arXiv subjects

Markus Pfannmueller

Publications and source records attributed to Markus Pfannmueller.

3 recordsLinked to original sources

arXiv1994

Finite-Size Scaling Studies of Reaction-Diffusion Systems, Part I: Periodic Boundary Conditions

The finite-size scaling function and the leading corrections for the single species 1D coagulation model $(A + A \rightarrow A)$ and the annihilation model $(A + A \rightarrow \emptyset)$ are calculated. The scaling functions are universal and independent of the initial conditions but do depend on the boundary conditions. A similarity transformation between the two models is derived and used to connect the corresponding scaling functions.

cond-mat↗

arXiv1994

Finite-Size-Scaling Studies of Reaction-Diffusion Systems Part II: Open Boundary Conditions

We consider the coagulation-decoagulation model on an one-dimensional lattice of length $L$ with open boundary conditions. Based on the empty interval approach the time evolution is described by a system of $\frac{L(L+1)}{2}$ differential equations which is solved analytically. An exact expression for the concentration is derived and its finite-size scaling behaviour is investigated. The scaling function is found to be independent of initial conditions. The scaling function and the correction function for open boundary conditions are different from those for periodic boundary conditions.

cond-mat↗

arXiv1994

Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods

The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\rightarrow A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial conditions as well. Two different numerical methods are used to compute the scaling properties: Monte Carlo simulations and extrapolations of exact finite lattice data. These methods are tested in a case where analytical results are available. It is shown that Monte Carlo simulations can be used to compute even the correction terms. To obtain reliable results from finite-size extrapolations exact numerical data for lattices up to ten sites are sufficient.

cond-mat↗