Models of cellulose physical structure from the viewpoint of the cellulose I → II transition

Supermolecular structure of linters cellulose at the cellulose I–II phase transition is investigated by wide-angle X-ray scattering (quantitative phase analysis, degree of crystallinity by the method of Ruland and Vonk, and lateral crystallite sizes via peak separation by Pearson VII functions). A survey of models of cellulose structure recently discussed in literature is given. The compatibility of these models with the obtained WAXS results is checked. As a conclusion, some of the models especially the parallel–antiparallel transition of chain arrangement are outruled and a nonuniform fringed fibrillar model in connection with a conformation transition from bent to bent and twisted single chain conformation is preferred.     

Time-varying autoregressions with model order uncertainty

We explore some aspects of the analysis of latent component structure in non-stationary time series based on time-varying autoregressive (TVAR) models that incorporate uncertainty on model order. Our modelling approach assumes that the AR coefficients evolve in time according to a random walk and that the model order may also change in time following a discrete random walk. In addition, we use a conjugate prior structure on the autoregressive coefficients and a discrete uniform prior on model order. Simulation from the posterior distribution of the model parameters can be obtained via standard forward filtering backward simulation algorithms. Aspects of implementation and inference on decompositions, latent structure and model order are discussed for a synthetic series and for an electroencephalogram (EEG) trace previously analysed using fixed order TVAR models.     

A model-based systems approach to pharmaceutical product-process design and analysis

This is a perspective paper highlighting the need for systematic model-based design and analysis in pharmaceutical product-process development. A model-based framework is presented and the role, development and use of models of various types are discussed together with the structure of the models for the product and the process. The need for a systematic modelling framework is highlighted together with modelling issues related to model identification, adaptation and extension. In the area of product design and analysis, predictive models are needed with a wide application range. In the area of process synthesis and design, the use of generic process models from which specific process models can be generated, is highlighted. The use of a multi-scale modelling approach to extend the application range of the property models is highlighted as well. Examples of different types of process models, model analysis and model generation are presented.     

On POD reduced models of tubular reactor with periodic regimes

The distributed model of a tubular reactor with recycle is reduced by approximating it first with a Continuous Stirred Tank Reactor (CSTR) cascade. Proper orthogonal decomposition (POD) with Galerkin projection is introduced to study oscillatory regimes. The dynamics of the resulting models is studied via numerical simulation, and solutions in the form of time series and phase plot diagrams are compared to those obtained for the original CSTR cascade model. Different methods to choose the minimum number of basis functions are compared and discussed. Solution diagrams built with POD models are compared with those from CSTR cascade, as a function of the Damköhler number. Features and limitations of POD models are discussed for different snapshot sampling policies and for different values of the Péclet number. Qualitative performance increases and quantitative performance decreases as samples from steady states are considered along with periodic solution samples. Performance becomes worse as the Péclet number increases.     

THE STATISTICAL ANALYSIS OF PERTURBED LIMIT CYCLE PROCESSES USING NONLINEAR TIME SERIES MODELS

Abstract. Statistical analysis of perturbed limit cycle process is discussed. Limit cycles of van der Pol equation type are considered and statistical time series models for the perturbed limit cycle processes are presented. It is shown that the model shares some interesting qualitative properties although the presented models are different, in appearance, from the van der Pol equation. Applications of the model to the statistical analysis of Canadian Lynx data are also discussed with numerical results.     

Nonlinear model reduction for dynamic analysis of cell population models

Transient cell population balance models consist of nonlinear partial differential-integro equations. An accurate discretized approximation typically requires a large number of nonlinear ordinary differential equations that are not well suited for dynamic analysis and model based controller design. In this paper, proper orthogonal decomposition (also known as the method of empirical orthogonal eigenfunctions and Karhunen Loéve expansion) is used to construct nonlinear reduced-order models from spatiotemporal data sets obtained via simulations of an accurate discretized yeast cell population model. The short-term and long-term behavior of the reduced-order models are evaluated by comparison to the full-order model. Dynamic simulation and bifurcation analysis results demonstrate that reduced-order models with a comparatively small number of differential equations yield accurate predictions over a wide range of operating conditions.     

Kinetic Modeling of Large‐Scale Reaction Systems

This review gives a brief account of basic ideas underlying approaches to analysis and modeling of large‐scale reaction systems. The emphasis is on model simplification and mechanism/dimension reduction via heuristic concepts and formal mathematical techniques. Among the key topics discussed are: top‐down and bottom‐up modeling approaches, graph/matrix representation of chemical reactions, mechanistic vs. pathways models, quantitative structure‐reactivity relationships, mathematical reduction of dimensionality, high‐fidelity surrogate models, continuum approximation, lumping of nonlinear kinetics, overall behavior/kinetics of many reactions, effect of pore diffusion, steady state multiplicity and stability. Some common features of dimension reduction methodologies are noted. Areas where further work will be valuable are identified.     

Techniques for incorporating longitudinal measurements into analyses of survival data from clinical trials

This article reviews existing approaches for joint analysis of longitudinal measurements, possibly measured with error or incompletely observed, and event-time data, possibly censored. The models take the form of selection or pattern-mixture models; estimation proceeds via the EM algorithm or Bayesian sampling techniques. The models are compared, their estimation and inferential procedures described, and advantages and disadvantages noted. Examples are discussed from several disease areas, including cancer and AIDS.     

Sequential Detection of Change-Points in Linear Models

Abstract

A new method for sequential detection of change-points in multivariate linear models is proposed. The main performance characteristics of this method are analyzed theoretically for finite sample volumes. Comparison with other well known methods for sequential detection of structural changes in linear models is carried out via Monte Carlo tests. Practical applications for the analysis of stability of the German quarterly model of demand for money (1961–1995) and the Russian monthly model of inflation (1994–2005) are considered.     

Dynamic modelling of a heterogeneously catalysed system with stiff Hopf bifurcations

We report the results of a detailed dynamic modelling of CO oxidation on a platinum catalytic wire, carried out via an iterative parameter estimation scheme which employs both experimental bifurcation-to-oscillation data as well as the actual oscillatory data. By exploiting the stiffness of the system's model equations, some algebraic equations that describe the oscillatory boundaries in the feed temperature/partial pressure parameter space are extracted. The resulting model is shown to fit quantitatively these boundaries and the dynamic oscillographs of the wire temperature and simulate, with satisfactory accuracy, the unfitted dynamic data. Following an extension of the independent parameters space of the model beyond the reported experimental one, interesting bifurcation sequences (including multiple steady states) obtained via a computational study are predicted. The utility of both the resulting model in catalytic reactor design and the novel iteration scheme in general parameter estimation work on catalytic models is discussed.     

Modeling for prediction of restrained shrinkage effect in concrete repair

A general model of autogenous shrinkage caused by chemical reaction (chemical shrinkage) is developed by means of Arrhenius' law and a degree of chemical reaction. Models of tensile creep and relaxation modulus are built based on a viscoelastic, three-element model. Tests of free shrinkage and tensile creep were carried out to determine some coefficients in the models. Two-dimensional FEM analysis based on the models and other constitutions can predict the development of tensile strength and cracking. Three groups of patch-repaired beams were designed for analysis and testing. The prediction from the analysis shows agreement with the test results. The cracking mechanism after repair is discussed.     

Bayesian selection of threshold autoregressive models

Abstract.  An approach to Bayesian model selection in self-exciting threshold autoregressive (SETAR) models is developed within a reversible jump Markov chain Monte Carlo (RJMCMC) framework. Our approach is examined via a simulation study and analysis of the Zurich monthly sunspots series. We find that the method converges rapidly to the optimal model, whilst efficiently exploring suboptimal models to quantify model uncertainty. A key finding is that the parsimony of the model selected is influenced by the specification of prior information, which can be examined and subjected to criticism. This is a strength of the Bayesian approach, allowing physical understanding to constrain the model selection algorithm.     

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

The focus of this work is on economic model predictive control (EMPC) that utilizes well‐conditioned polynomial nonlinear state‐space (PNLSS) models for processes with nonlinear dynamics. Specifically, the article initially addresses the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of PNLSS dynamic models which are well‐conditioned over a broad region of process operation in the sense that they can be correctly integrated in real‐time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state‐space models identified via existing techniques. Working within the framework of PNLSS models, additional constraints are imposed in the identification procedure to ensure well‐conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov‐based EMPC (LEMPC) systems for nonlinear processes using the well‐conditioned nonlinear models that can be readily implemented in real‐time as the computational burden required to compute the control actions within the process sampling period is reduced. A stability analysis for this LEMPC design is provided that guarantees closed‐loop stability of a process under certain conditions when an LEMPC based on a nonlinear empirical model is used. Finally, a classical chemical reactor example demonstrates both the system identification and LEMPC design techniques, and the significant advantages in terms of computation time reduction in LEMPC calculations when using the nonlinear empirical model. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3353–3373, 2015     

Safety aspects in modelling and operating of batch and semibatch stirred tank chemical reactors

Safety aspects in modelling of batch and semibatch stirred tank reactors as well as a model based safety analysis have been considered. Applicability of two basic types of models – i.e. the perfectly mixed reactor model and the CFD model, both formulated for laboratory scale as well as pilot plant scale reactors – has been discussed. A formulation of the appropriate reactor model, which is adequate to the considered case study has been demonstrated and tested experimentally. Particular attention has been devoted to the formulation of robust CFD models employed to simulate a performance of the stirred tank reactors. It has been found that models for perfectly mixed reactors may have quite wide range of application, while the CFD models should be definitely used in case of fast reactions, high viscosity of the reacting mixture as well as of failure leading to stopping of the impeller. The CFD models are able to predict a dynamic behaviour of reactors at any circumstances, so they can play a significant role in safety analysis carried out for industrial scale reactors, for which experimental safety tests are expensive and dangerous.     

Molecular mechanics modeling of carbon nanotube fracture

The fracture of carbon nanotubes (CNTs) is studied in this paper. Molecular mechanics models that incorporate the modified Morse potential and reactive empirical bond-order potential are developed to envisage the fracture behavior of perfect CNTs. The tensile strength, fracture strain, and fracture angle under tension are discussed, and special attention is paid to the effects of tube chirality. Explicit expressions for the fracture solutions for achiral carbon nanotubes are presented, but only numerical results are available for chiral carbon nanotubes. The predicted results of the present model are in good agreement with existing data and those of molecular mechanics simulations via the Materials Studio software package, which indicates the effectiveness of the developed models.     

Lag length estimation in large dimensional systems

We study the impact of the system dimension on commonly used model selection criteria (AIC, BIC, HQ) and LR based general to specific testing strategies for lag length estimation in VARs. We show that AIC's well known overparameterization feature becomes quickly irrelevant as we move away from univariate models, with the criterion leading to consistent estimates under sufficiently large system dimensions. Unless the sample size is unrealistically small, all model selection criteria will tend to point towards low orders as the system dimension increases, with the AIC remaining by far the best performing criterion. This latter point is also illustrated via the use of an analytical power function for model selection criteria. The comparison between the model selection and general to specific testing strategy is discussed within the context of a new penalty term leading to the same choice of lag length under both approaches.     

Modeling the mechanical response of polymers and nano-filled polymers: Effects of porosity and fillers content

In this study, models are developed to predict the mechanical behavior of porous polymer-based membranes, since they are exposed to temperature and pressure load under service conditions. To the best of our knowledge, existing studies related to numerical simulations of mechanical behavior of polymer nanocomposites do not explicitly report porosity in the modeling. Hence, the proposed models attempt to explicitly examine the effect of porosity. The first model predicts the elastic modulus of porous polymer nanocomposites which is based on Weibull statistical analysis. The results show the combined effects of fillers content and porosity on the modulus. The second model predicts the yield stress for porous polymer nanocomposites. The coupled effects of fillers content and porosity on the yield stress is examined via our proposed extension of the cooperative model. A parametric study is conducted to show the influence of a single parameter used to model the influence of porosity.     

下吸式生物质气化炉数值模拟的研究进展

使用数值模拟方法,建立下吸式生物质气化炉的数学模型,能够更好地理解气化炉内发生的各种化学和物理现象,进而对气化炉的设计和操作进行优化、对新工艺的开发进行指导。对几种基本的下吸式气化炉数值模拟方法(如热动力学平衡法、化学动力学方法、计算流体动力学(CFD)法、ASPEN Plus法)和多分区模拟法,进行了探讨和分析比较,并进一步总结了"结合单颗粒模型的多分区数值模拟"方法,提出结合单颗粒模型的多分区模拟法具有更加广阔的发展前景。     

Crystallization kinetics during polymer processing—Analysis of available approaches for process modeling

An analysis of available methods of dealing with polymer crystallization for process modeling is presented. Problems encountered in using isothermal data to predict nonisothermal results are discussed and illustrated using experimental data for nylon 6. A half-time analysis is used to evaluate and extrapolate the isothermal crystallization rates. It is concluded that none of the available models are entirely satisfactory for computing nonisothermal crystallization from isothermal data, though the Nakamura model is shown to be more satisfactory for process modeling than other models discussed in the literature. A nonlinear regression method is presented for directly fitting nonisothermal crystallinity data using the Nakamura model to obtain crystallization rate equation parameters. Two empirical methods for including amorphous orientation effects are also considered and evaluated by comparing predicted results to online experimental data for melt spinning of nylon 6.