A model for simultaneous and coupled diffusion and precipitation of chemical elements in metallic matrices is proposed, together with a scheme for its numerical solution and some applications to problems of internal oxidation. This model extends over a previous one of the authors, which itself stood as a generalization of many earlier ones. It includes the possibility that precipitates may be present in large fractions; if so, they may affect diffusion in the matrix phase by acting as ''barriers'', and/or by distorting this matrix. The possible re-dissolution of some or all precipitates may also be prohibited for kinetic reasons. A simple but robust numerical scheme based on 1D finite differences in space coupled with explicit integration in time is proposed to solve the equations of the problem. This scheme notably contains an efficient Newton-Raphson algorithm used to solve the laws of mass action. Numerical simulations of internal oxidation processes close to those encountered in actual industrial practice are finally presented. It is first shown that in simple cases, the simulations reproduce Wagner's classical analytical solution and related ones. More complex cases not amenable to analytic solutions are then envisaged.

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This paper presents a modelling framework for the Incremental Risk Charge (IRC) and Comprehensive Risk Measure (CRM) as the new capital requirements for market risks in a bank's trading book (‘Basel 2.5’). Both are Value‐at‐Risk‐type measures projecting losses over a one‐year capital horizon at a 99.9% confidence level and are applicable to credit flow and credit correlation instruments, respectively. With no consensus on industry standards for suitable internal models as yet, the article discusses selected risk factor models to derive simulation‐based loss distributions and the associated risk figures. Example calculations and implementation aspects complement the discussion.