Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

Shallow water equations: Magic and limitations

D Liang from Cambridge University explains the shallow water equations and their applications to the dam-break and other steep-fronted flow modeling. They assume that the horizontal scale of the flow is much greater than the vertical scale, which means the flow is restricted within a thin layer, thus the vertical momentum is insignificant and the pressure distribution is hydrostatic. The left hand sides of the two momentum equations represent the acceleration of the fluid particle in the horizontal plane. If the fluid acceleration is ignored, then the two momentum equations are simplified into the so-called diffusion wave equations. In contrast to the SWEs approach, it is much less convenient to model floods with the Navier-Stokes equations. In conventional computational fluid dynamics (CFD), cumbersome treatments are needed to accurately capture the shape of the free surface. The SWEs are derived using the assumptions of small vertical velocity component, smooth water surface, gradual variation and hydrostatic pressure distribution.

Accelerator-induced transients in Accelerator Driven Subcritical Reactors

Achieving higher particles energies and beam powers have long been the main focus of research in accelerator technology. Since Accelerator Driven Subcritical Reactors (ADSRs) have become the subject of increasing interest, accelerator reliability and modes of operation have become important matters that require further research and development in order to accommodate the engineering and economic needs of ADSRs. This paper focuses on neutronic and thermo-mechanical analyses of accelerator-induced transients in an ADSR. Such transients fall into three main categories: beam interruptions (trips), pulsed-beam operation, and beam overpower. The concept of a multiple-target ADSR is shown to increase system reliability and to mitigate the negative effects of beam interruptions, such as thermal cyclic fatigue in the fuel cladding and the huge financial cost of total power loss. This work also demonstrates the effectiveness of the temperature-to-reactivity feedback mechanisms in ADSRs. A comparison of shutdown mechanisms using control rods and beam cut-off highlights the intrinsic safety features of ADSRs. It is evident that the presence of control rods is crucial in an industrial-scale ADSR. This paper also proposes a method to monitor core reactivity online using the repetitive pattern of beam current fluctuations in a pulsed-beam operation mode. Results were produced using PTS-ADS, a computer code developed specifically to study the dynamic neutronic and thermal responses to beam transients in subcritical reactor systems. © 2012 Elsevier B.V.

Development of realistic liquid equations of state for multi-phase CFD modelling

Several equations of state (EOS) have been incorporated into a novel algorithm to solve a system of multi-phase equations in which all phases are assumed to be compressible to varying degrees. The EOSs are used to both supply functional relationships to couple the conservative variables to the primitive variables and to calculate accurately thermodynamic quantities of interest, such as the speed of sound. Each EOS has a defined balance of accuracy, robustness and computational speed; selection of an appropriate EOS is generally problem-dependent. This work employs an AUSM+-up method for accurate discretisation of the convective flux terms with modified low-Mach number dissipation for added robustness of the solver. In this paper we show a newly-developed time-marching formulation for temporal discretisation of the governing equations with incorporated time-dependent source terms, as well as considering the system of eigenvalues that render the governing equations hyperbolic.

Ultra-thin 242mAm fuel elements in nuclear reactors

There is a growing interest in using 242mAm as a nuclear fuel. The advantages of 242mAm as a nuclear fuel derive from the fact that 242mAm has the highest thermal fission cross section. The thermal capture cross section is relatively low and the number of neutrons per thermal fission is high. These nuclear properties make it possible to obtain nuclear criticality with ultra-thin fuel elements. The possibility of having ultra-thin fuel elements enables the use of these fission products directly, without the necessity of converting their energy to heat, as is done in conventional reactors. There are three options of using such highly energetic and highly ionized fission products. 1. Using the fission products themselves for ionic propulsion. 2. Using the fission products in an MHD generator, in order to obtain electricity directly. 3. Using the fission products to heat a gas up to a high temperature for propulsion purposes. In this work, we are not dealing with a specific reactor design, but only calculating the minimal fuel elements' thickness and the energy of the fission products emerging from these fuel elements. It was found that it is possible to design a nuclear reactor with a fuel element of less than 1 μm of 242mAm. In such a fuel element, 90% of the fission products' energy can escape.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.