Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMonte Carlo Simulations of Ultrathin Magnetic Dots
198
0
0.0
(
0
)
Added by
Marcella Rapini Braga
Publication date
2006
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this work we study the thermodynamic properties of ultrathin ferromagnetic dots using Monte Carlo simulations. We investigate the vortex density as a function of the temperature and the vortex structure in monolayer dots with perpendicular anisotropy and long-range dipole interaction. The interplay between these two terms in the hamiltonian leads to an interesting behavior of the thermodynamic quantities as well as the vortex density.
rate research
Read More
Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in the potential energy, and the two-body terms in the Jastrow factor. In the framework of variational Monte Carlo methods, the random batch algorithm is constructed based on the over-damped Langevin dynamics, so that updating the position of each particle in an $N$-particle system only requires $mathcal{O}(1)$ operations, thus for each time step the computational cost for $N$ particles is reduced from $mathcal{O}(N^2)$ to $mathcal{O}(N)$. For diffusion Monte Carlo methods, the random batch algorithm uses an energy decomposition to avoid the computation of the total energy in the branching step. The effectiveness of the random batch method is demonstrated using a system of liquid ${}^4$He atoms interacting with a graphite surface.
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection method, and Markov chain Monte Carlo to sample a probability distribution function, and methods for variance reduction to evaluate numerical integrals using the Monte Carlo simulation. We will also briefly introduce the quasi-Monte Carlo sampling at the end of this lecture.
Using the Ehrenfest urn model we illustrate the subtleties of error estimation in Monte Carlo simulations. We discuss how the smooth results of correlated sampling in Markov chains can fool ones perception of the accuracy of the data, and show (via numerical and analytical methods) how to obtain reliable error estimates from correlated samples.
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are considered to demonstrate the applicability of the MLMC method. The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal random field. A more general second extension is considered based on the work of [Xiao et al.(2017)], where the entire Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For two fundamental flows, we show that the MLMC method based on a hierarchy of meshes is asymptotically faster than plain Monte Carlo. Additionally, we demonstrate that for some flows an optimal multilevel estimator can be obtained for which the cost scales with the same order as a single CFD solve on the finest grid level.
We present extensive new emph{ab initio} path integral Monte Carlo (PIMC) simulations of normal liquid $^3$He without any nodal constraints. This allows us to study the effects of temperature on different structural properties like the static structure factor $S(mathbf{q})$, the momentum distribution $n(mathbf{q})$, and the static density response function $chi(mathbf{q})$, and to unambiguously quantify the impact of Fermi statistics. In addition, the dynamic structure factor $S(mathbf{q},omega)$ is rigorously reconstructed from imaginary-time PIMC data, and we find the familiar phonon-maxon-roton dispersion that is well known from $^4$He and has been reported previously for two-dimensional $^3$He films [Nature textbf{483}, 576-579 (2012)]. The comparison of our new results for both $S(mathbf{q})$ and $S(mathbf{q},omega)$ to neutron scattering measurements reveals an excellent agreement between theory and experiment.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
