Maplesoft: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=165
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 10 Feb 2016 12:52:07 GMTWed, 10 Feb 2016 12:52:07 GMTNew applications published by Maplesofthttp://www.mapleprimes.com/images/mapleapps.gifMaplesoft: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=165
EscapeTime Fractals
http://www.maplesoft.com/applications/view.aspx?SID=153882&ref=Feed
<P>
The <A HREF="/support/help/Maple/view.aspx?path=Fractals/EscapeTime">Fractals</A> package in Maple makes it easier to create and explore popular fractals, including the Mandelbrot, Julia, Newton, and other time-iterative fractals. The Fractals package can quickly apply various escape time iterative maps over rectangular regions in the complex plane, the results of which consist of images that approximate well-known fractal sets. In the following application, you can explore escape time fractals by manipulating parameters pertaining to the generation of Mandelbrot, Julia, Newton and Burning Ship fractals.</P>
<P>
<B>Also:</B> You can <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=5690839489576960">interact with this application</A> in the MapleCloud!</P><img src="/view.aspx?si=153882/escapetimefractal.png" alt="EscapeTime Fractals" align="left"/><P>
The <A HREF="/support/help/Maple/view.aspx?path=Fractals/EscapeTime">Fractals</A> package in Maple makes it easier to create and explore popular fractals, including the Mandelbrot, Julia, Newton, and other time-iterative fractals. The Fractals package can quickly apply various escape time iterative maps over rectangular regions in the complex plane, the results of which consist of images that approximate well-known fractal sets. In the following application, you can explore escape time fractals by manipulating parameters pertaining to the generation of Mandelbrot, Julia, Newton and Burning Ship fractals.</P>
<P>
<B>Also:</B> You can <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=5690839489576960">interact with this application</A> in the MapleCloud!</P>153882Fri, 25 Sep 2015 04:00:00 ZMaplesoftMaplesoftTips and Techniques: Working with Finitely Presented Groups in Maple
http://www.maplesoft.com/applications/view.aspx?SID=153852&ref=Feed
This Tips and Techniques article introduces Maple's facilities for working with finitely presented groups. A finitely presented group is a group defined by means of a finite number of generators, and a finite number of defining relations. It is one of the principal ways in which a group may be represented on the computer, and is virtually the only representation that effectively allows us to compute with many infinite groups.<img src="/view.aspx?si=153852/thumb.jpg" alt="Tips and Techniques: Working with Finitely Presented Groups in Maple" align="left"/>This Tips and Techniques article introduces Maple's facilities for working with finitely presented groups. A finitely presented group is a group defined by means of a finite number of generators, and a finite number of defining relations. It is one of the principal ways in which a group may be represented on the computer, and is virtually the only representation that effectively allows us to compute with many infinite groups.153852Tue, 25 Aug 2015 04:00:00 ZMaplesoftMaplesoftHollywood Math 2
http://www.maplesoft.com/applications/view.aspx?SID=153681&ref=Feed
<p>Over the years, Hollywood has entertained us with many mathematical moments in film and television, often in unexpected places. In this application, you’ll find several examples of Hollywood Math, including Fermat’s Last Theorem and <em>The Simpsons</em>, the Monty Hall problem in <em>21</em>, and a discussion of just how long that runway actually was in <em>The Fast and the Furious</em>. These examples are also presented in <a href="/webinars/recorded/featured.aspx?id=782">Hollywood Math 2: The Recorded Webinar</a>.</p>
<p>For even more examples, see <a href="/applications/view.aspx?SID=6611">Hollywood Math: The Original Episode</a>.</p><img src="/view.aspx?si=153681/HollywoodMath2.jpg" alt="Hollywood Math 2" align="left"/><p>Over the years, Hollywood has entertained us with many mathematical moments in film and television, often in unexpected places. In this application, you’ll find several examples of Hollywood Math, including Fermat’s Last Theorem and <em>The Simpsons</em>, the Monty Hall problem in <em>21</em>, and a discussion of just how long that runway actually was in <em>The Fast and the Furious</em>. These examples are also presented in <a href="/webinars/recorded/featured.aspx?id=782">Hollywood Math 2: The Recorded Webinar</a>.</p>
<p>For even more examples, see <a href="/applications/view.aspx?SID=6611">Hollywood Math: The Original Episode</a>.</p>153681Tue, 23 Sep 2014 04:00:00 ZMaplesoftMaplesoftState-Feedback and Observer-Based Control Design
http://www.maplesoft.com/applications/view.aspx?SID=153526&ref=Feed
<p>This application explores different control strategies for a cart supporting two inverted pendulums of different, but unknown, lengths. State-feedback, observer-based controllers are designed for the system. Controllers are parameterized, and interactive applications are created for each method to allow easy exploration and visualization.</p>
<p>This application requires the <a href="/products/toolboxes/control_design/">MapleSim Control Design Toolbox</a>.</p><img src="/view.aspx?si=153526/95d1242810308c9068f71961d5f5f9e4.gif" alt="State-Feedback and Observer-Based Control Design" align="left"/><p>This application explores different control strategies for a cart supporting two inverted pendulums of different, but unknown, lengths. State-feedback, observer-based controllers are designed for the system. Controllers are parameterized, and interactive applications are created for each method to allow easy exploration and visualization.</p>
<p>This application requires the <a href="/products/toolboxes/control_design/">MapleSim Control Design Toolbox</a>.</p>153526Wed, 19 Mar 2014 04:00:00 ZMaplesoftMaplesoftDesigning a PID Controller
http://www.maplesoft.com/applications/view.aspx?SID=153527&ref=Feed
<p>This worksheet illustrates how the MapleSim Control Design Toolbox can be used to design PID controllers using several methods. In the first section, we will use the Pole Placement method to design a PI controller for a second-order system so that we can confine the closed-loop poles to a desired region. In the second section, we will use the Exact Pole Placement method to design a PID controller so that we can specify the exact location of the dominant poles. In the third section, we will use the Gain-Phase Margin method to design a PID controller for a fifth-order system. Finally, in the last section, we will use a single tuning parameter - equivalent to the desired time constant of the closed-loop system - to design a PID controller for a third-order system applying Skogestad IMC tuning rules.</p>
<p>This application requires the <a href="/products/toolboxes/control_design/">MapleSim Control Design Toolbox</a>.</p><img src="/view.aspx?si=153527/3ac68242ca1f9edfc23fddc173ce6537.gif" alt="Designing a PID Controller" align="left"/><p>This worksheet illustrates how the MapleSim Control Design Toolbox can be used to design PID controllers using several methods. In the first section, we will use the Pole Placement method to design a PI controller for a second-order system so that we can confine the closed-loop poles to a desired region. In the second section, we will use the Exact Pole Placement method to design a PID controller so that we can specify the exact location of the dominant poles. In the third section, we will use the Gain-Phase Margin method to design a PID controller for a fifth-order system. Finally, in the last section, we will use a single tuning parameter - equivalent to the desired time constant of the closed-loop system - to design a PID controller for a third-order system applying Skogestad IMC tuning rules.</p>
<p>This application requires the <a href="/products/toolboxes/control_design/">MapleSim Control Design Toolbox</a>.</p>153527Wed, 19 Mar 2014 04:00:00 ZMaplesoftMaplesoftVehicle Ride and Handling Tool
http://www.maplesoft.com/applications/view.aspx?SID=153445&ref=Feed
<p>This interactive tool allows the user to try various combinations of steer- and camber-by-roll coefficients for a 3 degree-of-freedom vehicle model, and observe the effect on the yaw gain curve and the value of the understeer coefficient, <em>K<sub>us</sub></em>.</p><img src="/view.aspx?si=153445/3eef1d3c328ded1f1a2b2761f1f9bce4.gif" alt="Vehicle Ride and Handling Tool" align="left"/><p>This interactive tool allows the user to try various combinations of steer- and camber-by-roll coefficients for a 3 degree-of-freedom vehicle model, and observe the effect on the yaw gain curve and the value of the understeer coefficient, <em>K<sub>us</sub></em>.</p>153445Wed, 23 Oct 2013 04:00:00 ZMaplesoftMaplesoftFiltering Frequency Domain Noise
http://www.maplesoft.com/applications/view.aspx?SID=144593&ref=Feed
<p>This application demonstrates how you can filter low-power noise from the frequency domain representation of experimental data.</p><img src="/view.aspx?si=144593/10748a72d8047dfc094a9cdc7e3de5cd.gif" alt="Filtering Frequency Domain Noise" align="left"/><p>This application demonstrates how you can filter low-power noise from the frequency domain representation of experimental data.</p>144593Wed, 13 Mar 2013 04:00:00 ZMaplesoftMaplesoftPeriodicity of Sunspots
http://www.maplesoft.com/applications/view.aspx?SID=144592&ref=Feed
<p>This application finds the periodicity of sunspots with two independent approaches</p>
<ul>
<li>a frequency domain transformation of the data, </li>
<li>and autocorrelation. </li>
</ul>
<p>If implemented and interpreted correctly, both approaches should give the same sunspot period. The application uses routines from Maple 17’s new <a href="/products/maple/new_features/signal_processing.aspx">Signal Processing package</a>, and uses historical sunspot data from the National Geophysical Data Center. Additionally, an embedded video component demonstrates how you can zoom into a plot.</p><img src="/view.aspx?si=144592/sunspots.jpg" alt="Periodicity of Sunspots" align="left"/><p>This application finds the periodicity of sunspots with two independent approaches</p>
<ul>
<li>a frequency domain transformation of the data, </li>
<li>and autocorrelation. </li>
</ul>
<p>If implemented and interpreted correctly, both approaches should give the same sunspot period. The application uses routines from Maple 17’s new <a href="/products/maple/new_features/signal_processing.aspx">Signal Processing package</a>, and uses historical sunspot data from the National Geophysical Data Center. Additionally, an embedded video component demonstrates how you can zoom into a plot.</p>144592Wed, 13 Mar 2013 04:00:00 ZMaplesoftMaplesoftPole Locations and Performance Characteristics
http://www.maplesoft.com/applications/view.aspx?SID=139228&ref=Feed
<p>This control theory application explores how the behavior of a system is determined by the position of the poles and zeros.</p>
<p>This document is part of the collection of <a href="/contact/webforms/ControlTheory/">Classroom Content: Control Theory</a> package.</p><img src="/view.aspx?si=139228/139228_thumb.jpg" alt="Pole Locations and Performance Characteristics" align="left"/><p>This control theory application explores how the behavior of a system is determined by the position of the poles and zeros.</p>
<p>This document is part of the collection of <a href="/contact/webforms/ControlTheory/">Classroom Content: Control Theory</a> package.</p>139228Mon, 05 Nov 2012 05:00:00 ZMaplesoftMaplesoftStatistics Enhancements in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132195&ref=Feed
Statistical computations in Maple combine the ease of working in a high-level, interactive environment with a very large and powerful set of algorithms. Large data sets can be handled efficiently with 35 built-in statistical distributions, sampling, estimations, data smoothing, hypothesis testing, and visualization algorithms. In addition, integration with the Maple symbolic engine means that you can easily specify custom distributions by combining existing distributions or simply by giving a formula for the probability or cumulative distribution function. These examples illustrate the use of the Statistics package, with emphasis on enhancements in Maple 16.<img src="/view.aspx?si=132195/thumb.jpg" alt="Statistics Enhancements in Maple 16" align="left"/>Statistical computations in Maple combine the ease of working in a high-level, interactive environment with a very large and powerful set of algorithms. Large data sets can be handled efficiently with 35 built-in statistical distributions, sampling, estimations, data smoothing, hypothesis testing, and visualization algorithms. In addition, integration with the Maple symbolic engine means that you can easily specify custom distributions by combining existing distributions or simply by giving a formula for the probability or cumulative distribution function. These examples illustrate the use of the Statistics package, with emphasis on enhancements in Maple 16.132195Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftObject-Oriented Programming in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132199&ref=Feed
The Maple language is a full programming language designed for mathematical computation, combining the best principles from procedural, functional, and object-oriented programming. Maple 16 adds support for light-weight objects for enhanced object-oriented programming. Such objects integrate closely with Maple using operator overloading, making your objects almost indistinguishable from built-in Maple types. This example illustrates the use of light-weight objects.<img src="/view.aspx?si=132199/thumb.jpg" alt="Object-Oriented Programming in Maple 16" align="left"/>The Maple language is a full programming language designed for mathematical computation, combining the best principles from procedural, functional, and object-oriented programming. Maple 16 adds support for light-weight objects for enhanced object-oriented programming. Such objects integrate closely with Maple using operator overloading, making your objects almost indistinguishable from built-in Maple types. This example illustrates the use of light-weight objects.132199Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftPolynomial System Solving in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132208&ref=Feed
Computing and manipulating the real solutions of a polynomial system is a requirement for many application areas, such as biological modeling, robotics, program verification, and control design, to name just a few. For example, an important problem in computational biology is to study the stability of the equilibria (or steady states) of biological systems. This question can often be reduced to solving a parametric system of polynomial equations and inequalities. In this application, these techniques are used to perform stability analysis of a parametric dynamical system and verify mathematical identities through branch cut analysis.<img src="/view.aspx?si=132208/thumb.jpg" alt="Polynomial System Solving in Maple 16" align="left"/>Computing and manipulating the real solutions of a polynomial system is a requirement for many application areas, such as biological modeling, robotics, program verification, and control design, to name just a few. For example, an important problem in computational biology is to study the stability of the equilibria (or steady states) of biological systems. This question can often be reduced to solving a parametric system of polynomial equations and inequalities. In this application, these techniques are used to perform stability analysis of a parametric dynamical system and verify mathematical identities through branch cut analysis.132208Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftPhysics in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132209&ref=Feed
Maple 16 provides the most significant evolution of the Physics package since its introduction in Maple 11, underscoring Maple's goal of having a state-of-the-art environment for algebraic computations in physics. The Physics package in Maple 16 includes 17 new commands that extend its functionality in vector and tensor analysis, general relativity, and quantum fields. In addition, a vast number of changes were introduced to support the goal of making the computational experience as natural as possible, resembling the paper-and-pencil way of doing computations and providing textbook-quality display of results. This application illustrates some of the new features in the Physics package.<img src="/view.aspx?si=132209/thumb.jpg" alt="Physics in Maple 16" align="left"/>Maple 16 provides the most significant evolution of the Physics package since its introduction in Maple 11, underscoring Maple's goal of having a state-of-the-art environment for algebraic computations in physics. The Physics package in Maple 16 includes 17 new commands that extend its functionality in vector and tensor analysis, general relativity, and quantum fields. In addition, a vast number of changes were introduced to support the goal of making the computational experience as natural as possible, resembling the paper-and-pencil way of doing computations and providing textbook-quality display of results. This application illustrates some of the new features in the Physics package.132209Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftMath Apps in Maple
http://www.maplesoft.com/applications/view.aspx?SID=132220&ref=Feed
Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains a sampling of some of the many Math Apps available in Maple: drawing the graph of a quadratic, epicycloids, monte carlo approximations of pi, and throwing coconuts.<img src="/view.aspx?si=132220/mathapps_thumb.png" alt="Math Apps in Maple" align="left"/>Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains a sampling of some of the many Math Apps available in Maple: drawing the graph of a quadratic, epicycloids, monte carlo approximations of pi, and throwing coconuts.132220Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftInterpolation and Smoothing
http://www.maplesoft.com/applications/view.aspx?SID=132223&ref=Feed
These examples illustrate 3-D interpolation and smoothing. It shows the use of a smoothing algorithm to create a smooth surface that approximates your noisy data 3-D data, and interpolation methods that generate a surface that matches your data exactly, regardless of whether the data points lie on a uniform or non-uniform grid. Many of these techniques are new in Maple 16.<img src="/view.aspx?si=132223/thumb.jpg" alt="Interpolation and Smoothing" align="left"/>These examples illustrate 3-D interpolation and smoothing. It shows the use of a smoothing algorithm to create a smooth surface that approximates your noisy data 3-D data, and interpolation methods that generate a surface that matches your data exactly, regardless of whether the data points lie on a uniform or non-uniform grid. Many of these techniques are new in Maple 16.132223Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftDifferential Geometry in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132224&ref=Feed
With over 250 commands, the DifferentialGeometry package allows sophisticated computations from basic jet calculus to the realm of the mathematics behind general relativity. In addition, 19 differential geometry lessons, from beginner to advanced level, and 6 tutorials illustrate the use of the package in applications. This applications demonstrates some of the new functionality in Maple 16 for working with abstractly defined differential forms, general relativity, and Lie algebras.<img src="/view.aspx?si=132224/thumb.jpg" alt="Differential Geometry in Maple 16" align="left"/>With over 250 commands, the DifferentialGeometry package allows sophisticated computations from basic jet calculus to the realm of the mathematics behind general relativity. In addition, 19 differential geometry lessons, from beginner to advanced level, and 6 tutorials illustrate the use of the package in applications. This applications demonstrates some of the new functionality in Maple 16 for working with abstractly defined differential forms, general relativity, and Lie algebras.132224Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftDifferential Equations in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132225&ref=Feed
Maple 16 continues to push the frontiers in differential equation solving and extends its lead in computing closed-form solutions to differential equations, adding in even more classes of problems that can be handled. The numeric ODE, DAE, and PDE solvers also continue to evolve. Maple 16 shows significant performance improvements for these solvers, as well as enhanced event handling. This application illustrates many of these improvements.<img src="/view.aspx?si=132225/thumb2.jpg" alt="Differential Equations in Maple 16" align="left"/>Maple 16 continues to push the frontiers in differential equation solving and extends its lead in computing closed-form solutions to differential equations, adding in even more classes of problems that can be handled. The numeric ODE, DAE, and PDE solvers also continue to evolve. Maple 16 shows significant performance improvements for these solvers, as well as enhanced event handling. This application illustrates many of these improvements.132225Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftDouble Vitrage (Double Glazed Windows)
http://www.maplesoft.com/applications/view.aspx?SID=131043&ref=Feed
<p>Ce modèle compare trois types de vitrage:</p>
<ul>
<li>un simple vitrage</li>
<li>un double vitrage utilisant l'air comme isolant</li>
<li>un double vitrage utilisant l'argon comme isolant</li>
</ul>
<p>This model compares three types of glazing:</p>
<ul>
<li>Single glazing</li>
<li>Double glazing using air as insulation</li>
<li>Double glazing using argon as insulation</li>
</ul><img src="/applications/images/app_image_blank_lg.jpg" alt="Double Vitrage (Double Glazed Windows)" align="left"/><p>Ce modèle compare trois types de vitrage:</p>
<ul>
<li>un simple vitrage</li>
<li>un double vitrage utilisant l'air comme isolant</li>
<li>un double vitrage utilisant l'argon comme isolant</li>
</ul>
<p>This model compares three types of glazing:</p>
<ul>
<li>Single glazing</li>
<li>Double glazing using air as insulation</li>
<li>Double glazing using argon as insulation</li>
</ul>131043Wed, 22 Feb 2012 05:00:00 ZMaplesoftMaplesoftWater Hammer
http://www.maplesoft.com/applications/view.aspx?SID=129499&ref=Feed
<p>When a valve at the end of a pipeline rapidly closes, a pressure surge hits the valve, and a pressure wave travels along the pipeline. This is known as Water Hammer.</p>
<p>In this model, a discretized pipeline (with inertial and resistive properties) is initially pressurized at one end to create flow. After two seconds, a valve at the other end is closed. A pressure surge at the valve is observed.</p>
<p>Probes can be placed at various points to investigate the pressure dynamics along the pipeline.</p>
<p>The valve dynamics can be altered to reduce the magnitude of the pressure surge. Moreover, an accumulator can be enabled to further reduce the pressure surge.</p>
<p>Additionally, a Maple worksheet that models Water Hammer by solving the governing PDEs (through spatial discretization, giving a set of ODEs) is included as an attachment (see Project > Attachments > Documents > Water Hammer Application.mw.</p>
<p>The MapleSim model and Maple worksheet give consistent results, and the maximum pressure (for fully shut valves) corresponds to the <em>Joukowsky pressure. </em>This provides assurance that both approaches are correct.</p><img src="/view.aspx?si=129499/waterhammer_sm.jpg" alt="Water Hammer" align="left"/><p>When a valve at the end of a pipeline rapidly closes, a pressure surge hits the valve, and a pressure wave travels along the pipeline. This is known as Water Hammer.</p>
<p>In this model, a discretized pipeline (with inertial and resistive properties) is initially pressurized at one end to create flow. After two seconds, a valve at the other end is closed. A pressure surge at the valve is observed.</p>
<p>Probes can be placed at various points to investigate the pressure dynamics along the pipeline.</p>
<p>The valve dynamics can be altered to reduce the magnitude of the pressure surge. Moreover, an accumulator can be enabled to further reduce the pressure surge.</p>
<p>Additionally, a Maple worksheet that models Water Hammer by solving the governing PDEs (through spatial discretization, giving a set of ODEs) is included as an attachment (see Project > Attachments > Documents > Water Hammer Application.mw.</p>
<p>The MapleSim model and Maple worksheet give consistent results, and the maximum pressure (for fully shut valves) corresponds to the <em>Joukowsky pressure. </em>This provides assurance that both approaches are correct.</p>129499Mon, 09 Jan 2012 05:00:00 ZMaplesoftMaplesoftFitting 3D Data to a Bivariate Polynomial Surface
http://www.maplesoft.com/applications/view.aspx?SID=129500&ref=Feed
<p>This application:</p>
<ul>
<li>generates 3D data as a proxy for experimental data (i.e. a table of X, Y, Z points with random noise added to Z),</li>
<li>generates a bivariate polynomial (the order can be changed by the user),</li>
<li>fits the polynomial to the data with a least-squares fit,</li>
</ul>
<p>and plots the original data against the best-fit polynomial surface.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Fitting 3D Data to a Bivariate Polynomial Surface" align="left"/><p>This application:</p>
<ul>
<li>generates 3D data as a proxy for experimental data (i.e. a table of X, Y, Z points with random noise added to Z),</li>
<li>generates a bivariate polynomial (the order can be changed by the user),</li>
<li>fits the polynomial to the data with a least-squares fit,</li>
</ul>
<p>and plots the original data against the best-fit polynomial surface.</p>129500Mon, 09 Jan 2012 05:00:00 ZMaplesoftMaplesoft