675,269 research outputs found
A Monte Carlo Method for the Numerical Simulation of Tsallis Statistics
We present a new method devised to overcome the intrinsic difficulties
associated to the numerical simulations of the Tsallis statistics. We use a
standard Metropolis Monte Carlo algorithm at a fictitious temperature T',
combined with a numerical integration method for the calculation of the entropy
in order to evaluate the actual temperature T. We illustrate the method by
applying it to the 2d-Ising model using a standard reweighting technique.Comment: 7 LaTeX pages, 3 figures, submited to Physica
Discrete-time port-Hamiltonian systems: A definition based on symplectic integration
We introduce a new definition of discrete-time port-Hamiltonian systems
(PHS), which results from structure-preserving discretization of explicit PHS
in time. We discretize the underlying continuous-time Dirac structure with the
collocation method and add discrete-time dynamics by the use of symplectic
numerical integration schemes. The conservation of a discrete-time energy
balance - expressed in terms of the discrete-time Dirac structure - extends the
notion of symplecticity of geometric integration schemes to open systems. We
discuss the energy approximation errors in the context of the presented
definition and show that their order is consistent with the order of the
numerical integration scheme. Implicit Gauss-Legendre methods and Lobatto
IIIA/IIIB pairs for partitioned systems are examples for integration schemes
that are covered by our definition. The statements on the numerical energy
errors are illustrated by elementary numerical experiments.Comment: 12 pages. Preprint submitted to Systems & Control Letter
Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration
In the finite difference method which is commonly used in computational
micromagnetics, the demagnetizing field is usually computed as a convolution of
the magnetization vector field with the demagnetizing tensor that describes the
magnetostatic field of a cuboidal cell with constant magnetization. An
analytical expression for the demagnetizing tensor is available, however at
distances far from the cuboidal cell, the numerical evaluation of the
analytical expression can be very inaccurate.
Due to this large-distance inaccuracy numerical packages such as OOMMF
compute the demagnetizing tensor using the explicit formula at distances close
to the originating cell, but at distances far from the originating cell a
formula based on an asymptotic expansion has to be used. In this work, we
describe a method to calculate the demagnetizing field by numerical evaluation
of the multidimensional integral in the demagnetization tensor terms using a
sparse grid integration scheme. This method improves the accuracy of
computation at intermediate distances from the origin.
We compute and report the accuracy of (i) the numerical evaluation of the
exact tensor expression which is best for short distances, (ii) the asymptotic
expansion best suited for large distances, and (iii) the new method based on
numerical integration, which is superior to methods (i) and (ii) for
intermediate distances. For all three methods, we show the measurements of
accuracy and execution time as a function of distance, for calculations using
single precision (4-byte) and double precision (8-byte) floating point
arithmetic. We make recommendations for the choice of scheme order and
integrating coefficients for the numerical integration method (iii)
Improved Spin Dynamics Simulations of Magnetic Excitations
Using Suzuki-Trotter decompositions of exponential operators we describe new
algorithms for the numerical integration of the equations of motion for
classical spin systems. These techniques conserve spin length exactly and, in
special cases, also conserve the energy and maintain time reversibility. We
investigate integration schemes of up to eighth order and show that these new
algorithms can be used with much larger time steps than a well established
predictor-corrector method. These methods may lead to a substantial speedup of
spin dynamics simulations, however, the choice of which order method to use is
not always straightforward.Comment: J. Mod. Phys. C (in press
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