Mathematical Models

This paper deals with the solution of the stress, displacement, and pore pressure field induced by the drilling and~or the pressurization of a vertical borehole. The rock, which is permeated by fluid, is assumed to behave as a poroelastic material with compressible constituents, following the Biot theory. The analytical solution is derived in the Laplace transform space, and is transformed to the time domain using an approximate numerical inversion technique. The solution reveals a full range of coupled poroelastic effects which provide potential mechanisms for delayed borehole instability and shear fracture initiation inside the rock.

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.

This paper aims to develop an improved understanding of the critical response of structures to multicomponent seismic motion characterized by three uncorrelated components that are deÿned along its principal axes: two horizontal and the vertical component. An explicit formula, convenient for code applications, has been derived to calculate the critical value of structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. The critical response is deÿned as the largest value of response for all possible incident angles. The ratio rcr=rsrss between the critical value of response and the SRSS response-corresponding to the principal components of ground acceleration applied along the structure axes-is shown to depend on three dimensionless parameters: the spectrum intensity ratio between the two principal components of horizontal ground motion characterized by design spectra A(Tn) and A(Tn); the correlation coe cient of responses rx and ry due to design spectrum A(Tn) applied in the x-and y-directions, respectively; and ÿ = ry=rx. It is demonstrated that the ratio rcr=rsrss is bounded by 1 and (2=1 + 2 ). Thus the largest value of the ratio is √ 2, 1.26, 1.13 and 1.08 for = 0, 0.5, 0.75 and 0.85, respectively. This implies that the critical response never exceeds √ 2 times the result of the SRSS analysis, and this ratio is about 1.13 for typical values of , say 0.75. The correlation coe cient depends on the structural properties but is always bounded between −1 and 1. For a ÿxed value of , the ratio rcr=rsrss is largest if ÿ = 1 and = ± 1. The parametric variations presented for one-storey buildings indicate that this condition can be satisÿed by axial forces in columns of symmetric-plan buildings or can be approximated by lateral displacements in resisting elements of unsymmetrical-plan buildings.

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

In this paper we propose a dynamic model representing the temporal evolution of the levels of power generation (installed capacity) from two competing sources. These are renewable and conventional (fossil) sources. The percentage penetration rates of renewable and nonrenewable sources are considered as control or decision variables. We introduce an objective functional based on energy demand, production of pollution associated with usage of fossil fuels, and the cost of their systematic substitution by renewable sources. Pontryagin minimum principle is used to determine optimal control policy through minimizing energy generation from fossil fuels while meeting the energy demand as closely as possible through gradual replacement of nonrenewable sources by renewable ones. For different choices of plan periods, optimal generation path along with the corresponding control policies are presented. These results demonstrate that modern control theory can be used effectively to formulate optimal socio-economic policies.

The aim of this study was to determine the nutritional value of adult commercial cuttlefish, to develop a Quality Index Method (QIM) scheme, and to evaluate the application of some biochemical methods commonly used for freshness assessment of fish under ice storage. Additionally, shelf-life was to be determined based on both QIM and suitable biochemical methods. The nutritional value of the cuttlefish mantle in the first 24 h and after 13 days was determined. Captured cuttlefish was composed (g/100 g) by 16.60 AE 0.10 g protein, 0.09 AE 0.01 g fat, 79.55 AE 0.14 g moisture and 1.39 AE 0.03 g of ash. After 13 days of ice storage, cuttlefish was composed (g/100 g) of 11.90 AE 0.28 g protein, 0.17 AE 0.09 g fat, 87.04 AE 0.13 g moisture and 0.52 AE 0.01 g of ash. Differences (p < 0.001) were found in protein, ash and moisture but not in fat (p > 0.05). These results seem to indicate that there is impregnation of the iced water into the mantle tissue promoting protein leaching with the melting ice. TVB-N and TMA-N displayed a similar increasing tendency, peaking beyond EEC regulations proposed maximum between the 9th and 10th days. The developed QIM scheme for cuttlefish was composed of 29 demerit points, divided into 4 attributes and 13 parameters. The calculated quality index (QI) evolved linearly with storage time in ice (QI ¼ 2.68 Â days in ice À 0.61, R 2 ¼ 0.9866). Storage time could be estimated with an accuracy of AE 1 day, if five cuttlefish from each sample were included in the QIM assessment. The shelf-life was determined as 8 AE 1 days by both type of methods (QIM and biochemical). However, the suitability of some biochemical methods to assess freshness need to be more thoroughly researched.

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&#39;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)

Soft and semi-soft farm cheeses made from pasteurized milk and having high moisture content are common craft products in Ireland. Theses cheeses have limited shelf-life and needs to consider the release of CO 2 and consumption of O 2 for packaging design. The objective of this work was to analyze the effect of the storage temperature (4, 12 and 20°C) and different gas compositions (O 2 and CO 2) on the gas exchange rate of whole soft cheese (camembert-type). The O 2 consumption rate was found to be 26.21 ml kg À1 h À1 at 4°C when stored in 19% O 2 and 10% CO 2 gas composition. It increased to 91.03 ml kg À1 h À1 when temperature increased to 20°C at the same gas composition. A Pareto analysis showed that the temperature and O 2 concentration have a significant effect on the gas exchange rate, whereas the effect of CO 2 concentration was negligible. The effect of O 2 concentration on the gas exchange rate was found to be well described by a Michaelis-Menten equation whereas an Arrhenius equation was used to fit the effect of temperature. Combining the effect of O 2 and temperature, a global model was developed and validated which provided a good fit to the experimental data, explaining 94% of the variance of the data.

The first results of an axisymmetric MHD model of the interaction of an expanding cometary atmosphere with the solar wind are presented. The model assumes that far upstream the plasma flow lines are parallel to the magnetic field vector. The effects of mass loading and ion-neutral friction are taken into account by the governing equations, which are solved on an adaptively refined unstructured grid using a MUSCL-type numerical technique. The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the near nucleus of the comet. The main findings are the following: (1) A shock is formed • 0.45 Mkm upstream of the comet (its location is controlled by the sonic and Alfvenic Mach numbers of the ambient solar wind flow and by the cometary mass addition rate). (2) A contact surface is formed • 5,600 km upstream of the nucleus separating an outward expanding cometary ionosphere from the nearly stagnating solar wind flow. The location of the contact surface is controlled by the upstream flow conditions, the mass loading rate and the ion-neutral drag. The contact surface is also the boundary of the diamagnetic cavity. (3) A closed inner shock terminates the supersonic expansion of the cometary ionosphere. This inner shock is closer to the nucleus on dayside than on the nightside. flow. It should be noted that photo-ionization and impact-ionization add new mass to the plasma flow.

This report summarizes research advances pursued with award funding issued by the DOE to Drexel University through the Presidential Early Career Award (PECASE) program. Professor Rich Cairncross was the recipient of this award in 1997. With it he pursued two related research topics under Sandia's guidance that address the outstanding issue of fluid-structural interactions of liquids with deformable solid materials, focusing mainly on the ubiquitous dynamic wetting problem.

In an effort t o improve and automate the fluid dynamic design of rotary blood pumps, a coupled computational fluid dynamics (CFD) shape optimization methodology has been developed and implemented. This program couples a finite element flow simulation with a gradient-based optimization routine to modify automatically the shape of an initial candidate blood path, according to a variety of desired fluid dynamic criteria, including shear stress, vorticity/circulation, and viscous dissipation. Preliminary results have led to both intuitive and nonintuitive transformations of the initial blood flow

A new gasdynamic launcher is described, in which intact projectiles weighing at least 1 gram can be accelerated to mass velocities of 15-20 km/s. The system employs a conventional 2-stage light gas gun, with the barrel modified and filled with helium to act as a pump tube for a third stage. The key feature of the launcher is that the peak pressure in the third stage can be maintained below 2.5 GPa, thus assuring high efficiency and the integrity of the projectile.

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Satellite-based information on significant waves is increasingly being made available to ocean scientists and engineers at low costs. While such measurements have a number of useful applications the manner with which the satellites sense the waves limits their applications to nearshore locations. This paper discusses an approach based on the radial basis function (RBF) type of artificial neural networks to map remote-sensed deep-water waves with the coastal waves. Significant wave heights at a number of locations over a track parallel to the coastline are used to estimate the significant wave heights at a nearshore site. The success of the method adopted was confirmed from the satisfactory error measures it produced during the testing carried out following the network training. It was also found that the satellite data need a 'local tuning' as done in the RBF before their further use in network computations. This work also highlighted importance of innovative approaches to calibrate a network on the basis of a given data set.

This paper summarizes a mathematical model that relates the geometric and geotechnical features of a road construction site with the allocation of materials, searching for a minimum construction cost. This paper proposes a linear programming model to optimize excavation and paving services. With this model, it is possible to evaluate site alternatives with different soil strata and different degrees of compaction. The borrow pit materials are allocated in the most economical way, and it is possible to incorporate more inputs like materials mix. Software was used to solve the model, and a spreadsheet application was used as an interface for data input. The proposed model demonstrated possible cost savings in earthwork planning. It is expected that earthwork and paving optimization with linear programming will reduce road construction costs considerably.

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.

The present paper is aimed to investigate and develop cheap adsorption methods for colour removal from wastewater using waste material de-oiled mustard as adsorbent. De-oiled mustard, a biosorbent, was successfully utilized for removing a water-soluble xanthene dye, Erythrosine from wastewater. Kinetic studies of adsorption of Erythrosine at de-oiled mustard were carried out at 30 • C, using aqueous solutions with 5 × 10 −5 M concentration of Erythrosine. The adsorption process followed a pseudo-first order model. The equilibrium process can be well described by both Freundlich and Langmuir models, at 30, 40 and 50 • C. Free energy of adsorption (G •), enthalpy (H •), and entropy (S •) changes were calculated to predict the nature of adsorption. The estimated values for G • were −12.81 × 10 3 and −12.57 × 10 3 over activated carbon and activated de-oiled mustard at 203 K (30 • C), indicate toward a spontaneous process. The positive value for H • indicates that the adsorption of Erythrosine dye to de-oiled mustard is an endothermic process.

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 ...

Global ocean climatology Temperature and salinity observations Since the 1970s, the U.S. Navy has maintained a state-of-the-art gridded global monthly full-depth climatology of temperature and salinity and their standard deviations called the Generalized Digital Environmental Model (GDEM). The present document describes the development and evaluation of GDEM4, the newest version of GDEM. As part of the evaluation of GDEM4, comparisons are made in this report to GDEM3 and to four other ocean climatologies: the NODC World Ocean Atlas (WOA2005), the NODC 1/4 degree resolution climatology, the WOCE Global Hydrographic Climatology (WGHC), and the NRLMODAS 2D (MODAS2D) surface temperature climatology. GDEM4 combines the methodology originally developed for GDEM3 with an expanded observation data set. In the evaluations performed, the GDEM4 climatology has been shown to be a significant improvement over GDEM3 and to compare favorably and in many ways improve on fields from the other climatologies used in the evaluations.

The displacement field for an edge dislocation in an Earth model consisting of • l•yer welded to • h•lf-sp•ce of different m•terial is found in the form of • Fourier integral following the method given by Weeks et al. [1968]. There are four elementary solutions to be considered: the dislocation is either in the half-space or the l•yer •nd the Burgers vector is either p•rallel or perpendicular to the layer. A general two-dimensional solution for • dip-slip faulting or dike injection (arbitrary dip) c•n be constructed from • superposition of these elementary solutions. Surface deformations h•ve been c•lcul•ted for •n edge dislocation located •t the interface with Burgers vector inclined 0 ø, 30 ø, 60 ø, •nd 90 ø to the interface for the case where the rigidity of the l•yer is h•lf of that of the half-space and the Poisson ratios •re the same. Those displacement fields h•ve been compared to the displacement fields generated by similarly situated edge dislocations in a uniform half-space.

The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that allow different levels of description of the initial wording. Within these transformations, the passage between successive phases of the problem-solving process determines four operational categories: decoding (transposing the text into more explicit relations among the data and the operating schemes, induced by the constraints of the problem), representing (transposing the problem via a generated mental model), processing (identifying an associated mathematical model based on the mental configurations suggested by the problem and own mathematical competence), and implementing (applying identified mathematical techniques to the particular situation of the problem, with the purpose of drafting a conventional solution). The study of this framework in action offers insights for more effective teaching and can be used in problem posing and problem analysis in order to devise questions more relevant for deep learning.

The authors respond to a recent article in this journal by Ewald and Kiker in which a limited application of input-output techniques was used to develop a costing model for higher education. The Ewald-Kiker costing model, in addition to the ordinary restrictions on production relationships (fixed proportions, non-substitutability of inputs), requires that further restrictions be imposed. Specifically, the model assumes a limited set of possible interactions between the primary and support programs at an institution of higher education (product divisions and service centers in their terminology). This paper provides a costing methodology based on a similar application of input-output theory but one which is completely general with regard to possible program interrelationships. The paper concludes with some comments on the limitations on use of input-output models and information derived from them.

Aim The aims of this study are to resolve terminological confusion around different types of species-area relationships (SARs) and their delimitation from species sampling relationships (SSRs), to provide a comprehensive overview of models and analytical methods for SARs, to evaluate these theoretically and empirically, and to suggest a more consistent approach for the treatment of species-area data.

I. The first group consists of predictive D P (ε) models based only on ε. The first ε-based models were The soil gas diffusion coefficient (D P ) and its dependency on airintroduced a century ago. Edgar Buckingham, as filled porosity (ε) govern most gas diffusion-reaction processes in soil.

A modification of the TUCKALS3 algorithm is proposed that handles three-way arrays of order I x J × K for any I. When I is much larger than JK, the modified algorithm needs less work space to store the data during the iterative part of the algorithm than does the original algorithm. Because of this and the additional feature that execution speed is higher, the modified algorithm is highly suitable for use on personal computers.

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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Comments on the article by E. Brandstätter, G. Gigerenzer, and R. Hertwig. The authors discuss the priority heuristic, a recent model for decisions under risk. They reanalyze the experimental validity of this approach and discuss how these results compare with cumulative prospect theory, the currently most established model in behavioral economics. They also discuss how general models for decisions under risk based on a heuristic approach can be understood mathematically to gain some insight in their limitations. They finally consider whether the priority heuristic model can lead to some understanding of the decision process of individuals or whether it is better seen as an as-if model.

Many beginning university students struggle with the new approaches to mathematics that they find in their courses due to a shift in presentation of mathematical ideas, from a procedural approach to concept definitions and deductive derivations, with ideas building upon each other in quick succession. This paper highlights this situation by considering some conceptual processes and difficulties students find in learning about eigenvalues and eigenvectors. We use the theoretical framework of Tall's three worlds of mathematics, along with perspectives from process-object and representational theory. The results of the study describe the thinking about these concepts of groups by first and second year university students, and in particular the obstacles they faced, and the emerging links some were constructing between parts of their concept images formed from the embodied, symbolic and formal worlds. We also identify some fundamental problems with student understanding of the definition of eigenvectors that lead to problems using it, and some of the concepts underlying the difficulties.

 We describe new analytical techniques to help mitigate the disruptions to electric power grids caused by terrorist attacks. New bilevel mathematical models and algorithms identify critical system components (e.g., transmission lines, generators, transformers) by creating maximally disruptive attack plans for terrorists assumed to have limited offensive resources. We report results for standard reliability test networks to show that the techniques identify critical components with modest computational effort.

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 aim of this work was to analyze by means of simple mathematical models the effect of different integral doses of g irradiation on the mechanical properties of blends of polypropylene (PP) with virgin and recycled high density polyethylene (v-HDPE, r-HDPE), with and without woodflour-type filler. Analysis of the results at an integral irradiation dose between 0 and 50 kGy shows that crosslinking predominates in the PP/v-HDPE blend whereas degradation is predominant in the PP/r-HDPE blend, due to the characteristics of the recycled material. For the 50-70 kGy interval, both blends (PP/v-HDPE, PP/r-HDPE) suggest the possibility of competing processes, chain breaking being the most marked in the PP/r-HDPE blend. For the 0-50 kGy range in the blends with woodflour, the behavior of the PP/v-HDPE/woodflour composite was more complex since the polynomial equations are of third order for both tensile properties analyzed: Young's modulus and elongation at break. The behavior of the PP/r-HDPE/woodflour composite is complex suggesting simultaneous crosslinking and degradation. Both composites show a bimolecular process within the 50-70 kGy range which signifies a second-order dependence.

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of tliis collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 0MB control number.

This paper reports on the numerical modelling of flash flood propagation in urban areas after an excessive rainfall event or dam/dyke break wave. A two-dimensional (2-D) depth-averaged shallow-water model is used, with a refined grid of quadrilaterals and triangles for representing the urban area topography. The 2-D shallow-water equations are solved using the explicit second-order scheme that is adapted from MUSCL approach. Four applications are described to demonstrate the potential benefits and limits of 2-D modelling: (i) laboratory experimental dam-break wave in the presence of an isolated building; (ii) flash flood over a physical model of the urbanized Toce river valley in Italy; (iii) flash flood in October 1988 at the city of Nîmes (France) and (iv) dam-break flood in October 1982 at the town of Sumacárcel (Spain). Computed flow depths and velocities compare well with recorded data, although for the experimental study on dam-break wave some discrepancies are observed around buildings, where the flow is strongly 3-D in character. The numerical simulations show that the flow depths and flood wave celerity are significantly affected by the presence of buildings in comparison with the original floodplain. Further, this study confirms the importance of topography and roughness coefficient for flood propagation simulation.

A bidimensional finite element model that predicts temperature distribution and moisture migration of wheat stored in silobags due to seasonal variation of climatic conditions is described. The model includes grain respiration and calculates carbon dioxide and oxygen concentrations during storage as well as the associated dry matter loss.

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 ...

An attempt is made to develop a method for the presentation of temporal and spatial sociolinguistic data in order to study phenomena of bilingual interaction. Domain of language usage and other sociocultural variables are abstracted from extant sources, normalized and compared with the aim of studying sociolinguistic variation, its reflection on stability of language distribution and the relation of the latter to convergence processes in the languages in contact. The possibility of applying sociological-geographic models for the diffusion of innovation to linguistic diffusion is investigated. The case of the Macedorumanian nomads in the Balkans is used to illustrate the method.

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 ...

The purpose of, this paper is to present a generalisation of the =concept of item difficulty to test items,that. measure more than one dimension. Three common definitions of item difficulty were considered: Abe proportion of correct responses for a group of individuals;lhe probability of a correct response.to an item, for a specific person; and the' location of the 4tem along a difficulty continuum. This paper defines the difficulty of an item .