New Application Center Additions
https://www.maplesoft.com/applications
en-us2020 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 07 Jun 2020 09:11:08 GMTSun, 07 Jun 2020 09:11:08 GMTThe latest content added to the Application Centerhttps://www.maplesoft.com/images/Application_center_hp.jpgNew Application Center Additions
https://www.maplesoft.com/applications
Minimum Road Radius for Highway Superelevation
https://www.maplesoft.com/applications/view.aspx?SID=154647&ref=Feed
When a vehicle travels around a curve, a centripetal force is needed to keep the vehicle on the road. If the road is completely horizontal, this force is entirely provided by side friction (i.e. the friction of the tires on the road).
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However, road curves are usually banked - the outer edge is higher than the inner edge. This uses the weight of the vehicle to help keep the vehicle on the road, and is called superelevation.
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In this application, we derive an equation that describes the relationship between velocity, side friction, road radius and superelevation for a point-mass vehicle traveling around a bend. This relationship is then rearranged to give an explicit equation for the road radius.
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This equation is then used to calculate the road radius required to maintain the trajectory of a vehicle as it travels around a bend. For a specific set of parameters, the calculated road radius matches the minimum road radius given in the AASHTO Green Book.<img src="https://www.maplesoft.com/view.aspx?si=154647/superelevation.png" alt="Minimum Road Radius for Highway Superelevation" style="max-width: 25%;" align="left"/>When a vehicle travels around a curve, a centripetal force is needed to keep the vehicle on the road. If the road is completely horizontal, this force is entirely provided by side friction (i.e. the friction of the tires on the road).
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However, road curves are usually banked - the outer edge is higher than the inner edge. This uses the weight of the vehicle to help keep the vehicle on the road, and is called superelevation.
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In this application, we derive an equation that describes the relationship between velocity, side friction, road radius and superelevation for a point-mass vehicle traveling around a bend. This relationship is then rearranged to give an explicit equation for the road radius.
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This equation is then used to calculate the road radius required to maintain the trajectory of a vehicle as it travels around a bend. For a specific set of parameters, the calculated road radius matches the minimum road radius given in the AASHTO Green Book.https://www.maplesoft.com/applications/view.aspx?SID=154647&ref=FeedWed, 03 Jun 2020 04:00:00 ZSamir KhanSamir KhanHighway Pavement Design using the CALTRANS method
https://www.maplesoft.com/applications/view.aspx?SID=154646&ref=Feed
A highway pavement is several layers of materials above the natural soil. This application helps you design a flexible pavement using the approach outlined in the Highway Design Manual (6th edition) published by the California Department of Transportation (CALTRANS). Specifically, this application will determine the thickness of the subbase, base and asphalt concrete layers.<img src="https://www.maplesoft.com/view.aspx?si=154646/caltrans_highway_pavement.png" alt="Highway Pavement Design using the CALTRANS method" style="max-width: 25%;" align="left"/>A highway pavement is several layers of materials above the natural soil. This application helps you design a flexible pavement using the approach outlined in the Highway Design Manual (6th edition) published by the California Department of Transportation (CALTRANS). Specifically, this application will determine the thickness of the subbase, base and asphalt concrete layers.https://www.maplesoft.com/applications/view.aspx?SID=154646&ref=FeedFri, 29 May 2020 04:00:00 ZSamir KhanSamir KhanVenting of Gas From a Hole in a Pipe
https://www.maplesoft.com/applications/view.aspx?SID=154644&ref=Feed
This application calculates the rate at which gas flows out of a hole (or throat) in a pressurized pipe. Additionally, the Mach number, gas temperature and velocity, and speed of sound at the throat are computed.
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The same analysis can be applied to a pressurized tank venting gas through a hole, as long as the internal conditions are constant.
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The hole is small compared to the pipe diameter (so that the gas vents at a greater rate than the bulk flow of gas through the pipe), and the process is at steady-state and isentropic.
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The polytropic coefficient and molecular weight of the gas are computed with the <A HREF="/support/help/maple/view.aspx?path=ThermophysicalData">ThermophysicalData package</A>.<img src="https://www.maplesoft.com/view.aspx?si=154644/Venting_of_Gas_from_a_Hole_in_a_Pipe.png" alt="Venting of Gas From a Hole in a Pipe" style="max-width: 25%;" align="left"/>This application calculates the rate at which gas flows out of a hole (or throat) in a pressurized pipe. Additionally, the Mach number, gas temperature and velocity, and speed of sound at the throat are computed.
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The same analysis can be applied to a pressurized tank venting gas through a hole, as long as the internal conditions are constant.
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The hole is small compared to the pipe diameter (so that the gas vents at a greater rate than the bulk flow of gas through the pipe), and the process is at steady-state and isentropic.
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The polytropic coefficient and molecular weight of the gas are computed with the <A HREF="/support/help/maple/view.aspx?path=ThermophysicalData">ThermophysicalData package</A>.https://www.maplesoft.com/applications/view.aspx?SID=154644&ref=FeedMon, 25 May 2020 04:00:00 ZSamir KhanSamir KhanSpatially Varied Open-Channel Flow with Increasing Discharge
https://www.maplesoft.com/applications/view.aspx?SID=154645&ref=Feed
Consider a long rectangular concrete channel that ends in an abrupt freefall, with an inflow of water along its length.
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This application will calculate the profile of the water surface from the freefall to a specified distance upstream by numerically solving the governing differential equation.
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For a subcritical flow, downstream conditions determine the water surface profile. The water depth reaches the critical height (i.e. the minimum energy height) at a short distance before the freefall - this is the boundary condition on the solution of the governing differential equation.<img src="https://www.maplesoft.com/view.aspx?si=154645/Spatially_Varied_Open-Channel_Flow_with_Increasing_Discharge.png" alt="Spatially Varied Open-Channel Flow with Increasing Discharge" style="max-width: 25%;" align="left"/>Consider a long rectangular concrete channel that ends in an abrupt freefall, with an inflow of water along its length.
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This application will calculate the profile of the water surface from the freefall to a specified distance upstream by numerically solving the governing differential equation.
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For a subcritical flow, downstream conditions determine the water surface profile. The water depth reaches the critical height (i.e. the minimum energy height) at a short distance before the freefall - this is the boundary condition on the solution of the governing differential equation.https://www.maplesoft.com/applications/view.aspx?SID=154645&ref=FeedMon, 25 May 2020 04:00:00 ZSamir KhanSamir KhanIntegration by Pullback
https://www.maplesoft.com/applications/view.aspx?SID=154643&ref=Feed
The calculus of differential forms is a powerful tool that unifies and simplifies many mathematical concepts. We use the Pullback command in Maple's DifferentialGeometry package to perform double, triple, line and surface integrals in James Stewart's Calculus to demonstrate the method differential forms and show the connection among these integrals.<img src="https://www.maplesoft.com/view.aspx?si=154643/flux.png" alt="Integration by Pullback" style="max-width: 25%;" align="left"/>The calculus of differential forms is a powerful tool that unifies and simplifies many mathematical concepts. We use the Pullback command in Maple's DifferentialGeometry package to perform double, triple, line and surface integrals in James Stewart's Calculus to demonstrate the method differential forms and show the connection among these integrals.https://www.maplesoft.com/applications/view.aspx?SID=154643&ref=FeedSun, 24 May 2020 04:00:00 ZDr. Frank WangDr. Frank WangGradually Varied Flow in a Trapezoidal Channel
https://www.maplesoft.com/applications/view.aspx?SID=154642&ref=Feed
Water flows along a gently sloped trapezoidal channel; this is known as gradually varied flow.
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As the flow progresses along the channel, the water depth eventually reaches a uniform depth that no longer changes with distance along the channel; this is known as the normal depth.
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This application derives a fully analytical differential equation for gradually varied flow in a trapezoidal channel. The differential equation is solved numerically, and the resulting water surface profile is plotted.<img src="https://www.maplesoft.com/view.aspx?si=154642/Trapezoidal_Channel.png" alt="Gradually Varied Flow in a Trapezoidal Channel" style="max-width: 25%;" align="left"/>Water flows along a gently sloped trapezoidal channel; this is known as gradually varied flow.
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As the flow progresses along the channel, the water depth eventually reaches a uniform depth that no longer changes with distance along the channel; this is known as the normal depth.
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This application derives a fully analytical differential equation for gradually varied flow in a trapezoidal channel. The differential equation is solved numerically, and the resulting water surface profile is plotted.https://www.maplesoft.com/applications/view.aspx?SID=154642&ref=FeedThu, 21 May 2020 04:00:00 ZSamir KhanSamir KhanSimulation of DNA with Maple
https://www.maplesoft.com/applications/view.aspx?SID=154639&ref=Feed
This app shows the modeling and simulation of DNA carried out entirely in Maple. The mathematical model is inserted through the combination of trigonometric functions. It shows the graphs of the curvature vs time for its interpretation. Made for engineering and health science students. (In Spanish)<img src="https://www.maplesoft.com/view.aspx?si=154639/adn_2020.png" alt="Simulation of DNA with Maple" style="max-width: 25%;" align="left"/>This app shows the modeling and simulation of DNA carried out entirely in Maple. The mathematical model is inserted through the combination of trigonometric functions. It shows the graphs of the curvature vs time for its interpretation. Made for engineering and health science students. (In Spanish)https://www.maplesoft.com/applications/view.aspx?SID=154639&ref=FeedFri, 08 May 2020 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloMaple 2020 User Manual. Russian version.
https://www.maplesoft.com/applications/view.aspx?SID=154640&ref=Feed
A Russian translation of the Maple 2020 User Manual.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Maple 2020 User Manual. Russian version." style="max-width: 25%;" align="left"/>A Russian translation of the Maple 2020 User Manual.https://www.maplesoft.com/applications/view.aspx?SID=154640&ref=FeedFri, 08 May 2020 04:00:00 ZMaplesoftMaplesoftSpeed of Sound in Various Fluids
https://www.maplesoft.com/applications/view.aspx?SID=154641&ref=Feed
This application computes and tabulates the speed of sound in various fluids at standard temperature and pressure, as provided by the ThermophysicalData package (which uses the open-source CoolProp project for fluid properties).
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The list of fluids include water, ethanol, air, ammonia and several others. However, you can use any of the fluids in the ThermophysicalData package (this help page contains a list of available fluids).
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This application also demonstrates the use of the DocumentTools package for tabulating and formatting results.<img src="https://www.maplesoft.com/view.aspx?si=154641/thumb.png" alt="Speed of Sound in Various Fluids" style="max-width: 25%;" align="left"/>This application computes and tabulates the speed of sound in various fluids at standard temperature and pressure, as provided by the ThermophysicalData package (which uses the open-source CoolProp project for fluid properties).
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The list of fluids include water, ethanol, air, ammonia and several others. However, you can use any of the fluids in the ThermophysicalData package (this help page contains a list of available fluids).
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This application also demonstrates the use of the DocumentTools package for tabulating and formatting results.https://www.maplesoft.com/applications/view.aspx?SID=154641&ref=FeedFri, 08 May 2020 04:00:00 ZSamir KhanSamir KhanShifting the Pitch of Audio in the Frequency Domain
https://www.maplesoft.com/applications/view.aspx?SID=154638&ref=Feed
This application will shift the pitch of an audio file by scaling its frequency spectrum.
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Our simple approach will multiply each signal frequency by the same amount. For a piano or violin note, the harmonics will still be an integer multiple of the pitch with the same balance between amplitudes (baring some digital aliasing effects). This preserves the timbre of the sound.
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If your original audio is a piano note at F4 (a pitch of 349.2 Hz), you can convert it to an A4 note by scaling the frequencies by 4 semitones (a pitch of 349.2 Hz 4/12 = 440.0 Hz).<img src="https://www.maplesoft.com/view.aspx?si=154638/Pitch_Shift.png" alt="Shifting the Pitch of Audio in the Frequency Domain" style="max-width: 25%;" align="left"/>This application will shift the pitch of an audio file by scaling its frequency spectrum.
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Our simple approach will multiply each signal frequency by the same amount. For a piano or violin note, the harmonics will still be an integer multiple of the pitch with the same balance between amplitudes (baring some digital aliasing effects). This preserves the timbre of the sound.
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If your original audio is a piano note at F4 (a pitch of 349.2 Hz), you can convert it to an A4 note by scaling the frequencies by 4 semitones (a pitch of 349.2 Hz 4/12 = 440.0 Hz).https://www.maplesoft.com/applications/view.aspx?SID=154638&ref=FeedMon, 04 May 2020 04:00:00 ZSamir KhanSamir KhanPlus petit multiple non nul d'une liste d'entiers
https://www.maplesoft.com/applications/view.aspx?SID=154626&ref=Feed
Cette Maplet permet de calculer le plus petit nombre pouvant etre divisé par tout les nombres de 1 à n avec n entier supérieur ou égal à 1.
(challenge @universal_sci)<img src="https://www.maplesoft.com/view.aspx?si=154626/Capture1.JPG" alt="Plus petit multiple non nul d'une liste d'entiers" style="max-width: 25%;" align="left"/>Cette Maplet permet de calculer le plus petit nombre pouvant etre divisé par tout les nombres de 1 à n avec n entier supérieur ou égal à 1.
(challenge @universal_sci)https://www.maplesoft.com/applications/view.aspx?SID=154626&ref=FeedFri, 24 Apr 2020 04:00:00 Zxavier cormierxavier cormierPressure Drop of Gas and Liquid Flowing in a Pipe
https://www.maplesoft.com/applications/view.aspx?SID=154636&ref=Feed
This application calculates the two-phase pressure gradient for gas and liquid flowing in a pipe. The Lockhart-Martinelli separated flow approach is used.<img src="https://www.maplesoft.com/view.aspx?si=154636/pipe.png" alt="Pressure Drop of Gas and Liquid Flowing in a Pipe" style="max-width: 25%;" align="left"/>This application calculates the two-phase pressure gradient for gas and liquid flowing in a pipe. The Lockhart-Martinelli separated flow approach is used.https://www.maplesoft.com/applications/view.aspx?SID=154636&ref=FeedMon, 20 Apr 2020 04:00:00 ZSamir KhanSamir KhanBraking Distance of a Skidding Car
https://www.maplesoft.com/applications/view.aspx?SID=154632&ref=Feed
You're driving a car on an incline, but the brakes lock up. How far will your car skid?
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This application uses Newton's 2nd law and laws of motion to derive an equation that gives the distance your car will skid (also known as the braking distance). This equation shows that the braking distance is proportional to the square of the velocity at the start of the skid.<img src="https://www.maplesoft.com/view.aspx?si=154632/Braking_Distance_of_a_Skidding_Car.png" alt="Braking Distance of a Skidding Car" style="max-width: 25%;" align="left"/>You're driving a car on an incline, but the brakes lock up. How far will your car skid?
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This application uses Newton's 2nd law and laws of motion to derive an equation that gives the distance your car will skid (also known as the braking distance). This equation shows that the braking distance is proportional to the square of the velocity at the start of the skid.https://www.maplesoft.com/applications/view.aspx?SID=154632&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanHow Cold Can a Zeer Pot Get?
https://www.maplesoft.com/applications/view.aspx?SID=154633&ref=Feed
A Zeer pot is an evaporative cooler made of two clay or terracotta pots. One is placed inside the other and the gap filled with wet sand, and a wet cloth is placed on top. Vegetables or fruit are usually placed in the inner pot. As the water from the sand evaporates, the inner pot is cooled. Water wicks throughout the sand to maintain a consistent temperature throughout.
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The coldest possible temperature that can be achieved is the wet-bulb temperature, and can be computed with Maple's ThermophysicalData package. The wet bulb temperature is a function of the relative humidity (i.e. the water content) and temperature of the ambient air.
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This application plots the coldest possible temperature in a Zeer pot for a range of relative humidities.<img src="https://www.maplesoft.com/view.aspx?si=154633/ZeerPot.png" alt="How Cold Can a Zeer Pot Get?" style="max-width: 25%;" align="left"/>A Zeer pot is an evaporative cooler made of two clay or terracotta pots. One is placed inside the other and the gap filled with wet sand, and a wet cloth is placed on top. Vegetables or fruit are usually placed in the inner pot. As the water from the sand evaporates, the inner pot is cooled. Water wicks throughout the sand to maintain a consistent temperature throughout.
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The coldest possible temperature that can be achieved is the wet-bulb temperature, and can be computed with Maple's ThermophysicalData package. The wet bulb temperature is a function of the relative humidity (i.e. the water content) and temperature of the ambient air.
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This application plots the coldest possible temperature in a Zeer pot for a range of relative humidities.https://www.maplesoft.com/applications/view.aspx?SID=154633&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanExtract the Envelope and Instantaneous Phase of a Signal using the Hilbert Transform
https://www.maplesoft.com/applications/view.aspx?SID=154634&ref=Feed
The Hilbert transform has many practical applications. These include vibration analysis and amplitude modulation in communication systems
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This application compute the envelope and instantaneous frequency of a signal using the Hilbert transform.
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<LI>The signal envelope is the magnitude of the Hilbert transform
<LI>The instantaneous frequency is the derivative (wrt time) of the phase angle of the Hilbert transform (only for single-component signals)
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The magnitude of the analytic signal captures the slowly varying features of the signal, while the phase contains the high-frequency information.<img src="https://www.maplesoft.com/view.aspx?si=154634/Hilbert_Transform.png" alt="Extract the Envelope and Instantaneous Phase of a Signal using the Hilbert Transform" style="max-width: 25%;" align="left"/>The Hilbert transform has many practical applications. These include vibration analysis and amplitude modulation in communication systems
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This application compute the envelope and instantaneous frequency of a signal using the Hilbert transform.
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<LI>The signal envelope is the magnitude of the Hilbert transform
<LI>The instantaneous frequency is the derivative (wrt time) of the phase angle of the Hilbert transform (only for single-component signals)
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The magnitude of the analytic signal captures the slowly varying features of the signal, while the phase contains the high-frequency information.https://www.maplesoft.com/applications/view.aspx?SID=154634&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanThe Color of Noise
https://www.maplesoft.com/applications/view.aspx?SID=154635&ref=Feed
You've probably heard the sound of white noise. It's what we perceive as a hiss, and has a flat spectral content across all frequencies. But many other colors of noise exist, each with a different spectral "slope". Some emphasize lower frequencies, while others have a U-shape spectral weighting.
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Common noise colors include pink, red, blue and violet, each with different properties and applications.
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<LI>Pink noise, for example, better represents natural phenomena like rain and has been shown to aid sleep and memory
<LI>Blue noise is used in audio dithering to mask the effect of quantization
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This application generates 1D pink, red, blue and violet noise, and produces periodograms for each. Each noise sample is sonified so you can hear what it sounds like.
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Additionally, the sound can also be exported to a wave file for use in another tool (Maple will export high precision 32-bit and 64-bit wave files).<img src="https://www.maplesoft.com/view.aspx?si=154635/pinkNoise.png" alt="The Color of Noise" style="max-width: 25%;" align="left"/>You've probably heard the sound of white noise. It's what we perceive as a hiss, and has a flat spectral content across all frequencies. But many other colors of noise exist, each with a different spectral "slope". Some emphasize lower frequencies, while others have a U-shape spectral weighting.
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Common noise colors include pink, red, blue and violet, each with different properties and applications.
<UL>
<LI>Pink noise, for example, better represents natural phenomena like rain and has been shown to aid sleep and memory
<LI>Blue noise is used in audio dithering to mask the effect of quantization
</UL>
This application generates 1D pink, red, blue and violet noise, and produces periodograms for each. Each noise sample is sonified so you can hear what it sounds like.
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Additionally, the sound can also be exported to a wave file for use in another tool (Maple will export high precision 32-bit and 64-bit wave files).https://www.maplesoft.com/applications/view.aspx?SID=154635&ref=FeedFri, 17 Apr 2020 04:00:00 ZSamir KhanSamir KhanApplications of Differential Forms in Thermodynamics
https://www.maplesoft.com/applications/view.aspx?SID=154631&ref=Feed
We use Maple's DifferentialGeometry package to derive Maxwell and other mathematical identities in thermodynamics.<img src="https://www.maplesoft.com/view.aspx?si=154631/gradS.png" alt="Applications of Differential Forms in Thermodynamics" style="max-width: 25%;" align="left"/>We use Maple's DifferentialGeometry package to derive Maxwell and other mathematical identities in thermodynamics.https://www.maplesoft.com/applications/view.aspx?SID=154631&ref=FeedSat, 11 Apr 2020 04:00:00 ZDr. Frank WangDr. Frank WangGenerate the Sound of Plucked Instruments with the Karplus-Strong Algorithm
https://www.maplesoft.com/applications/view.aspx?SID=154630&ref=Feed
This application implements the Karplus-Strong string synthesis method to generate the sound of a plucked instrument.
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Despite its simplicity, this algorithm can create remarkably realistic sounds. You can even extend the application to generate the sound of strummed chords.
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As a further step (not shown here), you add special effects like reverb and echo by convolving the generated sound with an impulse response.<img src="https://www.maplesoft.com/view.aspx?si=154630/KarplusStrong.png" alt="Generate the Sound of Plucked Instruments with the Karplus-Strong Algorithm" style="max-width: 25%;" align="left"/>This application implements the Karplus-Strong string synthesis method to generate the sound of a plucked instrument.
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Despite its simplicity, this algorithm can create remarkably realistic sounds. You can even extend the application to generate the sound of strummed chords.
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As a further step (not shown here), you add special effects like reverb and echo by convolving the generated sound with an impulse response.https://www.maplesoft.com/applications/view.aspx?SID=154630&ref=FeedTue, 07 Apr 2020 04:00:00 ZSamir KhanSamir KhanCalculate Order of Butterworth Filter for User-Defined Design Requirements
https://www.maplesoft.com/applications/view.aspx?SID=154629&ref=Feed
This worksheet will help you calculate the order of a lowpass Butterworth filter with a user-defined minimum gain at a user-defined frequency. Additionally, once the order is known, the filter gain is plotted.<img src="https://www.maplesoft.com/view.aspx?si=154629/thumb.png" alt="Calculate Order of Butterworth Filter for User-Defined Design Requirements" style="max-width: 25%;" align="left"/>This worksheet will help you calculate the order of a lowpass Butterworth filter with a user-defined minimum gain at a user-defined frequency. Additionally, once the order is known, the filter gain is plotted.https://www.maplesoft.com/applications/view.aspx?SID=154629&ref=FeedFri, 03 Apr 2020 04:00:00 ZSamir KhanSamir KhanDouble Stub Matching
https://www.maplesoft.com/applications/view.aspx?SID=154628&ref=Feed
This application will calculate the lengths of two shunt stubs that match the load to the impedance of a transmission line.<img src="https://www.maplesoft.com/view.aspx?si=154628/double_stub.png" alt="Double Stub Matching" style="max-width: 25%;" align="left"/>This application will calculate the lengths of two shunt stubs that match the load to the impedance of a transmission line.https://www.maplesoft.com/applications/view.aspx?SID=154628&ref=FeedThu, 02 Apr 2020 04:00:00 ZSamir KhanSamir Khan