A Bayesian Approach to the Estimation of Parameters and Their Interdependencies in Environmental Modeling

We present a case study for Bayesian analysis and proper representation of distributions and dependence among parameters when calibrating process-oriented environmental models. A simple water quality model for the Elbe River (Germany) is referred to as an example, but the approach is applicable to a wide range of environmental models with time-series output. Model parameters are estimated by Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling. While the best-fit solution matches usual least-squares model calibration (with a penalty term for excessive parameter values), the Bayesian approach has the advantage of yielding a joint probability distribution for parameters. This posterior distribution encompasses all possible parameter combinations that produce a simulation output that fits observed data within measurement and modeling uncertainty. Bayesian inference further permits the introduction of prior knowledge, e.g., positivity of certain parameters. The estimated distribution shows to which extent model parameters are controlled by observations through the process of inference, highlighting issues that cannot be settled unless more information becomes available. An interactive interface enables tracking for how ranges of parameter values that are consistent with observations change during the process of a step-by-step assignment of fixed parameter values. Based on an initial analysis of the posterior via an undirected Gaussian graphical model, a directed Bayesian network (BN) is constructed. The BN transparently conveys information on the interdependence of parameters after calibration. Finally, a strategy to reduce the number of expensive model runs in MCMC sampling for the presented purpose is introduced based on a newly developed variant of delayed acceptance sampling with a Gaussian process surrogate and linear dimensionality reduction to support function-valued outputs.     

Aspects of Frequentism

Some aspects of the Frequentist approach to statistical data analysis are presented and discussed. The construction of confidence intervals for parameters is explained and made concrete with a detailed example. The intervals correspond to parameter ranges where the observed data is in a ‘favored’ part of the expected results distribution. Goodness‐of‐fit tests are defined similarly; here, a Bayesian argument is given for the usefulness of these tests. The possible over‐interpretation of Frequentist results is also discussed.     

A normalised residence time transport equation for the numerical simulation of combustion with high-temperature air

This study concerns the numerical simulation of turbulent non-premixed combustion in highly preheated air streams. One of the objectives is to settle an efficient computational procedure to proceed with the numerical simulation of large-scale industrial devices. It is also expected that the availability of such a computational framework may facilitate comprehensive sensitivity analyses as well as the development of mathematical models able to represent turbulence-chemistry interactions (TCI) in such conditions. Based on the salient physical ingredients that characterise scalar mixing, propagation, and self-ignition processes, a turbulent combustion modelling framework is thus introduced and applied to the numerical simulation of well-documented laboratory flames. In the corresponding geometries, the bulk flow velocities of the reactants streams can reach rather large values, which lead the flame to lift from the burner rim. Partially premixed flame edges thus stabilise the whole flame structure and the temperature of the oxidising stream can be increased by vitiation with burned gases so as to promote the corresponding flame-stabilisation processes. For sufficiently large values of the vitiated airstream temperature, self-ignition mechanisms may be triggered thus leading to a competition between mixing, propagation, and ignition processes. In this context, the ratio of the residence time to the self-ignition delay is thought to be a relevant variable to delineate the possible influence of ignition phenomena. Therefore, a modelled transport equation for this normalised residence time is considered. The performance of the corresponding modelling proposal is analysed with special emphasis placed on its ability to reproduce ‘memory’ or ‘lagrangian’ effects related to thermal aging processes. In this respect, it is noteworthy that the present set of computations makes use of tabulated quantities associated to (i) steady laminar one-dimensional diffusion flamelets, so as to describe the composition of combustion products, (ii) steady laminar one-dimensional premixed flamelets, to describe the flame brush propagation, and (iii) temporal evolution of zero-dimensional homogeneous mixtures to account for the possible occurrence of self-ignition phenomena. In particular, the tabulated self-ignition time value is used to evaluate the increase in the normalised residence time. Finally, two modelling parameters are put into evidence and studied through a detailed sensitivity analysis.     

Effect of Co-flowing Vapor during Vertical Falling-film Evaporation

A large number of industrial processes use falling-film evaporation to concentrate liquid products. This technology allows for small temperature differences during operation and is often significantly more energy efficient than other techniques. When processing dairy products, a reduction in the solvent fraction results in an increased product viscosity and may thus result in non-Newtonian features. The interaction between a co-flowing vapor that is produced during the evaporation process and the falling film is an important feature of the process. Few studies have accurately studied the effect of co-flow on evaporative falling films at high solid contents. In this work, an experimental study of the influence of co-flowing vapor on the heat transfer coefficient for a dairy product is presented as a function of both the solid content (from 10 to 50%) and the mass flow rate of the feed. The experimental set-up, consisting of a unique industrial pilot-scale evaporator, provides the possibility of obtaining results useful for realistic industrial conditions. An analytical approach that enables the simultaneous evaluation of heat transfer in every experimental condition, e.g., for Newtonian or non-Newtonian fluids and with or without co-flowing vapors, is presented.     

On the computation of steady Hopper flows: II: von Mises materials in various geometries

Similarity solutions are constructed for the flow of granular materials through hoppers. Unlike previous work, the present approach applies to nonaxisymmetric containers. The model involves ten unknowns (stresses, velocity, and plasticity function) determined by nine nonlinear first order partial differential equations together with a quadratic algebraic constraint (yield condition). A pseudospectral discretization is applied; the resulting problem is solved with a trust region method. The important role of the hopper geometry on the flow is illustrated by several numerical experiments of industrial relevance.     

The Characterisation of the Flow of Aerated Powders

This paper reviews the development of a new annular shear cell for the characterisation of aerated powders. The cell enables the measurement of the transmitted shear stress at degrees of aeration below fluidisation. Results are presented for three powders, Alumina, Phosphate Rock and Sodium Carbonate. These show a large reduction in shear stress for small quantities of air entrainment and a transition from normal coulomb-solid flow to liquid-type flow at high shear rates. This characterisation enables an explanation of the flooding phenomena experienced in powder handling processes.     

Measurement of pulsatile flow using MRI and a Bayesian technique of probability analysis

This work shows that complete spatial information of periodic pulsatile fluid flows can be rapidly obtained by Bayesian probability analysis of flow encoded magnetic resonance imaging data. These data were acquired as a set of two-dimensional images (complete two-dimensional sampling of k-space or reciprocal position space) but with a sparse (six point) and nonuniform sampling of q-space or reciprocal displacement space. This approach enables more precise calculation of fluid velocity to be achieved than by conventional two q-sample phase encoding of velocities, without the significant time disadvantage associated with the complete flow measurement required for Fourier velocity imaging. For experimental comparison with the Bayesian analysis applied to nonuniformly sampled q-space data, a Fourier velocity imaging technique was used with one-dimensional spatial encoding within a selected slice and a uniform sampling of q-space using 64 values of the pulsed gradients to encode fluid flow. Because the pulsatile flows were axially symmetric within the resolution of the experiment, the radial variation of fluid velocity, in the direction of the pulsed gradients, was reconstructed from one-dimensional spatial projections of the velocity by exploiting the central slice theorem. Data were analysed for internal consistency using linearised flow theories. The results show that nonuniform q-space sampling followed by Bayesian probability analysis is at least as accurate as the combined uniform q-space sampling with Fourier velocity imaging and projection reconstruction method. Both techniques give smaller errors than a two-point sampling of q-space (the conventional flow encoding experiment).     

Technological features of ‘gnathia’ pottery

‘Gnathia’ pottery samples, dating back to the mid‐fourth and third century BC, from the archaeological site of Egnazia (Fasano, Brindisi, Italy) have been characterised from the physical‐chemical, mineralogical and morphological points of view. Optical and scanning electron microscopy, X‐ray energy‐dispersive spectroscopy and X‐ray diffraction analyses have been carried out on the ceramic body, black gloss, white, yellow and red over‐paintings of fragments, with the aim of outlining technological features and defining the nature of coatings and decorations. Analytical results confirm from both a technological and morphological/decorative point of view the close relationship between ‘Gnathia’ pottery and red figured pottery, particularly with the Apulian red figured from which it takes its inspiration. At the same time the experimental results highlight shared characteristics and differences with both Attic and Apulian red figured productions. The biggest difference is in the utilisation of the ‘ingobbio rosso’ layer that covers the ceramic body. This does not seem to be based on aesthetic grounds, as in the case of Apulian red figured pottery, but on application of acquired production processes, since ‘Gnathia’ pottery was made in the same workshops as red figured pottery. Copyright © 2009 John Wiley & Sons, Ltd.     

A hybrid EDC/Flamelet approach for modelling biomass combustion of grate-firing furnace

This paper proposes a new combustion model for the simulation of biomass combustion. It is developed based on the framework of the well-known Eddy Dissipation Concept (EDC) approach, which has the ability to incorporate chemical kinetics in turbulent reacting flows and thus makes it suitable for modelling gas-phase combustion. However, its high computational cost when using detailed chemistry has made it impractical for modelling large/industrial setups. To address this handicap, the proposed approach decouples the real-time calculation of chemical and mixing processes by importing a pre-calculated steady laminar flamelet library into EDC. The development of this new model is performed based on a modified version of EDC (called Extended EDC), which is capable of modelling the gas-phase of biomass combustion over a wide range of turbulent flow conditions. The proposed model is validated by simulating the well-documented experiment of the piloted jet flames of Barlow and Frank. The performance of the model is then evaluated by simulating a small-scale grate firing biomass furnace. The results show that, overall, the proposed model can be used to model biomass combustion at substantially low computational cost.     

Fractal modelling of turbulent combustion

In a previous paper we proposed a new model for turbulent flows, called the fractal model (FM), which is applicable both to RANS and LES formulations. Here, the model is extended to the reactive case with the goal of simulating turbulent flames, both premixed and non-premixed.

FM is a subgrid model that describes the physics of the small scales of turbulence building on the phenomenological concept of vortex cascade and on fractal theory. The physics of the small scales is summarized by a turbulent ‘viscosity’ μ_t, to be added to the molecular one. μ_t is zero where the flow is laminar and, in particular, goes to zero at solid walls.

The fundamental assumption in treating combustion in this work is that chemical reactions take place only at the dissipative scales of turbulence, i.e. near the so-called ‘fine structures’ (the eddy dissipation concept). FM predicts the growth of dissipative scales due to heat release; therefore, it enables a local DNS in the hot regions of the flow where the dissipative scale may grow up to the cell dimension. FM can also estimate the volume fraction γ* occupied by the ‘fine structures’; this quantity is critical for modelling the reaction rate, and therefore the source terms in the energy and species equations. FM can also estimate the local surface of the reactive ‘fine structures’, that is, the local flame front area. It also takes into account, although in approximate manner, the formation of islands of unburnt mixture. In this paper, the model (in the isotropic formulation (IFM)) is used in conjunction with a time-dependent LES (but with the limitations of an isotropic model) approach and is validated through a three-dimensional axisymmetric diffusion flame studied experimentally by Correa and Gulati and numerically by many researchers. The time-dependent results obtained are in good agreement with the experiments. Moreover, the IFM solution offers a possible explanation for the stabilization process of this flame, which undergoes local stretching of the order of 46 000 s^?1.     

Characterization of colorants and opacifiers in roman glass mosaic tesserae through spectroscopic and spectrometric techniques

Several glass mosaic tesserae were recovered during the archeological excavation of the thermal baths at the ‘Villa dei Quintili’ in Rome and dated to the second century ad . This work reports the results of an archeometrical investigation performed, through a multi‐technique approach, on 19 colored opaque tesserae. The aims of the study were (1) the characterization of coloring and opacifying agents used for the production of the glass tesserae and (2) the definition of the technological processes involved. Colorimetric measurements allowed us to classify the tesserae in color groups, while the glassy matrix and the dispersed crystallites were characterized in detail through micro‐Raman spectroscopy, field emission scanning electron microscopy with energy dispersive X‐ray spectroscopy, laser ablation‐inductively coupled plasma‐mass spectrometry, and X‐ray powder diffraction analyses. Most of the glass shows the typical soda‐lime‐silicate composition (except for the orange and red tesserae). Raman results and elemental analysis prove the use of Sn–Pb antimonates to create yellow glass and of Ca‐antimonates for the white tesserae. A mixture of Sn–Pb antimonates and copper ions was used to obtain the emerald green color, while Ca‐antimonates were employed in both copper‐colored and cobalt‐colored blue glass to obtain different shades (blue‐green, dark, and light blue). X‐ray powder diffraction analyses reveal the presence of metallic copper (Cu⁰) and Cu₂O particles (cuprite) in red and orange tesserae, respectively. These results confirm the high technological level reached by the glassmakers of the Imperial Age. Copyright © 2014 John Wiley & Sons, Ltd.     

Hybrid Rayleigh,Raman and two‐photon excited fluorescence spectral confocal microscopy of living cells

A hybrid fluorescence–Raman confocal microscopy platform is presented, which integrates low‐wavenumber‐resolution Raman imaging, Rayleigh scatter imaging and two‐photon fluorescence (TPE) spectral imaging, fast ‘amplitude‐only’ TPE‐fluorescence imaging and high‐spectral‐resolution Raman imaging. This multi‐dimensional fluorescence–Raman microscopy platform enables rapid imaging along the fluorescence emission and/or Rayleigh scatter dimensions. It is shown that optical contrast in these images can be used to select an area of interest prior to subsequent investigation with high spatially and spectrally resolved Raman imaging. This new microscopy platform combines the strengths of Raman ‘chemical’ imaging with light scattering microscopy and fluorescence microscopy and provides new modes of correlative light microscopy. Simultaneous acquisition of TPE hyperspectral fluorescence imaging and Raman imaging illustrates spatial relationships of fluorophores, water, lipid and protein in cells. The fluorescence–Raman microscope is demonstrated in an application to living human bone marrow stromal stem cells. Copyright © 2009 John Wiley & Sons, Ltd.     

Sampling the posterior: An approach to non-Gaussian data assimilation

The viewpoint taken in this paper is that data assimilation is fundamentally a statistical problem and that this problem should be cast in a Bayesian framework. In the absence of model error, the correct solution to the data assimilation problem is to find the posterior distribution implied by this Bayesian setting. Methods for dealing with data assimilation should then be judged by their ability to probe this distribution. In this paper we propose a range of techniques for probing the posterior distribution, based around the Langevin equation; and we compare these new techniques with existing methods.

When the underlying dynamics is deterministic, the posterior distribution is on the space of initial conditions leading to a sampling problem over this space. When the underlying dynamics is stochastic the posterior distribution is on the space of continuous time paths. By writing down a density, and conditioning on observations, it is possible to define a range of Markov Chain Monte Carlo (MCMC) methods which sample from the desired posterior distribution, and thereby solve the data assimilation problem. The basic building-blocks for the MCMC methods that we concentrate on in this paper are Langevin equations which are ergodic and whose invariant measures give the desired distribution; in the case of path space sampling these are stochastic partial differential equations (SPDEs).

Two examples are given to show how data assimilation can be formulated in a Bayesian fashion. The first is weather prediction, and the second is Lagrangian data assimilation for oceanic velocity fields. Furthermore the relationship between the Bayesian approach outlined here and the commonly used Kalman filter based techniques, prevalent in practice, is discussed. Two simple pedagogical examples are studied to illustrate the application of Bayesian sampling to data assimilation concretely. Finally a range of open mathematical and computational issues, arising from the Bayesian approach, are outlined.     

Three-dimensional simulation of primary break-up in a close-coupled atomizer

Until now much of the modelling activity around close-coupled gas atomization has been mainly focused on gas-only flow with discrete phase interaction using Lagrangian-based models. However, this approach is unable to supply valuable information regarding the primary break-up mechanism of the melt being injected. Furthermore, much of existing numerical work is based on two-dimensional axisymmetric geometries, and therefore suffers the absence of three-dimensional flow features. In order to overcome these aspects the authors have carried out an analysis using a three-dimensional geometry by means of an Eulerian, Volume of Fluid, model to accurately present the early stages of melt stream behaviour at the atomizer’s melt inlet. The study investigates the mechanisms associated with primary break-up, and the results obtained highlight three modes under which a close-coupled atomizer may operate.     

基于贝叶斯分层模型的MCMC方法在闪光图像重建中的应用

针对闪光图像得到的光程数据,采用贝叶斯分层模型建立了后验概率模型,运用Gibbs抽样动态构造马尔可夫链;进而获得了关于线吸收系数的统计结果及其不确定度,并与约束共轭梯度(CCG)方法进行对比分析。数值实验结果表明,马尔可夫链蒙特卡罗(MCMC)方法对理想光程图像的重建结果与真值近似完全一致;在含模糊和噪声时,重建结果与CCG方法相当;当含模糊且噪声干扰较大时,MCMC方法的重建结果要略优于CCG;更重要的是MCMC方法能够给出重建结果的不确定度。     

It's not easy being green: Strategies for all‐nitrides,all‐colour solid state lighting

The design strategy presently employed to obtain ‘white’ light from semiconductors combines the emission of an InGaN blue or UV light‐emitting diode (LED) with that of one or more yellow‐orange phosphors. While commercially successful, this approach achieves good colour rendering only by increasing the number and spectral range of the phosphors used; compared to the alternative of combining ‘true’ red, green and blue (RGB) sources, it is intrinsically inefficient. The two major roadblocks to the RGB approach are 1. the green gap in the internal quantum efficiency (IQE) of LEDs; 2. the diode droop in the efficiency of LEDs at higher current densities. The physical origin of these effects, in the case of III‐nitrides, is generally thought to be a combination of Quantum Confined Stark Effect (QCSE) and Auger Effect (AE). These effects respectively reduce the electron–hole wave‐ function overlap of In‐rich InGaN quantum wells (QW), and provide a non‐radiative shunt for electron–hole recombination, particularly at higher excitation densities. SORBET, a novel band gap engineering strategy based upon quantum well intermixing (QWIM), offers solutions to both of the roadblocks mentioned above. In this introduction to SORBET, its great potential is tested and confirmed by the results of simulations of green InGaN diodes performed using the TiberCAD device modelling suite, which calculates the macroscopic properties of real‐world optoelectronic and electronic devices in a multiscale formalism. An alternative approach to the realisation of RGB GaN‐based LEDs through doping of an active layer by rare earth (RE) ions will also be briefly described. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical theory for the description of powder systems under compression

In this work, a new theoretical approach to modelling some properties of powder systems under compression is presented. This new theoretical route consists of modelling an actual powder system (with particles of unequal size and irregular form) by means of a system of deforming spheres in a simple cubic arrangement and with a certain global porosity that, in some way, makes it equivalent to the actual one. The study of the evolution of the effective contact area between particles and the effective path of the electric or thermal flow through the powder aggregate is the starting point for establishing the equivalence relationship between the actual system and the simple cubic one. In order to exemplify the utility of this new theoretical tool, two classic problems of practical interest have been studied: the electrical conduction in sintered powders and the law governing the powders’ cold die compaction. The proposed solutions to these problems, as well as the equations allowing one to obtain the equivalence relationship, are validated by experiments carried out in actual powder systems.     

Discharge flow of granular particles through an orifice on a horizontal hopper:Effect of the hopper angle

We experimentally investigate the effect of the hopper angle on the flow rate of grains discharged from a twodimensional horizontal hopper on a conveyor belt.The flow rate grows with the hopper angle,and finally reaches a plateau.The curve feature appears to be similar for different orifice widths and conveyor belt-driven velocities.On the basis of an empirical law of flow rate for a flat-bottom hopper,we propose a modified equation to describe the relation between the flow rate and hopper angle,which is in a good agreement with the experimental results.     

Application of the backscatter fundamental parameter method for in situ element determination using a portable energy‐dispersive x‐ray fluorescence spectrometer

The backscatter fundamental parameter (BFP) algorithm was adapted and modified for the use with a portable energy‐dispersive x‐ray fluorescence (EDXRF) spectrometer system. The method utilizes coherently and incoherently scattered peaks of primary radiation to estimate the ‘dark matrix’ of the analysed sample. A so‐called ‘full fundamental parameter’ model was implemented in the algorithm, allowing a simple calibration of the method using only one standard sample. To improve the accuracy of the method, the differential mass scattering cross‐sections were used. The algorithm also takes into account the secondary excitation effects. The method was applied to element determinations in various matrices with minimum sample preparation. It was tested in the laboratory with homogeneous samples prepared from standard reference materials and was also successfully applied to in situ element determinations in soil. The analyses were performed using a portable XRF spectrometer equipped with a ¹⁰⁹Cd radioisotope source and an Si‐PIN photodiode detector. The BFP algorithm was found to perform well for the analysis of loose powder samples containing an unknown fraction of ‘dark matrix,’ and therefore it is regarded as suitable for in situ element determinations. Copyright © 2003 John Wiley & Sons, Ltd.     

Quantum-Like Tunnelling and Levels of Arbitrage

We apply methods of wave mechanics to financial modelling. We proceed by assigning a financial interpretation to wave numbers. This paper makes a plea for the use of the concept of ‘tunnelling’ (in the mathematical formalism of quantum mechanics) in the modelling of financial arbitrage. Financial arbitrage is a delicate concept to model in social science (i.e. in this case economics and finance) as its presence affects the precision of benchmark financial asset prices. In this paper, we attempt to show how ‘tunnelling’ can be used to positive effect in the modelling of arbitrage in a financial asset pricing context.