tsunamiBTP

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15 years, 314 days

MaplePrimes Activity


These are replies submitted by tsunamiBTP

@Carl Love Thanks Carl,

Too bad others have to impose their arrogance on others (Tomleslie) as opposed to a professional demeanor that yields results.

@Carl Love 

"When you're entering a Question, there's a check-off for "Product", where you selected Maple for this Question. Then there's a pull-down list where you can select your Maple version. It'd be very helpful to the people who answer your Questions if you'd check off the appropriate version, so that it'll be clearly displayed in the Question's header. This'll save both of us, and the other readers, a lot of time, display space, confusion, and aggravation going back and forth suggesting that you try things that you can't and that you read help pages that don't apply to your version."

YEP, I found that feature a little bit after I posted the question.  Hopefully, I will remember it for future reference.  This website has been revised since the time I had frequented it before so there is a lack of familiarity with the website changes.

I will try you suggestion with th ZIP("^"A,3).

@tomleslie "at least for anyone who can read the help"

Tom, you should curtail snide comments!  I have been using MATLAB longer than you, but that may not be the case with MAPLE.

So if you have something constructive to say, stick with that.  You are behaving like the Twitter trolls many speak of.

In my situation I am not trying to raise a matrix to an exponential power.  I want to raise the individual elements to that power without having to do it individually.  How can I do that in MAPLE?

@acer 

I tried to do this, but to no avail.  How can I do this?  This is a trivial task in MATLAB.

@acer YEP, I am using MAPLE 12.  That is still a reasonably late version of MAPLE?  So the *~ was not incorporated even then?

@Christopher2222 I get NO MATCHES FOUND

@Carl Love 

I do not think this helps?

@Carl Love 

What am I missing?


 

Loading LinearAlgebra

Typesetting[delayDotProduct]((Matrix(3, 3, {(1, 1) = 5/32, (1, 2) = 1/6, (1, 3) = 1/2, (2, 1) = 5/4, (2, 2) = 4/3, (2, 3) = 4, (3, 1) = 5/32, (3, 2) = 1/6, (3, 3) = 1/2})).`~`, Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}), true)

Error, (in rtable/Product) invalid arguments

 

Typesetting[delayDotProduct]((Matrix(3, 3, {(1, 1) = 5/32, (1, 2) = 1/6, (1, 3) = 1/2, (2, 1) = 5/4, (2, 2) = 4/3, (2, 3) = 4, (3, 1) = 5/32, (3, 2) = 1/6, (3, 3) = 1/2}))*`~`, Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}), true)

Matrix([[(5/32)*`~`, (1/6)*`~`, (1/2)*`~`], [(5/4)*`~`, (4/3)*`~`, 4*`~`], [(5/32)*`~`, (1/6)*`~`, (1/2)*`~`]])

(1)

``


 

Download elementwise.mw

It would be helpful if there elementwise operations was listed in the LinearAlgebra[Multiply] help page as an option, but I do not believe it is mentioned.

@Carl Love 

My assumption for the particular solution was incorrect.  I needed:

C[1]*t*exp(-t)+C[2]*t^2*exp(-t) not C[1]*exp(-t)+C[2]*t*exp(-t)+C[3]*t^2*exp(-t)

I now need to carry this over to my .mw file.

 

@Carl Love 

The case where  t^2*exp(f*t) exists concurs with the case when C(3)<>0  in the particular solution given by eq #17 in my .mw file which I also listed below.

C[1]*exp(-t/tau)+C[2]*t*exp(-t/tau)+C[3]*t^2*exp(-t/tau)

In the case of the Friedlander waveform there is no t^2 term so C(3)=0 which I specified for eq #18 in my .mw file.

I now see your point of the possibility of 3 repeated roots that would yield the t^2 term could occur if one of the roots to the homogeneous characteristic equation is equal to the double REAL root of the nonhomogeneous source term.  This not likely to ever happen since the sensor behaves as a harmonic oscillator which means the 2 roots of the characteristic equation are a complex conjugate pair.  Nonetheless, I do not think this addresses the discrepancy among the coefficients A(3) to B(1) & A(4) to B(2) respectively for the homogeneous portion of the solution that I point out in eqs #24 through #26.

Your .mw file only addresses the solution method using the LaPlace transform.  I have reworked your equations #1 & #5 using the method of undetermined coeffcients that I included in the modified file, Download Laplace.mw.  The coefficients, a, b, & c to the characteristic equation are specified to match your equations #1 & #5.

In the case for #1 the eigenfunctions are exp(2t) & exp(-t) which concurs with your solution given by eq #2.  Now to account for nonhomogeneous source term I assume the form given by eq #11.  After backsubstitution I find that C(3) pertaining to the t^2 term = 0.  After resolving both C(1) & C(2) I apply the IC's to resolve B(1) & B(2) which are the coefficients to the homogeneous solution.  The results are given by eq #16.  Assembly of the total solution is given by eq #17.  My observations on the discrepancy are highlighted after eq #17.  Similar disrepancies occur for the other case.

So despite matching your coeffcients of equations #1 & #5 the resulting solutions do not concur.  Why does the discrepancy exist or where have I gone wrong with my coeffcients?

Download Laplace.mw

@Carl Love 

I will likely have further questions after I consume your information.

@Carl Love 

You are confusing the forcing function with the response of the system.  The repeated root  t^2*exp(-t/tau) to which you are referring is governed by a complete different set of physics.  Separate the forcing function from the homogeneous equation which deccribes the response of the sensor system..

The coefficients in both approaches should concur as long as I applied the initial conditions correctly.  This is where I am perplexed.  The eigenvalues to the problem are dictated by the homogeneous diff eq; whereas, the coefficents are dictated by the IC's which I am assuming the sensor is completely stationary before the blastfront arrives.

Again the repeated root in the forcing function is not associated with the sensor system.  If you have any doubts on this issue GOOGLE "Friedlander wavefront".  I could elaborate further, but it is a complete chapter in my dissertation so I think to avoid all of that messy detail look it up via GOOGLE.  You can also GOOGLE FG Friedlander whom is the namesake of the pressure profile associated with an explosive wavefront.  If you can follow his math in his first 4 sets of papers regarding the dispersion of wavefronts around abrupt barriers then you will realize what I am saying.  His math is VERY ELABORATE & COMPLICATED.  If you are the MAPLEPrimes person handling this case can you forward it on to someone else if you do not follow me.

Thank you

@Carl Love 

Well I appreciate your perspective I am not sure I follow what you are implying.  Z(1) & Z(2) are never equal nor do they ever equal tau unless very wierd coincidental physical circumstances prevail.  Nonetheless, can you create a .mw file to elucidate your point especially regarding the special cases you mention.  Maybe i can get something from that.

To give you a physical description of the mathematical background a sensor that behaves as a simple harmonic oscillator is exposed to a blast front that is described as the Friedlander wavefront profile which models the pressure as a function in time with a decay constant of tau.  If the oscillator has a modal frequency corresponding to tau than discerning the response of the sensor to the phenomena it is monitoring would become exceptionally difficult.  So Z(1) & Z(2) are targeted to avoid tau.& for the most part that is easy to accomplish.

@Carl Love 

@Carl Love 

@Carl Love & any others who might offer a different perspective to my discrepancy,

I use the TEST RELATION feature quite a bit to verify my formulae.  You might have to wade through that.  I highlghted the terms of interest so hopefully you can follow the progression in a logical manner.  At the end of the document I demonstrate how much the homogeneous solution differs & also that the particular solution in both cases does concur.  Since the governing differential equation in both cases is the same then the homogeneous solutions should be the same as long as I apply the initial conditions in both cases to be the same. That is perhaps where my error resides, but I have not been able to figure it out.  I hope a fresh pair of eyes will help find the problem. 

Download coeffs_of_homogen_soln_discrepancy.mw

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