PROGRAM SUMMARY
Title of program:
jacobi2.0
Catalogue identifier:
ADOE
Ref. in CPC:
137(2001)325
Distribution format: tar gzip file
Operating system: DEC-Unix, Irix, Solaris, Linux, Windows 98/NT
High speed store required:
2MK words
Number of bits in a word:
16
Number of lines in distributed program, including test data, etc:
2228
Keywords:
Computer algebra, Jacobi identity, Poisson brackets, GENERIC,
Nonequilibrium thermodynamics, Reversible motion,
Symbolic programming, Statistical physics, General purpose,
Algebras.
Programming language used: Mathematica
Computer:
Alpha-Workstation ,
Silicon Graphics ,
Sun ,
Linux-PC ,
Windows-PC ,
MacIntosh .
Nature of problem:
The problem is to evaluate single and nested arbitrary generalized
Poisson brackets and the cyclic sum of these in order to test the Jacobi
identity on a given state space for systems described in terms of
discrete or of continuous variables. The Jacobi identity has to be
fulfilled for Poisson brackets consistently describing the reversible
dynamics of physical systems as desired, e.g., within the framework of
nonequilibrium thermodynamics [1-3].
Method of solution:
By symbolic programming the algorithm inserts linear combinations of
discrete state variables or functionals of field variables into the
relevant terms of the Jacobi identity. Subsequent transformations such
as partial integrations, functional derivatives, and recognition rules
are used to perform the operation.
Restrictions:
The machine must provide the main memory needed (see Long Write-up Sec.
3.4). There is no restrictions concerning discrete problems. The
distributed version handles fixed and variable bounded and unbounded
integrals for continuous problems (concerning checkjacobi, see Tab.1).
Other methods, in particular directF and REDUCE (see Tab.1) disregard
any surface contributions, and apply partial integrations by neglecting
surface terms.
Typical running time:
The typical running time increases with the number of ingredients for
the Poisson bracket. For short brackets, e.g. with 5 terms, and
one-dimensional integration, the running time is of the order of seconds
to minutes on any modern computer.
References:
[1] A.N. Beris and B.J. Edwards, Thermodynamics of flowing systems with
internal microstructure (Oxford University Press, Oxford, U.K.,
1994).
[2] M. Grmela and H.C. Ottinger, Phys. Rev. E 56 (1997) 6620-32.
[3] H.C. Ottinger and M. Grmela, Phys. Rev. E 56 (1997) 6633-35.