scholarly journals A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks

2019 ◽  
Vol 6 (3) ◽  
pp. 181848 ◽  
Author(s):  
I. Kavrakov ◽  
D. Legatiuk ◽  
K. Gürlebeck ◽  
G. Morgenthal
Keyword(s):  
Mathematical Models ◽  
Category Theory ◽  
Structural Engineering ◽  
Model Comparison ◽  
Model Assessment ◽  
Adequate Description ◽  
Categorical Approach ◽  
Abstract Approach ◽  
Huge Variety ◽  
Modelling Approach

Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary. This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterization is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications.

scholarly journals Mathematical Modelling by Help of Category Theory: Models and Relations between Them

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1946
Author(s):  
Dmitrii Legatiuk
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Models ◽  
Category Theory ◽  
Model Comparison ◽  
Physical Phenomenon ◽  
Point Of View ◽  
Model Choice ◽  
Practical Applications ◽  
Abstract Description

The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are computation-based, and thus time consuming and computationally costly. Therefore, it is necessary to develop other approaches to working abstractly, i.e., without computations, with mathematical models. An abstract description of mathematical models can be achieved by the help of abstract mathematics, implying formalisation of models and relations between them. In this paper, a category theory-based approach to mathematical modelling is proposed. In this way, mathematical models are formalised in the language of categories, relations between the models are formally defined and several practically relevant properties are introduced on the level of categories. Finally, an illustrative example is presented, underlying how the category-theory based approach can be used in practice. Further, all constructions presented in this paper are also discussed from a modelling point of view by making explicit the link to concrete modelling scenarios.

scholarly journals Interdependence of friction, wear, and noise: A review

Friction ◽  
2021 ◽  
Author(s):  
Kevin Lontin ◽  
Muhammad Khan
Keyword(s):  
Mathematical Models ◽  
Friction And Wear ◽  
Review Paper ◽  
Acoustic Noise ◽  
Friction Noise ◽  
Mathematical Expressions ◽  
Mechanical Contacts ◽  
Exact Relationship ◽  
Modelling Approach ◽  
Frictional Noise

AbstractPhenomena of friction, wear, and noise in mechanical contacts are particularly important in the field of tribomechanics but equally complex if one wants to represent their exact relationship with mathematical models. Efforts have been made to describe these phenomena with different approaches in past. These efforts have been compiled in different reviews but most of them treated friction, wear mechanics, and acoustic noise separately. However, an in-depth review that provides a critical analysis on their interdependencies is still missing. In this review paper, the interdependencies of friction, wear, and noise are analysed in the mechanical contacts at asperitical level. The origin of frictional noise, its dependencies on contact’s mechanical properties, and its performance under different wear conditions are critically reviewed. A discussion on the existing mathematical models of friction and wear is also provided in the last section that leads to uncover the gap in the existing literature. This review concludes that still a comprehensive analytical modelling approach is required to relate the interdependencies of friction, noise, and wear with mathematical expressions.

scholarly journals Categories as Mathematical Models

2018 ◽  
Author(s):  
David I. Spivak
Keyword(s):  
Dynamical Systems ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Category Theory ◽  
Vector Spaces ◽  
Mathematical Objects ◽  
Working Definition ◽  
Modelling Framework ◽  
Categorical Models ◽  
Definition Of

Category theory is presented as a mathematical modelling framework that highlights the relationships between objects, rather than the objects in themselves. A working definition of model is given, and several examples of mathematical objects, such as vector spaces, groups, and dynamical systems, are considered as categorical models.

scholarly journals Technical note: Comparison of methane ebullition modelling approaches used in terrestrial wetland models

2018 ◽  
Vol 15 (3) ◽  
pp. 937-951 ◽  
Author(s):  
Olli Peltola ◽  
Maarit Raivonen ◽  
Xuefei Li ◽  
Timo Vesala
Keyword(s):  
Temporal Variability ◽  
Model Comparison ◽  
Technical Note ◽  
Scale Model ◽  
Emission Model ◽  
Ch4 Emission ◽  
Ch4 Emissions ◽  
Emission Models ◽  
Modelling Approach ◽  
Modelling Approaches

Abstract. Emission via bubbling, i.e. ebullition, is one of the main methane (CH4) emission pathways from wetlands to the atmosphere. Direct measurement of gas bubble formation, growth and release in the peat–water matrix is challenging and in consequence these processes are relatively unknown and are coarsely represented in current wetland CH4 emission models. In this study we aimed to evaluate three ebullition modelling approaches and their effect on model performance. This was achieved by implementing the three approaches in one process-based CH4 emission model. All the approaches were based on some kind of threshold: either on CH4 pore water concentration (ECT), pressure (EPT) or free-phase gas volume (EBG) threshold. The model was run using 4 years of data from a boreal sedge fen and the results were compared with eddy covariance measurements of CH4 fluxes.Modelled annual CH4 emissions were largely unaffected by the different ebullition modelling approaches; however, temporal variability in CH4 emissions varied an order of magnitude between the approaches. Hence the ebullition modelling approach drives the temporal variability in modelled CH4 emissions and therefore significantly impacts, for instance, high-frequency (daily scale) model comparison and calibration against measurements. The modelling approach based on the most recent knowledge of the ebullition process (volume threshold, EBG) agreed the best with the measured fluxes (R2 = 0.63) and hence produced the most reasonable results, although there was a scale mismatch between the measurements (ecosystem scale with heterogeneous ebullition locations) and model results (single horizontally homogeneous peat column). The approach should be favoured over the two other more widely used ebullition modelling approaches and researchers are encouraged to implement it into their CH4 emission models.

scholarly journals Investigation of a new effective bacterium for cellulosic degradation

2021 ◽  
Author(s):  
Weining Lin
Keyword(s):  
Growth Rate ◽  
Mathematical Models ◽  
Incubation Temperature ◽  
Biogas Production ◽  
Substrate Utilization ◽  
Gas Production ◽  
Biomass Growth ◽  
Growth Substrate ◽  
Wide Range ◽  
Modelling Approach

Clostridium phytofermentans, a newly isolated mesophilic anaerobic bacterium from forest soil, has received considerable attention for its potential application in producing ethanol directly from cellulose. This microorganism produces ethanol, acetate, CO₂ and H₂ as major metabolites from cellulose. Potential applications of this research include the transformation of waste materials into valuable products, such as fuels and organic acids. As an initial part of a multi-staged project, this study is to focus on the characerization of this microorganism growth and to verify the bacterium kinetics, including biomass growth, substrate utilization, and gas production. A series of batch fermentation experiments using cellulose substrate (GS-2C) was performed under the incubation temperature of 37°C. To investigate the effects of pH and substrate concentration (S₀) on growth, 12 trial experiments were conducted with various controlled pH values (7.0 to 8.5) and with various initial cellulose concentration settings (0.1 to 6.0 g/L). Our experimental results showed that the optimal growth condition for C. phytofermentans in batch culture was at pH = 8.4 amd S₀ = 6.0 g/L. Under such condition, the maximum growth rate of 0.37h⁻¹ was observed. Comparing results with other celluloytic clostridium studies, relatively high biomass growth rate using C. phytofermentans is confirmed by our experiments. Mathematical models, using a combination modelling approach with the logistic equation. Monod model, and Luedeking-Piret model, were developed for biomass growth, substrate degradation, and biogas production, respectively, base on our experiment results. This study demonstrated the determination of the four parameters (µmax, Ks, Y, and Smin), which can describe satisfactorily growth or degradation phenomena, using the proposed integration modelling approach. The experiments conducted under wide range conditions, such as changing pH and S₀, not only provide insight into growth kinetics but also provide an opportunity to evaluate the performance of the mathematical models and understand their limitations. This leads to look for improvement or modification to the models. It is foreseen that the findings in this study will enhance the overall understanding of the kinetics of growth and substrate utilization and product formation of this bacterium, and provide important information on the design of the bench-scale anaerobic bioreactor for future studies.

scholarly journals Yoneda Philosophy in Engineering

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Lambrini Seremeti ◽  
Ioannis Kougias
Keyword(s):  
Mathematical Models ◽  
Conceptual Framework ◽  
Category Theory ◽  
Formal Concept Analysis ◽  
Building Blocks ◽  
Ontology Engineering ◽  
Formal Concept ◽  
Physical Systems ◽  
Formal Concepts ◽  
Engineering Models

Mathematical models, such as sets of equations, are used in engineering to represent and analyze the behaviour of physical systems. The conventional notations in formulating engineering models do not clearly provide all the details required in order to fully understand the equations, and, thus, artifacts such as ontologies, which are the building blocks of knowledge representation models, are used to fulfil this gap. Since ontologies are the outcome of an intersubjective agreement among a group of individuals about the same fragment of the objective world, their development and use are questions in debate with regard to their competencies and limitations to univocally conceptualize a domain of interest. This is related to the following question: “What is the criterion for delimiting the specification of the main identifiable entities in order to consistently build the conceptual framework of the domain in question?” This query motivates us to view the Yoneda philosophy as a fundamental concern of understanding the conceptualization phase of each ontology engineering methodology. In this way, we exploit the link between the notion of formal concepts of formal concept analysis and a concluding remark resulting from the Yoneda embedding lemma of category theory in order to establish a formal process.

Mathematical models for coating processes

1982 ◽  
Vol 117 ◽  
pp. 443-455 ◽  
Author(s):  
M. D. Savage
Keyword(s):  
Surface Tension ◽  
Fluid Flow ◽  
Mathematical Models ◽  
Coating Thickness ◽  
Essential Difference ◽  
Narrow Gap ◽  
Adequate Description ◽  
Theoretical Predictions ◽  
Dimensional Parameters ◽  
Separation Model

The flow is considered of a Newtonian fluid, of viscosity η and surface tension T, in the narrow gap between a pair of rollers of radii R1 and R2, whose peripheral speeds are constant and equal to U1 and U2 respectively. The objective is to determine the coating thickness h1∞ on the upper roller as a function of the non-dimensional parameters H0/R, ηU/T and U1/U2, where H0 is the minimum gap thickness, U = ½(U1 + U2), and 2R−1 = R1−1 + R2−1.Using lubrication theory to provide an adequate description of the fluid flow, two mathematical models are derived whose essential difference lies in the specification of the boundary conditions. In the separation model it is assumed that the pressure distribution will terminate at a position which is both a stagnation point and a point of separation, whereas the Reynolds model incorporates the classical Reynolds conditions. In each case, theoretical predictions for the non-dimensional coating thickness, h1∞/H0 as a function of U1/U2 are found to compare well with experiment. However, theory does suggest that the two models are applicable to different and complementary regions of parameter space, and hence together they may form a basis for further investigations into the various features of coating processes.

scholarly journals Using ANN to Estimate the Critical Buckling Load of Y Shaped Cross-Section Steel Columns

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Thuy-Anh Nguyen ◽  
Hai-Bang Ly ◽  
Hai-Van Thi Mai ◽  
Van Quan Tran
Keyword(s):  
Correlation Coefficient ◽  
Cross Section ◽  
Structural Engineering ◽  
Buckling Load ◽  
Model Assessment ◽  
Ann Model ◽  
Critical Buckling Load ◽  
Steel Columns ◽  
Marquardt Algorithm ◽  
Shaped Cross Section

Accurate measurement of the critical buckling stress is crucial in the entire field of structural engineering. In this paper, the critical buckling load of Y-shaped cross-section steel columns was predicted by the Artificial Neural Network (ANN) using the Levenberg-Marquardt algorithm. The results of 57 buckling tests were used to generate the training and testing datasets. Seven input variables were considered, including the column length, column width, steel equal angles thickness, the width and thickness of the welded steel plate, and the total deviations following the Ox and Oy directions. The output was the critical buckling load of the columns. The accuracy assessment criteria used to evaluate the model were the correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE). The selection of an appropriate structure of ANN was first addressed, followed by two investigations on the highest accuracy models. The first one consisted of the ANN model that gave the lowest values of MAE = 40.0835 and RMSE = 30.6669, whereas the second one gave the highest value of R = 0.98488. The results revealed that taking MAE and RMSE for model assessment was more accurate and reasonable than taking the R criterion. The RMSE and MAE criteria should be used in priority, compared with the correlation coefficient.

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