A radiation-hydrodynamics scheme valid from the transport to the diffusion limit

We present in this paper the numerical treatment of the coupling between hydrodynamics and radiative transfer. The fluid is modeled by classical conservation laws (mass, momentum and energy) and the radiation by the grey moment $M_1$ system. The scheme introduced is able to compute accurate numerical solution over a broad class of regimes from the transport to the diffusive limits. We propose an asymptotic preserving modification of the HLLE scheme in order to treat correctly the diffusion limit. Several numerical results are presented, which show that this approach is robust and have the correct behavior in both the diffusive and free-streaming limits. In the last numerical example we test this approach on a complex physical case by considering the collapse of a gas cloud leading to a proto-stellar structure which, among other features, exhibits very steep opacity gradients.Comment: 29 pages, submitted to Journal of Computational physic

Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy

Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. Starting from these, we derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free-streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.Comment: 20 pages, 7 figure

Improving the analytical assessment of fish stocks by providing parameters of data quality via InterCatch

The last multiannual Community program for the collection, management and use of data in the fisheries sector (Commission Decision 2008/949/EC) stated the provision of precision levels and sampling intensities of the estimates at national level. However, the unequal compliance of this standard has hindered its application in stock assessment and the consequent scientific advice. The cost-benefit analysis of a sampling program, besides addressing logistical and economic constraints, should deepen the potential of the tools currently available. This article proposes to test the calculation, provision and use in stock assessment of extensively collected precision parameters. First, sampling intensities and coefficients of variation of fisheries-dependent parameters are calculated using the COST software, a statistical tool specifically designed to quantify uncertainty in marine sampled data. Secondly, alternative ways are explored to provide precision parameters to the stock assessment coordinators by using InterCatch, the existing ICES web-based system to submit national data and compile international catch matrices. Finally, the incorporation of these precision parameters in the assessment model is tested, through a stock assessed by statistical assessment models (such as SS3) which can account for sampling errors. Thus, it will be possible to quantify how errors in input data propagate through stock assessment models to affect harvest rules, and also to help identify the most cost-effective data collections that adequately support the advisory process

Simulations of protostellar collapse using multigroup radiation hydrodynamics. I. The first collapse

Radiative transfer plays a major role in the process of star formation. Many simulations of gravitational collapse of a cold gas cloud followed by the formation of a protostellar core use a grey treatment of radiative transfer coupled to the hydrodynamics. However, dust opacities which dominate extinction show large variations as a function of frequency. In this paper, we used frequency-dependent radiative transfer to investigate the influence of the opacity variations on the properties of Larson's first core. We used a multigroup M1 moment model in a 1D radiation hydrodynamics code to simulate the spherically symmetric collapse of a 1 solar mass cloud core. Monochromatic dust opacities for five different temperature ranges were used to compute Planck and Rosseland means inside each frequency group. The results are very consistent with previous studies and only small differences were observed between the grey and multigroup simulations. For a same central density, the multigroup simulations tend to produce first cores with a slightly higher radius and central temperature. We also performed simulations of the collapse of a 10 and 0.1 solar mass cloud, which showed the properties of the first core to be independent of the initial cloud mass, with again no major differences between grey and multigroup models. For Larson's first collapse, where temperatures remain below 2000 K, the vast majority of the radiation energy lies in the IR regime and the system is optically thick. In this regime, the grey approximation does a good job reproducing the correct opacities, as long as there are no large opacity variations on scales much smaller than the width of the Planck function. The multigroup method is however expected to yield more important differences in the later stages of the collapse when high energy (UV and X-ray) radiation is present and matter and radiation are strongly decoupled.Comment: 9 pages, 5 figures, accepted for publication in A&

Проблеми інноваційного розвитку підприємств вугільної галузі України

Метою статті є визначення проблем інноваційного розвитку вугільної галузі та напрями його забезпечення шляхом упровадження інновацій

Porosity and density of spark-processed silicon

Abstract Spark-processed Si (sp-Si) is a porous solid-state material. Due to the nature of its structure and morphology, the traditional methods for porosity measurements cannot be utilized. Using the measure theory and the expected value theorems of stereology, we have calculated the porosity of sp-Si to be 43%. Stereological analysis was applied to sp-Si specimen, prepared within a fixed set of growth parameters. Over 60 cross-sectional scanning electron micrographs of the specimen were utilized in this work. The sp-Si sample has a characteristic cylindrical symmetry due to the uniform surface resistance of the Si substrate and to the random nature of spark processing. However, sp-Si is not isotropic, uniform and random (IUR), exhibiting radial and axial anisotropy of porosity. To avoid bias in the calculation, we chose random areas of the cross-sectional surface of sp-Si and calculated their porosities. The calculated values entered into a weighted statistical distribution, in which the statistical weights were determined from the symmetry properties of the sample. The statistical approach and the fact that volume is an additive quantity, allowed us to use a two-dimensional population of points in the calculation of the three-dimensional pore volume fraction and to satisfy the requirement for IUR sample. In the course of the present work we examined fourteen sp-Si samples, prepared under different processing conditions. Ten of these samples were studied qualitatively by measuring the area of the pores relative to the total area in a cross-sectional cut of the sample. Four samples were studied quantitatively using the stereological method outlined above and exhibited porosities in the neighborhood of 43%. One of these studies is described in detail in the present paper and provides a consistent value for the porosity of sp-Si materials, processed in air. Small-spot X-ray photoelectron spectroscopy studies of sp-Si were used in the calculation of its density. In the case of inhomogeneous materials, the density is a weighted (with respect to volume) average of the densities of all participating phases. Taking into account the already calculated porosity, we have estimated the density of sp-Si to be 1.36 g/cm 3 . The main contribution to this value comes from amorphous SiO 2 , which occupies most of the volume of sp-Si