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PRODUCT ARCHIVE: MATHS (JUNE/JULY 05)
Love at first sightThe latest version of Maple changed Felix Grant's mathematical life in a weekend I've been familiar with Maple for a long time. It is the standard mathematics environment for many educational institutions, and many students turn in their assignments as Maple worksheets. Its power is beyond question. But 'easy to use' never seemed the most obvious way to describe it. Although a new, graphical page interface brought natural interaction a while ago, I was impressed but set in my ways. With release 10 comes yet another interface option, and I am won over. I have never been a fan of on-screen calculators, so when I installed the review copy of Maple 10, I paid no immediate attention to the icon labelled 'Maple Calculator'. Fortunately, my stepdaughter's nine-year-old son was less sniffy. 'Hey,' said his voice from the corner of the room, 'this is cool!' He was right. There is the usual scientific keypad: numerals, parentheses, exponent entry, trig and log functions, factorial and complex number unit. An additional alphabetic pad sits alongside, for variables. A matrix/list editor button, then the display area with scrolling tape session history. At top right, a secondary display area: help text by default, but showing other material in response to six tabs (Help, Graph, Data, Variables, Math, Settings) above it. And, behind it all, the power of a mainstream computer algebra package. Any problems are small. Options changed in the settings tab are not 'sticky' - set scientific notation or complex number system and they hold until shut down, but revert to normal decimal real at next start up. Some functions that report accurately in the conventional interfaces display minute inaccuracies: Sin(?), for example, shows as -2.07*10-13 in the calculator. Perhaps the biggest plus is that syntax considerations are all but removed. Each function is entered by a mouse click, a clear guide to the required parameters and their order being shown simultaneously. In the conventional worksheet, I frequently make syntax mistakes which then have to be corrected; less so in the newer graphical page environment; never in the calculator. The calculator icon is now permanently on my Windows quick start bar, a USB numeric keypad replacing the handheld one beside the laptop. For symbolics, Maple's graphical page is a natural progression (a psychological success for Maplesoft) and beyond that, for running programs or heavy weight masochism, lies the worksheet. Together, the three take me closer to 'electronic scribbling on an envelope' than I have ever been; my routine mathematical life has changed in a weekend.
Forward and inverse problem solversDynaFlow has expertise in the solution of forward and inverse problems arising from the boundary integral formulation of fluid flows and electric fields. 3DynaFS (or 2DynaFS, the axisymmetric version) provides solutions for 3D unsteady incompressible potential flows in the presence of free surfaces. The software can handle the dynamics of multiple bubbles near solid boundaries, free surfaces, submerged or floating objects, non-uniform flows, free surface waves, and body motions. In addition to its original application of cavitation bubbles, 3DynaFS was recently applied to propeller cavitation studies and ship hydrodynamics. It can be coupled with other general-purpose fluid dynamics and structure codes, such as Uncle and Dyna3D. DynaEIT is based on the same BEM method and employs efficient algorithms for electrical impedance tomography (EIT). EIT seeks to image the interior of a container, based on the electric measurements conducted on the outside, using algorithms for multi-dimensional minimisation. These EIT algorithms can be applied to medical imaging, multiphase flows encountered in chemical, oil and gas, and energy industries, non-destructive tests, and underground imaging and detection.
Extreme Optimization for .NETThe Extreme Optimization Mathematics Library for .NET is a numerical library for the Microsoft .NET framework. It includes classes for complex numbers, polynomials, curve fitting, equation solving, numerical integration and differentiation, vectors, matrices, matrix decompositions and various special functions commonly used in scientific computing. The linear algebra code uses processor-optimised versions of the standard BLAS and LAPACK routines. All routines are callable from any .NET language, including C#, Visual Basic, and Managed C++. The library lets developers exploit the enhanced productivity features of the .NET platform. Consistency, both with Microsoft's Design Guidelines for Class Library Developers and internally, ensures that developers can reuse what they have learnt building applications for the .NET framework. The objects in the library correspond to the concepts used to model mathematical problems. Upcoming companion products include a statistical library and an extended matrix library.
Multiphysics modellingFEMLAB is multiphysics modelling software for investigating scientific and engineering problems that involve partial differential equations. Users can simultaneously solve virtually any combination of physics, such as electromagnetics, heat transfer, and structural mechanics, without writing any code. This complete package includes CAD tools, predefined interfaces for physics and equation specifications, a choice of solvers, and multiple visualisation and post-processing tools. Extensive model libraries document and demonstrate hundreds of examples from technical literature and real-world applications. The software supports 64-bit platforms to handle large-scale computations. A seamless interface to MatLab allows users to combine both packages. Also available are add-on modules customised for particular areas of investigation; these modules supply PDE templates with pre-selected equations where users simply enter coefficients. Add-ons are available for chemical engineering, earth science, electromagnetics, heat transfer, MEMS, and structural mechanics.
CenterSpace for .NETThe NMath Suite of numerical component libraries from CenterSpace Software provides building blocks for mathematical, financial, engineering, and scientific applications on the .NET platform. Features include matrix and vector classes, linear algebra, random number generators, numerical integration methods, interpolation, statistics, biostatistics, multiple linear regression, and analysis of variance (ANOVA). For basic linear algebra operations, NMath libraries use proven, optimised versions of public-domain subroutine libraries, such as the BLAS (Basic Linear Algebra Subprograms) and LAPACK (Linear Algebra PACKage). This gives NMath routines performance levels comparable to C or FORTRAN, but with easy-to-use interfaces that use the full power of the .NET platform. Compliant with the Microsoft Common Language Specification, all NMath routines are callable from any .NET language, including C# and Visual Basic.NET.
Problem solving with differential equationsFlexPDE is a script-driven 'problem-solving environment' for partial differential equations, including heat flow, electric and magnetic fields, stress analysis, and other areas of science and engineering. Users can present their equations, boundary conditions, domain description and graphics output requests to FlexPDE in a readable, self-documenting script format. FlexPDE automatically builds a mesh, constructs a finite element model of the system, solves it, and presents graphical output. FlexPDE can process linear or nonlinear equations in one, two, or three space dimensions, steady-state, time-dependent or eigenvalues. It supports unlimited equation complexity, unlimited number of variables, adaptive mesh refinement and adaptive time-step control. Flexible graphic output is provided, or users can export to TecPlot, VisIt or other graphics systems for visualisations.
Mathsoft looks to the enterpriseMathsoft's calculation management suite is an enterprise software solution designed specifically to help engineering organisations create and manage engineering information. The suite includes Mathcad 12 with an open-data model, scalability, new flexibility to document engineering-critical values, greatly expanded units and dimensions handling, and new 2D plotting capabilities. Mathcad also features an XML architecture, which delivers an open-engineering data model, enabling powerful publishing, collaboration, integration and search capabilities, especially when deployed across an enterprise. The suite also includes Designate, a software framework for viewing searching and publishing Mathcad worksheets from a web browser.
Maths for optimised performanceMathematical software from The Numerical Algorithms Group (NAG) underpins thousands of applications spanning the globe in industries as diverse as financial analysis, science and engineering, and in academia and research. The latest release of the NAG Fortran Library now features more than 1,450 routines. In addition to numerical libraries in C, Fortran 77 and 90, recent developments have also included the production of a subset of routines in C# for developers using the Microsoft .NET environment. This environment allows rapid program development in the whole family of .NET languages, including C#, C++, J# and Visual Basic.
Solving intensive problemsThe latest release from The Mathworks is MatLab 7, which offers built-in support for integer and single- precision floating-point mathematics, as well as features for managing and analysing larger data sets. A large number of optimisations across data types, operations, functions, and hardware, result in improved computational performance, while the enhanced MatLab Compiler enables developers to deploy many more applications for use outside the MatLab environment.
Virtual prototyping of RF devicesSimulation software is essential to engineering design, with the concept of 'virtual prototyping' now commonplace in the design of RF and microwave devices as elsewhere. Concerto, from Vector Fields, is a three-dimensional high-frequency modelling package which uses the conformal finite-difference time-domain method. It can model all microwave devices including patch, slot, wire or horn antennas, waveguides, couplers, filters etc. A 3D geometric modeller permits simple or complex shapes to be created quickly, or models can be built using a library of predefined, parameterised objects. Other functions include blending, chamfering, twisting, lofting and 'morphing'. Thin sheets and wires can be embedded within the finite-difference grid. The Quickwave Simulator is based on the finite-difference time-domain (FDTD) technique, and uses conforming meshing technology to ensure complex geometries are easily and efficiently modelled. Conforming elements allow material boundaries to intersect with finite difference cells, so that cells can contain more than one material. Applications include telecommunications, microwave ovens, defence, microwave chemistry, space and atmosphere research, food processing, and electromagnetic impact on biological tissues.
Organisation-wide mathsWolfram Research develops computing software for science and technology, providing organisation-wide computing solutions. Mathematica, the company's main product, offers facilities ranging from simple calculator operations to large-scale programming and interactive-document preparation, and is in use at the frontiers of scientific research, in engineering analysis and modelling, in technical education from high school to graduate school, and wherever quantitative methods are used. Mathematica's features include symbolic and numeric computation, 2D and 3D data visualisation, broad programming capabilities, and one-step creation of web documents. Mathematica's native notebook format is Wolfram's universal document technology, with an open, structured syntax and active content. It allows for the generation of cross-platform, customisable files that provide professional mathematical typesetting and high-quality layout of electronic and printed media. Wolfram also has a growing library of add-on application packages for areas such as engineering, finance, statistics, data analysis, web deployment, and grid computing.
Non-linear applicationsInfinity, from Mathrevolt, is new maths software for non-linear applications. It can solve ordinary differential equations (ODE) and ODE systems, ordinary non-autonomous differential equations systems; nonlinear non-stationary differential equations and systems. In addition, the program solves derivatives, linear algebraic equations systems, and works with polynoms, including opening brackets and normalising expressions. The program can compute ordinary non-linear non-autonomous systems of differential equations with the limiting absolute local error top level given. Calculation step choice is adaptive and anticipates the dynamics of the solution change. The software can overcome first- and second-kind discontinuities, while revealing locally unstable areas in the solution.
Design and analyse pumps with Kreila and GridgenPointwise is helping solve a major problem facing engineering analysts: mesh generation for computational fluid dynamics. Manufacturing firms and research organisations use Pointwise's Gridgen software to create the 'digital geometry' enabling computer simulation of a product's performance in a fluid environment. One unique Gridgen application is a custom interface that reads geometry files directly from pump-design software, Kreila, and grids them automatically. Once a design is complete in Kreila, a complete, high-quality model is built and made ready for immediate CFD analysis at the push of a button. Gridgen will export the model in the native format of many CFD solvers, including CFX, STAR-CD, and Fluent. Gridgen gives users the flexibility to add other portions of the flowpath. Kreila and Gridgen provide highly automated design and analysis with the flexibility to make detailed changes if needed.
Vortices visualised2DFLOW, from Dynaflow, is a program for visualising flows induced by the distributions of point and line singularities, such as vortices, dipoles and sources. It graphically illustrates the use of potential flow theory, by the combination of a uniform flow with a variety of singularities to simulate a wide range of fluid-mechanics problems. 2DFLOW produces graphic representations of many classical fluid-dynamics problems. When used in conjunction with a fluid dynamics class, 2DFLOW can make visualisation of textbook theory as easy as clicking the mouse. It also allows the user to simulate and visualise complex flows making it a valuable tool for the professional. Highlights include: point-and-click singularity insertion and editing; solid boundaries and objects of arbitrary shapes can be inserted in the flow; study internal as well as external flows; problem simulation that allows the user to compute and view flow-trajectories, equipotential-lines, stream-lines, pressures and velocity vectors, using full-colour contours, iso-quantity lines and trajectories; circulation and force computation along a user defined elliptical or rectangular area and flux computation along a user-defined line; particle and strain-element emission from arbitrary regions in the flow-field; 2D and 3D graphical representations of flow quantities; interactive animation of the flow-field using scalar particle distributions and allowing motion of inserted vortices.
Fluid dynamics models enginesCD-adapco has announced the release of the Windows version of Star-CD v3.24, the latest release of its industrial CFD software, Star-CD. The new release is aimed directly at the engine modelling world, including the 3 Zone Extended Coherent Flame Model (ECFM-3Z) combustion model. ECFM-3Z is the first truly general purpose combustion model, capable of simulating the combustion process within gasoline, diesel, and hybrid concept engines.
webMathematica 2.2 includes version 5.1WebMathematica 2.2, from Wolfram Research, provides expanded web development options. Building on Mathematica Version 5.1's capabilities for working with large-scale, diverse types of data, webMathematica offers more than 50 new functions, toolkits, and performance improvements. Highlights include: built-in universal database connectivity; industrial-strength string manipulation; integrated web services support; authoring system preview; optimised binary data I/O; support for new 64-bit architectures; and additional graphic, web, and matrix import-export formats. New kinds of application development on a wider range of platforms can now be realised with webMathematica 2.2. Industrial-strength string manipulation makes it a good fit for data mining and bioinformatics applications, while support for web services makes it easy for users to harness financial, environmental, language translation, and other information resources.
Application libraries for modelling electric drivesThe MathWorks has made available SimPowerSystems 4, which enables engineers to use model-based design to model and simulate electrical circuits and power systems within Simulink. New application libraries include electric drives, flexible AC transmission systems (FACTS), and distributed resources, containing more than 150 blocks distributed in eight sub-libraries, including electric sources, electric machinery, and three-phase components. The libraries represent both simple and complex electric components, such as resistors, inductors, capacitors, and AC and DC electric drives. Together with SimMechanics and SimDriveline, SimPowerSystems 4 is the latest addition to The MathWorks' physical modelling tools, which provide electromechanical solutions and multi-domain capabilities for complex modelling and simulation. It is available immediately for Windows, UNIX/Linux, and Macintosh platforms.
Maplesoft announces suite of rapid control development toolsMaplesoft has announced ICP (Intelligent Controller Parameterisation) for Maple, a suite of rapid control development tools. The first product in the MapleConnect Premier Series, ICP for Maple enables easy identification of non-linear engineering systems and automatic development of the required controller structure and parameters to achieve design objectives. Users who need high-precision models of existing dynamic systems, particularly for control design, can capture the system output and generate continuous Laplace transfer functions that fully characterise the system across different operating points, by simply stimulating the system with an input signal. ICP then applies robust algorithms to the plant transfer functions to generate robust controller structures and optimal controller parameters without the need to be familiar with the underlying control theory.
Design Science support for MathMLXyEnterprise, a developer of XML content management and enterprise publishing software, has announced that its XML Professional Publisher (XPP) software now integrates with Design Science's standards-based MathFlow Editor. XPP is used to produce scientific, technical and medical journals, as well as many other types of print and electronic publications. Combined with MathFlow's graphical interface, which supports the creation of complex mathematical expressions, publishers of complex mathematical information now have a user-friendly publishing tool that supports the increasingly important MathML standard. MathFlow Editor is a native MathML equation editor that works within XPP. Its user interface is similar to that of Design Science's MathType and Equation Editor products with Microsoft Word. Equations appear in typeset form within the XPP and are saved as MathML within the document.
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