Application of a three-dimensional prognostic model during the ETEX real-time modeling exercise: Evaluation of results

Increases in computing capabilities and ready access to large-scale model output make it possible to employ advanced three-dimensional prognostic models to forecast the long-range transport of toxic or radioactive gases for emergency response. The Savannah River Technology Center (SRTC) of the U.S. Department of Energy`s Savannah River Site demonstrated this during the European Tracer EXperiment (ETEX). ETEX, conducted in the Fall of 1994, provided an opportunity to evaluate the performance of models for long-range atmospheric pollutant transport and dispersion. A comparison of SRTC forecast results for the first ETEX experiment with measured surface tracer gas concentrations shows that the predicted plume is transported too quickly and surface concentrations are low. However, modeling studies show that the forecast performance is significantly improved if convective parameterization is not employed

Development of a three-dimensional two-fluid code with transient neutronic feedback for LWR applications

The development of a three-dimensional coupled neutronics/thermalhydraulics code for LWR safety analysis has been initiated. The transient neutronics code QUANDRY has been joined to the two-fluid thermal-hydraulics code THERMIT with the appropriate feedback mechanisms modeled. A literature review of the existing coupled neutronics/thermal-hydraulics codes is presented. It indicates that all of the known codes have limitations in their neutronic and/or thermal-hydraulic models which limit their generality of application and accuracy. It was also found that a tandem coupling scheme was most often employed and generally performed well. A detailed steady-state and transient coupling scheme based on the tandem technique was devised, taking into account the important operational characteristics of QUANDRY and THERMIT. The two codes were combined and the necessary programming modifications were performed to allow steady-state calculations with feedback. A simple steady-state sample problem was produced for the purpose of testing and debugging the coupled code

Q2Q_2-free families in the Boolean lattice

For a family $\mathcal{F}$ of subsets of [n]=\{1, 2, ..., n} ordered by inclusion, and a partially ordered set P, we say that $\mathcal{F}$ is P-free if it does not contain a subposet isomorphic to P. Let $ex(n, P)$ be the largest size of a P-free family of subsets of [n]. Let $Q_2$ be the poset with distinct elements a, b, c, d, a<b, c<d; i.e., the 2-dimensional Boolean lattice. We show that $2N -o(N) \leq ex(n, Q_2)\leq 2.283261N +o(N),$ where $N = \binom{n}{\lfloor n/2 \rfloor}$. We also prove that the largest $Q_2$-free family of subsets of [n] having at most three different sizes has at most 2.20711N members.Comment: 18 pages, 2 figure

Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\Omega\left( \frac{n \log h}{\log \log h}\right)}$. This rules out the existence of a single-exponential algorithm and shows that the trivial upper bound $2^{{\mathcal O}(n\log{h})}$ is almost asymptotically tight. We also investigate what properties of graphs $G$ and $H$ make it difficult to solve HOM$(G,H)$. An easy observation is that an ${\mathcal O}(h^n)$ upper bound can be improved to ${\mathcal O}(h^{\operatorname{vc}(G)})$ where $\operatorname{vc}(G)$ is the minimum size of a vertex cover of $G$. The second lower bound $h^{\Omega(\operatorname{vc}(G))}$ shows that the upper bound is asymptotically tight. As to the properties of the "right-hand side" graph $H$, it is known that HOM$(G,H)$ can be solved in time $(f(\Delta(H)))^n$ and $(f(\operatorname{tw}(H)))^n$ where $\Delta(H)$ is the maximum degree of $H$ and $\operatorname{tw}(H)$ is the treewidth of $H$. This gives single-exponential algorithms for graphs of bounded maximum degree or bounded treewidth. Since the chromatic number $\chi(H)$ does not exceed $\operatorname{tw}(H)$ and $\Delta(H)+1$, it is natural to ask whether similar upper bounds with respect to $\chi(H)$ can be obtained. We provide a negative answer to this question by establishing a lower bound $(f(\chi(H)))^n$ for any function $f$. We also observe that similar lower bounds can be obtained for locally injective homomorphisms.Comment: 19 page

Mapping interactions between the sustainable development goals: lessons learned and ways forward

Pursuing integrated research and decision-making to advance action on the sustainable development goals (SDGs) fundamentally depends on understanding interactions between the SDGs, both negative ones (“trade-offs”) and positive ones (“co-benefits”). This quest, triggered by the 2030 Agenda, has however pointed to a gap in current research and policy analysis regarding how to think systematically about interactions across the SDGs. This paper synthesizes experiences and insights from the application of a new conceptual framework for mapping and assessing SDG interactions using a defined typology and characterization approach. Drawing on results from a major international research study applied to the SDGs on health, energy and the ocean, it analyses how interactions depend on key factors such as geographical context, resource endowments, time horizon and governance. The paper discusses the future potential, barriers and opportunities for applying the approach in scientific research, in policy making and in bridging the two through a global SDG Interactions Knowledge Platform as a key mechanism for assembling, systematizing and aggregating knowledge on interactions

Methods development for LWR transient analysis

The initial development of TITAN, a three-dimensional coupled neutronics/thermal-hydraulics code for LWR safety analysis, has been completed. The transient neutronics code QUANDRY has been joined to the two-fluid thermal-hydraulics code THERMIT with the appropriate feedback mechanisms modeled. A detailed steady-state and transient coupling scheme based on the tandem technique was implemented in accordance with the important structural and operational characteristics of QUANDRY and THERMIT. A two channel sample problem formed the basis for steady-state and transient analyses performed with TITAN. TITAN steady-state results were compared with those obtained with MEKIN and showed good agreement. A fuel pin model sensitivity study was performed for steady-state problems. Null transients, simulated turbine trip transients, and a rod withdrawal transient were analyzed with TITAN and reasonable results were obtained

Advanced three dimensional coupled neutronic/thermal-hydraulics code

The accurate analysis of nuclear reactor transients frequently requires that neutronics, thermal-hydraulics and feedback be included. A number of coupled neutronics/thermal-hydraulics codes have been developed for this purpose. Of these, only a few combine three-dimensional neutronics and thermal-hydraulics, and these are either not generally available or too expensive for many applications of interest. Therefore, TITAN, a coupled code combining state-of-the-art three-dimensional neutronics and thermal-hydraulics models, was developed and tested.The three-dimensional nodal neutronics code QUANDRY and the threedimensional two-fluid thermal-hydraulics code THERMIT are combined into TITAN. Steady-state and transient coupling methodologies based upon a tandem structure were devised and implemented. Additional models for nuclear feedback, equilibrium xenon and direct moderator heating were added. TITAN was tested using a boiling water two channel problem and the coupling methodologies were shown to be effective. Simulated turbine trip transients and several control rod withdrawal transients were analyzed with good results. Sensitivity studies indicated that the time-step size can affect transient results significantly.TITAN was also applied to a quarter core PWR problem based on a real reactor geometry. The steady-state results were compared to a solution produced by MEKIN-B and poor agreement between the horizontal power shapes was found. Calculations with various mesh spacings showed that the mesh spacings in the MEKIN-B analysis were too large to produce accurate results with a finite difference method. The TITAN results were shown to be reasonable. A pair of control rod ejection accidents were also analyzed with TITAN.The computing time requirements for these analyses were less than 1 hour c.p.u. time on a large mainframe computer. This is reasonable for a severe transient in a large reactor.A comparison of the TITAN PWR control rod ejection results with results from coupled point kinetics/thermal-hydraulics analyses showed that the point kinetics method used (adiabatic method for contol rod reactivities, steady-state flux shape for core-averaged reactivity feedback) underpredicted the power excursion in one case and overpredicted it in the other. It was therefore concluded that point kinetics methods should be used with caution and that three-dimensional codes like TITAN are superior for analyzing PWR control rod ejection transients

The perceived barriers to the inclusion of rainwater harvesting systems by UK house building companies

This work investigates the barriers that exist to deter the implementation of rainwater harvesting into new UK housing. A postal questionnaire was sent to a selection of large, medium and small house-builders distributed across the UK. Questions were asked concerning potential barriers to the inclusion of rainwater harvesting in homes separated into five sections; (1) institutional and regulatory gaps, (2) economic and financial constraints, (3) absence of incentives, (4) lack of information and technical knowledge, and (5) house-builder attitudes. The study concludes that although the knowledge of rainwater systems has increased these barriers are deterring house-builders from installing rainwater harvesting systems in new homes. It is further acknowledged that the implementation of rainwater harvesting will continue to be limited whilst these barriers remain and unless resolved, rainwater harvesting's potential to reduce the consumption of potable water in houses will continue to be limited