Note:
This conversation took place for the last 20 days till today.
All my friend's quarries are in blue...
On Thu, Jul 14, 2011 at 12:39 PM,
Dear Snp Gupta,
Thanks for your mail. But I am not quite sure what you are looking for, and what is this of solution of the N-body problem. It is well known that, at least for the moment, there is not an analytical solution for the N-body problem, but a numerical solution through out the N-body simulations. I do not see what makes your approach.
Best regards,
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2011/7/14 snp gupta <snp.gupta@gmail.com>
Hi,
Thank you for your fast reply and a very Good question.
There is no analytical solution till now in the conventional differential equations approach, you are correct. But this solution is from using Tensors. You can call it as analytical. No problem.
Regarding your question of simulations…
For Example take some equations like F= ma, s=ut+ 0.5at2 , E=mc2, These equations give simulated answers for simulated data, and the same equations will give real answers for real values. What do you say?
The actual tensor solution of Dynamic Universe model is subdivided into 21000 small equations for 133 point masses in SITA software. For all the equations in detail please see Book2….
Here I am proposing to simplify those equations in to about 3000 such equations, that’s what I wrote you in my mail…
If you call such above equations as simulations then SITA is also a simulation, if call above equations are Real, then SITA is real.
Hence, we can say,this SITA software is not actually SIMULATION in that sense when you use real data you will get real answers, but SITA is a set of Real equations as in the above example working together to calculate real values …
You can ask me any questions on this, or if you can invite me. I will come and show and give you the total set working software so that you can see them yourself and confirm and analyze…
Warm and best regards
=snp
For Books see the Books Published tab
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On Fri, Jul 15, 2011 at 1:48 AM, wrote;
Dear Snp Gupta,
I do not understand yet how you solve the N-body problem...Let me consider the generic case for a system composed with N masses. We have to find out 6N variables (3 spatial variables and 3 for the momentums for each mass), which can be reduced using some additional equations. It is well known that for N>2 the problem can not be solved analytically, but numerically (except special cases).
Let me consider now your proposal, you are talking about a problem with 133 masses (why 133 and not the general N case?), which involve 21000 equations!! (what kind of equations are?), that means as minimum as 21000/133*6=26.3 equations per variable!! Apart from the fact that there is not an exact number of equations per variable, how can you have a solution in the case that all the equations are independent? Answer: there is no solution. Even in the case that the equations are reduced to 3000 (as you say), you still have 3000/133*6=3.759 equations per variable...Did I miss anything??
Anyway, I do not know the details of your calculations, but if you actually think that solves the N-body problem, you should submit your results (with details) in the known peer review journals, so that other colleagues can discuss and study your approach.
Best regards,
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On Fri, Jul 15, 2011 at 3:29 PM, snp gupta<snp.gupta@gmail.com> wrote:
Hi,
I do not understand yet how you solve the N-body problem...Let me consider the generic case for a system composed with N masses. We have to find out 6N variables (3 spatial variables and 3 for the momentums for each mass), which can be reduced using some additional equations…….
You are correct sir, following conventional differential equations method; any one has to start and end up that way only. This Dynamic Universe Model and SITA uses a different approach. The mathematical background can be found in the chapter 3 of the attached book for your perusal.
….It is well known that for N>2 the problem cannot be solved analytically, but numerically (except special cases).
Numerical methods generally mean solving Differential and Integral equations by giving approximation values. There are different methods for that. Here in Dynamic Universe model there are no Differential and Integral equations. And there are no equations with multiple value results for the same inputs. Because of these two reasons this set is different. What I did was thinking that just giving just a set of resulting equations from the tensors, I thought it will be better to give numerical results also, to see if that matches with reality. Or else there is no need for a computer.
Let me consider now your proposal, you are talking about a problem with 133 masses (why 133 and not the general N case?), which involve 21000 equations!! (what kind of equations are?), that means as minimum as 21000/133*6=26.3 equations per variable!! Apart from the fact that there is not an exact number of equations per variable, how can you have a solution in the case that all the equations are independent? Answer: there is no solution. Even in the case that the equations are reduced to 3000 (as you say), you still have 3000/133*6=3.759 equations per variable...Did I miss anything??
No, no, you don’t miss anything, This Dynamic Universe Model and SITA uses a different approach. The mathematical background can be found in the chapter 3 of the attached book for your perusal. If you want to see all the 21000 equations you have to see the second book.
Anyway, I do not know the details of your calculations, but if you actually think that solves the N-body problem, you should submit your results (with details) in the known peer review journals, so that other colleagues can discuss and study your approach.
Mostly I find the peer review editors are not scientists, they don’t have much time and understanding to go through all the equations. They don’t bother to use their mind to understand the problem or the solution. They generally see who is standing at the back of this writer, nothing else. I feel workers of a steel plant are not allowed for solving problems. What I can show is 34 years of steel plant service.
The paper will come back like ball in the squash court. With some comments like ‘ You are not attached to university or institution,’ ‘your English is poor” or ‘ you should not solve the problem in a different way, you have to follow the methods used by earlier people only’
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Wed, Aug 3, 2011 at 11:55 AM Dear Snp Gupta,
Dear Snp Gupta,
Sorry for the delay, but I am in vacation and I can not check the mail everyday. I had a look on your book, specifically on the chapter 3, where you say that the mathematical background of your approach is given, and I found that is basically the demonstration of the well known Virial Theorem, which does not solve the N-body by itself, but it only introduces a constraint on the degrees of freedom.
Sorry for the delay, but I am in vacation and I can not check the mail everyday. I had a look on your book, specifically on the chapter 3, where you say that the mathematical background of your approach is given, and I found that is basically the demonstration of the well known Virial Theorem, which does not solve the N-body by itself, but it only introduces a constraint on the degrees of freedom.
I think your approach is more a simulation (or something like that) than an analytical solution. I am not an expert on N-body simulations, so you should ask to another person, but I know that N-body simulations are very complex programs written in fortran, c++.... However, if you still think that your approach solves the problem, you should apply the method to a known system and compare your results with the reality and/or other simulations, for example the galaxy formation or the Large Scale Structure surveys.
Best regards,
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Dear
Sorry for the delay, but I am in vacation and I can not check the mail everyday.
It is alright, I must say thank you for the continued interest in Dynamic Universe Model. I will try to reply all your quarries in your present mail.
I had a look on your book, specifically on the chapter 3, where you say that the mathematical background of your approach is given, and I found that is basically the demonstration of the well known Virial Theorem, which does not solve the N-body by itself, but it only introduces a constraint on the degrees of freedom.
No, No, I feel you are still confusing. Thanks for going through the mathematics in chapter 3. Dynamic Universe Model is uses Virial theorem, but it itself is not Virial theorem or an extension of Virial theorem. In the earlier method, we were to introduce constraints to reduce degrees of freedom. Not in Dynamic Universe Model. This Model uses tensors.
Dynamic Universe Model is totally and conceptually different from the usual Differential / Integral Equation method. It uses There are no equations with multiple value results for the same inputs. Because of these two reasons this set is different.
Dynamic Universe Model uses simple, single valued and individually tested 21000 equations like F= ma, s=ut+ 0.5at2 , E=mc2 (some equations are lengthy, some are small) for finding single and unique coordinate values in three Cartesian dimensions of Position, Velocity, Acceleration for each POINT MASS in the calculations at that particular time instant .
Dynamic Universe Model calculates and uses Universal Gravitation Force (UGF) on each POINT MASS in the calculations at the same particular time instant as mentioned above.
I think your approach is more a simulation (or something like that) than an analytical solution. I am not an expert on N-body simulations, so you should ask to another person, but I know that N-body simulations are very complex programs written in fortran, c++....
You need not be expert on n-body simulations FOR UNDERSTANDING Dynamic Universe Model. It is not a simulation. Dynamic Universe Model is a simple and straight forward usage of Newtonian gravitational equations using in the classical way and in simple and direct Excel.
It can be written Fortran or C++ by any expert or any knowledged person.
No problem. Probably this can be done for making this Dynamic Universe Model faster.
Regarding your question of simulations I answered it earlier also…
For Example take some equations like F= ma, s=ut+ 0.5at^2 , E=mc^2, These equations give simulated answers for simulated data, and the same equations will give real answers for real values. What do you say?
The actual tensor solution of Dynamic Universe model is subdivided into 21000 small equations for 133 point masses in SITA software. For all the equations in detail please see Book2.
However, if you still think that your approach solves the problem, you should apply the method to a known system and compare your results with the reality
Definitely yes, Many natural problems were solved, but for your proposal I need some institutional support to get that large data, computers etc……
...........and/or other simulations,.............
Results will match with reality, definitely yes. Other simulations I cant say. I don’t know. No comments…..
................for example the galaxy formation or the Large Scale Structure surveys.
……such project can be taken….No problem.
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Thu, Aug 4, 2011 at 7:57 AM, Spain, wrote...
Dear Snp Gupta,
I do not understand yet your approach and how you solve the N-body problem. But there is a difference between an analytical solution and a numerical one. Basically what we understand by an analytical solution is the resolution of a problem where the free parameters remains arbitrary, and by a numerical solution, when one has to introduce the numerical values of the free parameters in order to get a numerical solution, For example, the algebraic equation a2 x^2+a1 x+a0=0 has an analytical solution, i.e. it can be solved independently of the values of a2,a1,a0, but the general equation anx^{n}+a_{n-1} x^{n-1}+....+a1x+a0=0 can not be in general solved analytically unless one specifies the value of the constants an,a_{n-1},....that is basically the difference.
Looking at your chapter 3, I only see the usual equations of Newtonian gravity, and the demonstration of the virial theorem. For the moment, we know that those equations can not be solved for N>2 (except special cases). You say that you have 21000 equations, where are they coming from? an algebraic combination of Newtonian ones? I do not understand anything here.
Anyway, in order to test and check your approach, the scientific community has to have access to such approach, and for the moment, I have only seen a mathematical demonstration that is well known (your chapter 3), but no other calculation and/or solution.
In addition, you do not need support to test your model at least for simple systems, for example for the case of N=3 bodies you can test if your solution predicts the existence of the Lagrange points, which are very well known.
Best regards,
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Thank you for analyzing the problem nicely and expressing your doubts in such fast way….
I do not understand yet your approach and how you solve the N-body problem. But there is a difference between an analytical solution and a numerical one. Basically what we understand by an analytical solution is the resolution of a problem where the free parameters remains arbitrary, and by a numerical solution, when one has to introduce the numerical values of the free parameters in order to get a numerical solution, For example, the algebraic equation a2 x^2+a1 x+a0=0 has an analytical solution, i.e. it can be solved independently of the values of a2,a1,a0, but the general equation anx^{n}+a_{n-1} x^{n-1}+....+a1x+a0=0 can not be in general solved analytically unless one specifies the value of the constants an,a_{n-1},....that is basically the difference.
You are correct, any equation without such constants a1, a2 …an, will not be a solution. For our particular and specific need we have to supply such set of constants like a1, a2, … an…. So in order to have a specific solution from the general tensor solution given in Chapter 3 we tune the equation 25 to this need. In Chapter 2 we can find a table, which is one set of initial values that define these tuning constants in Dynamic Universe Model. That set was shown for the New Horizons satellite tracking equations.
These sets of values depend from application to application. This set will be entirely different for Galaxy calculations.
After fixing these initial values for the problem chosen for study, we have to do Numerical calculations. Use calculator or Computer Excel, no problem.
Looking at your chapter 3, I only see the usual equations of Newtonian gravity, and the demonstration of the virial theorem. For the moment, we know that those equations can not be solved for N>2 (except special cases).
Equations of Dynamic Universe Model work for any number of point masses, no problem. They are basically Newtonian equations, and of course use Virial theorem. When we go for the conventional equations with Differential and Integral equations, they can not be solved for n>2, which is true.
You say that you have 21000 equations, where are they coming from? an algebraic combination of Newtonian ones? I do not understand anything here.
The tensor formed in equation 25 ( Chapter 3) in Dynamic Universe Model, is to be sub-divided into final solution of 21000 equations for forming required solution.
Anyway, in order to test and check 'your approach', the scientific community has to have access to such approach, and for the moment, I have only seen a mathematical demonstration that is well known (your chapter 3), but no other calculation and/or solution.
I did not understand what you are mentioning as my approach...
Dynamic Universe model is my approach. The Book 1 is the total such solution…. Any further questions you are most welcome. All the calculations can be done manually or by using Excel using the subdivided set of equations.
Any further questions in this respect are welcome….
In addition, you do not need support to test your model at least for simple systems, for example for the case of N=3 bodies you can test if your solution predicts the existence of the Lagrange points, which are very well known.
I tested the equations of Dynamic Universe Model for n=3, it is ok, no problem. If you have any doubts on n= 3 you are welcome. That set was not yet published.
May I put this conversation into my blog…….?.....
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Thu, Aug 4, 2011 at 1:43 PM, Spain,
Dear Snp Gupta,
You can publish the conversation in your blog if you wish.
I do not understand your approach to the N-body simulations yet, and as I told you, I am not an expert on the topic. I have found also confusions in your treatment, as for example with the tensors that seem wrong defined.
Anyway, the way to proceed is basically obtain results and compare with other approaches and observations. That's all.
Anyway, the way to proceed is basically obtain results and compare with other approaches and observations. That's all.
Best regards,
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Shall i show the name? But the blog thing is not very important.
Your understanding and satisfactions on this subject is important.
Why are you telling that you are not an expert? You are an expert, that's why you asked so many questions..........
Irrespective of above, If you have any type of questions please feel free to ask me. If you want me will come to your office and explain everything to you in person, I will do it very gladly and demonstrate to you so that all your questions will be satisfied in person to you. Because such thing will be necessary to reduce all the confusions. You dont have to be so much formal about the invitations and all.
Any way don't stop your questions.
All the best
=snp
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Dear Snp Gupta,
I do not think my name is important, and it is better not refer my name. When I say that I am not an expert on the problem is because my research is not focused on N-body problem, which is a very complex issue. You should write to people which work with N-body simulations, they would probably give better advices to you.
I have only concerned on the mathematical tools that you write in your chapter 3, and which, as I said in my previous mails, is only the Virial theorem. I do not understand how you split your equation (25) in "many" equations, (also I do not understand what that external potential means in the problem?), or what kind of mathematical object is a tensor for you (eq. (25) seems to be a scalar, basically a tensor of order 0).
I do not think my name is important, and it is better not refer my name. When I say that I am not an expert on the problem is because my research is not focused on N-body problem, which is a very complex issue. You should write to people which work with N-body simulations, they would probably give better advices to you.
I have only concerned on the mathematical tools that you write in your chapter 3, and which, as I said in my previous mails, is only the Virial theorem. I do not understand how you split your equation (25) in "many" equations, (also I do not understand what that external potential means in the problem?), or what kind of mathematical object is a tensor for you (eq. (25) seems to be a scalar, basically a tensor of order 0).
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I will not write your name ( as you wish), I will write only Friend from Barcelona, Spain , I hope It will be ok. Your interest is quit good, even if your research is not focused on n-body problem. You should go further in n-body. Don't worry how that equation 25 looks. It will work. It can be subdivided no problem. You please ask any other questions, N-body problem will become easy for you...
Regards
=snp
