Mathematical Models

A method is proposed for deriving dynamical equations for systems with both rigid and flexible components. During the derivation, each flexible component of the system is represented by a ``surrogate element'''' which captures the response characteristics of that component and is easy to mathematically manipulate. The derivation proceeds essentially as if each surrogate element were a rigid body. Application of an extended form of Lagrange''s equation yields a set of simultaneous differential equations which can then be transformed to be the exact, partial differential equations for the original flexible system. This method''s use facilitates equation generation either by an analyst or through application of software-based symbolic manipulation.

We introduce models for cooperative mitigating response strategies to suppress large scale Internet worm attack. In our models, cooperating members communicate with oth- ers using a "friend protocol" that spreads attack reports to potentially vulnerable uninfected sites. We use mathemati- cal models for the simplest strategies and a simulation for more complex models of mitigation. We investigate the per- formance

This article is a contribution to the discussion on the utility of spatial models in the context of Small Area Estimation (SAE) (see Cressie 1991; Pfeffermann 2002; Saei and Chambers 2003, 2005; Singh et al. 2005; Pratesi and Salvati 2008). The attention is on the Fay–Herriot model and its Mean Squared Error (MSE) when a common autocorrelation parameter among small areas is included. Firstly, we discuss the extent to which the spatial effects in data used for SAE motivate the introduction of an autocorrelation parameter in the Fay–Herriot model. Secondly, the performance of MSE estimators is discussed through a simulation study where the joint effect of the area level sampling variance and of the parameter estimation is shown. The importance of the strength of spatial autocorrelation among small areas is confirmed. The results are tenable for different sampling variance patterns. A case study with spatial dependence in the data is presented and estimates at small area level are prov...

: Sutherland's theoretical expression for the absolute or dynamic viscosity of a gas has been modified to represent experimental viscosity data for air. The resulting semi-empirical equation accurately describes measured viscosities of air for temperatures ranging from the boiling point at 78 K to molecular dissociating conditions at 2500 K. Discrepancies between measured values and semi-empirical results rarely exceed 2%. Other more limited expressions for the viscosity of air are also compared to measured viscosity data and discussed. (Author)

The development of public housing has major traffic impacts on road networks, particularly in already congested cities. Hong Kong, being one of the most congested cities in the world, has a significant amount of public housing in town. Severe traffic congestion occurs in the adjacent road network if the forecast of traffic generation is not accurate. This technical note develops a multilinear regression model to forecast traffic generation for large-scale, high-density, multistory public residential housing estates in Hong Kong. Manual traffic counts were conducted at 36 housing development sites throughout Hong Kong. Regression analysis was undertaken for model evaluation. Many variables, such as the number of apartments, population, gross floor area, parking spaces, and accessibility, were included in the analysis, and the resulting model is both qualitatively and quantitatively reasonable.

By means of the model results, important harmonic constants of the tidal heights and currents, as well as the form factor, were computed. These results have revealed that there is a phase delay and an increase in amplitude of the major constituents as the tide ...

This paper presents a study for the development of first- and second-order tool-life models at 95% confidence level for turning high strength steel. The tool-life models are developed in terms of cutting speed, feed rate, and depth of cut, using response surface methodology and design of experiment. The effects of the main cutting variables (cutting speed, feed, and depth of cut) on tool life have been investigated by the application of the factorial design method. All of the cutting tests were performed using uncoated carbide tools under dry conditions. Tool-life contours have been generated from these model equations and are shown in different plots. Dual-response contours of metal removal rate and tool life are shown also. The results are presented in terms of mean values and confidence levels. © 1998 Elsevier Science S.A. All rights reserved.

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This paper introduces a mathematical model and an optimizer to optimize dynamic variables of construction operations in multi-project environment. Vulnerable nature of construction schedules, resource limitations, multiple objectives, project uncertainties, business priorities and other inevitable constraints make the operations very challenging. The ultimate outcome of the model is to improve construction business efficiency and productivity in terms of profitability and resource management. The model consists of two main components; theoretical model and an optimizer. The first part is the formulation of the theoretical model considering all the multi-objective variables using mathematical descriptions, assumptions and equations. The second part is the solution using special purpose discrete-event simulation and genetic algorithms (GA) . An example with real life project data is presented to demonstrate the application of the proposed model. The results offer the best solution for conflicting objectives of minimizing multi-project schedules, maximizing resource utilization and maximizing the profit while satisfying all the imposed constraints.

The paper deals with the application of fiber reinforced polymer (FRP) laminates or fabrics as shear strengthening materials for reinforced concrete beams. The study aims at increasing the experimental database on shear strengthening of concrete using composites and, most ...

Abstract: In this article, we review some of the theoretical solutions used to describe swirl dominated flows in both unidirectional and bidirectional flow orientations. This short survey starts with the Rankine vortex and culminates in the presentation of a compressible solution of the bidirectional vortex. After classifying representative swirl motions as external or internal depending on physical boundary conditions, their commonalities are identified along with their relevance to either geophysical or industrial applications. We also identify ...