On evaluation of the Heun functions

In the paper we deal with the Heun functions --- solutions of the Heun equation, which is the most general Fuchsian equation of second order with four regular singular points. Despite the increasing interest to the equation and numerous applications of the functions in a wide variety of physical problems, it is only Maple amidst known software packages which is able to evaluate the Heun functions numerically. But the Maple routine is known to be imperfect: even at regular points it may return infinities or end up with no result. Improving the situation is difficult because the code is not publicly available. The purpose of the work is to suggest and develop alternative algorithms for numerical evaluation of the Heun functions. A procedure based on power series expansions and analytic continuation is suggested which allows us to avoid numerical integration of the differential equation and to achieve reasonable efficiency and accuracy. Results of numerical tests are given

Microwave Subsurface Imaging Technology for Damage Detection

This paper presents a technology for detecting invisible damage inside concrete, which is based on reconstruction of dielectric profile (image) of the concrete illuminated with microwaves sent from and received by antenna arrays controlled by specialized software. The imaging system developed in this study consists of an 8X8 transmitting and an 8X8 receiving arrays, an innovative numerical bifocusing operator for improving image resolution, and imaging software for reconstructing a two-dimensional image from the scattered field. The effectiveness of the of the developed technology in detecting steel and voids inside concrete has been demonstrated through numerical simulation and experiments

Improving the regulatory acceptance and numerical performance of CFD based fire-modelling software

The research of this thesis was concerned with practical aspects of Computational Fluid Dynamics (CFD) based fire modelling software, specifically its application and performance. Initially a novel CFD based fire suppression model was developed (FIREDASS). The FIREDASS (FIRE Detection And Suppression Simulation) programme was concerned with the development of water misting systems as a possible replacement for halon based fire suppression systems currently used in aircraft cargo holds and ship engine rooms. A set of procedures was developed to test the applicability of CFD fire modelling software. This methodology was demonstrated on three CFD products that can be used for fire modelling purposes. The proposed procedure involved two phases. Phase 1 allowed comparison between different computer codes without the bias of the user or specialist features that may exist in one code and not another by rigidly defining the case set-up. Phase 2 allowed the software developer to perform the test using the best modelling features available in the code to best represent the scenario being modelled. In this way it was hoped to demonstrate that in addition to achieving a common minimum standard of performance, the software products were also capable of achieving improved agreement with the experimental or theoretical results. A significant conclusion drawn from this work suggests that an engineer using the basic capabilities of any of the products tested would be likely to draw the same conclusions from the results irrespective of which product was used. From a regulators view, this is an important result as it suggests that the quality of the predictions produced are likely to be independent of the tool used - at least in situations where the basic capabilities of the software were used. The majority of this work has focussed on the use of specialised proprietary hardware generally based around the UNIX operating system. The majority of engineering firms that would benefit from the reduced timeframes offered by parallel processing rarely have access to such specialised systems. However, in recent years with the increasing power of individual office PCs and the improved performance of Local Area Networks (LAN) it has now come to the point where parallel processing can be usefully utilised in a typical office environment where many such PCs maybe connected to a LAN. Harnessing this power for fire modelling has great promise. Modern low cost supercomputers are now typically constructed from commodity PC motherboards connected via a dedicated high-speed network. However, virtually no work has been published on using office based PCs connected via a LAN in a parallel manner on real applications. The SMARTFIRE fire field model was modified to utilise multiple PCs on a typical office based LAN. It was found that good speedup could be achieved on homogeneous PCs, for example for a problem composed of-100,000 cells would run on a network of 12 PCs with a speedup of 9.3 over a single PC. A dynamic load balancing scheme was devised to allow the effective use of the software on heterogeneous PC networks. This scheme also ensured that the impact of the parallel processing on other computer users was minimised. This scheme also minimised the impact of other computer users on the parallel processing performed by the FSE

Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models

Graphical models use graphs to compactly capture stochastic dependencies amongst a collection of random variables. Inference over graphical models corresponds to finding marginal probability distributions given joint probability distributions. In general, this is computationally intractable, which has led to a quest for finding efficient approximate inference algorithms. We propose a framework for generalized inference over graphical models that can be used as a wrapper for improving the estimates of approximate inference algorithms. Instead of applying an inference algorithm to the original graph, we apply the inference algorithm to a block-graph, defined as a graph in which the nodes are non-overlapping clusters of nodes from the original graph. This results in marginal estimates of a cluster of nodes, which we further marginalize to get the marginal estimates of each node. Our proposed block-graph construction algorithm is simple, efficient, and motivated by the observation that approximate inference is more accurate on graphs with longer cycles. We present extensive numerical simulations that illustrate our block-graph framework with a variety of inference algorithms (e.g., those in the libDAI software package). These simulations show the improvements provided by our framework.Comment: Extended the previous version to include extensive numerical simulations. See http://www.ima.umn.edu/~dvats/GeneralizedInference.html for code and dat

BCVEGPY2.0: A upgrade version of the generator BCVEGPY with an addendum about hadroproduction of the PP-wave BcB_c states

The generator BCVEGPY is upgraded by adding the hadroproduction of the $P$-wave excited $B_c$ states (denoted by $B_{cJ,L=1}^*$ or by $h_{B_c}$ and $\chi_{B_c}$) and by improving some features of the original one as well. We denote it as BCVEGPY2.0. The $P$-wave production is also calculated by taking only the dominant gluon-gluon fusion mechanism (with the subprocess $gg\to B_{cJ,L=1}^*+\bar{c}+b$ being dominated) into account as that for $S$-wave. In order to make the addendum piece of the upgraded generator as compact as possible so as to increase its efficiency, we manipulate the amplitude as compact as possible with FDC (a software for generating Feynman diagrams and the algebra amplitudes, and for manipulating algebra formulae analytically etc) and certain simplification techniques. The correctness of the program is tested by checking the gauge invariance of the amplitude and by comparing the numerical results with the existent ones in the literature carefully.Comment: 21 page, 4 figure

Development of software for easy prediction of process parameters in air bending with local heating

This paper presents a new software tool for sheet metal forming, based on an analytical model of the process. The advantages of this kind of tool, compared with numerical models based on finite element codes, are described. The analysis is focused on sheet metal bending at high temperature that is a promising method for metal forming, improving sheet formability and machines range of use.Publicad

Integrated aerodynamic-structural design of a forward-swept transport wing

The introduction of composite materials is having a profound effect on aircraft design. Since these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require an integrated multidisciplinary design process. Futhermore, because of the complexity of the design process, numerical optimization methods are required. The utilization of integrated multidisciplinary design procedures for improving aircraft design is not currently feasible because of software coordination problems and the enormous computational burden. Even with the expected rapid growth of supercomputers and parallel architectures, these tasks will not be practical without the development of efficient methods for cross-disciplinary sensitivities and efficient optimization procedures. The present research is part of an on-going effort which is focused on the processes of simultaneous aerodynamic and structural wing design as a prototype for design integration. A sequence of integrated wing design procedures has been developed in order to investigate various aspects of the design process