The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.

Two empirical hydrocyclone models revisited

There has been an abundance of literature on the modelling of hydrocyclones over the past 30 years. However, in the comminution area at least, the more popular commercially available packages (e.g. JKSimMet, Limn, MODSIM) use the models developed by Nageswararao and Plitt in the 1970s, either as published at that time, or with minor modification. With the benefit of 30 years of hindsight, this paper discusses the assumptions and approximations used in developing these models. Differences in model structure and the choice of dependent and independent variables are also considered. Redundancies are highlighted and an assessment made of the general applicability of each of the models, their limitations and the sources of error in their model predictions. This paper provides the latest version of the Nageswararao model based on the above analysis, in a form that can readily be implemented in any suitable programming language, or within a spreadsheet. The Plitt model is also presented in similar form. (C) 2004 Elsevier Ltd. All rights reserved.

Large-eddy simulation of heat transfer downstream of a backward-facing step

Large-eddy simulation is used to predict heat transfer in the separated and reattached flow regions downstream of a backward-facing step. Simulations were carried out at a Reynolds number of 28 000 (based on the step height and the upstream centreline velocity) with a channel expansion ratio of 1.25. The Prandtl number was 0.71. Two subgrid-scale models were tested, namely the dynamic eddy-viscosity, eddy-diffusivity model and the dynamic mixed model. Both models showed good overall agreement with available experimental data. The simulations indicated that the peak in heat-transfer coefficient occurs slightly upstream of the mean reattachment location, in agreement with experimental data. The results of these simulations have been analysed to discover the mechanisms that cause this phenomenon. The peak in heat-transfer coefficient shows a direct correlation with the peak in wall shear-stress fluctuations. It is conjectured that the peak in these fluctuations is caused by an impingement mechanism, in which large eddies, originating in the shear layer, impact the wall just upstream of the mean reattachment location. These eddies cause a 'downwash', which increases the local heat-transfer coefficient by bringing cold fluid from above the shear layer towards the wall.

Forecasting with serially correlated regression models

In this article we investigate the asymptotic and finite-sample properties of predictors of regression models with autocorrelated errors. We prove new theorems associated with the predictive efficiency of generalized least squares (GLS) and incorrectly structured GLS predictors. We also establish the form associated with their predictive mean squared errors as well as the magnitude of these errors relative to each other and to those generated from the ordinary least squares (OLS) predictor. A large simulation study is used to evaluate the finite-sample performance of forecasts generated from models using different corrections for the serial correlation.

The specification of vector autoregressive moving average models

In this paper we propose a new identification method based on the residual white noise autoregressive criterion (Pukkila et al. , 1990) to select the order of VARMA structures. Results from extensive simulation experiments based on different model structures with varying number of observations and number of component series are used to demonstrate the performance of this new procedure. We also use economic and business data to compare the model structures selected by this order selection method with those identified in other published studies.

High-pressure adsorption capacity and structure of CO2 in carbon slit pores: Theory and simulation

We present new simulation results for the packing of single-center and three-center models of carbon dioxide at high pressure in carbon slit pores. The former shows a series of packing transitions that are well described by our density functional theory model developed earlier. In contrast, these transitions are absent for the three-center model. Analysis of the simulation results shows that alternations of flat-lying molecules and rotated molecules can occur as the pore width is increased. The presence or absence of quadrupoles has negligible effect on these high-density structures.

Effects of potential models on the adsorption of ethane and ethylene on graphitized thermal carbon black. Study of two-dimensional critical temperature and isosteric heat versus loading

Adsorption of ethylene and ethane on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers is studied in detail to investigate the packing efficiency, the two-dimensional critical temperature, and the variation of the isosteric heat of adsorption with loading and temperature. Here we used a Monte Carlo simulation method with a grand canonical Monte Carlo ensemble. A number of two-center Lennard-Jones (LJ) potential models are investigated to study the impact of the choice of potential models in the description of adsorption behavior. We chose two 2C-LJ potential models in our investigation of the (i) UA-TraPPE-LJ model of Martin and Siepmann (J. Phys. Chem. B 1998,102, 25692577) for ethane and Wick et al. (J. Phys. Chem. B 2000,104, 8008-8016) for ethylene and (ii) AUA4-LJ model of Ungerer et al. (J. Chem. Phys. 2000,112, 5499-5510) for ethane and Bourasseau et al. (J. Chem. Phys. 2003, 118, 3020-3034) for ethylene. These models are used to study the adsorption of ethane and ethylene on graphitized thermal carbon black. It is found that the solid-fluid binary interaction parameter is a function of adsorbate and temperature, and the adsorption isotherms and heat of adsorption are well described by both the UA-TraPPE and AUA models, although the UA-TraPPE model performs slightly better. However, the local distributions predicted by these two models are slightly different. These two models are used to explore the two-dimensional condensation for the graphitized thermal carbon black, and these values are 110 K for ethylene and 120 K for ethane.

PVT behaviour of fluids with potential models optimised for phase equilibria

NPT and NVT Monte Carlo simulations are applied to models for methane and water to predict the PVT behaviour of these fluids over a wide range of temperatures and pressures. The potential models examined in this paper have previously been presented in the literature with their specific parameters optimised to fit phase coexistence data. The exponential-6 potential for methane gives generally good prediction of PVT behaviour over the full range of temperature and pressures studied with the only significant deviation from experimental data seen at high temperatures and pressures. The NSPCE water model shows very poor prediction of PVT behaviour, particularly at dense conditions. To improve this. the charge separation in the NSPCE model is varied with density. Improvements for vapour and liquid phase PVT predictions are achieved with this variation. No improvement was found in the prediction of the oxygen-oxygen radial distribution by varying charge separation under dense phase conditions. (C) 2004 Elsevier B.V. All rights reserved.

Adsorption of ethylene on graphitized thermal carbon black and in slit pores: A computer simulation study

In this paper, we studied vapor-liquid equilibria (VLE) and adsorption of ethylene on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers. Simple models of a one-center Lennard-Jones (LJ) potential and a two-center united atom (UA)-LJ potential are investigated to study the impact of the choice of potential models in the description of VLE and adsorption behavior. Here, we used a Monte Carlo simulation method with grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo ensembles. The one-center potential model cannot describe adequately the VLE over the practical range of temperature from the triple point to the critical point. On the other hand, the two-center potential model (Wick et al. J. Phys. Chem. B 2000, 104, 8008-8016) performs well in the description of VLE (saturated vapor and liquid densities and vapor pressure) over the wide range of temperature. This UA-LJ model is then used in the study of adsorption of ethylene on graphitized thermal carbon black and in slit pores. Agreement between the GCMC simulation results and the experimental data on graphitized thermal carbon black for moderate temperatures is excellent, demonstrating that the potential of the GCMC method and the proper choice of potential model are essential to investigate adsorption. For slit pores of various sizes, we have found that the behavior of ethylene exhibits a number of features that are not manifested in the study of spherical LJ particles. In particular, the singlet density distribution versus distance across the pore and the angle between the molecular axis and the z direction provide rich information about the way molecules arrange themselves when the pore width is varied. Such an arrangement has been found to be very sensitive to the pore width.

A parallel implementation of the lattice solid model for the simulation of rock mechanics and earthquake dynamics

The Lattice Solid Model has been used successfully as a virtual laboratory to simulate fracturing of rocks, the dynamics of faults, earthquakes and gouge processes. However, results from those simulations show that in order to make the next step towards more realistic experiments it will be necessary to use models containing a significantly larger number of particles than current models. Thus, those simulations will require a greatly increased amount of computational resources. Whereas the computing power provided by single processors can be expected to increase according to Moore's law, i.e., to double every 18-24 months, parallel computers can provide significantly larger computing power today. In order to make this computing power available for the simulation of the microphysics of earthquakes, a parallel version of the Lattice Solid Model has been implemented. Benchmarks using large models with several millions of particles have shown that the parallel implementation of the Lattice Solid Model can achieve a high parallel-efficiency of about 80% for large numbers of processors on different computer architectures.

Three-dimensional simulation of the rolling of a saturated fibro-porous media

This paper describes recent advances made in computational modelling of the sugar cane liquid extraction process. The saturated fibro-porous material is rolled between circumferentially grooved rolls, which enhance frictional grip and provide a low-resistance path for liquid flow during the extraction process. Previously reported two-dimensional (2D) computational models, account for the large deformation of the porous material by solving the fully coupled governing fibre stress and fluid-flow equations using finite element techniques. While the 2D simulations provide much insight into the overarching cause-effect relationships, predictions of mechanical quantities such as roll separating force and particularly torque as a function of roll speed and degree of compression are not satisfactory for industrial use. It is considered that the unsatisfactory response in roll torque prediction may be due to the stress levels that exist between the groove tips and roots which have been largely neglected in the geometrically simplified 2D model. This paper gives results for both two- and three-dimensional finite element models and highlights their strengths and weaknesses in predicting key milling parameters. (c) 2005 Elsevier B.V. All rights reserved.

Diagnostic goal driven modelling and simulation of multiscale process systems

A systematic goal-driven top-down modelling methodology is proposed that is capable of developing a multiscale model of a process system for given diagnostic purposes. The diagnostic goal-set and the symptoms are extracted from HAZOP analysis results, where the possible actions to be performed in a fault situation are also described. The multiscale dynamic model is realized in the form of a hierarchical coloured Petri net by using a novel substitution place-transition pair. Multiscale simulation that focuses automatically on the fault areas is used to predict the effect of the proposed preventive actions. The notions and procedures are illustrated on some simple case studies including a heat exchanger network and a more complex wet granulation process.

Impact of potential models on adsorption of linear molecules on carbon black

In this paper, we investigate the effects of potential models on the description of equilibria of linear molecules (ethylene and ethane) adsorption on graphitized thermal carbon black. GCMC simulation is used as a tool to give adsorption isotherms, isosteric heat of adsorption and the microscopic configurations of these molecules. At the heart of the GCMC are the potential models, describing fluid-fluid interaction and solid-fluid interaction. Here we studied the two potential models recently proposed in the literature, the UA-TraPPE and AUA4. Their impact in the description of adsorption behavior of pure components will be discussed. Mixtures of these components with nitrogen and argon are also studied. Nitrogen is modeled a two-site plus discrete charges while argon as a spherical particle. GCMC simulation is also used for generating simulation mixture isotherms. It is found that co-operation between species occurs when the surface is fractionally covered while competition is important when surface is fully loaded.

Evaluation of 1-site and 5-site models of methane on its adsorption on graphite and in graphitic slit pores

In this paper, we evaluate the performance of the 1- and 5-site models of methane on the description of adsorption on graphite surfaces and in graphitic slit pores. These models have been known to perform well in the description of the fluid-phase behavior and vapor-liquid equilibria. Their performance in adsorption is evaluated in this work for nonporous graphitized thermal carbon black, and simulation results are compared with the experimental data of Avgul and Kiselev (Chemistry and Physics of Carbon; Dekker: New York, 1970; Vol. 6, p 1). On this nonporous surface, it is found that these models perform as well on isotherms at various temperatures as they do on the experimental isosteric heat for adsorption on a graphite surface. They are then tested for their performance in predicting the adsorption isotherms in graphitic slit pores, in which we would like to explore the effect of confinement on the molecule packing. Pore widths of 10 and 20 angstrom are chosen in this investigation, and we also study the effects of temperature by choosing 90.7, 113, and 273 K. The first two are for subcritical conditions, with 90.7 K being the triple point of methane and 113 K being its boiling point. The last temperature is chosen to represent the supercritical condition so that we can investigate the performance of these models at extremely high pressures. We have found that for the case of slit pores investigated in this paper, although the two models yield comparable pore densities (provided the accessible pore width is used in the calculation of pore density), the number of particles predicted by the I-site model is always greater than that predicted by the 5-site model, regardless of whether temperature is subcritical or supercritical. This is due to the packing effect in the confined space such that a methane molecule modeled as a spherical particle in the I-site model would pack better than the fused five-sphere model in the case of the 5-site model. Because the 5-site model better describes the liquid- and solid-phase behavior, we would argue that the packing density in small pores is better described with a more detailed 5-site model, and care should be exercised when using the 1-site model to study adsorption in small pores.

Effects of potential models in the vapor-liquid equilibria and adsorption of simple gases on graphitized thermal carbon black

In this paper, we investigate the effects of various potential models in the description of vapor–liquid equilibria (VLE) and adsorption of simple gases on highly graphitized thermal carbon black. It is found that some potential models proposed in the literature are not suitable for the description of VLE (saturated gas and liquid densities and the vapor pressure with temperature). Simple gases, such as neon, argon, krypton, xenon, nitrogen, and methane are studied in this paper. To describe the isotherms on graphitized thermal carbon black correctly, the surface mediation damping factor introduced in our recent publication should be used to calculate correctly the fluid–fluid interaction energy between particles close to the surface. It is found that the damping constant for the noble gases family is linearly dependent on the polarizability, suggesting that the electric field of the graphite surface has a direct induction effect on the induced dipole of these molecules. As a result of this polarization by the graphite surface, the fluid–fluid interaction energy is reduced whenever two particles are near the surface. In the case of methane, we found that the damping constant is less than that of a noble gas having the similar polarizability, while in the case of nitrogen the damping factor is much greater and this could most likely be due to the quadrupolar nature of nitrogen.