arXiv subjects

R. D. Schram

Publications and source records attributed to R. D. Schram.

2 recordsLinked to original sources

arXiv2013

Reaction-diffusion model Monte Carlo simulations on the GPU

We created an efficient algorithm suitable for graphics processing units (GPUs) to perform Monte Carlo simulations of a subset of reaction-diffusion models. The algorithm uses techniques that are specific to GPU programming, and combines these with the multispin technique known from CPU programming to create one of the fastest algorithms for reaction-diffusion models. As an example, the algorithm is applied to the pair contact process with diffusion (PCPD). Compared to a simple algorithm on the CPU, our GPU algorithm is approximately 4000 times faster. If we compare the performance of the GPU algorithm, between the GPU and CPU, we find a speed-up of about 130x.

physics.comp-ph↗

arXiv2012

Critical exponents of the pair contact process with diffusion

We study the pair contact process with diffusion (PCPD) using Monte Carlo simulations, and concentrate on the decay of the particle density $ρ$ with time, near its critical point, which is assumed to follow $ρ(t) \approx ct^{-δ} +c_2t^{-δ_2}+...$. This model is known for its slow convergence to the asymptotic critical behavior; we therefore pay particular attention to finite-time corrections. We find that at the critical point, the ratio of $ρ$ and the pair density $ρ_p$ converges to a constant, indicating that both densities decay with the same powerlaw. We show that under the assumption $δ_2 \approx 2 δ$, two of the critical exponents of the PCPD model are $δ= 0.165(10)$ and $β= 0.31(4)$, consistent with those of the directed percolation (DP) model.

cond-mat.stat-mech↗