Samir Khan: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=613
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 08 Feb 2016 06:13:34 GMTMon, 08 Feb 2016 06:13:34 GMTNew applications published by Samir Khanhttp://www.mapleprimes.com/images/mapleapps.gifSamir Khan: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=613
Holiday Greetings and Tupper’s Self-Referential Formula
http://www.maplesoft.com/applications/view.aspx?SID=153935&ref=Feed
Want to send a Holiday greeting to a fellow Maple user? Then send them this worksheet - it's a seasonal spin on the classic Tupper’s Self-Referential Formula.<img src="/view.aspx?si=153935/teaserimage.png" alt="Holiday Greetings and Tupper’s Self-Referential Formula" align="left"/>Want to send a Holiday greeting to a fellow Maple user? Then send them this worksheet - it's a seasonal spin on the classic Tupper’s Self-Referential Formula.153935Fri, 11 Dec 2015 05:00:00 ZSamir KhanSamir KhanGain of an Ideal and Non-Ideal Amplifier
http://www.maplesoft.com/applications/view.aspx?SID=153907&ref=Feed
This application models the ideal and non-ideal behavior of an amplifier.<img src="/view.aspx?si=153907/amplifiergain.png" alt="Gain of an Ideal and Non-Ideal Amplifier" align="left"/>This application models the ideal and non-ideal behavior of an amplifier.153907Fri, 30 Oct 2015 04:00:00 ZSamir KhanSamir KhanPV Diode Parameter Estimation
http://www.maplesoft.com/applications/view.aspx?SID=153908&ref=Feed
This application fits experimental I-V data to an equation that describes a photovoltaic diode.<img src="/view.aspx?si=153908/pvdiode.png" alt="PV Diode Parameter Estimation" align="left"/>This application fits experimental I-V data to an equation that describes a photovoltaic diode.153908Fri, 30 Oct 2015 04:00:00 ZSamir KhanSamir KhanSending Emails from the Maple Command Line
http://www.maplesoft.com/applications/view.aspx?SID=153912&ref=Feed
You can send emails from the Maple command line via Mailgun (http://mailgun.com) a free email delivery service with an web-based API. The code in this application communicates with this API to send an email; you'll need to replace certain parts with details from your own Mailgun account.<img src="/applications/images/app_image_blank_lg.jpg" alt="Sending Emails from the Maple Command Line" align="left"/>You can send emails from the Maple command line via Mailgun (http://mailgun.com) a free email delivery service with an web-based API. The code in this application communicates with this API to send an email; you'll need to replace certain parts with details from your own Mailgun account.153912Fri, 30 Oct 2015 04:00:00 ZSamir KhanSamir KhanFitting Wave Height Data to a Probability Distribution
http://www.maplesoft.com/applications/view.aspx?SID=153864&ref=Feed
<p>The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.</p>
<p>This application:</p>
<ul>
<li>downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W),</li>
</ul>
<ul>
<li>fits the significant wave height to a Weibull distribution via two methods: maximum likelihood estimation and moment matching,</li>
</ul>
<ul>
<li>and plots the fitted distributions on top of a histogram of the experimental data</li>
</ul>
<p>The location of buoy PR206 is given in a Google Maps component.</p><img src="/view.aspx?si=153864/distribution.jpg" alt="Fitting Wave Height Data to a Probability Distribution" align="left"/><p>The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.</p>
<p>This application:</p>
<ul>
<li>downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W),</li>
</ul>
<ul>
<li>fits the significant wave height to a Weibull distribution via two methods: maximum likelihood estimation and moment matching,</li>
</ul>
<ul>
<li>and plots the fitted distributions on top of a histogram of the experimental data</li>
</ul>
<p>The location of buoy PR206 is given in a Google Maps component.</p>153864Wed, 09 Sep 2015 04:00:00 ZSamir KhanSamir KhanParameter Estimation for a Chemical Reaction
http://www.maplesoft.com/applications/view.aspx?SID=153782&ref=Feed
<p>This application estimates the rate parameters for a reversible reaction with dimerization of an intermediate. It does this by</p>
<ul>
<li>parameterizing the numerical solution of the different equations that describe the reaction kinetics (with respect to the rate constants)</li>
<li>defining a procedure that calculates the sum of the square of the errors between the model predictions and experimental data,</li>
<li>and minimizing the sum of the square of the errors to find the best fit values of the rate constants</li>
</ul><img src="/view.aspx?si=153782/chemical_kinetics.png" alt="Parameter Estimation for a Chemical Reaction" align="left"/><p>This application estimates the rate parameters for a reversible reaction with dimerization of an intermediate. It does this by</p>
<ul>
<li>parameterizing the numerical solution of the different equations that describe the reaction kinetics (with respect to the rate constants)</li>
<li>defining a procedure that calculates the sum of the square of the errors between the model predictions and experimental data,</li>
<li>and minimizing the sum of the square of the errors to find the best fit values of the rate constants</li>
</ul>153782Thu, 09 Apr 2015 04:00:00 ZSamir KhanSamir KhanCalibrating Response Curves for the Concentration of Melatonin Sulfate in Human Urine
http://www.maplesoft.com/applications/view.aspx?SID=153783&ref=Feed
<p>This application calibrates response curves against data from an immunoassay that records the concentration of melatonin in human urine and its optical density.</p>
<p>Melatonin is excreted by the pineal gland and regulates human circadian rhythms. Deviations outside of normal boundaries may indicate sleep disorders, depression, schizophrenia, or a range of other conditions.</p><img src="/view.aspx?si=153783/melatonin.png" alt="Calibrating Response Curves for the Concentration of Melatonin Sulfate in Human Urine" align="left"/><p>This application calibrates response curves against data from an immunoassay that records the concentration of melatonin in human urine and its optical density.</p>
<p>Melatonin is excreted by the pineal gland and regulates human circadian rhythms. Deviations outside of normal boundaries may indicate sleep disorders, depression, schizophrenia, or a range of other conditions.</p>153783Thu, 09 Apr 2015 04:00:00 ZSamir KhanSamir KhanInteraural Time Delay
http://www.maplesoft.com/applications/view.aspx?SID=153780&ref=Feed
<p>Humans locate the origin of a sound with several cues. One technique employs the small difference in the time taken for the sound to reach either ear; this is known as the interaural time delay (ITD). This application modifies a single-channel audio file so that the sound appears to originate at an angle from the observer. It does this by introducing an extra channel of sound. Despite both channels having the same amplitude, the sound appears to come from an angle simply by delaying one channel.</p><img src="/view.aspx?si=153780/interaural.png" alt="Interaural Time Delay" align="left"/><p>Humans locate the origin of a sound with several cues. One technique employs the small difference in the time taken for the sound to reach either ear; this is known as the interaural time delay (ITD). This application modifies a single-channel audio file so that the sound appears to originate at an angle from the observer. It does this by introducing an extra channel of sound. Despite both channels having the same amplitude, the sound appears to come from an angle simply by delaying one channel.</p>153780Tue, 31 Mar 2015 04:00:00 ZSamir KhanSamir KhanGas Orifice Flow Meter Calculator
http://www.maplesoft.com/applications/view.aspx?SID=153739&ref=Feed
<p>This application calculates the flowrate through a large-diameter orifice using the approach outlined in ISO 5167 2:2003</p>
<p>Orifice meters use the pressure loss across a constriction (that is, the orifice plate) in a pipe to determine the flowrate. </p>
<p>The formulas are valid for</p>
<ul>
<li>pipes diameters between 50mm and 1000 mm, </li>
<li>and pressure ratios greater than 0.75.</li>
</ul>
<p>Reference: <span ><a href="http://en.wikipedia.org/wiki/Orifice_plate">http://en.wikipedia.org/wiki/Orifice_plate</a></span></p><img src="/view.aspx?si=153739/gasorifice.png" alt="Gas Orifice Flow Meter Calculator" align="left"/><p>This application calculates the flowrate through a large-diameter orifice using the approach outlined in ISO 5167 2:2003</p>
<p>Orifice meters use the pressure loss across a constriction (that is, the orifice plate) in a pipe to determine the flowrate. </p>
<p>The formulas are valid for</p>
<ul>
<li>pipes diameters between 50mm and 1000 mm, </li>
<li>and pressure ratios greater than 0.75.</li>
</ul>
<p>Reference: <span ><a href="http://en.wikipedia.org/wiki/Orifice_plate">http://en.wikipedia.org/wiki/Orifice_plate</a></span></p>153739Tue, 20 Jan 2015 05:00:00 ZSamir KhanSamir KhanIs a Stock Overvalued or Undervalued?
http://www.maplesoft.com/applications/view.aspx?SID=153740&ref=Feed
<p>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.</p>
<p>Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.</p>
<p>The stock is undervalued If the fair value is greater than the current market price, and vice-versa.</p>
<p>This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols. This spreadsheet is used to populate the interface with industries, exchanges and companies, and must be saved in the same location as the Maple worksheet.</p><img src="/view.aspx?si=153740/stockovervalued.png" alt="Is a Stock Overvalued or Undervalued?" align="left"/><p>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.</p>
<p>Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.</p>
<p>The stock is undervalued If the fair value is greater than the current market price, and vice-versa.</p>
<p>This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols. This spreadsheet is used to populate the interface with industries, exchanges and companies, and must be saved in the same location as the Maple worksheet.</p>153740Tue, 20 Jan 2015 05:00:00 ZSamir KhanSamir KhanEconomic Pipe Sizer for Process Plants
http://www.maplesoft.com/applications/view.aspx?SID=153659&ref=Feed
<p>Pipework is a large part of the cost of a process plant. Plant designers need to minimize the total cost of this pipework across the lifetime of the plant. The total overall cost is a combination of individual costs related to the:</p>
<ul>
<li>pipe material,</li>
<li>installation, </li>
<li>maintenance, </li>
<li>depreciation, </li>
<li>energy costs for pumping, </li>
<li>liquid parameters, </li>
<li>required flowrate,</li>
<li>pumping efficiencies,</li>
<li>taxes,</li>
<li>and more.</li>
</ul>
<p>The total cost is not a simple linear sum of the individual costs; a more complex relationship is needed.</p>
<p>This application uses the approach described in [1] to find the pipe diameter that minimizes the total lifetime cost. The method involves the iterative solution of an empirical equation using <a href="/support/help/Maple/view.aspx?path=fsolve">Maple’s fsolve function</a> (the code for the application is in the Startup code region).</p>
<p>Users can choose the pipe material (carbon steel, stainless steel, aluminum or brass), and specify the desired fluid flowrate, fluid viscosity and density. The application then solves the empirical equation (using Maple’s fsolve() function) and returns the economically optimal pipe diameter.</p>
<p>Bear in mind that the empirical parameters used in the application vary as economic conditions change. Those used in this application are correct for 1998 and 2008.</p>
<p><em>[1]: "Updating the Rules for Pipe Sizing", Durand et al., Chemical Engineering, January 2010</em></p><img src="/applications/images/app_image_blank_lg.jpg" alt="Economic Pipe Sizer for Process Plants" align="left"/><p>Pipework is a large part of the cost of a process plant. Plant designers need to minimize the total cost of this pipework across the lifetime of the plant. The total overall cost is a combination of individual costs related to the:</p>
<ul>
<li>pipe material,</li>
<li>installation, </li>
<li>maintenance, </li>
<li>depreciation, </li>
<li>energy costs for pumping, </li>
<li>liquid parameters, </li>
<li>required flowrate,</li>
<li>pumping efficiencies,</li>
<li>taxes,</li>
<li>and more.</li>
</ul>
<p>The total cost is not a simple linear sum of the individual costs; a more complex relationship is needed.</p>
<p>This application uses the approach described in [1] to find the pipe diameter that minimizes the total lifetime cost. The method involves the iterative solution of an empirical equation using <a href="/support/help/Maple/view.aspx?path=fsolve">Maple’s fsolve function</a> (the code for the application is in the Startup code region).</p>
<p>Users can choose the pipe material (carbon steel, stainless steel, aluminum or brass), and specify the desired fluid flowrate, fluid viscosity and density. The application then solves the empirical equation (using Maple’s fsolve() function) and returns the economically optimal pipe diameter.</p>
<p>Bear in mind that the empirical parameters used in the application vary as economic conditions change. Those used in this application are correct for 1998 and 2008.</p>
<p><em>[1]: "Updating the Rules for Pipe Sizing", Durand et al., Chemical Engineering, January 2010</em></p>153659Fri, 15 Aug 2014 04:00:00 ZSamir KhanSamir KhanDrawdown of Historical Stock Prices
http://www.maplesoft.com/applications/view.aspx?SID=153624&ref=Feed
<p>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.</p>
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol (this requires a connection to the Internet),</li>
<li>defines a procedure that calculates the drawdown of the historical stock price</li>
<li>and plots the drawdown against the adjusted close price of the asset</li>
</ul>
<p>By changing the ticker symbol and the two dates, you can examine drawdown of any stock between any period.</p>
<p>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL into a matrix using <span><a href="/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</p><img src="/view.aspx?si=153624/2def9a8f2111f9b47d0bee568aed6035.gif" alt="Drawdown of Historical Stock Prices" align="left"/><p>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.</p>
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol (this requires a connection to the Internet),</li>
<li>defines a procedure that calculates the drawdown of the historical stock price</li>
<li>and plots the drawdown against the adjusted close price of the asset</li>
</ul>
<p>By changing the ticker symbol and the two dates, you can examine drawdown of any stock between any period.</p>
<p>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL into a matrix using <span><a href="/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</p>153624Mon, 07 Jul 2014 04:00:00 ZSamir KhanSamir KhanOptimizing the Design of a Coil Spring
http://www.maplesoft.com/applications/view.aspx?SID=153608&ref=Feed
<p>The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.</p>
<p>Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.</p>
<p>This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency and the maximum stress, and a loading condition.</p>
<ul>
<li>the minimum deflection, </li>
<li>the minimum surge wave frequency, </li>
<li>the maximum stress, </li>
<li>and a loading condition.</li>
</ul>
<p>The design variables are the</p>
<ul>
<li>diameter of the wire, </li>
<li>the outside diameter of the spring,</li>
<li>and the number of coils</li>
</ul>
<p> Reference: "Introduction to Optimum Design", Jasbir S. Arora, 3<sup>rd</sup> Edition 2012.</p><img src="/view.aspx?si=153608/695d991fff8fb4975d1e1dcd90bb771d.gif" alt="Optimizing the Design of a Coil Spring" align="left"/><p>The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.</p>
<p>Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.</p>
<p>This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency and the maximum stress, and a loading condition.</p>
<ul>
<li>the minimum deflection, </li>
<li>the minimum surge wave frequency, </li>
<li>the maximum stress, </li>
<li>and a loading condition.</li>
</ul>
<p>The design variables are the</p>
<ul>
<li>diameter of the wire, </li>
<li>the outside diameter of the spring,</li>
<li>and the number of coils</li>
</ul>
<p> Reference: "Introduction to Optimum Design", Jasbir S. Arora, 3<sup>rd</sup> Edition 2012.</p>153608Tue, 17 Jun 2014 04:00:00 ZSamir KhanSamir KhanCircle Packing in an Ellipse
http://www.maplesoft.com/applications/view.aspx?SID=153598&ref=Feed
<p>This application optimizes the packing of circles in an ellipse, such that the area of the ellipse is minimized. A typical solution is visualized here.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 35 circles generates 666 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.</p>
<p>Applications like this are used to stress-test global optimizers.</p>
<p>The constraints and ellipse parameterization are taken from "Packing circles within ellipses", Birgin et al., International Transactions in Operational Research , Volume 20, Issue 3, pages 365–389, May 2013.</p><img src="/view.aspx?si=153598/5f52383daddaeb53aec548d14ebd6ce0.gif" alt="Circle Packing in an Ellipse" align="left"/><p>This application optimizes the packing of circles in an ellipse, such that the area of the ellipse is minimized. A typical solution is visualized here.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 35 circles generates 666 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.</p>
<p>Applications like this are used to stress-test global optimizers.</p>
<p>The constraints and ellipse parameterization are taken from "Packing circles within ellipses", Birgin et al., International Transactions in Operational Research , Volume 20, Issue 3, pages 365–389, May 2013.</p>153598Wed, 04 Jun 2014 04:00:00 ZSamir KhanSamir KhanPacking Circles into a Triangle
http://www.maplesoft.com/applications/view.aspx?SID=153596&ref=Feed
<p>This application finds the best packing and largest radius of equal-sized circles, such that they fit in a pre-defined triangle. One solution, as visualized by this application, is given below.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="http://www.maplesoft.com/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 310 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations. The vertices of the triangle can also be modified</p>
<p>Applications like this are used to stress-test global optimizers.</p><img src="/view.aspx?si=153596/2ac6ca1378717b3d939f3d8107616b35.gif" alt="Packing Circles into a Triangle" align="left"/><p>This application finds the best packing and largest radius of equal-sized circles, such that they fit in a pre-defined triangle. One solution, as visualized by this application, is given below.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="http://www.maplesoft.com/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 310 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations. The vertices of the triangle can also be modified</p>
<p>Applications like this are used to stress-test global optimizers.</p>153596Wed, 04 Jun 2014 04:00:00 ZSamir KhanSamir KhanCircle Packing in a Square
http://www.maplesoft.com/applications/view.aspx?SID=153599&ref=Feed
<p>This application optimizes the packing of circles (of varying radii) in a square, such that the side-length of the square is minimized. One solution for 20 circles (with integer radii of 1 to 20) is visualized here.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 230 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.</p>
<p>Applications like this are used to stress-test global optimizers.</p><img src="/view.aspx?si=153599/071f7b81258c5cad651a5030370d824f.gif" alt="Circle Packing in a Square" align="left"/><p>This application optimizes the packing of circles (of varying radii) in a square, such that the side-length of the square is minimized. One solution for 20 circles (with integer radii of 1 to 20) is visualized here.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 230 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.</p>
<p>Applications like this are used to stress-test global optimizers.</p>153599Wed, 04 Jun 2014 04:00:00 ZSamir KhanSamir KhanPacking Disks into a Circle
http://www.maplesoft.com/applications/view.aspx?SID=153600&ref=Feed
<p>This application finds the best packing of unequal non-overlapping disks in a circular container, such that the radius of the container is minimized. This is a tough global optimization problem that demands strong solvers; this application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>. You must have the Global Optimization Toolbox installed to use this application.</p>
<p>One solution for the packing of 50 disks with the integer radii 1 to 50 (as found by this application) is visualized here.</p>
<p>Other solutions for similar packing problems are documented at <a href="http://www.packomania.com">http://www.packomania.com</a>.</p>
<p>Packing optimization is industrially important, with applications in pallet loading, the arrangement of fiber optic cables in a tube, or the placing of components on a circuit board.</p><img src="/view.aspx?si=153600/32183b61c1bca332d0c71924ae09f73a.gif" alt="Packing Disks into a Circle" align="left"/><p>This application finds the best packing of unequal non-overlapping disks in a circular container, such that the radius of the container is minimized. This is a tough global optimization problem that demands strong solvers; this application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>. You must have the Global Optimization Toolbox installed to use this application.</p>
<p>One solution for the packing of 50 disks with the integer radii 1 to 50 (as found by this application) is visualized here.</p>
<p>Other solutions for similar packing problems are documented at <a href="http://www.packomania.com">http://www.packomania.com</a>.</p>
<p>Packing optimization is industrially important, with applications in pallet loading, the arrangement of fiber optic cables in a tube, or the placing of components on a circuit board.</p>153600Wed, 04 Jun 2014 04:00:00 ZSamir KhanSamir KhanWelded Beam Design Optimization
http://www.maplesoft.com/applications/view.aspx?SID=153592&ref=Feed
<p>A rigid member is welded onto a beam, with a load applied to the end of the member. The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.</p>
<p>The design of the beam is optimized to minimize the production costs by varying the weld and member dimensions.</p>
<p>The constraints include limits on the shear stress, bending stress, buckling load and end deflection, and several size constraints.</p>
<p>The application uses Maple’s non-linear optimizers</p><img src="/view.aspx?si=153592/0621a9aba622112f66506495e21f68d9.gif" alt="Welded Beam Design Optimization" align="left"/><p>A rigid member is welded onto a beam, with a load applied to the end of the member. The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.</p>
<p>The design of the beam is optimized to minimize the production costs by varying the weld and member dimensions.</p>
<p>The constraints include limits on the shear stress, bending stress, buckling load and end deflection, and several size constraints.</p>
<p>The application uses Maple’s non-linear optimizers</p>153592Fri, 30 May 2014 04:00:00 ZSamir KhanSamir KhanPrincipal Component Analysis
http://www.maplesoft.com/applications/view.aspx?SID=153591&ref=Feed
<p>Principal Component Analysis transforms a multi-dimensional data set to a new set of perpendicular axes (or components) that describe decreasing amounts of variance. </p>
<p>This worksheet reduces the complexity of a data set using principal component analysis. Those components that have the least impact on the variance are discarded, and the simplified data reconstructed from the remaining components.</p><img src="/view.aspx?si=153591/PrincipalComponentAn.jpg" alt="Principal Component Analysis" align="left"/><p>Principal Component Analysis transforms a multi-dimensional data set to a new set of perpendicular axes (or components) that describe decreasing amounts of variance. </p>
<p>This worksheet reduces the complexity of a data set using principal component analysis. Those components that have the least impact on the variance are discarded, and the simplified data reconstructed from the remaining components.</p>153591Mon, 26 May 2014 04:00:00 ZSamir KhanSamir KhanOptimizing the Design of a Fuel Pod with NX and Maple
http://www.maplesoft.com/applications/view.aspx?SID=153573&ref=Feed
<p>A manufacturer has designed a fuel pod in NX. The fuel pod has a hemispherical and conical end, and a cylindrical mid-section. To minimize material costs, the manufacturer wants to minimize the surface area of the fuel pod while maintaining the existing volume.</p>
<p>This application:</p>
<ul>
<li>pulls the current dimensions of the fuel pod (radius of the hemispherical end, length of the cylindrical midsection, and height of the conical end) from the NX CAD model, </li>
<li>calculates the current volume of the fuel pod,</li>
<li>optimizes the dimensions to minimize the surface area while maintaining the existing volume,</li>
<li>and pushes the optimized dimensions back into the NX CAD model.</li>
</ul>
<p>NOTE: To use this application, you must</p>
<ul>
<li>have a supported version of NX installed, </li>
<li>load canisterOptimization.prt in NX (this is the CAD model of the fuel pod),</li>
<li>ensure the NX-Maple link works correctly.</li>
</ul><img src="/view.aspx?si=153573/fuelpod.jpg" alt="Optimizing the Design of a Fuel Pod with NX and Maple" align="left"/><p>A manufacturer has designed a fuel pod in NX. The fuel pod has a hemispherical and conical end, and a cylindrical mid-section. To minimize material costs, the manufacturer wants to minimize the surface area of the fuel pod while maintaining the existing volume.</p>
<p>This application:</p>
<ul>
<li>pulls the current dimensions of the fuel pod (radius of the hemispherical end, length of the cylindrical midsection, and height of the conical end) from the NX CAD model, </li>
<li>calculates the current volume of the fuel pod,</li>
<li>optimizes the dimensions to minimize the surface area while maintaining the existing volume,</li>
<li>and pushes the optimized dimensions back into the NX CAD model.</li>
</ul>
<p>NOTE: To use this application, you must</p>
<ul>
<li>have a supported version of NX installed, </li>
<li>load canisterOptimization.prt in NX (this is the CAD model of the fuel pod),</li>
<li>ensure the NX-Maple link works correctly.</li>
</ul>153573Wed, 07 May 2014 04:00:00 ZSamir KhanSamir Khan