Welcome Guest! To enable all features please Login or Register.

Notification

Icon
Error

Options
Go to last post Go to first unread
Offline Ber7  
#1 Posted : 27 January 2016 22:12:50(UTC)
Ber7


Rank: Advanced Member

Groups: Registered
Joined: 15/07/2010(UTC)
Posts: 328
Man
Israel
Location: Beer-Sheva

Was thanked: 425 time(s) in 230 post(s)
Zad 4a.sm (38kb) downloaded 77 time(s). Zad 4a.pdf (298kb) downloaded 70 time(s).Examples of solutions of nonlinear equations by Draghilev method in problems in chemistry, electrical
and structural mechanics. There are links to sources.

1.SH Model metabolism thiols. Solution equations of chemical processes,
occurring during the oxidation of low molecular weight thiols in cell
proteins. (Holodniok M., Klich A., Kubichek M., Marek M. Metody analiza nelinejnyh dinamicheskih modelej (Mir, 1991)(ru))

Edited by user 21 October 2018 20:25:39(UTC)  | Reason: Not specified

thanks 2 users thanked Ber7 for this useful post.
on 28/01/2016(UTC),  on 06/02/2016(UTC)
Offline Ber7  
#2 Posted : 27 January 2016 22:32:03(UTC)
Ber7


Rank: Advanced Member

Groups: Registered
Joined: 15/07/2010(UTC)
Posts: 328
Man
Israel
Location: Beer-Sheva

Was thanked: 425 time(s) in 230 post(s)
2. Example of the theory of polymerization (Volterra model-Salnikov)

thanks 1 user thanked Ber7 for this useful post.
on 06/02/2016(UTC)
Offline Ber7  
#3 Posted : 27 January 2016 22:33:16(UTC)
Ber7


Rank: Advanced Member

Groups: Registered
Joined: 15/07/2010(UTC)
Posts: 328
Man
Israel
Location: Beer-Sheva

Was thanked: 425 time(s) in 230 post(s)
bukov.pdf (721kb) downloaded 35 time(s). bukov.sm (132kb) downloaded 36 time(s).3. Example of the theory of catalytic reactions (stationary equation
Slin'ko-Chumakov)(Быков В. И.,Цыбенова С. Б.РЕАЛИЗАЦИЯ МЕТОДА
ПРОДОЛЖЕНИЯ ПО ПАРАМЕТРУ ДЛЯ СИСТЕМЫ ДВУХ УРАВНЕНИЙ.ВЫЧИСЛИТЕЛЬНЫЕ TЕХНОЛОГИИ.Выпуск № 5 / том 7 / 2002)

Edited by user 28 January 2016 10:48:22(UTC)  | Reason: Not specified

thanks 1 user thanked Ber7 for this useful post.
on 06/02/2016(UTC)
Offline Ber7  
#4 Posted : 28 January 2016 12:33:12(UTC)
Ber7


Rank: Advanced Member

Groups: Registered
Joined: 15/07/2010(UTC)
Posts: 328
Man
Israel
Location: Beer-Sheva

Was thanked: 425 time(s) in 230 post(s)
elektro1b.sm (70kb) downloaded 51 time(s). elektro1b.pdf (306kb) downloaded 33 time(s).Nonlinear circuit with Tunnel Diode

(A M. Dąbrowski.The use of mathematical programs and numerical methods in teaching
selected topics in circuit theory.GJEE,v13)
The circuit consists of a DC voltage source E, resistors R1, Ro and resistor R2, which can
change the resistance from 0 to 1000 om. Determine the dependence of current Id and the diode
voltage Vd of the resistance rheostat. Under what resistance rheostat current will be maximized?



Edited by user 28 January 2016 18:17:39(UTC)  | Reason: Not specified

thanks 1 user thanked Ber7 for this useful post.
on 06/02/2016(UTC)
Offline Ber7  
#5 Posted : 28 January 2016 19:34:40(UTC)
Ber7


Rank: Advanced Member

Groups: Registered
Joined: 15/07/2010(UTC)
Posts: 328
Man
Israel
Location: Beer-Sheva

Was thanked: 425 time(s) in 230 post(s)
Arca.pdf (259kb) downloaded 46 time(s). Arca.sm (80kb) downloaded 52 time(s).5.The dependence of the longitudinal force in the arch of the vertical load
Shallow arch (Fig.1), the ends of which are fixed on the displacement along the axis x,
loaded with a uniform vertical load q. N-longitudinal force at the ends of the arch, E,
F, J-elastic modulus, area and moment of inertia of the cross section of the arch, h-height,
L-distance between supports . Is known that the relationship between the load q and thrust
force N has a kind of loop curve . The intersection point on the curve is a bifurcation point (Fig.2).
Find function N of q.

(Григолюк Э.И.,Шалашилин В.И.Проблемы нелинейного деформирования. Метод
продолжения решения по параметру в нелинейных задачах механики твердого
деформируемого тела,1988,Наука.)
The solution is shown in the graph, which consists of three curves. Each curve emerges from
its starting point, and terminates near the bifurcation point.

Edited by user 28 January 2016 19:49:44(UTC)  | Reason: Not specified

thanks 1 user thanked Ber7 for this useful post.
on 06/02/2016(UTC)
Offline Ber7  
#6 Posted : 25 June 2016 13:11:58(UTC)
Ber7


Rank: Advanced Member

Groups: Registered
Joined: 15/07/2010(UTC)
Posts: 328
Man
Israel
Location: Beer-Sheva

Was thanked: 425 time(s) in 230 post(s)
6.Cascade of Two Continuous Stirred-Tank Reactors with Recycle

http://demonstrations.wolfram.c...TankReactorsWithRecycle/

Consider a cascade of two continuous stirred-tank reactors with recycle undergoing
exothermic first-order chemical reactions. The steady state is described by four
nonlinear equations for the reaction conversions x1,x2 ,dimensionless temperature T1,T2 ,
and parameter α(Damköhler number).



Wolfram.smz (98kb) downloaded 33 time(s). Wolfram4.pdf (519kb) downloaded 30 time(s).
thanks 2 users thanked Ber7 for this useful post.
on 25/06/2016(UTC),  on 25/06/2016(UTC)
Offline Ber7  
#7 Posted : 05 July 2016 22:10:41(UTC)
Ber7


Rank: Advanced Member

Groups: Registered
Joined: 15/07/2010(UTC)
Posts: 328
Man
Israel
Location: Beer-Sheva

Was thanked: 425 time(s) in 230 post(s)
Two problems from the Wolfram Demonstrations Project
1.The Semenov Model.2.Continuously Stirred Tank Reactor
http://demonstrations.wolfram.com/TheSemenovModel/
http://demonstrations.wolfram.c...UsingArcLengthParameter/


W.smz (9kb) downloaded 49 time(s).
WPdf.pdf (345kb) downloaded 31 time(s).

Edited by user 06 July 2016 06:44:27(UTC)  | Reason: Not specified

thanks 1 user thanked Ber7 for this useful post.
on 06/07/2016(UTC)
Offline loha  
#8 Posted : 15 August 2016 20:00:14(UTC)
loha


Rank: Member

Groups: Registered
Joined: 13/09/2011(UTC)
Posts: 13
Location: Kolkata

Was thanked: 1 time(s) in 1 post(s)
Hello Ber7,

I have seen your brilliant worksheets some years ago, but only today it seems to me that they could help me to solve a specific problem. Unfortunately, the graph does not appear in the plot window, it says type does not match. What can I do? Is there any specific plugin to install?

Also, is there any general introduction, for engineers, to Dragilev's method in English or French? I'm an architect and not very good at abstract maths!

I have a specific problem of calculating the width of a diagonal compression strut in a shallow brick dome on a rectangular room, tied by a single steel rod, (NOT by a beam), and the differential equation is a little difficult for me. Basically, I have to satisfy 2 conditions: 1) that the lateral stress on the steel tie is proportional to the curvature of the tie, and 2) that the same lateral stress is also related to the strain, it means to the lateral displacement, of the rod via the strain-stress relationship of masonry. This should give a very specific curve, with given boundary conditions: maximum strain at the corner and minimum strain at mid-span (minimum means almost zero), which are dictated by the masonry properties. I am trying with Maxima but I am a little lost, I felt that by following the examples given by you (particularly the snap-through of arch) I could get hold of the problem better.

Thanks for reading and for any help or advice that you may have.

Laurent
Offline Andrey Ivashov  
#9 Posted : 16 August 2016 00:43:55(UTC)
Andrey Ivashov


Rank: Administration

Groups: Developers, Registered, Knovel Developers, Administrators, Advanced Member
Joined: 11/07/2008(UTC)
Posts: 1,373
Man
Russian Federation

Was thanked: 1605 time(s) in 538 post(s)
Hello Laurent.

Originally Posted by: loha Go to Quoted Post
I have seen your brilliant worksheets some years ago, but only today it seems to me that they could help me to solve a specific problem. Unfortunately, the graph does not appear in the plot window, it says type does not match. What can I do? Is there any specific plugin to install?

Just checked this and I see this is an error in latest SMath Studio builds. Will fix it asap.

Best regards, Andrey Ivashov.
Offline Jean Giraud  
#10 Posted : 16 August 2016 05:54:31(UTC)
Jean Giraud


Rank: Advanced Member

Groups: Registered
Joined: 04/07/2015(UTC)
Posts: 3,887
Canada

Was thanked: 697 time(s) in 545 post(s)
Salut Laurent,

PLusieurs choses dans la même capsule:

1. It was created in a version apparently older than mine [5346 April 2014]
So, some of the animation code does not work for example 2. It plays once
and stops. I found no way to "repeat indefinitely". You can repeat as many
times as you wish, how ? => delete some 't' in the input data, retype 't',
it will repeat the single complete cycle.

2. I noticed that if you want to get the graph of the 2nd example, it is
wise to have Smath not open. Then reach were it downloads and click 'open'.
I noticed this behaviour with other work sheets not created in Smath 5346.

3. If you delete the if/else and conserve augment(col(el(K,tt),3),col(el(K,tt),2))
you can have each individual "Frame" by setting tt => 6..30 and export each
individual "Frame" solution.

4. The first example works well as viewed in the forum animated demo.

5. Draghilev module looks a complicated version of some discrete Runge-Kutta,
4th order. I don't understand what Jacobi is doing in there ... just
checking convergence the hard way ?

6. I know nothing about your "brick/cement" wall but I'm familiar with the
maths of the arc length. Simple if the function can be expressed in
analytical function or if not in discrete mode.

7. Close your Smath, follow step [2]. If it does not work, the problem
is with your actual more recent version than 5346.

Jean

Draghilev Stirred Tank.sm (45kb) downloaded 45 time(s).
Offline Jean Giraud  
#11 Posted : 16 August 2016 06:31:23(UTC)
Jean Giraud


Rank: Advanced Member

Groups: Registered
Joined: 04/07/2015(UTC)
Posts: 3,887
Canada

Was thanked: 697 time(s) in 545 post(s)
... like this:

Forum Laurent Multisol.gif
Offline loha  
#12 Posted : 16 August 2016 07:11:51(UTC)
loha


Rank: Member

Groups: Registered
Joined: 13/09/2011(UTC)
Posts: 13
Location: Kolkata

Was thanked: 1 time(s) in 1 post(s)
Originally Posted by: Andrey Ivashov Go to Quoted Post
Hello Laurent.

Originally Posted by: loha Go to Quoted Post
I have seen your brilliant worksheets some years ago, but only today it seems to me that they could help me to solve a specific problem. Unfortunately, the graph does not appear in the plot window, it says type does not match. What can I do? Is there any specific plugin to install?

Just checked this and I see this is an error in latest SMath Studio builds. Will fix it asap.

Best regards, Andrey Ivashov.


Thank you Andrey! I wonder if it is not related to the "Maple V wrapper" plugin. It also says the plugin update is not available. Visibly the plot is not the original smath plot window, but an extension from a plugin. But I have no idea which one. Is there a way to find out which command has created the window, so that we can learn by example? (general question for everyone)

Congratulations for making such a powerful, fast, easy-to-learn and clean-looking software. What I like the most in Smath is the incomparable speed with which you can put together all your material for a project, while keeping it clear and documented effortlessly. (That's important because generally, what is not effortlessly documented is not documented at all! And the work is lost after a few years, or even months). I use also Maxima and Geogebra for specialised purposes, but Smath is always the starting point and also the support of the final synthesis, for the reasons above.

And it's also a great advantage that such a nice, creative community has gathered around Smath!
thanks 1 user thanked loha for this useful post.
on 16/08/2016(UTC)
Offline loha  
#13 Posted : 16 August 2016 07:21:46(UTC)
loha


Rank: Member

Groups: Registered
Joined: 13/09/2011(UTC)
Posts: 13
Location: Kolkata

Was thanked: 1 time(s) in 1 post(s)
Originally Posted by: Jean Giraud Go to Quoted Post
Salut Laurent,

PLusieurs choses dans la même capsule:

1. It was created in a version apparently older than mine [5346 April 2014]
So, some of the animation code does not work for example 2. It plays once
and stops. I found no way to "repeat indefinitely". You can repeat as many
times as you wish, how ? => delete some 't' in the input data, retype 't',
it will repeat the single complete cycle.

2. I noticed that if you want to get the graph of the 2nd example, it is
wise to have Smath not open. Then reach were it downloads and click 'open'.
I noticed this behaviour with other work sheets not created in Smath 5346.

3. If you delete the if/else and conserve augment(col(el(K,tt),3),col(el(K,tt),2))
you can have each individual "Frame" by setting tt => 6..30 and export each
individual "Frame" solution.

4. The first example works well as viewed in the forum animated demo.

5. Draghilev module looks a complicated version of some discrete Runge-Kutta,
4th order. I don't understand what Jacobi is doing in there ... just
checking convergence the hard way ?

6. I know nothing about your "brick/cement" wall but I'm familiar with the
maths of the arc length. Simple if the function can be expressed in
analytical function or if not in discrete mode.

7. Close your Smath, follow step [2]. If it does not work, the problem
is with your actual more recent version than 5346.

Jean

Draghilev Stirred Tank.sm (45kb) downloaded 45 time(s).


Merci Jean! I will need some time to explore your explanations. My level in maths does not allow me to understand the difference between Dragilev and Runge-Kutta! And I like to use the latest version, since someone has worked on it! (Not always true, sometimes the newest version is a deliberate, clever sabotage of the previous one, but at least it's true for such a honest piece of software like Smath!)
Offline Jean Giraud  
#14 Posted : 16 August 2016 17:37:06(UTC)
Jean Giraud


Rank: Advanced Member

Groups: Registered
Joined: 04/07/2015(UTC)
Posts: 3,887
Canada

Was thanked: 697 time(s) in 545 post(s)
Salut Laurent,

The attached work sheet has been rescued, Smath version 5346.
Animation works fine as is. It could be that there is also
a problem in the transmission [freaks the code].
More collabs: please check if it works in your latest or actual
version. If it does not work, I will make an image of all
elements as I have in 5346.

Jacobi is one fo those things like Cholesky, i.e: some math
construction that renders maths more useful and productive.

Cholesky is the core algorithmic component of all LS methods,
so common that few know how it works. Two examples attached.

The Smath Jacobi code is not very visual [to me].

Jean

Draghilev Stirred Tank [5346].sm (31kb) downloaded 47 time(s).
PolyFit QUICK.sm (17kb) downloaded 34 time(s).
PolyFit QUICK_Scale [Rational Pade].sm (37kb) downloaded 37 time(s).
Offline loha  
#15 Posted : 16 August 2016 20:05:56(UTC)
loha


Rank: Member

Groups: Registered
Joined: 13/09/2011(UTC)
Posts: 13
Location: Kolkata

Was thanked: 1 time(s) in 1 post(s)
Cher Jean: CA MARCHE! It works.

I have uninstalled the latest version (which Andrey says is beta) and tried with 5346 and your modified worksheet works just fine. The way you have rewritten it is very interesting. Thanks for that!

Your "compactum" method -in my understanding- is that you have actually defined a function, which is interpreted at a later stage with whatever values in the variables that you want. It works with parameters as well as with global variables. A little like LISP, SMath evaluates a function only when it has to. It's very helpful, you can define whatever you want as a preamble without worrying if the variable exist or not, etc.

A very interesting point: Your modified worksheet works also perfectly well with the latest "stable" version, 5935. I guess that's why Andrey differentiates between "nightly builds" and "stable"!!! There is so much work to make these things turn smoothly, I can't imagine!!!

By the way, why do you stick to 5346?

The original "stirred tank" worksheet half-works, until and including the plot window "Dependence T of on the parameter γ", and the "arca.sm" worksheet does not work in any of the stable versions. I guess these are simply a matter of some outdated/too-much-updated plug-ins!

Anyway, you helped me a lot, I now can understand better the Dragilev method and try to use it.

In the mean time, today I've been using for the first time the software CALCODE by C.K. Raju, to study my ODEs. It's extremely simple, works in real time (instead of the 4 minutes you have to wait for Dragilev in Smath), it shows exactly what you need, and seems to be very powerful. Only problem it's a little rigid (you have to put your system of ODEs in standard form) but at least this rigidity forces you to do a little work by hand and to really understand what you are doing exactly before jumping in the computer screen...

I will look at Choleski and Jacobi when I will have time...

Regards,
Laurent
Offline Jean Giraud  
#16 Posted : 17 August 2016 00:13:48(UTC)
Jean Giraud


Rank: Advanced Member

Groups: Registered
Joined: 04/07/2015(UTC)
Posts: 3,887
Canada

Was thanked: 697 time(s) in 545 post(s)
Salut Laurent,

3 quicky, short:

1. In the original work sheet from the download, down the work sheet, several pages
there are 3 leftover item. Better remove them if you print or PDF. If they remain,
it will print or PDf very many blank sheets !

2. Why stick to 5346 ? In the mean time between 5346 and next stable, most of my
precious Mathcad 11 were done. Many, largely based on Maple.

3. Ordinary RK, Fhelberg ... are for one dependent variable. Here Draghilev is for 2 !
Thus it needs a two var companion ... something like Fourier two var.

Cheers, Jean

___________________________

I believe Andrey was born in a magic pot.

I discovered the "compactum" from observation and trial,
define something simple x:=2, click to see the collection bar
try to collect two and more definitions ...it works.
Very handy in Engineering works
Offline Andrey Ivashov  
#17 Posted : 17 August 2016 19:25:08(UTC)
Andrey Ivashov


Rank: Administration

Groups: Developers, Registered, Knovel Developers, Administrators, Advanced Member
Joined: 11/07/2008(UTC)
Posts: 1,373
Man
Russian Federation

Was thanked: 1605 time(s) in 538 post(s)
loha,

I've fixed a bug, so worksheet in interest can be opened in latest version of SMath Studio now. Please see http://en.smath.info/for...gust-2016.aspx#post35126
thanks 1 user thanked Andrey Ivashov for this useful post.
on 18/08/2016(UTC)
Offline loha  
#18 Posted : 18 August 2016 15:04:27(UTC)
loha


Rank: Member

Groups: Registered
Joined: 13/09/2011(UTC)
Posts: 13
Location: Kolkata

Was thanked: 1 time(s) in 1 post(s)
Fantastic! Thanks a lot Andrey. I don't know how many authors of free software would solve a problem so fast. I'm really impressed.
Users browsing this topic
Forum Jump  
You cannot post new topics in this forum.
You cannot reply to topics in this forum.
You cannot delete your posts in this forum.
You cannot edit your posts in this forum.
You cannot create polls in this forum.
You cannot vote in polls in this forum.