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…

            http://members.wap.org/kevin.parker/Densemass/VakPioneerAnom.doc

            Some questions raised by Baut forum can be seen here in this link…

            http://www.bautforum.com/against-mainstream/82024-pioneer-anomaly-dynamic-universe-model-cosmology.html

6.             SNP.GUPTA, “DYNAMIC UNIVERSE MODEL of cosmology: Missing mass in Galaxy” Presented in 7^th 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…

            http://www.bautforum.com/against-mainstream/85940-unanswered-questions-about-dynamic-universe-model.html

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).

10.       http://en.wikipedia.org/wiki/Olbers'_paradox

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: 15^th 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  17^th 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 12^th  to 15^th, 2005. And “DYNAMIC UNIVERSE MODEL of cosmology: Missing mass in Galaxy” Presented in 7^th 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

31    http://en.wikipedia.org/wiki/N-body_problem

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

Comparison between Dynamic Universe and Bigbang model

Now I feel it is high time to consider the other possible cosmological models also. People have seen both positive and negative sides of Bigbang based cosmologies. However, it is not that the Dynamic Universe Model explains every aspect of cosmology. Nevertheless, it tries to explain many aspects. Now let us compare the Dynamic Universe Model as an Alternative Cosmological model with Bigbang based cosmologies. I am requesting you to see the Comparison Table 30. Here we can see the Bigbang based cosmological models and their problems with achievements of Dynamic Universe Model.

Below is a Comparison Table: Here Bigbang vs. Dynamic Universe Model comparison done. The general questions and cosmological conditions which are supposed to be answered by any Cosmology model are given and comparison of various respective answers given by Bigbang based cosmological models with Dynamic Universe Model is shown.

	General question answered by any theory (Cosmology condition) ………	Bigbang based cosmology	Dynamic Universe Model
1	It should say something about the creation of Universe / matter.	Required, In the form of Bigbang Singularity.	Not required, NO Bigbang Singularity, No SINGULARITY
2	It should explain about the expansion of Universe.	Says Universe is expanding, But keeps mum about explaining the force behind expansion.	Says Universe is expanding, But explains the force behind expansion.
3	It should say about the universe closed-ness,	Due to Space-time continuum and curvature.	Due to Classical Physics
4	It should explain Large scale structures etc.	Explained Using General relativity	Explained Using Total Universal Gravitational Force on Bodies
5	Dark matter	Cannot explain missing mass, Concept of UNKNOWN dark matter required to explain many things	Explains missing mass, dark matter NOT required
6	Dark energy	Concept of UNKNOWN dark energy required to explain many things	NOT required
7	It should tell about existence of Blue shifted Galaxies	Keeps mum No answer	Blue and red-shifted Galaxies can co-exist
8	It should explain about universe starting assumptions like uniform density of matter	Uniform density of matter required	Can explain large VOIDs, Based on NON uniform mass densities........
9	It should deal correctly with celestial mechanics Like pioneer anomaly	Predicts away from SUN Observed is TOWARDS SUN	Predicts towards SUN as Observed (Important)
10	It should calculate correctly the Trajectory of New horizons satellite to Pluto.	At present trajectory predictions done using thumb-rules not from any model	Theoretically Calculates Trajectory accurately

The disagreement here seems to be over what constitutes a "solution" for the N-body Problem.. The original prize announced by King Oscar II of Sweden for the N body problem was for an analytical solution. My understanding is that this means that you have a set of equations where you put in the initial values for various parameters (mass, velocity, etc) at t0 and then you can then calculate the positions, velocities, etc at any given value of t, say tn. That is, a single step to calculate the result at tn What you are presenting appears to be a simulation or numerical solution where you put in the initial values at time t and then to get to the value at tn you have to run through a series of steps from t=t0, t1, t2, t3, .... tn.

The original prize announcement by King Oscar II of Sweden:

…. is for a solution of N-body problem with advice given by Gösta Mittag-Leffler in 1887. He announced:

‘Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.’ See Ref [1]

Here we have taken a ‘a system of arbitrarily many mass points that attract each according to Newton's law’ in Dynamic Universe model. We have not changed the NEWTON’s law anywhere.

And the assumption ‘that no two points ever collide’ is a valid assumption in Dynamic universe model. Due to this model’s fundamental ideology and mathematic formulation the collisions will not happen. But they may happen if uniform density of matter is used. For heterogeneous distributions the point masses will not colloid with each other. They start moving about each other for any formation of point masses as observed physically.

The announcement further says we have to find the ‘coordinates of each point as a series in a variable’, the words ‘analytical solution’ is not mentioned in the announcement. Here in Dynamic universe Model we find the representation of each point exactly from an ‘analytical solution’ derived here in Mathematical Background section (#3) and its Resulting Equation 25 of this monograph. The value of the variables converges uniformly for each point and gives only single value.

 So, the original announcement as stated above says about a series, that should converge uniformly, and it should not give chaotic results. In Dynamic Universe model case, the series converges uniformly, gives a unique value. He did not mention that it should not run through a series of steps from t=t₀, t₁, t₂, t₃, .... t_n. Of course we can calculate the result directly ‘t_n’ with limited accuracy on single time step. In the literature of science, there are many simulation methods for the last 120 years and almost all have changed the Newton’s laws. Some of the recent approaches were using iterative methods with high speed computers. None of them claim that they are singularity free and collision free.

My solution is Equation 25; it is analytical and is derived analytically. Just by saying that Equation 25, is the solution is not sufficient. People may not understand its complexity and depth. To make it understandable, SITA was developed. I want to stress that point again, that SITA is one of the many solutions possible for Equation 25. Many other solutions are possible for this Tensor. Then question comes how to prove and check SITA validity?

The tensor at the equation 25 is subdivided into many equations and calculations are done. Tensor is the basic equation. I am using basic methodology of calculations. It may be called a simulation, but should it be called Calculation? I don’t know. If you don’t want testing of Equation 25, then SITA is not required. I could not find any other method of testing Equation 25.

          This equation 25 can be tested by any person who has pencil and a paper. Depending on the budget available with him, he can use logarithmic tables, Simple calculators, scientific calculators, PC, Laptop, Main Frame computers or Super computers.

          This Dynamic Universe Model (SITA) is NOT a ‘simulation or numerical solution’ when we are calculating the positions / velocities / accelerations of point masses using actual data. It is simply another calculation method. When we use factitious data which is not real or some data used for testing purposes then the results can be called as ‘simulation or numerical solution’.

           It is well known that for N>2 the problem cannot be solved analytically in present day physics. Numerical methods generally mean solving Differential and Integral equations by giving approximation values. 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. This N-body problem thus solved is called Dynamic Universe Model.

            Just giving resulting equations from the tensors will not be sufficient, it will be better to give numerical results also, to see if that matches with reality. SITA is set of 21000 equations, an Excel solution for Dynamic Universe Model for checking these results of Dynamic Universe Model.

            Or else there is no need for a computer. For checking these solutions even a pencil and a paper with a calculator is sufficient.

Please form the differential equation that describes the motion and solve it.

No differential equation is formed here in Dynamic Universe Model. Only simple and tested engineering equations are used in SITA. These are all outcomes after solving equation 25, which I referred in Dynamic universe model.

This approach is slightly different from forming differential equations and solving. We cannot get solutions with that approach. People have tried in vain and have not been able to arrive at a solution and we already know that. That’s why there was no singularity free solution earlier.