Enabling Radiative Transfer on AMR grids in CRASH

We introduce CRASH-AMR, a new version of the cosmological Radiative Transfer (RT) code CRASH, enabled to use refined grids. This new feature allows us to attain higher resolution in our RT simulations and thus to describe more accurately ionisation and temperature patterns in high density regions. We have tested CRASH-AMR by simulating the evolution of an ionised region produced by a single source embedded in gas at constant density, as well as by a more realistic configuration of multiple sources in an inhomogeneous density field. While we find an excellent agreement with the previous version of CRASH when the AMR feature is disabled, showing that no numerical artifact has been introduced in CRASH-AMR, when additional refinement levels are used the code can simulate more accurately the physics of ionised gas in high density regions. This result has been attained at no computational loss, as RT simulations on AMR grids with maximum resolution equivalent to that of a uniform cartesian grid can be run with a gain of up to 60% in computational time.Comment: 19 pages, 17 figures. MNRAS, in pres

Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

Modelling social identification and helping in evacuation simulation

Social scientists have criticised computer models of pedestrian streams for their treatment of psychological crowds as mere aggregations of individuals. Indeed most models for evacuation dynamics use analogies from physics where pedestrians are considered as particles. Although this ensures that the results of the simulation match important physical phenomena, such as the deceleration of the crowd with increasing density, social phenomena such as group processes are ignored. In particular, people in a crowd have social identities and share those social identities with the others in the crowd. The process of self categorisation determines norms within the crowd and influences how people will behave in evacuation situations. We formulate the application of social identity in pedestrian simulation algorithmically. The goal is to examine whether it is possible to carry over the psychological model to computer models of pedestrian motion so that simulation results correspond to observations from crowd psychology. That is, we quantify and formalise empirical research on and verbal descriptions of the effect of group identity on behaviour. We use uncertainty quantification to analyse the model’s behaviour when we vary crucial model parameters. In this first approach we restrict ourselves to a specific scenario that was thoroughly investigated by crowd psychologists and where some quantitative data is available: the bombing and subsequent evacuation of a London underground tube carriage on July 7th 2005

The long-term consequences of hybridization between the two Daphnia species, D. galeata and D. dentifera, in mature habitats

<p>Abstract</p> <p>Background</p> <p>Ecological specializations such as antipredator defense can reinforce morphological and distributional divergence within hybridizing species. Two hybridizing species of <it>Daphnia </it>(<it>D. galeata </it>and <it>D. dentifera</it>) are distributed in both Japan and North America; however, these populations have a longer history in Japan than in North America due to the differing impact of the last glaciation on these two regions. We tested the hypothesis that this longer coexistence in Japan would lead to extensive genetic admixture in nuclear and mitochondrial DNA whilst the distinct morphological traits and distributional patterns would be maintained.</p> <p>Results</p> <p>The high level of correspondence among morphological traits, distribution, and mitochondrial and nuclear DNA types for the specimens with <it>D. dentifera </it>mtDNA indicated that the species distinction has been maintained. However, a discordance between mtDNA and nuclear ITS-1 types was observed for most specimens that had <it>D. galeata </it>mtDNA, consistent with the pattern seen between the two species in North America. This observation suggests nuclear introgression from <it>D. dentifera </it>into <it>D. galeata </it>without mitochondrial introgression.</p> <p>Conclusions</p> <p>The separation of morphological traits and distribution ranges of the two hybridizing species in Japan, as well as in North America, has been maintained, despite large differences in climatic and geographical histories of these two regions. Variations in environmental factors, such as predation pressure, might affect maintenance of the distribution, although the further studies are needed to confirm this.</p