A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

Bed expansion:extending correlations for fluidized beds with inserts to open fluidized beds

Bed expansion occurs during the operation of gas-fluidized beds and is influenced by particle properties, gas properties and distributor characteristics. It has a significant bearing on heat and mass transfer phenomena within the bed. A method of predicting bed expansion behavior from other fluidizing parameters would be a useful tool in the design process, dispensing with the need for small-scale trials. This study builds on previous work on fluidized beds with vertical inserts to produce a correlation that links a modified particle terminal velocity, minimum fluidizing velocity and distributor characteristics with bed voidage in the relationship with P as the pitch between holes in the perforated distributor plate. © 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

Internet search:subdivision-based interactive query expansion and the soft semantic web

The expansion of the Internet has made the task of searching a crucial one. Internet users, however, have to make a great effort in order to formulate a search query that returns the required results. Many methods have been devised to assist in this task by helping the users modify their query to give better results. In this paper we propose an interactive method for query expansion. It is based on the observation that documents are often found to contain terms with high information content, which can summarise their subject matter. We present experimental results, which demonstrate that our approach significantly shortens the time required in order to accomplish a certain task by performing web searches.

The role of environmental factors in industrial site selection activities:a case of limestone quarry expansion in Barbados, West Indies

Site selection is a key activity for quarry expansion to support cement production, and is governed by factors such as resource availability, logistics, costs, and socio-environmental factors. Adequate consideration of all factors facilitates both industrial productivity and sustainable economic growth. This study illustrates the site selection process that was undertaken for the expansion of limestone quarry operations to support cement production in Barbados. First, alternate sites with adequate resources to support a 25-year development horizon were identified. Second, socio-environmental conditions were described and potential impacts identified. Third, a comparative matrix was constructed to evaluate relative site characteristics with respect to physical, ecological, socio-cultural and economic factors. The study shows that environmental factors were essential to the final site recommendation.

Review of low-temperature vapour power cycle engines with quasi-isothermal expansion

External combustion heat cycle engines convert thermal energy into useful work. Thermal energy resources include solar, geothermal, bioenergy, and waste heat. To harness these and maximize work output, there has been a renaissance of interest in the investigation of vapour power cycles for quasi-isothermal (near constant temperature) instead of adiabatic expansion. Quasi-isothermal expansion has the advantage of bringing the cycle efficiency closer to the ideal Carnot efficiency, but it requires heat to be transferred to the working fluid as it expands. This paper reviews various low-temperature vapour power cycle heat engines with quasi-isothermal expansion, including the methods employed to realize the heat transfer. The heat engines take the form of the Rankine cycle with continuous heat addition during the expansion process, or the Stirling cycle with a condensable vapour as working fluid. Compared to more standard Stirling engines using gas, the specific work output is higher. Cryogenic heat engines based on the Rankine cycle have also been enhanced with quasi-isothermal expansion. Liquid flooded expansion and expander surface heating are the two main heat transfer methods employed. Liquid flooded expansion has been applied mainly in rotary expanders, including scroll turbines; whereas surface heating has been applied mainly in reciprocating expanders. © 2014 Elsevier Ltd.

Using a Query Expansion Technique to Improve Document Retrieval

Query expansion (QE) is a potentially useful technique to help searchers formulate improved query statements, and ultimately retrieve better search results. The objective of our query expansion technique is to find a suitable additional term. Two query expansion methods are applied in sequence to reformulate the query. Experiments on test collections show that the retrieval effectiveness is considerably higher when the query expansion technique is applied.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.

Porosity and Variational Principles

We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

A Perturbed Iterative Method for a General Class of Variational Inequalities

The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.

On a Variational Approach to some Quasilinear Problems

We prove some multiplicity results concerning quasilinear elliptic equations with natural growth conditions. Techniques of nonsmooth critical point theory are employed.

Nonlinear Variational Inequalities Depending on a Parameter

This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.

Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

* This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged.