Benchmark problems for continuum radiative transfer. High optical depths, anisotropic scattering, and polarisation

Solving the continuum radiative transfer equation in high opacity media requires sophisticated numerical tools. In order to test the reliability of such tools, we present a benchmark of radiative transfer codes in a 2D disc configuration. We test the accuracy of seven independently developed radiative transfer codes by comparing the temperature structures, spectral energy distributions, scattered light images, and linear polarisation maps that each model predicts for a variety of disc opacities and viewing angles. The test cases have been chosen to be numerically challenging, with midplane optical depths up 10^6, a sharp density transition at the inner edge and complex scattering matrices. We also review recent progress in the implementation of the Monte Carlo method that allow an efficient solution to these kinds of problems and discuss the advantages and limitations of Monte Carlo codes compared to those of discrete ordinate codes. For each of the test cases, the predicted results from the radiative transfer codes are within good agreement. The results indicate that these codes can be confidently used to interpret present and future observations of protoplanetary discs.Comment: 15 pages, 10 figures, accepted for publication in A&

The finite-temperature Monte Carlo method and its application to superfluid helium clusters

We review the use of the path integral Monte Carlo (PIMC) methodology to the study of finite-size quantum clusters, with particular emphasis on recent applications to pure and impurity-doped He clusters. We describe the principles of PIMC, the use of the multilevel Metropolis method for sampling particle permutations, and the methods used to accurately incorporate anisotropic molecule-helium interactions into the path integral scheme. Applications to spectroscopic studies of embedded atoms and molecules are summarized, with discussion of the new concepts of local and nanoscale superfluidity that have been generated by recent PIMC studies of the impurity-doped He clusters.Comment: P. Huang, Y. Kwon, and K. B. Whaley, in "Quantum Fluids in Confinement", Vol. 4 of "Advances in Quantum Many-Body Theories", edited by E. Krotscheck and J. Navarro (World Scientific, Singapore, 2002), in pres

Kinetics of electron-positron pair plasmas using an adaptive Monte Carlo method

A new algorithm for implementing the adaptive Monte Carlo method is given. It is used to solve the relativistic Boltzmann equations that describe the time evolution of a nonequilibrium electron-positron pair plasma containing high-energy photons and pairs. The collision kernels for the photons as well as pairs are constructed for Compton scattering, pair annihilation and creation, bremsstrahlung, and Bhabha & Moller scattering. For a homogeneous and isotropic plasma, analytical equilibrium solutions are obtained in terms of the initial conditions. For two non-equilibrium models, the time evolution of the photon and pair spectra is determined using the new method. The asymptotic numerical solutions are found to be in a good agreement with the analytical equilibrium states. Astrophysical applications of this scheme are discussed.Comment: 43 pages, 7 postscript figures, to appear in the Astrophysical Journa

Criticality in coupled quantum spin-chains with competing ladder-like and two-dimensional couplings

Motivated by the geometry of spins in the material CaCu$_2$O$_3$, we study a two-layer, spin-half Heisenberg model, with nearest-neighbor exchange couplings J and \alpha*J along the two axes in the plane and a coupling J_\perp perpendicular to the planes. We study these class of models using the Stochastic Series Expansion (SSE) Quantum Monte Carlo simulations at finite temperatures and series expansion methods at T=0. The critical value of the interlayer coupling, J_\perp^c, separating the N{\'e}el ordered and disordered ground states, is found to follow very closely a square root dependence on $\alpha$. Both T=0 and finite-temperature properties of the model are presented.Comment: 9 pages, 11 figs., 1 tabl

Analysis of Sample Correlations for Monte Carlo Rendering

Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.publishe

Is the Yb2Ti2O7 pyrochlore a quantum spin ice?

We use numerical linked cluster (NLC) expansions to compute the specific heat, C(T), and entropy, S(T), of a quantum spin ice model of Yb2Ti2O7 using anisotropic exchange interactions recently determined from inelastic neutron scattering measurements and find good agreement with experimental calorimetric data. In the perturbative weak quantum regime, this model has a ferrimagnetic ordered ground state, with two peaks in C(T): a Schottky anomaly signalling the paramagnetic to spin ice crossover followed at lower temperature by a sharp peak accompanying a first order phase transition to the ferrimagnetic state. We suggest that the two C(T) features observed in Yb2Ti2O7 are associated with the same physics. Spin excitations in this regime consist of weakly confined spinon-antispinon pairs. We suggest that conventional ground state with exotic quantum dynamics will prove a prevalent characteristic of many real quantum spin ice materials.Comment: 8 pages (two-column), 9 figure

End-to-end Sampling Patterns

Sample patterns have many uses in Computer Graphics, ranging from procedural object placement over Monte Carlo image synthesis to non-photorealistic depiction. Their properties such as discrepancy, spectra, anisotropy, or progressiveness have been analyzed extensively. However, designing methods to produce sampling patterns with certain properties can require substantial hand-crafting effort, both in coding, mathematical derivation and compute time. In particular, there is no systematic way to derive the best sampling algorithm for a specific end-task. Tackling this issue, we suggest another level of abstraction: a toolkit to end-to-end optimize over all sampling methods to find the one producing user-prescribed properties such as discrepancy or a spectrum that best fit the end-task. A user simply implements the forward losses and the sampling method is found automatically -- without coding or mathematical derivation -- by making use of back-propagation abilities of modern deep learning frameworks. While this optimization takes long, at deployment time the sampling method is quick to execute as iterated unstructured non-linear filtering using radial basis functions (RBFs) to represent high-dimensional kernels. Several important previous methods are special cases of this approach, which we compare to previous work and demonstrate its usefulness in several typical Computer Graphics applications. Finally, we propose sampling patterns with properties not shown before, such as high-dimensional blue noise with projective properties

Computational spectroscopy of helium-solvated molecules: effective inertia, from small He clusters toward the nano-droplet regime

Accurate computer simulations of the rotational dynamics of linear molecules solvated in He clusters indicate that the large-size (nano-droplet) regime is attained quickly for light rotors (HCN, CO) and slowly for heavy ones (OCS, N$_2$O, CO$_2$), thus challenging previously reported results. Those results spurred the view that the different behavior of light rotors with respect to heavy ones - including a smaller reduction of inertia upon solvation of the former - would result from the lack of adiabatic following of the He density upon molecular rotation. We have performed computer experiments in which the rotational dynamics of OCS and HCN molecules was simulated using a fictitious inertia appropriate to the other molecule. These experiments indicate that the approach to the nano-droplet regime, as well as the reduction of the molecular inertia upon solvation, is determined by the anistropy of the potential, more than by the molecular weight. Our findings are in agreement with recent infrared and/or microwave experimental data which, however, are not yet totally conclusive by themselves.Comment: 11 pages, 13 figure

Power spectrum of the maxBCG sample: detection of acoustic oscillations using galaxy clusters

We use the direct Fourier method to calculate the redshift-space power spectrum of the maxBCG cluster catalog -- currently by far the largest existing galaxy cluster sample. The total number of clusters used in our analysis is 12,616. After accounting for the radial smearing effect caused by photometric redshift errors and also introducing a simple treatment for the nonlinear effects, we show that currently favored low matter density "concordance" LCDM cosmology provides a very good fit to the estimated power. Thanks to the large volume (~0.4 h^{-3}Gpc^{3}), high clustering amplitude (linear effective bias parameter b_{eff} ~3x(0.85/sigma_8)), and sufficiently high sampling density (~3x10^{-5} h^{3}Mpc^{-3}) the recovered power spectrum has high enough signal to noise to allow us to find evidence (~2 sigma CL) for the baryonic acoustic oscillations (BAO). In case the clusters are additionally weighted by their richness the resulting power spectrum has slightly higher large-scale amplitude and smaller damping on small scales. As a result the confidence level for the BAO detection is somewhat increased: ~2.5 sigma. The ability to detect BAO with relatively small number of clusters is encouraging in the light of several proposed large cluster surveys.Comment: MNRAS accepted, extended analysis of arXiv:0705.1843, 15 page