A hybrid smoothed finite element method (H-SFEM) to solid mechanics problems

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and Node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained by adjusting ; (2) there exists a preferable at which the H-SFEM can produce the ultrasonic accurate solution.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

A new framework of measuring national nutrients balance for international and global comparison

Nutrients balance such as nitrogen and phosphorus balance are increasingly used as an indicator of the environmental performance of agricultural sector in international and global context. However there still is a lack of harmony in the use of methods for estimating the nutrients balance among countries. This is because of the disagreement regarding the accuracy and uncertainty of different accounting methods. The lack of harmony in the methods used in different countries further increases the uncertainty in the context of the international comparisons. This paper provides a new framework for nutrients balance calculation using the farm-gate accounting method. The calculation under this new framework takes advantage of availability of data from FAO and other reliable national and international sources. Due to this, the proposed framework is highly adaptable in many countries, making the global comparison feasible. The paper also proposes three criteria including adaptability, accuracy and interpretability to assess the appropriateness of nutrients accounting method. Based on these criteria, the paper provides a comprehensive comparison of the farm-gate and soil-surface methods in accounting country-level nutrients balance of agricultural production. The paper identifies some shortcomings of the soil-surface balance and shows that the farm-gate method has a greater potential of providing a more accurate and meaningful estimation of national nutrients balance.

Swept source OCT with air puff chamber for corneal dynamics measurements

None of currently used tonometers produce estimated IOP values that are free of errors. Measurement incredibility arises from indirect measurement of corneal deformation and the fact that pressure calculations are based on population averaged parameters of anterior segment. Reliable IOP values are crucial for understanding and monitoring of number of eye pathologies e.g. glaucoma. We have combined high speed swept source OCT with air-puff chamber. System provides direct measurement of deformation of cornea and anterior surface of the lens. This paper describes in details the performance of air-puff ssOCT instrument. We present different approaches of data presentation and analysis. Changes in deformation amplitude appears to be good indicator of IOP changes. However, it seems that in order to provide accurate intraocular pressure values an additional information on corneal biomechanics is necessary. We believe that such information could be extracted from data provided by air-puff ssOCT.

A prototype system dynamic model for assessing the sustainability of construction projects

There is a worldwide demand for an increasingly sustainable built environment. This has resulted in the need for a more accurate evaluation of the level of sustainability of construction projects. To do this it involves the development of better measurement and benchmarking methods. One approach is to use a theoretical model to assess construction projects in terms of their sustainable development value (SDV) and sustainable development ability (SDA) for implementation in the project life cycle, where SDA measures the contribution of a project to development sustainability and as a major criterion for assessing its feasibility. This paper develops an improved SDA prototype model that incorporates the effects of dynamical factors on project sustainability. This involves the introduction of two major factors concerning technological advancement and changes in people's perceptions. A case study is used to demonstrate the procedures involved in simulation and modeling, one outcome of which is to demonstrate the greater influence of technological advancement on project sustainability than changes in perception.