Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

Critical discontinuous phase transition in the threshold contact process

We analyze a threshold contact process on a square lattice in which particles are created on empty sites with at least two neighboring particles and are annihilated spontaneously. We show by means of Monte Carlo simulations that the process undergoes a discontinuous phase transition at a definite value of the annihilation parameter, in accordance with the Gibbs phase rule, and that the discontinuous transition exhibits critical behavior. The simulations were performed by using boundary conditions in which the sites of the border of the lattice are permanently occupied by particles.

Conformational behavior of different possible ways of oligoglycine formation in a solvent-free environment

The possible ways for glycine oligopeptide formation in gas phase, both in the extended P-strand like conformation and folded 2(7)-ribbon like conformations are analyzed using quantum chemical calculations. We focus on the sequential formation of peptide bond through upgradation of the immediate lower order molecule and observe the consequences in other related processes like oligoglycine formation through simultaneous peptide linkage of n glycine monomers and interchange of molecular conformation through peptide linkage. A comparison is made between the structures and binding energies obtained for both conformers. All binding energies are increased by the zero-point energy contribution. The role of electron correlation effects is briefly analyzed. The folded 2(7)-ribbon-like conformations in vacuo are found to be more stable in comparison to the extended structure. (c) 2007 Elsevier B.V. All rights reserved.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Accurate and Precise Zinc Isotope Ratio Measurements in Urban Aerosols

We developed an analytical method and constrained procedural boundary conditions that enable accurate and precise Zn isotope ratio measurements in urban aerosols. We also demonstrate the potential of this new isotope system for air pollutant source tracing. The procedural blank is around 5 ng and significantly lower than published methods due to a tailored ion chromatographic separation. Accurate mass bias correction using external correction with Cu is limited to Zn sample content of approximately 50 ng due to the combined effect of blank contribution of Cu and Zn from the ion exchange procedure and the need to maintain a Cu/Zn ratio of approximately 1. Mass bias is corrected for by applying the common analyte internal standardization method approach. Comparison with other mass bias correction methods demonstrates the accuracy of the method. The average precision of delta(66)Zn determinations in aerosols is around 0.05% per atomic mass unit. The method was tested on aerosols collected in Sin Paulo City, Brazil. The measurements reveal significant variations in delta(66)Zn(Imperial) ranging between -0.96 and -0.37% in coarse and between -1.04 and 0.02% in fine particular matter. This variability suggests that Zn isotopic compositions distinguish atmospheric sources. The isotopic light signature suggests traffic as the main source. We present further delta(66)Zn(Imperial) data for the standard reference material NIST SRM 2783 (delta 66Z(Imperial) = 0.26 +/- 0.10%).

Six-Day System Test and Component test and System Simulation for Combitanks with Internal heat Exchangers

An international standard, ISO/DP 9459-4 has been proposed to establish a uniform standard of quality for small, factory-made solar heating systerns. In this proposal, system components are tested separatelyand total system performance is calculated using system simulations based on component model parameter values validated using the results from the component tests. Another approach is to test the whole system in operation under representative conditions, where the results can be used as a measure of the general system performance. The advantage of system testing of this form is that it is not dependent on simulations and the possible inaccuracies of the models. Its disadvantage is that it is restricted to the boundary conditions for the test. Component testing and system simulation is flexible, but requires an accurate and reliable simulation model.The heat store is a key component conceming system performance. Thus, this work focuses on the storage system consisting store, electrical auxiliary heater, heat exchangers and tempering valve. Four different storage system configurations with a volume of 750 litre were tested in an indoor system test using a six -day test sequence. A store component test and system simulation was carried out on one of the four configurations, applying the proposed standard for stores, ISO/DP 9459-4A. Three newly developed test sequences for intemalload side heat exchangers, not in the proposed ISO standard, were also carried out. The MULTIPORT store model was used for this work. This paper discusses the results of the indoor system test, the store component test, the validation of the store model parameter values and the system simulations.

Techno-economic Appraisal of Concentrating Solar Power Systems (CSP)

The diffusion of Concentrating Solar Power Systems (CSP) systems is currently taking place at a much slower pace than photovoltaic (PV) power systems. This is mainly because of the higher present cost of the solar thermal power plants, but also for the time that is needed in order to build them. Though economic attractiveness of different Concentrating technologies varies, still PV power dominates the market. The price of CSP is expected to drop significantly in the near future and wide spread installation of them will follow. The main aim of this project is the creation of different relevant case studies on solar thermal power generation and a comparison betwwen them. The purpose of this detailed comparison is the techno-economic appraisal of a number of CSP systems and the understanding of their behaviour under various boundary conditions. The CSP technologies which will be examined are the Parabolic Trough, the Molten Salt Power Tower, the Linear Fresnel Mirrors and the Dish Stirling. These systems will be appropriatly sized and simulated. All of the simulations aim in the optimization of the particular system. This includes two main issues. The first is the achievement of the lowest possible levelized cost of electricity and the second is the maximization of the annual energy output (kWh). The project also aims in the specification of these factors which affect more the results and more specifically, in what they contribute to the cost reduction or the power generation. Also, photovoltaic systems will be simulated under same boundary conditions to facolitate a comparison between the PV and the CSP systems. Last but not leats, there will be a determination of the system which performs better in each case study.

Replacing Finned Copper withCorrugated Stainless Steel, forthe Heat Exchangers of a SolarCombisystem Store : Performance and EconomicEvaluation

The importance of investigating cost reduction in materials and components for solar thermal systems is crucial at the present time. This work focuses on the influence of two different heat exchangers on the performance of a solar thermal system. Both heat exchangers studied are immersed helically coiled, one made with corrugated stainless steel tube, and the other made with finned copper tube with smooth inner surface.A test apparatus has been designed and a simple test procedure applied in order to study heat transfer characteristics and pressure drop of both coils. Thereafter, the resulting experimental data was used to perform a parameter identification of the heat exchangers, in order to obtain a TRNSYS model with its corresponding numerical expression. Also a representative small-scale combisystem model was designed in TRNSYS, in order to study the influence of both heat exchangers on the solar fraction of the system, when working at different flow rates.It has been found that the highest solar fraction is given by the corrugated stainless steel coil, when it works at the lowest flow rate (100 l/hr). For any higher flow rate, the studied copper coil presents a higher solar fraction. The advantageous low flow performance of stainless steel heat exchanger turns out to be beneficial for the particular case of solar thermal systems, where it is well known that low flow collector loops lead to enhanced store stratification, and consequently higher solar fractions.Finally, an optimization of the stainless steel heat exchanger length is carried out, according to economic figures. For the given combisystem model and boundary conditions, the optimum length value is found between 10 and 12 m.

Influence of hydraulics and control of thermal storage in solar assisted heat pump combisystems

This paper studies the influence of hydraulics and control of thermal storage in systems combined with solar thermal and heat pump for the production of warm water and space heating in dwellings. A reference air source heat pump system with flat plate collectors connected to a combistore was defined and modeled together with the IEA SHC Task 44 / HPP Annex 38 (T44A38) “Solar and Heat Pump Systems” boundary conditions of Strasbourg climate and SFH45 building. Three and four pipe connections as well as use of internal and external heat exchangers for DHW preparation were investigated as well as sensor height for charging of the DHW zone in the store. The temperature in this zone was varied to ensure the same DHW comfort was achieved in all cases. The results show that the four pipe connection results in 9% improvement in SPF compared to three pipe and that the external heat exchanger for DHW preparation leads to a 2% improvement compared to the reference case. Additionally the sensor height for charging the DHW zone of the store should not be too low, otherwise system performance is adversely affected

Testing of combined heating systems for small houses: Improved procedures for whole system test methods : Deliverable 2.3

Dynamic system test methods for heating systems were developed and applied by the institutes SERC and SP from Sweden, INES from France and SPF from Switzerland already before the MacSheep project started. These test methods followed the same principle: a complete heating system – including heat generators, storage, control etc., is installed on the test rig; the test rig software and hardware simulates and emulates the heat load for space heating and domestic hot water of a single family house, while the unit under test has to act autonomously to cover the heat demand during a representative test cycle. Within the work package 2 of the MacSheep project these similar – but different – test methods were harmonized and improved. The work undertaken includes:  • Harmonization of the physical boundaries of the unit under test. • Harmonization of the boundary conditions of climate and load. • Definition of an approach to reach identical space heat load in combination with an autonomous control of the space heat distribution by the unit under test. • Derivation and validation of new six day and a twelve day test profiles for direct extrapolation of test results.   The new harmonized test method combines the advantages of the different methods that existed before the MacSheep project. The new method is a benchmark test, which means that the load for space heating and domestic hot water preparation will be identical for all tested systems, and that the result is representative for the performance of the system over a whole year. Thus, no modelling and simulation of the tested system is needed in order to obtain the benchmark results for a yearly cycle. The method is thus also applicable to products for which simulation models are not available yet. Some of the advantages of the new whole system test method and performance rating compared to the testing and energy rating of single components are:  • Interaction between the different components of a heating system, e.g. storage, solar collector circuit, heat pump, control, etc. are included and evaluated in this test. • Dynamic effects are included and influence the result just as they influence the annual performance in the field. • Heat losses are influencing the results in a more realistic way, since they are evaluated under "real installed" and representative part-load conditions rather than under single component steady state conditions.   The described method is also suited for the development process of new systems, where it replaces time-consuming and costly field testing with the advantage of a higher accuracy of the measured data (compared to the typically used measurement equipment in field tests) and identical, thus comparable boundary conditions. Thus, the method can be used for system optimization in the test bench under realistic operative conditions, i.e. under relevant operating environment in the lab.   This report describes the physical boundaries of the tested systems, as well as the test procedures and the requirements for both the unit under test and the test facility. The new six day and twelve day test profiles are also described as are the validation results.

Temperature Dynamics Investigation At Small And Shallow Lakes Using Hydrodynamic Model

A three-dimensional time-dependent hydrodynamic and heat transport model of Lake Binaba, a shallow and small dam reservoir in Ghana, emphasizing the simulation of dynamics and thermal structure has been developed. Most numerical studies of temperature dynamics in reservoirs are based on one- or two-dimensional models. These models are not applicable for reservoirs characterized with complex flow pattern and unsteady heat exchange between the atmosphere and water surface. Continuity, momentum and temperature transport equations have been solved. Proper assignment of boundary conditions, especially surface heat fluxes, has been found crucial in simulating the lake’s hydrothermal dynamics. This model is based on the Reynolds Average Navier-Stokes equations, using a Boussinesq approach, with a standard k − ε turbulence closure to solve the flow field. The thermal model includes a heat source term, which takes into account the short wave radiation and also heat convection at the free surface, which is function of air temperatures, wind velocity and stability conditions of atmospheric boundary layer over the water surface. The governing equations of the model have been solved by OpenFOAM; an open source, freely available CFD toolbox. As its core, OpenFOAM has a set of efficient C++ modules that are used to build solvers. It uses collocated, polyhedral numerics that can be applied on unstructured meshes and can be easily extended to run in parallel. A new solver has been developed to solve the hydrothermal model of lake. The simulated temperature was compared against a 15 days field data set. Simulated and measured temperature profiles in the probe locations show reasonable agreement. The model might be able to compute total heat storage of water bodies to estimate evaporation from water surface.

Análise dinâmica de vigas assimétricas em curva com parede fina e aberta submetidas a ação de carga móveis

Fundamentalmente, o presente trabalho faz uma análise elástica linear de pontes ou vigas curvas assimétricas de seção transversal aberta e de parede fina, com propriedades físicas, geométricas e raio de curvatura constantes ao longo do eixo baricêntrico. Para tanto, utilizaram-se as equações diferenciais de VLASOV considerando o acoplamento entre as deformações nas direções vertical, transversal, axial de torcão nal. Na solução do sistema de quatro equações com derivadas parciais foi utilizado um apropriado método numérico de integração (Diferenças Finitas Centrais). A análise divide-se, basicamente, em dois tipos: análise DINÂMICA e ESTATICA. Ambas são utilizadas também na determinação do coeficiente de impacto (C.M.D.). A primeira refere-se tanto na determinação das características dinâmicas básicas (frequências naturais e respectivos modos de vibração), como também na determinação da resposta dinâmica da viga, em tensões e deformações, para cargas móveis arbitrárias. Vigas com qualquer combinação das condições de contorno, incluindo bordos rotulados e engastados nas três direções de flexão e na torção, são consideradas. 0s resultados da análise teórica, obtidos pela aplicação de programas computacionais implementados em microcomputador (análise estática) e no computador B-6700 (análise dinâmica), são comparados tanto com os da bibliografia técnica como também com resultados experimentais, apresentando boa correlação.

Respostas dinâmicas em sistemas distribuídos e decomposição forçada da superfície livre para um modelo acoplado Oceano-Atmosfera

O objetivo deste trabalho é a introdução e desenvolvimento de uma metodologia analítico-simbólica para a obtenção de respostas dinâmicas e forçadas (soluções homogêneas e não homogêneas) de sistemas distribuídos, em domínios ilimitados e limitados, através do uso da base dinâmica gerada a partir da resposta impulso. Em domínios limitados, a resposta impulso foi formulada pelo método espectral. Foram considerados sistemas com condições de contorno homogêneas e não homogêneas. Para sistemas de natureza estável, a resposta forçada é decomposta na soma de uma resposta particular e de uma resposta livre induzida pelos valores iniciais da resposta particular. As respostas particulares, para entradas oscilatórias no tempo, foram calculadas com o uso da fun»c~ao de Green espacial. A teoria é desenvolvida de maneira geral permitindo que diferentes sis- temas evolutivos de ordem arbitrária possam ser tratados sistematicamente de uma forma compacta e simples. Realizou-se simulações simbólicas para a obtenção de respostas dinâmicas e respostas for»cadas com equações do tipo parabólico e hiperbólico em 1D,2D e 3D. O cálculo das respostas forçadas foi realizado com a determinação das respostas livres transientes em termos dos valores iniciais das respostas permanentes. Foi simulada a decomposição da resposta forçada da superfície livre de um modelo acoplado oceano-atmosfera bidimensional, através da resolução de uma equação de Klein-Gordon 2D com termo não-homogêneo de natureza dinâmica, devido a tensão de cisalhamento na superfície do oceano pela ação do vento.

Exploratory semiparametric analysis of two-dimensional diffusions in finance

We examine bivariate extensions of Aït-Sahalia’s approach to the estimation of univariate diffusions. Our message is that extending his idea to a bivariate setting is not straightforward. In higher dimensions, as opposed to the univariate case, the elements of the Itô and Fokker-Planck representations do not coincide; and, even imposing sensible assumptions on the marginal drifts and volatilities is not sufficient to obtain direct generalisations. We develop exploratory estimation and testing procedures, by parametrizing the drifts of both component processes and setting restrictions on the terms of either the Itô or the Fokker-Planck covariance matrices. This may lead to highly nonlinear ordinary differential equations, where the definition of boundary conditions is crucial. For the methods developed, the Fokker-Planck representation seems more tractable than the Itô’s. Questions for further research include the design of regularity conditions on the time series dependence in the data, the kernels actually used and the bandwidths, to obtain asymptotic properties for the estimators proposed. A particular case seems promising: “causal bivariate models” in which only one of the diffusions contributes to the volatility of the other. Hedging strategies which estimate separately the univariate diffusions at stake may thus be improved.

Contributions to the Theory of Optimal Tests

This paper considers tests which maximize the weighted average power (WAP). The focus is on determining WAP tests subject to an uncountable number of equalities and/or inequalities. The unifying theory allows us to obtain tests with correct size, similar tests, and unbiased tests, among others. A WAP test may be randomized and its characterization is not always possible. We show how to approximate the power of the optimal test by sequences of nonrandomized tests. Two alternative approximations are considered. The rst approach considers a sequence of similar tests for an increasing number of boundary conditions. This discretization allows us to implement the WAP tests in practice. The second method nds a sequence of tests which approximate the WAP test uniformly. This approximation allows us to show that WAP similar tests are admissible. The theoretical framework is readily applicable to several econometric models, including the important class of the curved-exponential family. In this paper, we consider the instrumental variable model with heteroskedastic and autocorrelated errors (HAC-IV) and the nearly integrated regressor model. In both models, we nd WAP similar and (locally) unbiased tests which dominate other available tests.