Improving the modelling of redshift-space distortions: I. A bivariate Gaussian description for the galaxy pairwise velocity distributions

As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation $\vec{r}$, such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean $\mu$ and dispersion $\sigma$. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. We also show how this description naturally allows for the Taylor expansion of $1+\xi_S(\vec{s})$ around $1+\xi_R(r)$, which leads to the Kaiser linear formula when truncated to second order, expliciting its connection with the moments of the velocity distribution functions. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.Comment: 11 pages, 3 figures, 2 table

CFD Applications in Energy Engineering Research and Simulation: An Introduction to Published Reviews

Computational Fluid Dynamics (CFD) has been firmly established as a fundamental discipline to advancing research on energy engineering. The major progresses achieved during the last two decades both on software modelling capabilities and hardware computing power have resulted in considerable and widespread CFD interest among scientist and engineers. Numerical modelling and simulation developments are increasingly contributing to the current state of the art in many energy engineering aspects, such as power generation, combustion, wind energy, concentrated solar power, hydro power, gas and steam turbines, fuel cells, and many others. This review intends to provide an overview of the CFD applications in energy and thermal engineering, as a presentation and background for the Special Issue “CFD Applications in Energy Engineering Research and Simulation” published by Processes in 2020. A brief introduction to the most significant reviews that have been published on the particular topics is provided. The objective is to provide an overview of the CFD applications in energy and thermal engineering, highlighting the review papers published on the different topics, so that readers can refer to the different review papers for a thorough revision of the state of the art and contributions into the particular field of interest

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Econometrics: A bird's eye view

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledge and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treatment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks and forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of the "real time econometrics". This paper attempts to provide an overview of some of these developments

Planning horizons and end conditions for sustained yield studies in continuous cover forests

The contemporary forestry preoccupation with non-declining even-flow during yield simulations detracts from more important questions about the constraints that should bind the end of a simulation. Whilst long simulations help to convey a sense of sustainability, they are inferior to stronger indicators such as the optimal state and binding conditions at the end of a simulation. Rigorous definitions of sustainability that constrain the terminal state should allow flexibility in the planning horizon and relaxation of non-declining even-flow, allowing both greater economic efficiency and better environmental outcomes. Suitable definitions cannot be divorced from forest type and management objectives, but should embrace concepts that ensure the anticipated value of the next harvest, the continuity of growing stock, and in the case of uneven-aged management, the adequacy of regeneration.Comment: 8 pages, 1 figure, 54 references, Ecological Indicators (2014

Physics-related epistemic uncertainties in proton depth dose simulation

A set of physics models and parameters pertaining to the simulation of proton energy deposition in matter are evaluated in the energy range up to approximately 65 MeV, based on their implementations in the Geant4 toolkit. The analysis assesses several features of the models and the impact of their associated epistemic uncertainties, i.e. uncertainties due to lack of knowledge, on the simulation results. Possible systematic effects deriving from uncertainties of this kind are highlighted; their relevance in relation to the application environment and different experimental requirements are discussed, with emphasis on the simulation of radiotherapy set-ups. By documenting quantitatively the features of a wide set of simulation models and the related intrinsic uncertainties affecting the simulation results, this analysis provides guidance regarding the use of the concerned simulation tools in experimental applications; it also provides indications for further experimental measurements addressing the sources of such uncertainties.Comment: To be published in IEEE Trans. Nucl. Sc

De/construction sites: Romans and the digital playground

The Roman world as attested to archaeologically and as interacted with today has its expression in a great many computational and other media. The place of visualisation within this has been paramount. This paper argues that the process of digitally constructing the Roman world and the exploration of the resultant models are useful methods for interpretation and influential factors in the creation of a popular Roman aesthetic. Furthermore, it suggests ways in which novel computational techniques enable the systematic deconstruction of such models, in turn re-purposing the many extant representations of Roman architecture and material culture

Numerical simulation of conservation laws with moving grid nodes: Application to tsunami wave modelling

In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite volume scheme is conservative and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed, thus unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.Comment: 46 pages, 7 figures, 7 tables, 94 references. Accepted to Geosciences. Other author's papers can be downloaded at http://www.denys-dutykh.com

Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them