961 resultados para analytical solution


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Textual cultural heritage artefacts present two serious problems for the encoder: how to record different or revised versions of the same work, and how to encode conflicting perspectives of the text using markup. Both are forms of textual variation, and can be accurately recorded using a multi-version document, based on a minimally redundant directed graph that cleanly separates variation from content.

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Today, polarisation of the fashion textile industry has already begun as smart, intelligent and conscientious fashion emerges as a backlash to the experience of choice fatigue, poor quality, dumb design and greenwash. But the process, development and manufacture of fashion textiles is complex. And the demand, both customer and industry driven, for new integrated product policies,2 designed to minimise environmental impacts by looking at all phases of a product's life cycle, is problematic due to complexity and a lack of networking tools. This article explores these issues through the construct of the department store of the future.

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The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

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HDTMA+ pillared montmorillonites were obtained by pillaring different amounts of the surfactant hexadecyltrimethylammonium bromide (HDTMAB) into sodium montmorillonite (Na-Mt) in an aqueous solution. The optimum conditions and batch kinetics of sorption of p-nitrophenol from aqueous solutions were reported. The solu-tion pH had a very important effect on the sorption of p-nitrophenol. The maximum p-nitrophenol absorption/adsorption occurs when solution pH (7.15~7.35) is approx-imately equal to the pKa (7.16) of the p-nitrophenol ion deprotonation reaction. X-ray diffraction analysis showed that surfactant cations had been pillared into the interlayer and the p-nitrophenol affected the arrangement of surfactant. With the increased con-centration of surfactant cations, the arrangement of HDTMA+ within the clay inter-layer changes and the sorption of p-nitrophenol increases. HDTMA+ pillared mont-morillonites are more effective than Na-Mt for the adsorption of p-nitrophenol from aqueous solutions. The Langmuir, Freundlich and dual-mode sorption were tested to fit the sorption isotherms.

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Columns are one of the key load bearing elements that are highly susceptible to vehicle impacts. The resulting severe damages to columns may leads to failures of the supporting structure that are catastrophic in nature. However, the columns in existing structures are seldom designed for impact due to inadequacies of design guidelines. The impact behaviour of columns designed for gravity loads and actions other than impact is, therefore, of an interest. A comprehensive investigation is conducted on reinforced concrete column with a particular focus on investigating the vulnerability of the exposed columns and to implement mitigation techniques under low to medium velocity car and truck impacts. The investigation is based on non-linear explicit computer simulations of impacted columns followed by a comprehensive validation process. The impact is simulated using force pulses generated from full scale vehicle impact tests. A material model capable of simulating triaxial loading conditions is used in the analyses. Circular columns adequate in capacity for five to twenty story buildings, designed according to Australian standards are considered in the investigation. The crucial parameters associated with the routine column designs and the different load combinations applied at the serviceability stage on the typical columns are considered in detail. Axially loaded columns are examined at the initial stage and the investigation is extended to analyse the impact behaviour under single axis bending and biaxial bending. The impact capacity reduction under varying axial loads is also investigated. Effects of the various load combinations are quantified and residual capacity of the impacted columns based on the status of the damage and mitigation techniques are also presented. In addition, the contribution of the individual parameter to the failure load is scrutinized and analytical equations are developed to identify the critical impulses in terms of the geometrical and material properties of the impacted column. In particular, an innovative technique was developed and introduced to improve the accuracy of the equations where the other techniques are failed due to the shape of the error distribution. Above all, the equations can be used to quantify the critical impulse for three consecutive points (load combinations) located on the interaction diagram for one particular column. Consequently, linear interpolation can be used to quantify the critical impulse for the loading points that are located in-between on the interaction diagram. Having provided a known force and impulse pair for an average impact duration, this method can be extended to assess the vulnerability of columns for a general vehicle population based on an analytical method that can be used to quantify the critical peak forces under different impact durations. Therefore the contribution of this research is not only limited to produce simplified yet rational design guidelines and equations, but also provides a comprehensive solution to quantify the impact capacity while delivering new insight to the scientific community for dealing with impacts.

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In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small � (ii) the asymptotic solution for large � (iii) the implicit finite difference method for all � where � is the transpiration parameter. Perturbation solutions for small and large values of � are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.