer
Solenoid Elements in COSY Infinity: K. Makino, M. Berz, Institute of Physics CS 175 (2004) 219-228
High Order Map Treatment of Superimposed Cavities, Absorbers, and Magnetic Multipole and Solenoid Fields: K. Makino, M. Berz, C. J. Johnstone, D. Errede, Nuclear Instruments and Methods A519 (2004) 162-174
The COSY Language Independent Architecture: Porting COSY Source Files: L. M. Chapin, J. Hoefkens, M. Berz, Institute of Physics CS 175 (2004) 37-45
Muon Beam Ionization Cooling in a Linear Quadrupole Channel: C. Johnstone, M. Berz, D. Errede, K. Makino, Nuclear Instruments and Methods A519 (2004) 472-482
Muon Beam Ring Cooler Simulations Using COSY Infinity: C. Maidana, M. Berz, K. Makino, Institute of Physics CS 175 (2004) 211-218
Stochastic Processes in Muon Ionization Cooling: D. Errede, K. Makino, M. Berz, C. Johnstone, A. van Ginneken, Nuclear Instruments and Methods A519 (2004) 466-471
Higher Order Multivariate Automatic Differentiation and Validated Computation of Remainder Bounds: M. Berz, K. Makino, Transactions on Mathematics 3(1) (2004) 37-44
COSY Infinity's EXPO Symplectic Tracking for LHC: M. L. Shashikant, M. Berz, B. Erdelyi, Institute of Physics CS 175 (2004) 299-306
Local Theory and Applications of Extended Generating Functions: B. Erdelyi, M. Berz, International Journal of Pure and Applied Mathematics 11(3) (2004) 241-282
New Approaches for the Validation of Transfer Maps using Remainder-Enhanced Differential Algebra: M. Berz, K. Makino, Nuclear Instruments and Methods A519 (2004) 53-62
Suppression of the Wrapping Effect by Taylor Model- based Validated Integrators: K. Makino, M. Berz, MSU HEP Report 40910 (2003)
Computing Validated Solutions of Implicit Differential Equations: J. Hoefkens, M. Berz, K. Makino, Advances in Computational Mathematics 19 (2003) 231-253
Taylor Models and Other Validated Functional Inclusion Methods: K. Makino, M. Berz, International Journal of Pure and Applied Mathematics 4(4) (2003) 379-456
Constructive Generation and Verification of Lyapunov Functions around Fixed Points of Nonlinear Dynamical Systems: M. Berz, K. Makino, International Journal of Computer Research 12,2 (2003) 235-244
Recent Progress in Neutrino Factory and Muon Collider Research within the Muon Collaboration: M. Alsharoa et al., Physical Review STAB 6(081001) (2003) 1-52
High-Order Maps with Acceleration for Optimization of Electrostatic and Radio-Frequency Ion-Optical Elements: A. Geraci, T. Barlow, M. Portillo, J. Nolen, K. Shepard, K. Makino, M. Berz, Review of Scientific Instruments 73(9) (2002) 3174-3180
Measure Theory and Integration on the Levi-Civita Field: K. Shamseddine, M. Berz, Contemporary Mathematics 319 (2002) 369-387
Cauchy Theory on Levi-Civita Fields: M. Berz, Contemporary Mathematics 319 (2002) 39-52
Intermediate Values and Inverse Functions on Non-Archimedean Fields: K. Shamseddine, M. Berz, International Journal of Mathematics and Mathematical Sciences 30(3) (2002) 165-176
Verification of Invertibility of Complicated Functions over Large Domains: J. Hoefkens, M. Berz, Reliable Computing 8(1) (2002) 1-16
Verified High-Order Inversion of Functional Dependencies and Interval Newton Methods: M. Berz, J. Hoefkens, Reliable Computing 7(5) (2001) 379-398
Verified Integration of Dynamics in the Solar System: M. Berz, K. Makino, J. Hoefkens, Nonlinear Analysis 47 (2001) 179-190
Verified High-Order Integration of DAEs and Higher-order ODEs: J. Hoefkens, M. Berz, K. Makino, in "Scientific Computing, Validated Numerics and Interval Methods", W. Kraemer and J. W. v. Gudenberg (Eds.) (2001) Kluwer
New Applications of Taylor Model Methods: K. Makino, M. Berz, in: "Automatic Differentiation: From Simulation to Optimization", G. Corliss, C. Faure, A. Griewank, L. Hascoet, and U. Naumann (Eds.) (2001) Springer
Higher Order Verified Inclusions of Multidimensional Systems by Taylor Models: K. Makino, M. Berz, Nonlinear Analysis 47 (2001) 3503-3514
Towards a Universal Data Type for Scientific Computing: M. Berz, in: "Automatic Differentiation: From Simulation to Optimization", G. Corliss, C. Faure, A. Griewank, L. Hascoet, and U. Naumann (Eds.) (2001) Springer
Efficient High-Order Methods for ODEs and DAEs: J. Hoefkens, M. Berz, K. Makino, in: "Automatic Differentiation: From Simulation to Optimization", G. Corliss, C. Faure, A. Griewank, L. Hascoet, and U. Naumann (Eds.) (2001) Springer
Optimal Symplectic Approximation of Hamiltonian Flows: B. Erdelyi, M. Berz, Physical Review Letters 87(11) (2001) 114302
Towards Accurate Simulation of Fringe Field Effects: M. Berz, B. Erdelyi, K. Makino, Nuclear Instruments and Methods A472(3) (2001) 533-540
The WebCOSY System for Course Management in Distance Education: J. Hoefkens, L. Diening, M. Berz, B. Erdelyi, Journal of Computers in Mathematics and Science Teaching 20(3) (2001) 307-321
Distance Education in Beam Physics: B. Erdelyi, J. Hoefkens, K. Makino, M. Berz, in: "Towards the Virtual University - International On-Line Learning Perspectives", Mihai Jalobeanu, Nicolae Nistor, Susan English, and Steve Wheeler (Eds.) (2001) Information Age Publishing
The Michigan State University M.Sc. and Ph.D. Online Degree Programs in Beam Physics: B. Erdelyi, J. Hoefkens, L. Diening, K. Makino, M. Berz, Quarterly Review of Distance Education 1(4) (2000) 345-350
Perturbative Equations of Motion and Differential Operators in Nonplanar Curvilinear Coordinates: K. Makino, M. Berz, International Journal of Applied Mathematics 3(4) (2000) 421-440
Preservation of Canonical Structure in Nonplanar Curvilinear Coordinates: M. Berz, K. Makino, International Journal of Applied Mathematics 3(4) (2000) 401-419
Analytical and Computational Methods for the Levi-Civita Field: M. Berz, Lecture Notes in Pure and Applied Mathematics 222 (2000) 21-34
Convergence on the Levi-Civita Field and Study of Power Series: K. Shamseddine, M. Berz, Lecture Notes in Pure and Applied Mathematics 222 (2000) 283-299
The Differential Algebraic Structure of the Levi-Civita Field and Applications: K. Shamseddine, M. Berz, International Journal of Applied Mathematics 3(4) (2000) 449-464
Non-Archimedean Analysis and Rigorous Computation: M. Berz, International Journal of Applied Mathematics 2(5) (2000) 889-930
Fringe Field Effects in Small Rings of Large Acceptance: M. Berz, B. Erdelyi, K. Makino, Physical Review STAB 3, 124001 (2000)
The Influence of Fringe Fields on Particle Dynamics in the Large Hadron Collider: W. Wan, C. Johnstone, J. Holt, M. Berz, K. Makino, M. Lindemann, B. Erdelyi, Nuclear Instruments and Methods A427, 74-78 (1999)
High-Accuracy Field Description of Particle Spectrographs,: R. Degenhardt, M. Berz, Nuclear Instruments and Methods A427, 151-156 (1999)
Differential Algebraic Techniques: M. Berz, Chapter in: "Handbook of Accelerator Physics and Engineering", M. Tigner, A.Chao (Eds.) (1999) World Scientific
Differential Algebraic Determination of High-Order Off-Energy Closed Orbits, Chromaticities, and Momentum Compactions: M. Berz, B. Erdelyi, W. Wan, K.-Y. Ng, Nuclear Instruments and Methods A427 (1999) 310-314
COSY Infinity Version 8: K. Makino, M. Berz, Nuclear Instruments and Methods A427 (1999) 338-343
Design of a Fifth-Order Achromat: W. Wan, M. Berz, Nuclear Instruments and Methods A423, 1 (1999) 1-6
Experiences with Interactive Remote Graduate Instruction in Beam Physics: M. Berz, B. Erdelyi, J. Hoefkens, Journal of Interactive Learning Research 10,1 (1999) 49-58
New Methods for High-Dimensional Verified Quadrature: M. Berz, K. Makino, Reliable Computing 5 (1999) 13-22
Efficient Control of the Dependency Problem Based on Taylor Model Methods: K. Makino, M. Berz, Reliable Computing 5 (1999) 3-12
Verified Integration of ODEs and Flows using Differential Algebraic Methods on High-Order Taylor Models: M. Berz, K. Makino, Reliable Computing 4 (1998) 361-369
Computation and Application of Taylor Polynomials with Interval Remainder Bounds: M. Berz, G. Hoffstätter, Reliable Computing 4 (1998) 83-97
From Taylor Series to Taylor Models: M. Berz, Chapter in: "Nonlinear Problems in Accelerator Physics" (1997) 1-27, American Institute of Physics CP405
Remainder Differential Algebras and their Applications: K. Makino, M. Berz, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 63-75, SIAM
Calculus and Numerics on Levi-Civita Fields: M. Berz, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 19-37, SIAM
Exception Handling in Derivative Computation with Nonarchimedean Calculus: K. Shamseddine, M. Berz, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 37-52, SIAM
Rigorous Lower Bounds on the Survival Time in Particle Accelerators: G. Hoffstätter, M. Berz, Particle Accelerators 54 (1996) 193-202
COSY Infinity Version 7: K. Makino, M. Berz, American Institute of Physics CP 391 (1996) 253-258
Symplectic Scaling of Transfer Maps including Fringe Fields: G. Hoffstätter, M. Berz, Physical Review E 54,4 (1996) 5664-5672
An Analytical Theory of Arbitrary Order Achromats: W. Wan, M. Berz, Physical Review E 54,3 (1996) 2870-2883
COSY Infinity and its Applications to Nonlinear Dynamics: M. Berz, K. Makino, K. Shamseddine, G. Hoffstätter, W. Wan, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 363-367, SIAM
Modern Map Methods for Charged Particle Optics: M. Berz, Nuclear Instruments and Methods A363 (1995) 100-104
Exact Bounds on the Long Term Stability of Weakly Nonlinear Systems Applied to the Design of Large Storage Rings: M. Berz, G. Hoffstätter, Interval Computations 2 (1994) 68-89
Reconstructive Correction of Aberrations in Nuclear Particle Spectrographs: M. Berz, K. Joh, J. A. Nolen, B. M. Sherrill, A. F. Zeller, Physical Review C 47,2 (1993) 537-544
Differential Algebraic Formulation of Normal Form Theory: M. Berz, in "Proc. Nonlinear Effects in Accelerators", M. Berz, S. Martin and K. Ziegler (Eds.) (1992) 77-86, IOP Publishing
High-Order Computation and Normal Form Analysis of Repetitive Systems: M. Berz, Chapter in: "Physics of Particle Accelerators", Melvin Month (Ed.) (1992) 456-489, AIP Publishing
Design Overview of a Highly Stable Infrared Free Electron Laser at LBL: K.J. Kim, M. Berz, S. Chattopadhyay, C. Kim, J. Edighofer, R. Gough, C. Kim, A.H. Kung, W. Stein, M. Xie, Nuclear Instruments and Methods A304 (1991) 233-237
Isochronous Beamlines for Free Electron Lasers: M. Berz, Nuclear Instruments and Methods A298 (1990) 106-112
Automatic Differentiation as Nonarchimedean Analysis: M. Berz, in: "Computer Arithmetic and Enclosure Methods" (1992) 439-450, Elsevier
Algorithms for Higher Order Automatic Differentiation in Many Variables with Applications to Beam Physics: M. Berz, in: "Automatic Differentiation of Algorithms: Theory, Implementation and Application" (1991) SIAM
Symplectic Tracking in Circular Accelerators with High Order Maps: M. Berz, in: "Nonlinear Problems in Future Particle Accelerators" (1991) 288-296, World Scientific
The Computation of the Aberrations of Fringing Fields of Magnetic Multipoles and Sector Magnets Using Differential Algebra: B. Hartmann, M. Berz, H. Wollnik, Nuclear Instruments and Methods A297 (1990) 343-353
Arbitrary Order Description of Arbitrary Particle Optical Systems: M. Berz, Nuclear Instruments and Methods A298 (1990) 426-440
Differential Algebraic Description of Beam Dynamics to Very High Orders: M. Berz, Particle Accelerators 24 (1989) 109-124
Simulation of Intense Particle Beams with Regularly Distributed Gaussian Subbeams: M. Berz, H. Wollnik, Nuclear Instruments and Methods A267 (1988) 25-34
The Method of Power Series Tracking for the Mathematical Description of Beam Dynamics: M. Berz, Nuclear Instruments and Methods A258 (1987) 431-436
The Program HAMILTON for the Analytic Solution of the Equations of Motion in Particle Optical Systems through Fifth Order: M. Berz, H. Wollnik, Nuclear Instruments and Methods A258 (1987) 364-373
COSY 5.0 - The Fifth Order Code for Corpuscular Optical Systems: M. Berz, H. C. Hoffmann, H. Wollnik, Nuclear Instruments and Methods A258 (1987) 402-406
Relations between Elements of Transfer Matrices due to the Condition of Symplecticity: H. Wollnik, M. Berz, Nuclear Instruments and Methods A238 (1985) 127-140

Theses

Damping Higher Order Modes in the PEP-II B-Factory Storage Ring Collider: S. Weathersby (2007)
Optimization of Accelerator Parameters using Normal Form Methods on Higher-Order Transfer Maps: P. Snopok (2007)
High Order Finite Element Methods to Compute Taylor Transfer Maps: S. L. Manikonda (2006)
A Timeline of Major Particle Accelerators: A. R. Steere (2005)
Development of a HPGe Detector for the Longitudinal Emittance Measurement: R. Taki (2003)
Rigorous Numerical Analysis with High-Order Taylor Models: J. Hoefkens (2001)
Symplectic Approximation of Hamiltonian Flows and Accurate Simulation of Fringe Field Effects: B. Erdelyi (2001)
New Elements of Analysis on the Levi-Civita Field: K. Shamseddine (1999)
Rigorous Analysis of Nonlinear Motion in Particle Accelerators: K. Makino (1998)
Rigorous Field Analysis of Superconducting Magnets and the Influence on Nonlinear Dynamics in Particle Accelerators: M. Lindemann (1998)
Theory and Applications of Arbitrary-Order Achromats: W. Wan (1995)
Rigorous Bounds on Survival Times in Circular Accelerators and Efficient Computation of Fringe-Field Transfer Maps: G. H. Hoffstätter (1994)

Other

Taylor Model Methods and Computer Assisted Proofs: M. Berz and K. Makino, Lecture Notes, Course Presented at Department of Mathematics, University of Barcelona, June 2008, MSUHEP-080609, Michigan State University (2008)
Studies on Performance of the COSY Infinity Optimizers on Constraint Satisfaction: A. Poklonskiy, MSUHEP-083117, Michigan State University (2008)
Detailed Analysis of Fringe Field Effects in the Large Hadron Collider: B. Erdelyi, M. Berz, and K. Makino, MSUCL-1129, Michigan State University (1999).
Differential Algebra-based Magnetic Field Computations and Accurate Fringe Field Maps: B. Erdelyi, M. Berz, and M. Lindemann
Analysis on a Nonarchimedean Extension of the Real Numbers: M. Berz, Lecture Notes, 1992 and 1995 Mathematics Summer Graduate Schools of the German National Merit Foundation, MSUCL-933, Department of Physics and Astronomy, Michigan State University (1994)
Introduction to Beam Physics: M. Berz, Lecture Notes, MSUPA PHY861

COSY Infinity

In addition to these publications you can access the COSY Infinity Reference Manual online.

This page is maintained by Alexander Wittig. Please contact him if there are any problems with it.