Comparison among MCNP-based depletion codes applied to burnup calculations of pebble-bed HTR lattices

The double-heterogeneity characterising pebble-bed high temperature reactors (HTRs) makes Monte Carlo based calculation tools the most suitable for detailed core analyses. These codes can be successfully used to predict the isotopic evolution during irradiation of the fuel of this kind of cores. At the moment, there are many computational systems based on MCNP that are available for performing depletion calculation. All these systems use MCNP to supply problem dependent fluxes and/or microscopic cross sections to the depletion module. This latter then calculates the isotopic evolution of the fuel resolving Bateman's equations. In this paper, a comparative analysis of three different MCNP-based depletion codes is performed: Montburns2.0, MCNPX2.6.0 and BGCore. Monteburns code can be considered as the reference code for HTR calculations, since it has been already verified during HTR-N and HTR-N1 EU project. All calculations have been performed on a reference model representing an infinite lattice of thorium-plutonium fuelled pebbles. The evolution of k-inf as a function of burnup has been compared, as well as the inventory of the important actinides. The k-inf comparison among the codes shows a good agreement during the entire burnup history with the maximum difference lower than 1%. The actinide inventory prediction agrees well. However significant discrepancy in Am and Cm concentrations calculated by MCNPX as compared to those of Monteburns and BGCore has been observed. This is mainly due to different Am-241 (n,γ) branching ratio utilized by the codes. The important advantage of BGCore is its significantly lower execution time required to perform considered depletion calculations. While providing reasonably accurate results BGCore runs depletion problem about two times faster than Monteburns and two to five times faster than MCNPX. © 2009 Elsevier B.V. All rights reserved.

Efficient generation of one-group cross sections for coupled Monte Carlo depletion calculations

Coupled Monte Carlo depletion systems provide a versatile and an accurate tool for analyzing advanced thermal and fast reactor designs for a variety of fuel compositions and geometries. The main drawback of Monte Carlo-based systems is a long calculation time imposing significant restrictions on the complexity and amount of design-oriented calculations. This paper presents an alternative approach to interfacing the Monte Carlo and depletion modules aimed at addressing this problem. The main idea is to calculate the one-group cross sections for all relevant isotopes required by the depletion module in a separate module external to Monte Carlo calculations. Thus, the Monte Carlo module will produce the criticality and neutron spectrum only, without tallying of the individual isotope reaction rates. The onegroup cross section for all isotopes will be generated in a separate module by collapsing a universal multigroup (MG) cross-section library using the Monte Carlo calculated flux. Here, the term "universal" means that a single MG cross-section set will be applicable for all reactor systems and is independent of reactor characteristics such as a neutron spectrum; fuel composition; and fuel cell, assembly, and core geometries. This approach was originally proposed by Haeck et al. and implemented in the ALEPH code. Implementation of the proposed approach to Monte Carlo burnup interfacing was carried out through the BGCORE system. One-group cross sections generated by the BGCORE system were compared with those tallied directly by the MCNP code. Analysis of this comparison was carried out and led to the conclusion that in order to achieve the accuracy required for a reliable core and fuel cycle analysis, accounting for the background cross section (σ0) in the unresolved resonance energy region is essential. An extension of the one-group cross-section generation model was implemented and tested by tabulating and interpolating by a simplified σ0 model. A significant improvement of the one-group cross-section accuracy was demonstrated.

The stochastic implicit Euler method - A stable coupling scheme for Monte Carlo burnup calculations

Existing Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the coupling schemes of the existing Monte Carlo burnup codes can be numerically unstable. Here we develop the Stochastic Implicit Euler method - a stable and efficient new coupling scheme. The implicit solution is obtained by the stochastic approximation at each time step. Our test calculations demonstrate that the Stochastic Implicit Euler method can provide an accurate solution to problems where the methods in the existing Monte Carlo burnup codes fail. © 2013 Elsevier Ltd. All rights reserved.

Growth of straight InAs-on-GaAs nanowire heterostructures.

One of the main motivations for the great interest in semiconductor nanowires is the possibility of easily growing advanced heterostructures that might be difficult or even impossible to achieve in thin films. For III-V semiconductor nanowires, axial heterostructures with an interchange of the group III element typically grow straight in only one interface direction. In the case of InAs-GaAs heterostructures, straight nanowire growth has been demonstrated for growth of GaAs on top of InAs, but so far never in the other direction. In this article, we demonstrate the growth of straight axial heterostructures of InAs on top of GaAs. The heterostructure interface is sharp and we observe a dependence on growth parameters closely related to crystal structure as well as a diameter dependence on straight nanowire growth. The results are discussed by means of accurate first principles calculations of the interfacial energies. In addition, the role of the gold seed particle, the effect of its composition at different stages during growth, and its size are discussed in relation to the results observed.

Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

Between scylla and charybdis: Hydrophobic graphene-guided water diffusion on hydrophilic substrates

The structure of water confined in nanometer-sized cavities is important because, at this scale, a large fraction of hydrogen bonds can be perturbed by interaction with the confining walls. Unusual fluidity properties can thus be expected in the narrow pores, leading to new phenomena like the enhanced fluidity reported in carbon nanotubes. Crystalline mica and amorphous silicon dioxide are hydrophilic substrates that strongly adsorb water. Graphene, on the other hand, interacts weakly with water. This presents the question as to what determines the structure and diffusivity of water when intercalated between hydrophilic substrates and hydrophobic graphene. Using atomic force microscopy, we have found that while the hydrophilic substrates determine the structure of water near its surface, graphene guides its diffusion, favouring growth of intercalated water domains along the C-C bond zigzag direction. Molecular dynamics and density functional calculations are provided to help understand the highly anisotropic water stripe patterns observed.

Climb-enabled discrete dislocation plasticity

A small strain two-dimensional discrete dislocation plasticity framework coupled to vacancy diffusion is developed wherein the motion of edge dislocations is by a combination of glide and climb. The dislocations are modelled as line defects in a linear elastic medium and the mechanical boundary value problem is solved by the superposition of the infinite medium elastic fields of the dislocations and a complimentary non-singular solution that enforces the boundary conditions. Similarly, the climbing dislocations are modelled as line sources/sinks of vacancies and the vacancy diffusion boundary value problem is also solved by a superposition of the fields of the line sources/sinks in an infinite medium and a complementary non-singular solution that enforces the boundary conditions. The vacancy concentration field along with the stress field provides the climb rate of the dislocations. Other short-range interactions of the dislocations are incorporated via a set of constitutive rules. We first employ this formulation to investigate the climb of a single edge dislocation in an infinite medium and illustrate the existence of diffusion-limited and sink-limited climb regimes. Next, results are presented for the pure bending and uniaxial tension of single crystals oriented for single slip. These calculations show that plasticity size effects are reduced when dislocation climb is permitted. Finally, we contrast predictions of this coupled framework with an ad hoc model in which dislocation climb is modelled by a drag-type relation based on a quasi steady-state solution. © 2013 Elsevier Ltd. All rights reserved.

First-principles energetics of water clusters and ice: a many-body analysis.

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.

The Random Forest Kernel and other kernels for big data from random partitions

We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random Forest. To demonstrate the potential of this method, we propose two new kernels, the Random Forest Kernel and the Fast Cluster Kernel, and show that these kernels consistently outperform standard kernels on problems involving real-world datasets. Finally, we show how the form of these kernels lend themselves to a natural approximation that is appropriate for certain big data problems, allowing $O(N)$ inference in methods such as Gaussian Processes, Support Vector Machines and Kernel PCA.