Fundamental Modeling Approach Research Articles

Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters

Despite the simplicity and practicality of (deterministic) fundamental diagram models in highway traffic flow theory, the wide scattering effect observed in empirical data remains highly controversial, particularly for explaining traffic state variations. Owing to the analytical properties of the fundamental diagram modeling approach, in this study, we proposed an analytical and quantitative method for analyzing traffic state variations. We investigated the scattering effect in the fundamental diagram and proposed two stochastic fundamental diagram (SFD) models with lognormal and skew-normal distributions to explain the variations in traffic states. The first SFD model assumes that the scattering effect results from stochasticity in both the free-flow speed and the speed at critical density. Both random variables were assumed to follow the lognormal distribution. In the second SFD model, an integrated error term that was assumed to follow the skew-normal distribution over different density ranges was appended to the deterministic fundamental diagram. The properties of these two SFD models were analyzed and compared, and the parameters in these SFD models were calibrated using real-world loop detector data. The observed scatters from the empirical data were reproduced well by the simulated fundamental diagram model, indicating the validity of the proposed SFD models for explaining traffic state variations. Using these two analytical SFD models, we can analyze the stochastic capacity of freeways with closed forms. More importantly, the sources of stochasticity in freeway capacity can be traced in terms of randomly distributed parameters in fundamental diagram models.

Modelling Building Energy Systems using Electric Circuit Analogy

Modelling energy systems is of great interest since it can help to analyse building energy behaviour and to optimize control strategies. Grey-box modelling is one of the three fundamental modelling approaches for developing energy models. Due to its simplicity and offering several benefits, it has been widely used to handle building-technology challenges such as building load estimate, control and optimization, synthetic data generation for prediction, load peak management and grid integration. This review research looked at several areas of grey box modelling for building energy systems. Here we analyse three main directions, first one is modelling thermal dynamics of buildings, second one analysing approach used to model most used building electrical appliances and third one is renewable systems used to produce thermal water for residential use.

Evaluation of housing stock indoor air quality models: A review of data requirements and model performance

To develop and evaluate housing strategies and interventions for improving indoor air quality (IAQ) at a city or national scale, housing stock IAQ models are required. Without such models, reliable prediction of residential indoor pollution concentrations and exposures at various spatial-temporal scales cannot be achieved. To address the areas not covered by past review articles in housing stock performance modelling, this paper presents the first comprehensive review of the housing stock IAQ models published during 2012–2020. Our review was carried out to achieve three outcomes: (1) to identify and summarize the fundamental IAQ modelling approaches including model assumptions, (2) to review the housing stock IAQ modelling methods (engineering and/or statistical), sampling methods, data sources in use and the underlying computation assumptions, and (3) to propose a descriptive framework and a performative matrix. The review resulted in a set of 11 key model attributes with which housing stock IAQ models can be evaluated in terms of data requirements and model performance. To improve robustness and accuracy in concentration and exposure predictions, future housing stock IAQ models should be developed to account for the dynamic interaction between heat transfer, inter-zone airflow and indoor contaminant transport through IAQ-Energy co-simulation.

Analysis of dynamic psychological processes to understand and promote physical activity behaviour using intensive longitudinal methods: a primer

ABSTRACT Physical activity behaviour displays temporal variability, and is influenced by a range of dynamic psychological processes (e.g., affect) and shaped by various co-occurring events (e.g., social/environmental factors, interpersonal dynamics). Yet, most physical activity research tends not to examine the dynamic psychological processes implicated in adopting and maintaining physical activity. Intensive longitudinal methods (ILM) represent one particularly salient means of studying the complex psychological dynamics that underlie and result from physical activity behaviour. With the increased recent interest in using intensive longitudinal data to understand specific dynamic psychological processes, the field of exercise and health psychology is well-positioned to draw from state-of-the-art measurement and statistical approaches that have been developed and operationalised in other fields of enquiry. The purpose of this review is to provide an overview of some of the fundamental dynamic measurement and modelling approaches applicable to the study of physical activity behaviour change, as well as the dynamic psychological processes that contribute to such change.

Experimental Validation of a Direct Fiber Model for Orientation Prediction

Predicting the fiber orientation of reinforced molded components is required to improve their performance and safety. Continuum-based models for fiber orientation are computationally very efficient; however, they lack in a linked theory between fiber attrition, fiber–matrix separation and fiber alignment. This work, therefore, employs a particle level simulation which was used to simulate the fiber orientation evolution within a sliding plate rheometer. In the model, each fiber is accounted for and represented as a chain of linked rigid segments. Fibers experience hydrodynamic forces, elastic forces, and interaction forces. To validate this fundamental modeling approach, injection and compression molded reinforced polypropylene samples were subjected to a simple shear flow using a sliding plate rheometer. Microcomputed tomography was used to measure the orientation tensor up to 60 shear strain units. The fully characterized microstructure at zero shear strain was used to reproduce the initial conditions in the particle level simulation. Fibers were placed in a periodic boundary cell, and an idealized simple shear flow field was applied. The model showed a faster orientation evolution at the start of the shearing process. However, agreement with the steady-state aligned orientation for compression molded samples was found.

A review of analogue modelling of geodynamic processes: Approaches, scaling, materials and quantification, with an application to subduction experiments

We present a review of the analogue modelling method, which has been used for 200 years, and continues to be used, to investigate geological phenomena and geodynamic processes. We particularly focus on the following four components: (1) the different fundamental modelling approaches that exist in analogue modelling; (2) the scaling theory and scaling of topography; (3) the different materials and rheologies that are used to simulate the complex behaviour of rocks; and (4) a range of recording techniques that are used for qualitative and quantitative analyses and interpretations of analogue models. Furthermore, we apply these four components to laboratory-based subduction models and describe some of the issues at hand with modelling such systems. Over the last 200 years, a wide variety of analogue materials have been used with different rheologies, including viscous materials (e.g. syrups, silicones, water), brittle materials (e.g. granular materials such as sand, microspheres and sugar), plastic materials (e.g. plasticine), visco-plastic materials (e.g. paraffin, waxes, petrolatum) and visco-elasto-plastic materials (e.g. hydrocarbon compounds and gelatins). These materials have been used in many different set-ups to study processes from the microscale, such as porphyroclast rotation, to the mantle scale, such as subduction and mantle convection. Despite the wide variety of modelling materials and great diversity in model set-ups and processes investigated, all laboratory experiments can be classified into one of three different categories based on three fundamental modelling approaches that have been used in analogue modelling: (1) The external approach, (2) the combined (external+internal) approach, and (3) the internal approach. In the external approach and combined approach, energy is added to the experimental system through the external application of a velocity, temperature gradient or a material influx (or a combination thereof), and so the system is open. In the external approach, all deformation in the system is driven by the externally imposed condition, while in the combined approach, part of the deformation is driven by buoyancy forces internal to the system. In the internal approach, all deformation is driven by buoyancy forces internal to the system and so the system is closed and no energy is added during an experimental run. In the combined approach, the externally imposed force or added energy is generally not quantified nor compared to the internal buoyancy force or potential energy of the system, and so it is not known if these experiments are properly scaled with respect to nature. The scaling theory requires that analogue models are geometrically, kinematically and dynamically similar to the natural prototype. Direct scaling of topography in laboratory models indicates that it is often significantly exaggerated. This can be ascribed to (1) The lack of isostatic compensation, which causes topography to be too high. (2) The lack of erosion, which causes topography to be too high. (3) The incorrect scaling of topography when density contrasts are scaled (rather than densities); In isostatically supported models, scaling of density contrasts requires an adjustment of the scaled topography by applying a topographic correction factor. (4) The incorrect scaling of externally imposed boundary conditions in isostatically supported experiments using the combined approach; When externally imposed forces are too high, this creates topography that is too high. Other processes that also affect surface topography in laboratory models but not in nature (or only in a negligible way) include surface tension (for models using fluids) and shear zone dilatation (for models using granular material), but these will generally only affect the model surface topography on relatively short horizontal length scales of the order of several mm across material boundaries and shear zones, respectively.

Fundamental FEM Modeling Approach of Residual Stress Propagation in Sn-Based Electroplated Films Prone to Sn Whiskers Growth

The evolution of residual stress gradients in three different cases of electrodeposited Sn-based films on brass substrate has been evaluated using thermomechanical finite element model (FEM), with temperature as the only loading condition. The FEM model for each of the three cases consists of a brass substrate with the following films: 1) pure Sn film; 2) pure Sn film with the Ni-underlayer; and 3) composite Ni/Sn film. The simulations consider the stress behavior under temperature loading, in the electrodeposited Sn-based films with and without the Ni-underlayer(s). A simple analytical model has been developed to estimate the resulting stress gradient (considered as one of the main causes for Sn whiskers growth) in each film. The modeled stress in the films is shown to be in good agreement with the previously published experimental measurements [Dimitrovska et al. , Journal of Electronic Materials 38, 2516 (2009)].

Are fundamentals enough? Explaining price variations in the German day-ahead and intraday power market

European electricity market participants are encouraged to balance intraday deviations from their day-ahead schedules via trades in the intraday market. Together with the increasing production of variable renewable energy sources (RES), the intraday market is gaining importance. We investigate the explanatory power of a fundamental modeling approach explicitly accounting for must-run operations of combined heat and power plants (CHP) and intraday peculiarities such as a shortened intraday supply stack. The fundamental equilibria between every hour's supply stack and aggregated demand in 2012 and 2013 are modeled to yield hourly price estimates. The major benefits of a fundamental modeling approach are the ability to account for non-linearities in the supply stack and the ability to combine time-varying information consistently. The empirical results show that fundamental modeling explains a considerable share of spot price variance. However, differences between the fundamental and actual prices persist and are explored using regression models. The main differences can be attributed to (avoided) start up-costs, market states and trading behavior.

Perfect competition vs. strategic behaviour models to derive electricity prices and the influence of renewables on market power

A variety of fundamental modelling approaches exist using different competition concepts with and without strategic behaviour to derive electricity prices. To investigate the quality and practicability of these different approaches in energy economics, a perfect competition model, a Cournot model and a Bilevel model are introduced and applied to different situations in the German electricity market. The three electricity market approaches are analysed with respect to their ability to represent electricity prices and the possibility of market power abuse. Market prices are taken as a benchmark for model validity. As a result, the perfect competition model fits best to today's market situation in most hours of the year. The Bilevel approach explains prices in high load hours sometimes better than the competition model. But complexity and calculation time increase disproportionately. In addition to the analysis of model quality, we use three scenarios to quantify how a high renewable feed-in influences the ability to abuse market power. Results show that the ability to address market power strongly depends on the amount of installed capacities.

Specifications of Fundamental Diagrams for Dynamic Traffic Modeling

This paper studies different specifications of fundamental diagrams for first-order dynamic traffic modeling. The fundamental diagram, which refers to the relationship between traffic flow and density at a given location, plays an important role in modeling the dynamics of traffic propagation. Many forms of fundamental diagrams have been proposed since the seminal work of Greenshields 80 years ago. Nevertheless, empirical validation of fundamental diagrams, in particular, for dynamic modeling purposes, is limited. The study is conducted with an extensive dataset collected from the U.K. M25 motorway. This paper highlights the difficulty in modeling congested traffic with single-valued fundamental diagrams and fine-grained loop detector data. Consequently, this paper first analyzes and discusses the effect of data granularity on model calibration and application. Following this, a set-valued fundamental diagram modeling approach with fine-grained data is also presented. This paper contributes to the development and validation of dynamic traffic simulation tools.

Comparison of phenomenological and fundamental modelling approaches for predicting fluidized bed reactor performance

Two approaches to modelling fluidized bed reactors were evaluated and compared in this work: a phenomenological 1D approach based on empirical closures and a more fundamental 2D approach based on computational fluid dynamics (CFD). The fundamental modelling approach should be more accurate and generic, but is several orders of magnitude more computationally expensive than the phenomenological approach. Therefore, the development of accurate, but computationally affordable phenomenological models is a matter of great importance. This work evaluated the behaviour of both modelling approaches over a wide range of operating variables spanning the bubbling fluidization regime. These variables included fluidization velocity, bed height, operating temperature and particle size. Several different closure models were evaluated for the phenomenological approach and it was shown that models for the bubble size, bubble-to-emulsion mass transfer coefficient and solids inside the bubble all have a significant impact on model performance. An optimal combination of closure models used in the phenomenological approach succeeded in providing a good match to data gathered from the more generic fundamental approach. The response of the model to changes in particle size was identified as the area with the greatest potential for further development. More detailed comparisons of axial distributions of important flow variables showed some differences between the predictions of the phenomenological and fundamental modelling approaches. In particular, the hydrodynamic measures of axial void distribution and bubble rise velocity predicted by these two approaches showed some significant differences.

A Fundamental Modeling Approach for Nano-Grinding of Silicon Wafers

The advantages of ductile regime grinding of silicon wafer such as smooth surface roughness (Ra < 10 nm) and minimum subsurface damage layer (< 10μm) have great impact on the production process of wafer. With ductile regime grinding, the subsequent processes such as etching and rough polishing processes can be minimized. To achieve ductile regime grinding, a fundamental concept is the application of grain depth of cut being less than the critical cut depth, dc, of the silicon wafer. However, dc is dependent on material properties, cutting conditions, and crystallographic orientation [1].The objective of this paper is to derive, and to investigate by experiment, the dc value for silicon wafer grinding. Following these key steps, the effects of dc on various major grinding parameters are studied.

An Empirical Investigation of Product Differentiation and Pricing Strategy: An Application to the Household Goods Motor Carrier Industry

Analysis of interfirm rivalry has long been an important focus in microeconomic theory and, in particular, the field of industrial organization. While the theoretical literature is both rich and broad-based, its empirical counterpart has generally been far more limited in scope and is, in fact, still very much in its infancy. The seminal work of Iwata [17] provided the fundamental modeling approach for empirical estimation of the conjectural variation. According to theory, this term measures the anticipated response of competitors to a change in some strategic variable. Since in long run equilibrium, these anticipated responses in fact represent actual behavior, conjectures can be interpreted not only as ex ante strategic assumptions, but also as ex post indicators of the actual competitive process.' Thus, estimated conjectures serve as a means to econometrically capture firm interdependence. Iwata's research motivated a series of subsequent empirical analyses, for example, Gollop and Roberts [9], Appelbaum [3], and Roberts and Samuelson [25]. These studies are more ambitious and sophisticated in terms of interpretation and econometric technique. However, none have fully abandoned the restrictive assumption of product homogeneity. This assumption not only constrains the selection of an institutional context for oligopoly models, but also, by definition, disallows analysis of product differentiation as a strategic instrument. Despite recognition of this latter issue in the theoretical literature, empirical work has apparently been discouraged by the inherent complexities associated with modeling product differences. This research extends the boundary of empirical interdependent firm models to incorporate an environment of product heterogeneity. In so doing, a model is formulated in which the profit motive operates via the simultaneous determination of price and product differentiation. Ultimately, this allows testing not only for the existence of product differentiation as a competitive instrument but also for the relative import of this activity vis-a-vis strategic pricing decisions.

Separating polymer solutions using high pressure lower critical solution temperature (LCST) phenomena

AbstractA lower critical solution temperature (LCST) phase split can be used as an alternative to steam stripping for separating polymer solutions, By adding a supercritical fluid (SCF) additive to the polymer solution, the LCST can be lowered, thus minimizing the possibility of polymer degradation and also reducing the thermal energy requirements for the process. Experimental results for the poly(ethylene‐co‐propylene)‐hexane‐SCF ethylene system are shown as an example of the type of phase behavior observed with polymer‐solvent‐SCF additive solutions. Adding 20 percent (w/w) ethylene to the polymer solution lowers the temperature of the LCST by 109°C. The addition of 30 percent (w/w) ethylene to the polymer solution lowers the temperature of the LCST curve sufficiently to merge this curve with the upper critical solution temperature (UCST) curve. When the lower critical end point (LCEP) is plotted against the critical temperature of the solvent the data for poly(ethylenie‐co‐propylene)‐solvent systems are well represented by a single curve. A more fundamental modeling approach is needed to estimate the pressure of the LCEP and the concentration of SCF additive necessary to merge the LCST and the UCST curves. Patterson's theory of corresponding states can be used for these calculations.