Non-Realist Cognitivism,Truth and Objectivity

In On What Matters, Derek Parfit defends a new metaethical theory, which he calls non-realist cognitivism. It claims that (i) normative judgments are beliefs; (ii) that some normative beliefs are true; (iii) that the normative concepts that are a part of the propositions that are the contents of normative beliefs are irreducible, unanalysable and of their own unique kind; and (iv) that neither the natural features of the reality nor any additional normative features of the reality make the relevant normative beliefs true. The aim of this article is to argue that Parfit’s theory is problematic because its defenders have no resources to make sense of the nature of normative truth, which is an essential element of their view. I do this by showing how the traditional theories of truth are not available for the non-realist cognitivists.     

In situ migration of tritiated water and iodine in Grimsel granodiorite,part II: assessment of the diffusion coefficients by TDD modelling

Diffusive transport of iodine (I) and tritiated water (HTO) in granodiorite is studied in the framework of the long term diffusion project (LTD) at the Grimsel Test Site, Switzerland. In this paper we modelled the tracer profiles measured in a long term (780 days) in situ diffusion test was carried out as part of LTD. The main outcome of the modelling tends to prove that the in situ apparent diffusion coefficients of I and HTO are close to the reference apparent diffusion coefficient determined in the laboratory (D _a = 3 × 10⁻¹⁰ m² s⁻¹).

     

Multi-scale study of the mineral porosity of veined gneiss and pegmatitic granite from Olkiluoto,Western Finland

The purpose of this work was to support the long-term experiments for investigation of rock matrix retention properties at the spent nuclear fuel repository site ONKALO, in Olkiluoto, Western Finland. Towards this end, rock samples were characterised in terms of porosity connected to mineralogy, with emphasis on pore sizes, and fillings. Both filled and unfilled pores were found with unfilled pores being majority in the pegmatitic granite veins of the mostly veined gneiss samples. It was found that the fillings were often connected to local alteration and the alteration caused variation in the range of pore sizes.     

Solutions to and Validation of Matrix-Diffusion Models

A model transport system is considered in which a pulse of tracer molecules is advected along a flow channel with porous walls. The advected tracer thus undergoes diffusion, matrix-diffusion, inside the walls, which affects the breakthrough curve of the tracer. Analytical solutions in the form of series expansions are derived for a number of situations which include a finite depth of the porous matrix, varying aperture of the flow channel, and longitudinal diffusion and Taylor dispersion of the tracer in the flow channel. Novel expansions for the Laplace transforms of the concentration in the channel facilitated closed-form expressions for the solutions. A rigorous result is also derived for the asymptotic form of the breakthrough curve for a finite depth of the porous matrix, which is very different from that for an infinite matrix. A specific experimental system was created for validation of matrix-diffusion modeling for a matrix of finite depth. A previously reported fracture-column experiment was also modeled. In both cases model solutions gave excellent fits to the measured breakthrough curves with very consistent values for the diffusion coefficients used as the fitting parameters. The matrix-diffusion modeling performed could thereby be validated.     

Diffusion of Tracer in Altered Tonalite: Experiments and Simulations with Heterogeneous Distribution of Porosity

Numerical time-domain-diffusion simulations were used for studying the diffusion behavior of tracer molecules in rock matrix with homogeneous and heterogeneous porosity. As the heterogeneous sample in these simulations, a 3D tomographic image of altered tonalite was used, in which the mineral components and the pores resolved by X-ray microtomography were represented by their respective intragranular porosities determined previously by the ¹⁴C-PMMA method. The apparent diffusion coefficient of a tracer in altered tonalite was determined experimentally, and was then used in the simulations. In the altered tonalite analyzed, inclusion of heterogeneity in the porosity increased the diffusion coefficient by 16 %. Altered and pristine feldspar was the main mineral component in the sample (72 %), and it also provided the dominant contribution to tracer diffusion, explaining alone 52 % of the diffusion coefficient. The large pores resolved by microtomography (6 %) and altered and pristine mica (22 %) gave an equal contribution to the diffusion coefficient. The simulation method applied was also validated by comparing the results to both an analytical and a numerical solution to the diffusion equation in a homogenous medium. In addition, the method was compared to discrete-time random-walk simulations in the case of randomly placed overlapping spheres.     

On Kre?n's formula

Kre?n's formula provides a parametrization of the generalized resolvents and Štraus extensions of a closed symmetric operator with equal possibly infinite defect numbers in a Hilbert space in terms of Nevanlinna families in a parameter space. The aim of this note is to give a simple complete analytical proof of Kre?n's formula.