Use of third generation data for the elements to model the thermodynamics of binary alloy systems: Part 1 – The critical assessment of data for the Al-Zn system

Over the last four years there has been a renewed interest in the development of new critically assessed data using physically based models. Nearly all work so far has been concerned with the critical assessment of data for the elements. This has involved the selection of Einstein or Debye temperatures for the stable crystalline phases and the liquid phase and associated parameters. However, until now, these data have not been extended in a comprehensive way to model the thermodynamic properties of binary, ternary and multicomponent systems. In this paper the way in which the parameters underlying these physical models vary with composition is explored. This includes a method to define the Einstein temperature for metastable phases of the elements and its relation to the so-called lattice stabilities used in the past, and the variation of the Einstein temperature with composition to account for the composition dependence of the excess entropy. This approach is demonstrated for the Al-Zn system which shows extensive regions of solid solution and complete miscibility in the liquid phase. Here Einstein temperatures are derived for Al in the HCP_ZN phase and Zn in the FCC_A1 phase together with parameters describing the variation of the Einstein temperature with composition for the HCP_ZN, FCC_A1 and liquid phases.     

Parameterized energy–latency trade-offs for data propagation in sensor networks

We study the problem of greedy, single path data propagation in wireless sensor networks, aiming mainly to minimize the energy dissipation. In particular, we first mathematically analyze and experimentally evaluate the energy efficiency and latency of three characteristic protocols, each one selecting the next hop node with respect to a different criterion (minimum projection, minimum angle and minimum distance to the destination). Our analytic and simulation findings suggest that any single criterion does not simultaneously satisfy both energy efficiency and low latency. Towards parameterized energy–latency trade-offs we provide as well hybrid combinations of the two criteria (direction and proximity to the sink). Our hybrid protocols achieve significant performance gains and allow fine-tuning of desired performance. Also, they have nice energy balance properties, and can prolong the network lifetime.     

Methods for constraint violation suppression in the numerical simulation of constrained multibody systems – A comparative study

Multibody systems are frequently modeled as constrained systems, and the arising governing equations incorporate the closing constraint equations at the acceleration level. One consequence of accumulation of integration truncation errors is the phenomenon of violation of the lower-order constraint equations by the numerical solutions to the governing equations. The constraint drift usually tends to increase in time and may spoil reliability of the simulation results. In this paper a comparative study of three methods for constraint violation suppression is presented: the popular Baumgarte’s constraint violation stabilization method, a projective scheme for constraint violation elimination, and a novel scheme patterned after that proposed recently by Braun and Goldfarb [D.J. Braun, M. Goldfarb, Eliminating constraint drift in the numerical simulation of constrained dynamical systems, Comput. Meth. Appl. Mech. Engrg., 198 (2009) 3151–3160]. The methods are confronted with respect to simplicity in applications, numerical effectiveness and influence on accuracy of the constraint-consistent motion.     

Gravitating to rigidity: Patterns of schema evolution – and its absence – in the lives of tables

Like all software maintenance, schema evolution is a process that can severely impact the lifecycle of a data-intensive software projects, as schema updates can drive depending applications crushing or delivering incorrect data to end users. In this paper, we study the schema evolution of eight databases that are part of larger open source projects, publicly available through open source repositories. In particular, the focus of our research was the understanding of which tables evolve and how. We report on our observations and patterns on how evolution related properties, like the possibility of deletion, or the amount of updates that a table undergoes, are related to observable table properties like the number of attributes or the time of birth of a table.A study of the update profile of tables, indicates that they are mostly rigid (without any updates to their schema at all) or quiet (with few updates), especially in databases that are more mature and heavily updated. Deletions are significantly outnumbered by table insertions, leading to schema expansion. Delving deeper, we can highlight four patterns of schema evolution. The Γ pattern indicating that tables with large schemata tend to have long durations and avoid removal, the Comet pattern indicating that the tables with most updates are the ones with medium schema size, the Inverse Γ pattern, indicating that tables with medium or small durations produce amounts of updates lower than expected, and, the Empty Triangle pattern indicating that deletions involve mostly early born, quiet tables with short lives, whereas older tables are unlikely to be removed. Overall, we believe that the observed evidence strongly indicates that databases are rigidity-prone rather than evolution-prone. We call the phenomenon gravitation to rigidity and we attribute it to the implied impact to the surrounding code that a modification to the schema of a database has.     

Dissipative exponentially-fitted methods for the numerical solution of the Schrödinger equation

The first dissipative exponentially fitted method for the numerical integration of the Schr?dinger equation is developed in this paper. The technique presented is a nonsymmetric multistep (dissipative) method. An application to the bound-states problem and the resonance problem of the radial Schr?dinger equation indicates that the new method is more efficient than the classical dissipative method and other well-known methods. Based on the new method and the method of Raptis and Allison (Comput. Phys. Commun. 14 (1978) 1-5) a new variable-step method is obtained. The application of the new variable-step method to the coupled differential equations arising from the Schr?dinger equation indicates the power of the new approach.     

Comparing global land-cover products – implications for geoscience applications: an investigation for the trans-boundary Mekong Basin

In this article we present the results of a comparison of six globally available land-cover products for the Mekong Basin – an area that spans 795,000 km² and comprises parts of six riparian countries: China, Myanmar, Thailand, Laos, Cambodia, and Vietnam. The basin covers most climatic zones: from high-altitude, snow-covered mountainous regions in the north, to subtropical and tropical rainforest areas and agricultural land further south. The geopolitically important region not only is home to over 72,000,000 inhabitants, but also is a centre of attention of several environmental modelling experts, trying to assess future hydrologic dynamics, climate variability, as well probable land-use developments in the area.

We compare land-cover products of the University of Maryland, UMD 1992–1993, the GLC 2000 product, the GlobCover products of 2004–2006 and 2009, as well as the MODIS-derived land-cover products of 2001 and 2009. For harmonization of individual legends, the Land Cover Classification System, LCCS, has been employed. However, even after harmonization, cross-tabulation among the products reveals extreme differences, where the impact of differing classification algorithms weighs higher than the impact of temporal coincidence of products. Especially, differences within mixed-vegetation classes are large, strongly impacting the overall assessment of forested land, other vegetated land, and even cultivated land in the Mekong Basin. The findings presented here are of high relevance for the modelling community as well as Mekong-related environmental studies, which should consider global remote-sensing-derived products with caution and solid background knowledge.     

An expert system for the numerical solution of the radial Schrödinger equation

An expert system for the numerical solution of the phase shift problem of the radial Schrödinger equation is developed in this paper.     

On kalandiya’ method for the numerical solution of singular integral equations

For the numerical solution of one-dimensional singular integral equations with Cauchy type kernels, one can use an appropriate quadrature rule and an appropriate set of collocation points for the reduction of this equation to a system of linear equations. In this short paper, we use as collocation points the nodes of the quadrature rule and we rederive, in a more direct manner, Kalandiya’ method for the numerical solution of the aforementioned class of equations, which was originally based on a trigonometric interpolation formula. Furthermore, we test this method in numerical applications. Finally, a discussion on the accuracy of the same method is made.     

A numerical investigation of the quadratic numerical range of Hain-Lüst operators

The quadratic numerical range (QNR) was introduced by Langer and Tretter [Spectral decomposition of some non-self-adjoint block operator matrices, J. Oper. Theory 39 (1998), pp. 339–359] as a tool for estimating the spectra of operators which admit a natural block matrix representation with respect to a decomposition of the underlying Hilbert space. We consider the problem of computing the QNR numerically for block differential operators, particularly these of Hain-Lüst type and Stokes type.     

Fully coupled algorithm for heat and water transport – Estimation of non-linear parameters based on the experimental data

We solve the problem of coupled heat conduction and water transport in bentonite with water present in vapour and adsorbed form in a non-equilibrium state. The problem is governed by a system of two parabolic PDE and one ODE. Most of the coefficients are non-linear functions, defined either by underlying physical phenomena or empirically. We present a numerical scheme using FEM with linear base functions, implicit time discretization, and simple iterations for the non-linear terms. The model is verified against experiments (one 1D and one 3D) and we demonstrate the use of optimization algorithm for parameter calibration. Some of the parameters could be estimated successfully while others with limited confidence, which is explained by the particular character of the non-linear parameter dependence and resulting small sensitivity of the model on some parameters.     

Evidential reasoning-based Fuzzy AHP approach for the evaluation of design alternatives’ environmental performances

With the growing general awareness of the need to protect the environment as well as the increasingly stringent regulatory requirements imposed by various national and cross-national bodies, manufacturers have to minimise the environmental impacts of their products. Environmental considerations have therefore become a new key criterion for evaluating design alternatives during the product development stage. To facilitate non-Life Cycle Assessment (LCA) experts, such as most product designers, in evaluating the design alternatives in terms of environmental friendliness, this paper introduces a decision-making mechanism that combines the multiple criteria decision making (MCDM) approaches with LCA methodology. This evidential reasoning-based approach is a fast-track and objective tool which ranks the available design alternatives according to their potential environmental impacts. The environmental impacts of design alternatives assessed by the LCA are used for the weight elicitation processes of the proposed approach. A case application is conducted to illustrate the use of the proposed method to evaluate the environmental performances of design alternatives.     

A family of Numerov-type exponentially fitted methods for the numerical integration of the Schrödinger equation

A family of predictor-corrector exponential Numerov-type methods is developed for the numerical integration of the one-dimensional Schrödinger equation. The Numerov-type methods considered contain free parameters which allow it to be fitted to exponential functions. The new fourth algebraic order methods are very simple and integrate more exponential functions than both the well-known fourth order Numerov-type exponentially fitted methods and the sixth algebraic order Runge-Kutta-type methods. Numerical results also indicate that the new methods are much more accurate than the other exponentially fitted methods mentioned above.     

High order Bessel fitting methods for the numerical integration of the Schrödinger equation

In this paper we show how to construct explicit multistep algorithms for an accurate and efficient numerical integration of the radial Schr?dinger equation. The proposed methods are Bessel fitting, that is to say, they integrate exactly any linear combination of Bessel and Newman functions and ordinary polynomials. They are the first of the like methods that can achieve any order.     

A variable step method for the numerical integration of the one-dimensional Schrödinger equation

Most numerical methods which have been proposed for the approximate integration of the one-dimensional Schrödinger equation use a fixed step length of integration. Such an approach can of course result in gross inefficiency since the small step length which must normally be used in the initial part of the range of integration to obtain the desired accuracy must then be used throughout the integration. In this paper we consider the method of embedding, which is widely used with explicit Runge-Kutta methods for the solution of first order initial value problems, for use with the special formulae used to integrate the Schrödinger equation. By adopting this technique we have available at each step an estimate of the local truncation error and this estimate can be used to automatically control the step length of integration. Also considered is the problem of estimating the global truncation error at the end of the range of integration. The power of the approaches considered is illustrated by means of some numerical examples.     

An eighth order exponentially-fitted method for the numerical integration of the Schrödinger equation

An eighth order exponentially-fitted method is developed for the numerical solution of the Schrödinger equation. The formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions. An error analysis is also given. Numerical and theoretical results indicate that the new method is much more accurate than other classical and exponentially fitted methods.     

Comparing the Adomian decomposition method and the Runge–Kutta method for solutions of the Stefan problem

The solution of the one-phase Stefan problem is presented. A Stefan's task is first approximated with a system of ordinary differential equations. A comparison between the Adomian decomposition method and the fourth-order Runge–Kutta method for solving this system is then presented.     

A meshless method for numerical solution of the coupled Schrödinger-KdV equations

This paper presents meshless method using RBF collocation scheme for the coupled Schrödinger-KdV equations. Instead of traditional mesh oriented methods such as finite element method (FEM) or finite difference method (FDM), this method requires only a scattered set of nodes in the domain. For this scheme, error estimates and stability analysis are studied. L ₂ and L _∞ error norms between the results and exact solution is used as a performance measure. Moreover the results of numerical experiments are presented, and are compared with the findings of Finite Element method, finite difference Crank–Nicolson (CN) scheme and analytical solution to confirm the good accuracy of the presented scheme.