Tuesday 29 November 2011

Conference on “Emerging Areas in Pure & Applied Mathematics” held on 25-26 Nov2011at Kalyan P.G. Autonomous College Bhilai


Conference ended nicely with lots of interactions and collaborations.

Official report on the conference…

Gopikant Goswami gk.goswami9@gmail.com
Nov 27 2011, (1 day ago)

to dr.djena, aditi_infotech, ajayddumath, aka, amit_ray786, amitabh_61, anish_mathuria, anjalioudhia, anu_chouhan, anurakeshbhilai, apoct0185, apurvadas1985, aradhana_sharm., artishree, arunrai18, arunpandey_2009, dr_arvindsinha., ashu_1959, ashwini_01g, asranadive04, avishek.adh, bacharya.etc, bld_1508, bsrmathou, kn, bnwaph

Dear Lourents! the two days seminar was successful in so many ways
we had invited talks from  a very able group of cosmologists headed by Prof Anirudh Pradhan who equipped us with the latest developments in cosmology. Prof. Pradhan gave talk on dark energy, the energy responsible for acceleration of the universe where as Prof Anil Yadav who was from Physics stream, presented a cosmological model in which he fitted the 350 observational datas and with the help of chi squire test he tried to show that his model fits best with the observations.In this sequel three feculties from Nagpur and Gorakhpur presented their research papers. There was also an invited talk by Prof Saubha Kotambker who presented basics of cosmology and relativity through pictures, diagrams and charts.She also presented his one cosmological model which underwent with healthy discussions amongst the participents.


We had a very academic and informative invited talk from Prof D.R.Sahu of Varanasi who presented latest developments,results and applications in the application of fixed points in varieties of functions, functionals and transformations The veteran Prof B.K.Sharma of Pt. Ravi shanker University appreciated and had given applauds to him.there were paper presentations by six researchers of Prof. Sahu.


 We heard a very interesting  invited talk from Prof Pankaj Srivastava who presented a mathematical heart machine in which if one inters his age ,blood pressure, kollostroy(spelling I don't Know), yogic and physical exercises etc, his heart conditions can be obtained.


Invited talk from Prof  P.Jha on  Super compact Topological vector space gathered interest and  The various participents and experts felt the need of its application. The researchers of Prof. Jha group presented their papers in varieties of domains of Mathematics.


There were presentations from a veteran Er. S.N.P. Gupta of B S P   who applied multi body dynamic problem based on Newtonian theory with computer aided simulations to form Dynamic model universe and Prof A.Narayan of B I T, Durg used it in getting the effect of oblateness and magnetic field of earth in the artificial two or more satellite.


There was an invited talk by Prof Rakesh Tiwari of Govt. College Durg and the Bilaspur group of faculties presented their papers on Approximation theory.
Above all  the key note address by Prof H K Pathak of  Pt. Ravi shanker University on the topic "From Geometry to Cryptography" had spoken his depth of knowledge and devotion towards the great subject Mathematics. The presentations with  informations and applications by young energetic scholars Miss Deepmala rai, Mrs Suja vergese and Mrs manju can not be overlooked. There are research scholars of Pt. Ravi shanker University.






Conference Photos can be found at

Friday 25 November 2011

Tensors without Differential and Integral equations used in Dynamic Universe Model

Abstract:
Newtonian two body problem used differential equations. Einstein’s general relativity used tensors which in turn unwrap into differential equations. Dynamic Universe Model uses tensors that will give simple equations with interdependencies. Differential equations will not give unique solutions. Whereas Dynamic Universe Model gives a unique solution of positions, velocities and accelerations for each point mass in the system for every instant of time. This new method of Dynamic Universe Model is different from earlier method of solving general N-body problem.


This is an invited talk in U. G. C. Sponsored National Conference on “Emerging Areas in Pure & Applied Mathematics”  to be held on 25-26 Nov2011at Kalyan P.G. Autonomous College Bhilai 

Wednesday 2 November 2011

A simple question to all…………….. VLBI solar gravitational deflection angle vs Solar Elongation angle:


There is a large variation in the observational results of VLBI, the Very long baseline interferometry techniques used all over the world, in the field of Radio astronomical observations.  This variation is clearly visible when the when the solar gravitational deflection angle is plotted against Solar Elongation angle. Why such variation  comes between different measurements? General Relativity predicts only one angle, not any variation is possible…………..

Can someone please give an explanation……

Saturday 15 October 2011

Differences between Steady state model and Dynamic Universe Model


There was an anonymous question in the Blog...
'What are the differences between the steady state model and Dynamic Universe Model?'

What are the differences between the steady state model and Dynamic Universe Model? In order to understand this question, we have to go  into the basic formation of mathematics of these models. But in simple words, both Steady state and Dynamic Universe Model are based on the same philosophy that the universe appeared the same yesterday as it does today and will look same tomorrow.

The Hoyle’s Steady state Universe Model is based on Einstein’s General theory of relativity. It supports expansion of universe and red-shifted Galaxies. To maintain the constant matter density in space, Hoyle proposed the creation of matter from empty space. He did not like the idea of Big Bang.  It was he who  coined the term ‘Big Bang’ to make fun of the concept of ‘the start and creation of Universe from a singularity from nowhere’, in a scientific gathering.
The main problem faced by Hoyle, with his Steady state Model is the occurrence  of Big Bang in his own model. He disliked the concept of Big Bang all his life; yet there would be a Big Bang in his Steady state Model. This was proven mathematically by Stephen Hawking and Roger Penrose, in their singularity theorem. The singularity theorem says that any Universe model which is based on Einstein’s General theory of relativity, supports expansion of Universe will have a Big Bang Singularity in some distant Past.
Now let’s come to Dynamic Universe Model.    
The Dynamic Universe Model is conceptually different from Einstein’s General theory of relativity. This model is also based on Tensors. But there will be no differential and integral equations on the expansion of these Tensors. No differential and integral equations are used as in the case of Newtonian two body problem. No differential and integral equations at all !
This Dynamic Universe Model supports simultaneous expansion and contraction of the universe. There will be red-shifted as well as blue shifted Galaxies in this Universe. The universe is dynamically balanced. All bodies in this universe are moving. Nothing stays static.  Some will go far away and some will come near. There will always be change.
This Dynamic Universe Model is a closed universe model. No energy flows out of universe. There are no other universes, No baby universes. No infinities.

Dynamic Universe model is a singularity free tensor based math model. The tensors used are linear without using any differential or integral equations. Only one calculated output set of values exists.  Data means properties of each point mass like its three dimensional coordinates, velocities, accelerations and it’s mass. Newtonian two-body problem used differential equations. Einstein’s general relativity used tensors, which in turn unwrap into differential equations. Dynamic Universe Model uses tensors that give simple equations with inter-dependencies. Differential equations will not give unique solutions. Whereas Dynamic Universe Model gives a unique solution of positions, velocities and accelerations; for each point mass in the system for every instant of time. This new method of Mathematics in Dynamic Universe Model is different from all earlier methods of solving general N-body problem.


This universe exists now in the present state, it existed earlier, and it will continue to exist in future also in a similar way. All physical laws will work at any time and at any place. Evidences for the three dimensional rotations or the dynamism of the universe can be seen in the streaming motions of local group and local cluster. Here in this dynamic universe, both the red shifted and blue shifted Galaxies co-exist simultaneously.


In this Dynamic Universe Model, different sets of point masses were taken at different 3 dimensional positions at different distances. These masses were allowed to move according to the universal gravitation force (UGF) acting on each mass at that instant of time at its position. In other words each point mass is under the continuous and Dynamical influence of all the other masses. For any N-body problem calculations, the more accurate our input data the better will be the calculated results; one should take extreme care, while collecting the input data. One may think that ‘these are simulations of the Universe, taking 133 bodies is too less.’ But all these masses are not same, some are star masses, some are Galaxy masses some clusters of Galaxies situated at their appropriate distances. All these positions are for their gravitational centres. The results of these simulation calculations are taken here. 

Here in these simulations the universe is assumed to be heterogeneous and anisotropic. From the output data graphs and pictures are formed from this Model.   These pictures show from the random starting points to final stabilized orbits of the point masses involved.   Because of this dynamism built in the model, the universe does not collapse into a lump (due to Newtonian gravitational static forces). This Model depicts the three dimensional orbit formations of involved masses or celestial bodies like in our present universe. From the resulting graphs one can see the orbit formations of the point masses, which were positioned randomly at the start. An orbit formation means that some Galaxies are coming near (Blue shifted) and some are going away (Red shifted) relative to an observer’s viewpoint.

Tuesday 11 October 2011

Problems in SITA software

Do you face any problems in SITA software?

Please post them here.....

Speeds faster than Light using Dynamic Universe Model


In a recent discovery, CERN found speeds of neutrinos faster than light.
In some of the theoretical experiments, Dynamic Universe Model  also gives speeds faster than light.. , this Dynamic Universe model solves many unexplainable present day physics problems.....

Like to collaborate in this new theoretical project, which will prove the this concept, using super computers and some satellites….?

Please contact me at 
snp.gupta@gmail.com

Sunday 21 August 2011

Third Book: SITA software simplification


Third book
Dynamic Universe Model: SITA software simplified
978-3-639-36469-9  Published by VDM Germany on 30th Aug 2011

This is the Third book in the series on Dynamic Universe Model, describing the SITA software in EXCEL in the accompanying CD / DVD emphasizing mainly HANDS ON usage of a simplified version. It explains 3000 equations for 133 masses [instead of earlier 21000 (Twenty one thousand)], in 17 different groups with additional 14 Index functions and 56 single equations. There are 16 ranges, 11 macros & processes and 18 graphs to view and monitor various parameters.   SITA is singularity-free, inter-body collision free and dynamically stable. Here basically how to tune, select input values, how to iterate & run to get the
results in EXCEL, how to select time step values, to analyze data and using Graphs etc., are presented. This SITA solution can be used by anyone who knows a
little about EXCEL and little bit interested in Physics for solving presently unsolved applications like Pioneer anomaly, New Horizons satellite trajectory at the Solar system level, Missing mass due to Star circular velocities and Galaxy disk formation at Galaxy level etc., that is from the Solar system level, to Cosmology level via Galaxy level.



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Two books were published by me on Dynamic Universe Model. First one is on its singularity-free N-body problem solution [ISBN 978-3-639-29436-1] and the second one on SITA singularity free software, [ISBN 978-3-639-33501-9] during the last October and this
year March by VDM Publications Germany.

After these two books publication, I was hearing the comments like people could not comprehend the equations of Dynamic Universe Model, mainly because there are 21000 equations in the Dynamic Universe Model in SITA software, making the general understanding is very difficult.

In addition these 21000 equations on the general PC or the Laptop are computationally intensive. Sometimes these PCs or Laptops of today takes about 24 hours even for as low as   500 iterations.

Because of all these practical difficulties,   a COST EFFECTIVE project was thought to be developed reducing the equation count to about 3000 from 21000. It is aimed to be faster, easy to use, and computationally less intensive.

This COST EFFECTIVE  project on Dynamic Universe Model, aims to development of the SITA software simplification project in EXCEL to 3000 equations for 133 masses [instead of earlier 21000 (Twenty one thousand)]. Work was already done in 16 different groups with additional 10 Index functions and 50 single equations. There are 14 ranges, 8 macros & processes and 10 graphs to view and monitor various parameters. Say it is 75 % of total work completed.

 SITA is singularity-free, inter-body collision free and dynamically stable. Here we will discuss basically how to tune, select input values, how to iterate & run to get the results in EXCEL, how to select time step values, to analyze data and using Graphs etc., are also intended to be developed

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Tuesday 9 August 2011

Queries on Book 2 Equations; of friend from Barcelona , Spain, on Dynamic Universe model


Note:
This conversation took place for the last 3 days till today after the first set of converstions.
All my friend's  quarries are in blue...

from snp gupta snp.gupta@gmail.com
date Sat, Aug 6, 2011 at 5:58 AM

Dear
Thank you for comments.

Please go through the attached file of equations, and please ask me any doubts / questions...

Best regards
=snp

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To snp.gupta <snp.gupta@gmail.com>
date Sat, Aug 6, 2011 at 1:40 PMsubject

I have had a look on the file you sent to me, and it seems very confusing because of the notation and the concepts, which are not written in a usual way, and does not look very formal from a mathematical point of view. However, it seems you introduce a lot of constraints on the system, so that the problem does not depend on initial values only!


Anyway, you should contact experts on N-body simulations, I am not.


Best regards,



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from snp gupta snp.gupta@gmail.com
date Sat, Aug 6, 2011 at 7:23 PM

Dear

Thank you once again for your fast reply. You always seem to understand the problem and various present day  mathematical procedures. And you always doubt on your self.  what i sent were the actual equations used in excel worksheet of Dynamic Universe model, as it is. They will work for you if you copy them to a sheet as written and prepare the sheet without mistakes. I want to be as accurate as possible to you.

Some equations give intermediate results, which will be used in next set of equations. Our task is to calculate x,y,z values of velocities, positions and accelerations for every point mass in the system for every time step. There will be so many equations and naturally so many variables.

Please don't imagine that there are some constraints. There aren't any.

Here some columns were designated as mass values in KG, some are  initial distances in meters with respect to some reference frame of Cartesian coordinate axes etc. Every thing is expressed and explained in that booklet, i sent  you. What else explanation you need? I gave the actual mathematics set in Chapter 3, which you already saw and gave your comments.  

For your kind information as I told you there are no additional constraints except initial values and time steps. You look for your self. Rows are with numbers, columns are with a,b,c, d's ( alphabets).

I thought you know how to use excel.....You did not seem to understand excel notations probably.

Please try again and tell me....

Best regards
=snp



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to snp gupta <snp.gupta@gmail.com>
date Sun, Aug 7, 2011 at 11:22 AM
Dear Snp,


As I told you, I do not work on N-body simulations, so I think you should contact people working on this. I do not have enough time to check your entire  model in excel. You should test simple models as N=3 and compare it with well known results.


Regards,



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from snp gupta snp.gupta@gmail.com
date Sun, Aug 7, 2011 at 1:29 PM

Dear

I already tested the Dynamic Universe Model with n= 2 and n=3, do you want me to show you...

Dear Diego, I want say one more thing, as I did not follow any body to work out these things in Dynamic Universe Model, I am getting rejected from every place,  nobody want to say a good word, or they dont want to test this. Every body say it is not his work or specialization.  In fact nobody worked in this line earlier.


Warm Regards
=snp



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Friday 5 August 2011

Queries of friend from Barcelona, Spain, on Dynamic Universe model

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.
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.
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). 
 


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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



Tuesday 19 July 2011

SITA & CUDA comparison

Comparison of SITA with NVIDIA’s CUDA implementation: Present CUDA implementation is not singularity free.


Let’s make a comparison study with CUDA here. SITA does not implement any portion of CUDA in its algorithm or in theory or development. Only differences are brought out here, so that SITA can be better understood.

Comparison Table SITA & CUDA


One of the contemporary N-body simulations ‘the CUDA implementation’ done by Lars Nyland, & Mark Harris, of NVIDIA Corporation Jan Prins of University of North Carolina at Chapel Hill [ref] was taken for studying the differences in implementations of SITA &CUDA. The following table gives the comparison. The column on the left side data from Chapter 31 of NVIDIA Corporation describing CUDA,  while right side is SITA implementation of Dynamic Universe Model. This CUDA is given for comparison only, SITA is not using any portion of CUDA. Basic idea why this table is given is for better understanding of SITA. SITA also can be implemented on NVIDIA hardware.

I could not add the comparison TABLE  in the blog, as this Blog is not showing mathematics. Those who are interested in the math, may please contact me by mail or phone  or this is available in my books

Mathematical background

I could not add this post / page in the blog, as this Blog is not showing mathematics. Those who are interested in the math, may please contact me by mail or phone or this is available in my books,

For mathematics you can down load this paper ...................
http://members.wap.org/kevin.parker/Densemass/VakPioneerAnom.doc

Comparison with other cosmologies


Our universe is not having a uniform mass distribution.  Isotropy & homogeneity in mass distribution is not observable at any scale. We can see present day observations in ‘2dFGRS survey’ publications for detailed surveys and technical papers [1]. The universe is lumpy as you can see in the picture given here in wikipedia [2]. There are Great voids, of the order of 1 billion light years where nothing is seen and then there is the Sloan Great Wall, the largest known structure, a giant wall of galaxies. These two observations indicate that our Universe is lumpy.  After seeing all these we can say that uniform density as prevalent in Bigbang based cosmologies is not a valid assumption.  Hence in this paper we have taken the mass of moon as moon & Galaxy as Galaxy employing non uniform mass densities.
This universe is now in the present state, as existed earlier and will continue to exist in the same way. This is something like Hoyle’s Steady state model philosophy [7] but without creation of matter. PCP (Perfect Cosmological Principle) was not considered true here as in steady state universe. We need not assume any homogeneity and isotropy here at any point of time. Matter need not be created to keep the density constant. Here Bigbang like creation of matter is also not required. Blue shifted galaxies also exist along with red shifted ones. No dark energy and dark matter is required to explain physical phenomena here. Here in this model the present measured CMB is from stars, galaxies and other astronomical bodies. This Dynamic Universe Model is a closed universe model.
Our Universe is not empty. For example De Sitter’s universe model explains everything but his Universe has no matter in it [8]. It may not hold a sink to hold all the energy that is escaped from the universe at infinity.[ref Einstein] It is a finite and closed universe. Absolute Rest frame of reference is not necessary. The time and space coordinates can be chosen as required. Dynamic Universe Model is different from Fritz Zwicky’s tired light theory as light does not loose energy here [9].   Gravitational red shift is present here.
Dynamic Universe Model gives a daring new approach. It is different from Newtonian static model and Olber’s paradox [10]. Here masses don’t collapse due to self gravitation and even though the masses are finite in number, they balance with each other dynamically and expanding. There is no space-time continuum. Hawking and Penrose [11,12] (1969, 1996) in their singularity theorem said that ‘In an Isotropic and homogeneous expanding universe, there must be a Big bang singularity some time in the past according to General theory of relativity . Since Isotropy and Homogeneity is not an assumption in Dynamic Universe Model, singularity theorem is not applicable here and Hawking’s Imaginary time axis perpendicular to time axis is not required. No baby universes, Blackhole or wormhole singularity [13] is built in. No Bigbang singularity [14 ] as in Friedmann-Robertson-Walker models. JV Narlikars’ many mini Bigbangs are also not present here [15]. Also this Dynamic Universe Model is poles apart from, M-theory & String theories or any of the Unified field theories. The basic problem in all these models, including String theory [16] and M-theory [17]  is that the matter density is significantly low and they push Bigbang singularity into some other dimensions.
There is a fundamental difference between galaxies / systems of galaxies and systems that normally use statistical mechanics, such as molecules in a box. The molecules repel each other but in gravitation we have not yet experienced any repulsive forces. Only attraction forces were seen in Newtonian and Bigbang based cosmologies. (See for ref: Binny and Tremaine  1987 [18]). But here in Dynamic Universe Model masses when distributed heterogeneously experience repulsive forces as well as attractive forces due to the total resulting universal force acting on the particular mass. Einstein’s cosmological constant l[19] to introduce repulsive forces at large scales like inter galactic distances (as also in MOND), is not required here.

REFERENCES


1.                  See 2dFGRS publications   http://www.mso.anu.edu.au/2dFGRS/

2.                  See in Wikipedia “The Large scale structure of cosmos”  http://en.wikipedia.org/wiki/Large-scale_structure_of_the_cosmos 
            Biggest void in space is 1 billion light years across see http://www.newscientist.com/article/dn12546
            The Sloan Great Wall is a giant wall of galaxies, (a galactic filament). See http://en.wikipedia.org/wiki/Sloan_Great_Wall


3.                  SNP.GUPTA, DYNAMIC UNIVERSE MODEL of cosmology and SITA (Simulation of Inter-intra-Galaxy Tautness and Attraction forces  with variable time step). The simulations in above  paper were changed to small time steps and  were accepted in British Gravity Meeting, in UK. 15-18 Sept 2004 the  international conference on gravitation.

4.             SNP.GUPTA, “DYNAMIC UNIVERSE MODEL of cosmology: Missing mass in Galaxy” Presented at OMEG05 Origin of Matter and Evolution of Galaxies,   November 8-11, 2005  at Koshiba Hall, University of Tokyo, Tokyo
5.       A copy of my earlier paper was kept here on the link below…
            Some questions raised by Baut forum can be seen here in this link…


6.             SNP.GUPTA, “DYNAMIC UNIVERSE MODEL of cosmology: Missing mass in Galaxy” Presented in 7th Astronomical conf by HEL.A.S,. Kefallinia, Greece 8-11,Sept, 2005.
             Some questions raised by the Baut forum can be seen in this link…

7.       Hoyle, F, On the Cosmological Problem, 1949MNRAS.109..365H.

8.         W. de Sitter, On Einstein's theory of gravitation and its astronomical consequences,    1916MNRAS..77..155D

9.       Zwicky, F. 1929. On the Red Shift of Spectral Lines through Interstellar Space. PNAS 15:773-779. Abstract (ADS) Full article (PDF).


11.       S.W. Hawking, Singularities in collapsing stars and Expanding Universes with Dennis William Sciama, Comments on Astrophysics and space Physics Vol 1#1, 1969,  MNRAS 142, 129, (1969).

12.      Stephen Hawking and Roger Penrose, ‘The Nature of space and time’, Princeton University press, 1996.

13.    -Einstein, A. 1916, “The foundation of General theory of relativity ”, Methuen and company, 1923, Reprinted, Dover publications, 1952, New York, USA.
            -Einstein, A. 1911, “On the influence of Gravitation on the propagation of light”, Methuen and company, 1923, Reprinted, Dover publications, 1952, New York, USA.

14.      A. G. Walker, On Milines theory of World Structure, 1937, Volume s2-42, Number 1, pp 90-127
            H.P. Robertson, Kinematics and world Structure III , The Astrophysical Journal, May 1936, vol 83 pp 257.

15.      JVNarlikar, Mini-bangs in Cosmology and astrophysics, Pramana ( Springer India), Vol 2, No.3, 1974, pp-158-170

16.     String theory M. J. Duff, James T. Liu, and R Minasian , Eleven dimensional origin of STRING / string duality.: arXiv:hep-th/9506126v2

17.       A. Miemiec, I. Schnakenburg : Basics of M-theory; Fortsch.Phys. 54(2006) Page 5-72 and preprints at arXiv:hep-th/0509137v2, Sept 2005

18.       James Binny and Scott Tremaine : Text book ‘Galactic Dynamics’ 1987

19.    Einstein, A. 1917, “Cosmological considerations of General theory of relativity  ”, Methuen and company, 1923, Reprinted, Dover publications, 1952, New York, USA.

20.       S.N.P. Gupta, ‘Absolute Rest frame of reference is not necessary’, presented in Symposium on Early Universe SEU, Dec 20-22; 1994, IIT, Madras, India, Proceedings Page 54.

28                Pioneer Anomaly :John D. Anderson, Philip A. Laing, Eunice L. Lau, Anthony S. Liu, Michael Martin Nieto, Slava G. Turyshev (1998). "Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration". Phys. Rev. Lett. 81: 2858–2861. doi:10.1103/PhysRevLett.81.2858. http://prola.aps.org/abstract/PRL/v81/i14/p2858_1.  (preprint) arXiv:gr-qc/9808081
    
29   For new Horizons satellite details please see: http://pluto.jhuapl.edu/index.php.   Ephemeris from Jet propulsion lab http://ssd.jpl.nasa.gov/horizons.cgi#top. Starting data given at http://ssd.jpl.nasa.gov/horizons.cgi#top . The website [ http://ssd.jpl.nasa.gov/horizons.cgi#results  gives output as in Table 4.

30  SNP.Gupta (The following results were publicized by me in the earlier seminars / conferences.) ‘Absolute Rest frame of reference is not necessary’, presented in Symposium on Early Universe SEU, Dec 20-22; 1994, IIT, Madras, India, Proceedings Page 54. MULTIPLE BENDING OF LIGHT RAY IN OUR DYNAMIC UNIVERSE; A COMPUTER SIMULATION. Gr15: 15th international conference on gravitational conference on gravitation and relativity, pune, India. 16-21 DEC 1995\7. P116; a6.32 (1997),; SNP. GUPTA, and ’  presented in SIGRAV, 18-22 September 2000 , Italy; Edited by R. Cianci, R. Collina, M. Francaviglia, and P. Fré (Eds) in Book  “Recent Developments in General relativity  Genoa 2000” published by Springer- Verlag Italia, Milano 2002, Page 389. On DYNAMIC UNIVERSE MODEL of cosmology and SITA (Simulation of Inter-intra-Galaxy Tautness and Attraction forces  with variable time step). The simulations in above  paper were changed to small time steps and  were accepted in British Gravity Meeting, in UK. 15-18 Sept 2004 the  international conference on gravitation. SNP.GUPTA, DYNAMIC UNIVERSE MODEL of cosmology and SITA (Simulation of Inter-intra-Galaxy Tautness and Attraction forces  with higher time step). This paper was formally presented in GR17; The  17th international conference on  gravitation and relativity, in Dublin, Ireland, 18-24 July 2004.  And on DYNAMIC UNIVERSE MODEL of cosmology and SITA  again Presented in ICR 2005 (International  Conference on Relativity) , at Amravati University , India, Jan 11- 14, 2005 . On Missing mass , “DYNAMIC UNIVERSE MODEL of cosmology: Missing mass in Galaxy” Presented at OMEG05 Origin of Matter and Evolution of Galaxies,   November 8-11, 2005  at Koshiba Hall, University of Tokyo, Tokyo . also in  Missing mass in Galaxy  using regression analysis in DYNAMIC UNIVERSE MODEL of cosmology” Presented at PHYSTAT05 Conference on 'Statistical Problems in Particle Physics, Astrophysics and Cosmology'’  held in Oxford, UK on Sept 12th  to 15th, 2005. And “DYNAMIC UNIVERSE MODEL of cosmology: Missing mass in Galaxy” Presented in 7th Astronomical conf by HEL.A.S,. Kefallinia, Greece 8-11,Sept, 2005. Copies of my earlier papers were kept here on the links below… http://members.wap.org/kevin.parker/Densemass/VakPioneerAnom.doc and http://members.wap.org/kevin.parker/Densemass/VDUMOC%20kp%20.doc


32     Ref Book ‘Celestial mechanics: the waltz of the planets’ By Alessandra Celletti, Ettore Perozzi,  page 27.