Samir Khan: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=613
en-us2019 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 16 Dec 2019 00:56:59 GMTMon, 16 Dec 2019 00:56:59 GMTNew applications published by Samir Khanhttps://www.maplesoft.com/images/Application_center_hp.jpgSamir Khan: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=613
Calculating the Latent Heats of Vaporization and Fusion of Water
https://www.maplesoft.com/applications/view.aspx?SID=154552&ref=Feed
This application demonstrates how you can calculate the latent heat of vaporization and the latent heat of fusion of water.
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The application uses empirical data from the <A HREF="/products/maple/features/thermophysicaldata.aspx">ThermophysicalData package</A><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Calculating the Latent Heats of Vaporization and Fusion of Water" style="max-width: 25%;" align="left"/>This application demonstrates how you can calculate the latent heat of vaporization and the latent heat of fusion of water.
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The application uses empirical data from the <A HREF="/products/maple/features/thermophysicaldata.aspx">ThermophysicalData package</A>https://www.maplesoft.com/applications/view.aspx?SID=154552&ref=FeedThu, 12 Sep 2019 04:00:00 ZSamir KhanSamir KhanGenerating Parametric Curves from 2-D Data using Discrete Fourier Transforms
https://www.maplesoft.com/applications/view.aspx?SID=154546&ref=Feed
This application will generate parametric equations for a set of 2-D points. When plotted, the parametric equations resemble the shape of the points.
<BR><BR>
This application has an interactive plot that lets you draw a curve. Maple will generate discrete points on this curve as it is drawn. Maple will then
<UL>
<LI>compute the discrete Fourier transforms (DFT) of the X and Y coordinates.
<LI>generate two parametric equations that consist of a sum of sines. The frequency and amplitude of each sine term are extracted from the DFT.
<LI>assign the equations to two variables
</UL><img src="https://www.maplesoft.com/view.aspx?si=154546/maple.png" alt="Generating Parametric Curves from 2-D Data using Discrete Fourier Transforms" style="max-width: 25%;" align="left"/>This application will generate parametric equations for a set of 2-D points. When plotted, the parametric equations resemble the shape of the points.
<BR><BR>
This application has an interactive plot that lets you draw a curve. Maple will generate discrete points on this curve as it is drawn. Maple will then
<UL>
<LI>compute the discrete Fourier transforms (DFT) of the X and Y coordinates.
<LI>generate two parametric equations that consist of a sum of sines. The frequency and amplitude of each sine term are extracted from the DFT.
<LI>assign the equations to two variables
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154546&ref=FeedMon, 12 Aug 2019 04:00:00 ZSamir KhanSamir KhanFinding the Sutherland Equation Coefficients with Least-Squares Curve Fitting
https://www.maplesoft.com/applications/view.aspx?SID=154547&ref=Feed
The Sutherland equation is commonly used to describe the variation of gas viscosity with temperature.
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There are two constants in the equation. These are typically found by fitting experimental data for viscosity to the equation.
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This application finds the Sutherland coefficients for Helium.
<UL>
<LI>Frist, data for the viscosity of Helium at several temperatures is generated with the ThermophysicalData:-Property command.
<LI>Then, the Statistics:-NonlinearFit command is used to find the value of the two constants.
</UL>
This gives us the constants in the equation. The principles can be extended to any gas.<img src="https://www.maplesoft.com/view.aspx?si=154547/sutherland.png" alt="Finding the Sutherland Equation Coefficients with Least-Squares Curve Fitting" style="max-width: 25%;" align="left"/>The Sutherland equation is commonly used to describe the variation of gas viscosity with temperature.
<BR><BR>
There are two constants in the equation. These are typically found by fitting experimental data for viscosity to the equation.
<BR><BR>
This application finds the Sutherland coefficients for Helium.
<UL>
<LI>Frist, data for the viscosity of Helium at several temperatures is generated with the ThermophysicalData:-Property command.
<LI>Then, the Statistics:-NonlinearFit command is used to find the value of the two constants.
</UL>
This gives us the constants in the equation. The principles can be extended to any gas.https://www.maplesoft.com/applications/view.aspx?SID=154547&ref=FeedMon, 12 Aug 2019 04:00:00 ZSamir KhanSamir KhanCompressor Power for a Supersonic Wind Tunnel at Steady-state and Start-up
https://www.maplesoft.com/applications/view.aspx?SID=154548&ref=Feed
This application calculates the compressor power (at steady-state and at start-up) for a fixed geometry supersonic wind tunnel. The test section will operate at Mach 2.5, simulate an altitude of 21 km and has a circular cross-sectional area with a diameter of 30 cm. A supersonic fixed-area diffuser follows the test section.
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A cooler between the compressor and the nozzle ensures that the air at the compressor inlet and in the test section have the same stagnation temperature.
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The air entering the compressor and in the test section has the same stagnation temperature. The compressor is isentropic, and friction and boundary layer effects are not considered.<img src="https://www.maplesoft.com/view.aspx?si=154548/wind_tunnel.png" alt="Compressor Power for a Supersonic Wind Tunnel at Steady-state and Start-up" style="max-width: 25%;" align="left"/>This application calculates the compressor power (at steady-state and at start-up) for a fixed geometry supersonic wind tunnel. The test section will operate at Mach 2.5, simulate an altitude of 21 km and has a circular cross-sectional area with a diameter of 30 cm. A supersonic fixed-area diffuser follows the test section.
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A cooler between the compressor and the nozzle ensures that the air at the compressor inlet and in the test section have the same stagnation temperature.
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The air entering the compressor and in the test section has the same stagnation temperature. The compressor is isentropic, and friction and boundary layer effects are not considered.https://www.maplesoft.com/applications/view.aspx?SID=154548&ref=FeedMon, 12 Aug 2019 04:00:00 ZSamir KhanSamir KhanUnpowered Glide Analysis of a Baron 58 Light Aircraft
https://www.maplesoft.com/applications/view.aspx?SID=154544&ref=Feed
This application presents an unpowered glide analysis of a Baron 58 aircraft.
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An aircraft with no engine power will glide to the ground. The best glide angle is the flight angle at which the airplane will travel the greatest distance, and occurs at the maximum lift-to-drag ratio.
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For the parameters used in this application, a Baron 58 aircraft has a maximum lift-to-drag ratio of about 12.2. This means an unpowered Baron will fall 1 m for every 12.2 m of travel. This application also calculates the best glide velocity, drag and lift coefficients, and the dynamic pressure.<img src="https://www.maplesoft.com/view.aspx?si=154544/Drag_force.png" alt="Unpowered Glide Analysis of a Baron 58 Light Aircraft" style="max-width: 25%;" align="left"/>This application presents an unpowered glide analysis of a Baron 58 aircraft.
<BR><BR>
An aircraft with no engine power will glide to the ground. The best glide angle is the flight angle at which the airplane will travel the greatest distance, and occurs at the maximum lift-to-drag ratio.
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For the parameters used in this application, a Baron 58 aircraft has a maximum lift-to-drag ratio of about 12.2. This means an unpowered Baron will fall 1 m for every 12.2 m of travel. This application also calculates the best glide velocity, drag and lift coefficients, and the dynamic pressure.https://www.maplesoft.com/applications/view.aspx?SID=154544&ref=FeedThu, 18 Jul 2019 04:00:00 ZSamir KhanSamir KhanUS Standard Atmosphere 1976
https://www.maplesoft.com/applications/view.aspx?SID=154545&ref=Feed
Standard atmospheric models describe how the properties of air change with altitude. The properties reflect conditions typically expected at that altitude, and do not vary with current climatic conditions. The results are typically used for flight studies, rocketry and ballistics.
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This application implements the US Standard Atmosphere model for the lower atmosphere, published by the US Committee on Extension to the Standard Atmosphere (COESA) in 1976.
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The model gives the pressure, temperature, density and viscosity of air as a function of geopotential altitude, and is valid from a geopotential altitude of 0 m to 84852 m.
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Reference: <A HREF="https://ntrs.nasa.gov/search.jsp?R=19770009539" TARGET="_blank">US Standard Atmosphere 1976</A><img src="https://www.maplesoft.com/view.aspx?si=154545/US_Standard_Atmosphere_1976.png" alt="US Standard Atmosphere 1976" style="max-width: 25%;" align="left"/>Standard atmospheric models describe how the properties of air change with altitude. The properties reflect conditions typically expected at that altitude, and do not vary with current climatic conditions. The results are typically used for flight studies, rocketry and ballistics.
<BR><BR>
This application implements the US Standard Atmosphere model for the lower atmosphere, published by the US Committee on Extension to the Standard Atmosphere (COESA) in 1976.
<BR><BR>
The model gives the pressure, temperature, density and viscosity of air as a function of geopotential altitude, and is valid from a geopotential altitude of 0 m to 84852 m.
<BR><BR>
Reference: <A HREF="https://ntrs.nasa.gov/search.jsp?R=19770009539" TARGET="_blank">US Standard Atmosphere 1976</A>https://www.maplesoft.com/applications/view.aspx?SID=154545&ref=FeedThu, 18 Jul 2019 04:00:00 ZSamir KhanSamir KhanMUSIC Method for Spectral Estimation
https://www.maplesoft.com/applications/view.aspx?SID=154543&ref=Feed
The <A HREF="https://en.wikipedia.org/wiki/MUSIC_(algorithm)">MUtiple SIgnal Classifier (MUSIC)</A> method is an approach for spectral estimation that is particularly appropriate for signals that consists of multiple sinusoids polluted with white (i.e. Gaussian) noise.
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Since the power estimate offered by the MUSIC method can be evaluated at any frequency, the MUSIC method offers a form of superesolution - that is, frequencies smaller than one sample (i.e. smaller than one DFT bin).
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This application generates a noisy sinusoidal signal, and then applies the MUSIC method to identify the frequencies used to generate the signal.<img src="https://www.maplesoft.com/view.aspx?si=154543/music.png" alt="MUSIC Method for Spectral Estimation" style="max-width: 25%;" align="left"/>The <A HREF="https://en.wikipedia.org/wiki/MUSIC_(algorithm)">MUtiple SIgnal Classifier (MUSIC)</A> method is an approach for spectral estimation that is particularly appropriate for signals that consists of multiple sinusoids polluted with white (i.e. Gaussian) noise.
<BR><BR>
Since the power estimate offered by the MUSIC method can be evaluated at any frequency, the MUSIC method offers a form of superesolution - that is, frequencies smaller than one sample (i.e. smaller than one DFT bin).
<BR><BR>
This application generates a noisy sinusoidal signal, and then applies the MUSIC method to identify the frequencies used to generate the signal.https://www.maplesoft.com/applications/view.aspx?SID=154543&ref=FeedWed, 10 Jul 2019 04:00:00 ZSamir KhanSamir KhanKinematic Analysis of a Quick Return Device
https://www.maplesoft.com/applications/view.aspx?SID=154541&ref=Feed
This is a quick return device.
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This application will:
<UL>
<LI>determine the range of motion of this device
<li>and its behavior if the crank driven at (i) a constant angular velocity, and (ii) a constant angular acceleration
</UL>
The latter involves numerically solving differential equations. These are symbolically derived by differentiating the geometric relationships with respect to time. The resulting equations contain the first and second derivative of the crank angle with respect to time; these will be set to constant values to reveal the behavior of the system.<img src="https://www.maplesoft.com/view.aspx?si=154541/kinematic.png" alt="Kinematic Analysis of a Quick Return Device" style="max-width: 25%;" align="left"/>This is a quick return device.
<BR><BR>
This application will:
<UL>
<LI>determine the range of motion of this device
<li>and its behavior if the crank driven at (i) a constant angular velocity, and (ii) a constant angular acceleration
</UL>
The latter involves numerically solving differential equations. These are symbolically derived by differentiating the geometric relationships with respect to time. The resulting equations contain the first and second derivative of the crank angle with respect to time; these will be set to constant values to reveal the behavior of the system.https://www.maplesoft.com/applications/view.aspx?SID=154541&ref=FeedMon, 08 Jul 2019 04:00:00 ZSamir KhanSamir KhanForces in a 4 Member Frame
https://www.maplesoft.com/applications/view.aspx?SID=154542&ref=Feed
This frame is subject to a load P at point G. This application will determine the forces at the supports and in members BE and CF.
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Since the frame is in equilibrium, the sum of horizontal forces, sum of vertical forces, and sum of momentum about a point is zero. This allows us to identify the unknown forces in a system.<img src="https://www.maplesoft.com/view.aspx?si=154542/frame.png" alt="Forces in a 4 Member Frame" style="max-width: 25%;" align="left"/>This frame is subject to a load P at point G. This application will determine the forces at the supports and in members BE and CF.
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Since the frame is in equilibrium, the sum of horizontal forces, sum of vertical forces, and sum of momentum about a point is zero. This allows us to identify the unknown forces in a system.https://www.maplesoft.com/applications/view.aspx?SID=154542&ref=FeedMon, 08 Jul 2019 04:00:00 ZSamir KhanSamir KhanPositions of Two Objects Suspended and Connected by Ropes
https://www.maplesoft.com/applications/view.aspx?SID=154535&ref=Feed
Two objects are connected and suspended by a system of ropes, as illustrated in the diagram.
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This application finds the position of the objects and the tension in the ropes with a horizontal and vertical force balance.<img src="https://www.maplesoft.com/view.aspx?si=154535/thumb.png" alt="Positions of Two Objects Suspended and Connected by Ropes" style="max-width: 25%;" align="left"/>Two objects are connected and suspended by a system of ropes, as illustrated in the diagram.
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This application finds the position of the objects and the tension in the ropes with a horizontal and vertical force balance.https://www.maplesoft.com/applications/view.aspx?SID=154535&ref=FeedWed, 05 Jun 2019 04:00:00 ZSamir KhanSamir KhanWorst Case Circuit Analysis with Monte Carlo Simulation
https://www.maplesoft.com/applications/view.aspx?SID=154534&ref=Feed
Electrical components are manufactured in large quantities. Inconsistencies in the raw materials and the manufacturing process means that component parameters have a statistical distribution. That is, the resistance of a batch of resistors might be described by a normal distribution.
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Given the components in a circuit their parameter distribution, the circuit may not perform as specified. This is a risk that must be identified and mitigated early in the design process.
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Worst Case Circuit Analysis is a set of techniques used to analyze how variations in parameters influence circuit performance. One approach is Monte Carlo analysis, in which parameters are randomly selected from a distribution, and the circuit simulated, anywhere from 1000 to 100000 times.
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This application performs a worst case circuit analysis of an electrical circuit using a Monte Carlo approach.<img src="https://www.maplesoft.com/view.aspx?si=154534/WCCA_MC.png" alt="Worst Case Circuit Analysis with Monte Carlo Simulation" style="max-width: 25%;" align="left"/>Electrical components are manufactured in large quantities. Inconsistencies in the raw materials and the manufacturing process means that component parameters have a statistical distribution. That is, the resistance of a batch of resistors might be described by a normal distribution.
<BR><BR>
Given the components in a circuit their parameter distribution, the circuit may not perform as specified. This is a risk that must be identified and mitigated early in the design process.
<BR><BR>
Worst Case Circuit Analysis is a set of techniques used to analyze how variations in parameters influence circuit performance. One approach is Monte Carlo analysis, in which parameters are randomly selected from a distribution, and the circuit simulated, anywhere from 1000 to 100000 times.
<BR><BR>
This application performs a worst case circuit analysis of an electrical circuit using a Monte Carlo approach.https://www.maplesoft.com/applications/view.aspx?SID=154534&ref=FeedWed, 29 May 2019 04:00:00 ZSamir KhanSamir KhanExtreme Value Analysis of an Electrical Circuit
https://www.maplesoft.com/applications/view.aspx?SID=154533&ref=Feed
An electrical component, such as a resistor or capacitor, is usually quantified with a nominal value and a tolerance. Given the number of components in a circuit and their compounded tolerances, the actual performance of a circuit may not necessarily match its desired performance.
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Extreme Value Analysis (EVA) is a process in which the behavior of a circuit is simulated for every permutation of extreme component parameters in combination with every permutation of extreme values for all other components. This application performs an extreme value analysis of a circuit with a photodiode-generated current and an op-amp, though the principles can be extended to any circuit.<img src="https://www.maplesoft.com/view.aspx?si=154533/circuit.png" alt="Extreme Value Analysis of an Electrical Circuit" style="max-width: 25%;" align="left"/>An electrical component, such as a resistor or capacitor, is usually quantified with a nominal value and a tolerance. Given the number of components in a circuit and their compounded tolerances, the actual performance of a circuit may not necessarily match its desired performance.
<BR><BR>
Extreme Value Analysis (EVA) is a process in which the behavior of a circuit is simulated for every permutation of extreme component parameters in combination with every permutation of extreme values for all other components. This application performs an extreme value analysis of a circuit with a photodiode-generated current and an op-amp, though the principles can be extended to any circuit.https://www.maplesoft.com/applications/view.aspx?SID=154533&ref=FeedTue, 28 May 2019 04:00:00 ZSamir KhanSamir KhanPhysical Properties of Natural Gas
https://www.maplesoft.com/applications/view.aspx?SID=154532&ref=Feed
Oil and gas engineers need accurate values of the transport and thermodynamic properties of natural gas, over a broad range of temperatures, pressures, and compositions.
<BR><BR>
This data is needed to size pipes, pumps, valves, heat exchangers, compressors and other items of a process plant.
<BR><BR>
Inaccurate data compounded over the many items of process equipment can amplify risk, both to cost and safety.
<BR><BR>
Maple lets you calculate the transport properties of several standard natural gas mixtures (Gulf Coast, Amarillo, Ekofisk, High N2 and High N2/O2), and your own custom mixtures. The functionality is available in the ThermophysicalData package, powered by the open source <A HREF="http://www.coolprop.org" TARGET="_blank">CoolProp</A> project.
<BR><BR>
Properties are calculated with a Helmholtz energy approach, and includes density, viscosity, specific heat capacity, compressibility factor, Joule-Thomson coefficient and more.
<BR><BR>
This data is instantly accessible in Maple's interactive computing environment - this means you can use all of Maple's plotting, solving and optimization routines, and employ units as a dimensionality check.<img src="https://www.maplesoft.com/view.aspx?si=154532/thumb.png" alt="Physical Properties of Natural Gas" style="max-width: 25%;" align="left"/>Oil and gas engineers need accurate values of the transport and thermodynamic properties of natural gas, over a broad range of temperatures, pressures, and compositions.
<BR><BR>
This data is needed to size pipes, pumps, valves, heat exchangers, compressors and other items of a process plant.
<BR><BR>
Inaccurate data compounded over the many items of process equipment can amplify risk, both to cost and safety.
<BR><BR>
Maple lets you calculate the transport properties of several standard natural gas mixtures (Gulf Coast, Amarillo, Ekofisk, High N2 and High N2/O2), and your own custom mixtures. The functionality is available in the ThermophysicalData package, powered by the open source <A HREF="http://www.coolprop.org" TARGET="_blank">CoolProp</A> project.
<BR><BR>
Properties are calculated with a Helmholtz energy approach, and includes density, viscosity, specific heat capacity, compressibility factor, Joule-Thomson coefficient and more.
<BR><BR>
This data is instantly accessible in Maple's interactive computing environment - this means you can use all of Maple's plotting, solving and optimization routines, and employ units as a dimensionality check.https://www.maplesoft.com/applications/view.aspx?SID=154532&ref=FeedThu, 23 May 2019 04:00:00 ZSamir KhanSamir KhanRobot Arm Writing "Maplesoft" in Handwritten Cursive Script
https://www.maplesoft.com/applications/view.aspx?SID=154531&ref=Feed
This application models a 3 DoF robot arm, with the motion of the tip writing "Maplesoft" in handwritten cursive script.
<BR><BR>
To model the arm, the worksheet:
<UL>
<LI>Analytically derives the Denavit & Hartenberg transformation matrix for each of the three joints
<LI>Lets the user specify a parametric path for the tip of the robot to follow. The default equations in the worksheet writes "Maplesoft" in cursive script
<LI>Animates the robot arm following the specified path
</UL><img src="https://www.maplesoft.com/view.aspx?si=154531/thumb.png" alt="Robot Arm Writing "Maplesoft" in Handwritten Cursive Script" style="max-width: 25%;" align="left"/>This application models a 3 DoF robot arm, with the motion of the tip writing "Maplesoft" in handwritten cursive script.
<BR><BR>
To model the arm, the worksheet:
<UL>
<LI>Analytically derives the Denavit & Hartenberg transformation matrix for each of the three joints
<LI>Lets the user specify a parametric path for the tip of the robot to follow. The default equations in the worksheet writes "Maplesoft" in cursive script
<LI>Animates the robot arm following the specified path
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154531&ref=FeedMon, 06 May 2019 04:00:00 ZBryon ThurBryon ThurGame of Thrones and Graph Theory
https://www.maplesoft.com/applications/view.aspx?SID=154529&ref=Feed
Graph theory can help you understand the social landscape of the television series Game of Thrones, based upon the A Song of Ice and Fire books. With the judicious use of Maple, you can ask yourself really pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over each season?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the television series. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154530">A Song of Ice and Fire and Graph Theory</A> to ask these types of questions using data for the books.<img src="https://www.maplesoft.com/view.aspx?si=154529/thumb.png" alt="Game of Thrones and Graph Theory" style="max-width: 25%;" align="left"/>Graph theory can help you understand the social landscape of the television series Game of Thrones, based upon the A Song of Ice and Fire books. With the judicious use of Maple, you can ask yourself really pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over each season?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the television series. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154530">A Song of Ice and Fire and Graph Theory</A> to ask these types of questions using data for the books.https://www.maplesoft.com/applications/view.aspx?SID=154529&ref=FeedWed, 27 Mar 2019 04:00:00 ZSamir KhanSamir KhanA Song of Ice and Fire and Graph Theory
https://www.maplesoft.com/applications/view.aspx?SID=154530&ref=Feed
Graph theory can help you understand the social landscape of the books in the series A Song of Ice and Fire by G. R. R. Martin. With the judicious use of Maple, you can ask yourself <i>really</i> pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over the five books?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the books. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154529">A Game of Thrones and Graph Theory</A> to ask these types of questions using data for the television series.<img src="https://www.maplesoft.com/view.aspx?si=154530/thumb.png" alt="A Song of Ice and Fire and Graph Theory" style="max-width: 25%;" align="left"/>Graph theory can help you understand the social landscape of the books in the series A Song of Ice and Fire by G. R. R. Martin. With the judicious use of Maple, you can ask yourself <i>really</i> pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over the five books?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the books. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154529">A Game of Thrones and Graph Theory</A> to ask these types of questions using data for the television series.https://www.maplesoft.com/applications/view.aspx?SID=154530&ref=FeedWed, 27 Mar 2019 04:00:00 ZSamir KhanSamir KhanLomb-Scargle Spectral Analysis of Irregularly Sampled Data
https://www.maplesoft.com/applications/view.aspx?SID=154521&ref=Feed
This application
<UL>
<LI>generates an irregularly sampled signal of a sum of two sinusoids (i.e. a time vector at irregular intervals, and a signal vector containing a value at each of those times)
<LI>and then generates a Lomb-Scargle periodogram of that data.
</UL>
The periodogram correctly identifies the frequencies used to generate the irregularly sampled signal.<img src="https://www.maplesoft.com/view.aspx?si=154521/lomb-thumbnailbnail.jpg" alt="Lomb-Scargle Spectral Analysis of Irregularly Sampled Data" style="max-width: 25%;" align="left"/>This application
<UL>
<LI>generates an irregularly sampled signal of a sum of two sinusoids (i.e. a time vector at irregular intervals, and a signal vector containing a value at each of those times)
<LI>and then generates a Lomb-Scargle periodogram of that data.
</UL>
The periodogram correctly identifies the frequencies used to generate the irregularly sampled signal.https://www.maplesoft.com/applications/view.aspx?SID=154521&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanBlurring an Image in the Spatial Frequency Domain
https://www.maplesoft.com/applications/view.aspx?SID=154522&ref=Feed
ere, we will blur in an image with a Gaussian Filter (effectively a low-pass filter) applied in the spatial frequency domain.
<UL>
<LI>First an image is imported
<LI>The fourier transform of the image is then computed, and the image periodogram plotted.
<LI>The fourier transform is multiplied by a Gaussian filter (this attenuates higher spatial frequencies - i.e. the finer detail is removed, leaving only the broad outline).
<LI>The resulted is inverted to the image domain, giving a blurry image
</UL>
This application uses the new Maple 2019 FFTShift function to swap data in a matrix or a vector into a different position. The Fourier transform of an image places lower frequency data near all four corners, with higher frequency data near the center. In this instance, FFTShift is typically applied to move the lowest frequencies to the center and the highest frequencies to the corners.
<BR><BR>
This results in a more meaningful visualization of the power spectrum where the lowest frequency data is contiguous, and simplifies the manipulation of image frequency data.<img src="https://www.maplesoft.com/view.aspx?si=154522/blurimage.jpg" alt="Blurring an Image in the Spatial Frequency Domain" style="max-width: 25%;" align="left"/>ere, we will blur in an image with a Gaussian Filter (effectively a low-pass filter) applied in the spatial frequency domain.
<UL>
<LI>First an image is imported
<LI>The fourier transform of the image is then computed, and the image periodogram plotted.
<LI>The fourier transform is multiplied by a Gaussian filter (this attenuates higher spatial frequencies - i.e. the finer detail is removed, leaving only the broad outline).
<LI>The resulted is inverted to the image domain, giving a blurry image
</UL>
This application uses the new Maple 2019 FFTShift function to swap data in a matrix or a vector into a different position. The Fourier transform of an image places lower frequency data near all four corners, with higher frequency data near the center. In this instance, FFTShift is typically applied to move the lowest frequencies to the center and the highest frequencies to the corners.
<BR><BR>
This results in a more meaningful visualization of the power spectrum where the lowest frequency data is contiguous, and simplifies the manipulation of image frequency data.https://www.maplesoft.com/applications/view.aspx?SID=154522&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanLocate a Signal in Audio in the Presence of Noise
https://www.maplesoft.com/applications/view.aspx?SID=154523&ref=Feed
This application demonstrates how you can estimate the location of a signal that might exist in a larger (perhaps noisy) measurement. In this instance, we find the location of a small segment of audio in a larger audio file.
<UL>
<LI>First, an audio file is first loaded, a small segment is extracted, and random Gaussian noise is added to both.
<LI>The cross-correlation of the full audio and the extract is computed, and the maximum lag computed.
</UL>
The maximum lag is the index at which the extract is predicted to exist in the audio.<img src="https://www.maplesoft.com/view.aspx?si=154523/thumbnail.jpg" alt="Locate a Signal in Audio in the Presence of Noise" style="max-width: 25%;" align="left"/>This application demonstrates how you can estimate the location of a signal that might exist in a larger (perhaps noisy) measurement. In this instance, we find the location of a small segment of audio in a larger audio file.
<UL>
<LI>First, an audio file is first loaded, a small segment is extracted, and random Gaussian noise is added to both.
<LI>The cross-correlation of the full audio and the extract is computed, and the maximum lag computed.
</UL>
The maximum lag is the index at which the extract is predicted to exist in the audio.https://www.maplesoft.com/applications/view.aspx?SID=154523&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanFundamental Frequency and Harmonics of a Violin Note
https://www.maplesoft.com/applications/view.aspx?SID=154524&ref=Feed
This application finds the fundamental frequency and harmonics of a violin using information from the amplitude spectrum. Then, we generate a sinusoidal signal with the same frequency-amplitude characteristics of the violin note, and play the resulting sound.
The analysis uses the new Maple 2019 command for finding the peaks and valleys of a 1D data set - FindPeaks. This command offers several options that let you filter out peaks or valleys that are too close, what defines a peak or valley, and more.<img src="https://www.maplesoft.com/view.aspx?si=154524/thumnbail.jpg" alt="Fundamental Frequency and Harmonics of a Violin Note" style="max-width: 25%;" align="left"/>This application finds the fundamental frequency and harmonics of a violin using information from the amplitude spectrum. Then, we generate a sinusoidal signal with the same frequency-amplitude characteristics of the violin note, and play the resulting sound.
The analysis uses the new Maple 2019 command for finding the peaks and valleys of a 1D data set - FindPeaks. This command offers several options that let you filter out peaks or valleys that are too close, what defines a peak or valley, and more.https://www.maplesoft.com/applications/view.aspx?SID=154524&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir Khan