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Deterministic and stochastic algorithms for mechanical systems under constraints.

Giovanni Ciccotti1, Galina Kalibaeva

  • 1INFM and Dipartimento di Fisica, Università degli Studi di Roma La Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy. giovanni.ciccotti@roma1.infn.it

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 13, 2004
PubMed
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This study explores constraint systems, linking statistical behavior and dynamics to non-Hamiltonian systems. New algorithms based on the Trotter formula are introduced for time-dependent fields and stochastic differential equations.

Area of Science:

  • Physics
  • Computational Science
  • Mathematical Physics

Background:

  • Understanding the behavior of constrained systems is crucial in various scientific fields.
  • General non-Hamiltonian systems present unique challenges in dynamical analysis.

Purpose of the Study:

  • To elucidate the philosophical underpinnings of statistical behavior and dynamical evolution in constrained systems.
  • To connect constrained systems with the broader framework of non-Hamiltonian dynamics.
  • To develop novel computational algorithms for simulating these systems.

Main Methods:

  • Discussion of the general philosophy for statistical behavior and dynamical evolution.
  • Integration of equations of motion for constrained systems.
  • Application of approximations to the evolution operator via the Trotter formula.

Related Experiment Videos

  • Generalization to time-dependent force fields.

    • Main Results:

    • Established a link between constrained systems and general non-Hamiltonian systems.
    • Introduced a family of algorithms derived from Trotter formula approximations.
    • Adapted algorithms for ordinary stochastic differential equations.

    Conclusions:

    • The presented framework provides a unified approach to constrained and non-Hamiltonian dynamics.
    • The developed algorithms offer a practical method for simulating complex systems.
    • The work extends to the analysis of stochastic processes in time-varying fields.