Adaptive symplectic and reversible integrators

The so-called structure-preserving methods which reproduce the fundamental properties like symplecticness, time reversibility, volume and energy preservation of the original model of the underlying physical problem became very important in recent years. It has been shown theoretically and experimentally, that these methods are superior to the standard integrators, especially in long term computation. In the paper the adaptivity issues are discussed for symplectic and reversible methods designed for integration of Hamiltonian systems. Molecular dynamics models and N-body problems, as Hamiltonian systems, are challenging mathematical models in many aspects; the wide range of time scales, very large number of differential equations, chaotic nature of trajectories, restriction to very small step sizes in time, etc. Recent results on variable step size integrators, multiple time stepping methods, regularization techniques with applications to classical and quantum molecular dynamics, to N- body atomic problems and planetary motion will be presented.


Theory of impurity induced lattice distortions in the normal phase of charge density wave systems
Turgut, Sadi (1994-05-01)
A phenomenological Ginzburg-Laundau theory is applied to the normal phase of one-dimensional charge-density-wave systems with a finite concentration of impurities. It is found that the interaction between the impurities and the highly polarizable electron gas leads to a strong and oscillatory impurityimpurity interaction, which in turn leads to ordered impurity arrangements and to sizeable periodic lattice distortions. The effect is very strongly dependent on the charge of the impurities, their concentratio...
Noncommutative nonlinear sigma models and integrability
Kürkcüoğlu, Seçkin (American Physical Society (APS), 2008-09-01)
We first review the result that the noncommutative principal chiral model has an infinite tower of conserved currents and discuss the special case of the noncommutative CP1 model in some detail. Next, we focus our attention to a submodel of the CP1 model in the noncommutative spacetime A(theta)(R2+1). By extending a generalized zero-curvature representation to A(theta)(R2+1) we discuss its integrability and construct its infinitely many conserved currents. A supersymmetric principal chiral model with and wi...
Magnetic transitions in two novel mixed-valence iron(II)–iron(III) metal formate frameworks: Two sublattice model
Yurtseven, Hasan Hamit; Tari, O. (2022-03-15)
We study the two-sublattice model in the mean field theory by expanding the Gibbs free energy in terms of the magnetizations M1 (Mup) and M2 (Mdown) with the quadratic coupling M12M22 (quadrupolar interactions) for the order–disorder transition in the two mixed-valence iron (II)-iron (III) metal formate frameworks, C2H5NH3FeIIFeIIIHCOO6 and C2H52NH2FeIIFeIIIHCOO6. Expressions derived from the Gibbs free energy for the temperature dependence of the magnetizations M1 and M2, are fitted to the observed data (H...
Direct Calculation of Entropy Generation by Solving Reynolds-Averaged Entropy Transport Equation in an Air-Cooled Turbine Cascade
Orhan, Omer Emre; Uzol, Oğuz (2012-06-15)
This paper presents an implementation of directly solving Reynolds-Averaged Entropy Transport equation as a part of the CFD solution to predict entropy generation rates in a two-dimensional turbine blade stator section. The Reynolds Averaged Entropy Transport and the necessary modeling. equations are implemented to a commercial CFD solver as a User Defined Scalar (UDS). The results are compared with those obtained by post-processing the temperature and velocity fields obtained by solving full Navier-Stokes ...
Angle of graph energy - A spectral measure of resemblance of isomeric molecules
Gutman, I; Türker, Burhan Lemi (2003-11-01)
A method, elaborated earlier by one of the present authors, for measuring the structural resemblance of isomeric alternant conjugated hydrocarbons, based on a graph-spectral quantity theta, called the angle of total pi-electron energy approach has been extended now to arbitrary molecules. Some general properties of theta have been established.
Citation Formats
B. Karasözen, “Adaptive symplectic and reversible integrators,” 1998, vol. 536, Accessed: 00, 2020. [Online]. Available: