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Normal Form Defect (2D Projection)
A six dimensional function with up to a million terms that all cancel nearly completely.
Finding exact bounds of the function allows prediction of long-term stability of particle accelerators and other dynamical systems.
Solved rigorously for the first time with global optimization techniques based on Taylor Model methods. |
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COSY INFINITY |
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News September 2008: Kyoko Makino and Martin Berz were awarded the R.E. Moore Prize for the development of some of the newest additions to COSY, which allow the rigorous treatment of remainder bounds of Taylor expansion, in particular those of the solutions of flows or maps of ODEs. April 2008: Martin Berz was awarded an Honorary Doctorate from Saint Petersburg University in Russia “For His Eminent Contributions to the Solution of Important Problems of Applied Mathematics”. Much of this work forms the mathematical basis of the algorithms in COSY. August 2007: Version 9.0 of COSY is released. New features include enhancements to the treatment of remainder bounds, many updates to existing data types, and external tools for the computation of field expansions from surface data.
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What Is COSY? COSY is a system for the use of various advanced concepts of modern scientific computing. COSY currently has more than 1000 registered users and has been extensively cross-checked and verified. The COSY system consists of the following parts. 1) A collection of advanced highly optimized Data Types. In particular: - The Differential Algebraic types for high-order multivariate study of ODEs, Flows, and PDEs. Also allow high-order multivariate automatic differentiation. - The Taylor Model type for rigorous high-order computing with often far-reaching suppression of dependency. Tools for range bounding, derivative-based box rejection, constraint satisfaction, ODEs and PDEs. 2) The COSYScript environment for the use of these types. It is object oriented and supports polymorphism, has a compact and simple syntax, and is compiled and executed on the fly. It has built-in optimization constructs, and is used for high turn around simulation. 3) Interfaces for C++ and F90 to seamlessly use the types in external programs in these object oriented languages. New User Registration
User's Agreement
As part of the registration process, new users will be asked to print the User's Agreement on the official letterhead of their organization, and fax a signed copy of that document to +1-815- 301-9725. (These instructions will be repeated after using the online registration form.)
Download COSY Source
The Beam Physics Package
COSY INFINITY is an arbitrary order beam dynamics simulation and analysis code. It allows the study of accelerator lattices, spectrographs, beamlines, electron microscopes, and many other devices. It can determine high-order maps of combinations of particle optical elements of arbitrary field configurations. The elements can either be based on a large library of existing elements with realistic field configurations including fringe fields, or described in detail by measured data.
Analysis options include computation of high-order nonlinearities; analysis of properties of repetitive motion via chromaticities, normal form analysis, and symplectic tracking; analysis of single-pass systems resolutions, reconstructive aberration correction, and consideration of detector errors; and analysis of spin dynamics via computation of spin maps, spin normal form and spin tracking.
Beam Physics Input Converters
Michigan State University - B149 Biomedical & Physical Sciences Building, East Lansing, MI 48824 Web page maintained by Kyoko Makino |