Abstraction and Structures in Energy

Subhajit Ganguly

Zero postulation and the principles of the Theory of Abstraction are used to study structures of energy inside a black hole, which is incredibly heavy and incredibly small. We chase the questions, how matter (with various structures) is formed from energy and the energy making up matter has to be in what orientation to form the matter that we see. We arrive at the fundamental model and the equations describing the formation of structure in energy.

Ganguly, Subhajit (2014): Abstraction and Structures in Energy. figshare.
http://dx.doi.org/10.6084/m9.figshare.1035785
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Abstraction and the Standard Model

Subhajit Ganguly

Description:

We study the Standard Model in light of the Zero-Postulation of the Theory of Abstraction. Yukawa Coupling, chiral superfields, the SUSY model, Interacting Boson Models (IBMs), Clebsch-Gordan coefficients, Interacting Boson-Fermion Model (IBFM), etc., are some of the concepts that we study in this paper. Non-commutative geometry seems to come very handy in describing the quantum world. Bosons and fermions both seem to be governed by the rules of such geometry. The principle of conservation of boson number inside a system is seen to follow directly from the Abstraction Model. The IBMs are seen to obey the Laws of Physical Transaction that follows from Zero-Postulation. The chaotic superfields at the requisite scaling-ratio yields necessary equation-parameters needed to describe them at that given scaling-ratio. This is seen to be independent of the choice of scale, but at smaller scaling-ratios, we have less loss of information. At a higher scale, we seem to have less number of parameters required to describe them.

Cite as:    Ganguly, Subhajit (2013): Abstraction and the Standard Model, figshare.

http://figshare.com/articles/Abstraction_and_the_Standard_Model/848625

Propagation of stationary exothermic transition front with nonstationary oscillatory tail

V.V. Smirnov, O.V.Gendelman, L.I. Manevitch

Description:

We consider a propagation of exotermic transition front in a discrete conservative oscillatory chain. Adequate description of such fronts is a key point in prediction of important transient phenomena, including phase transitions and topochemical reactions. Due to constant energy supply, the transition front can propagate with high velocities, precluding any continuum-based considerations. Stationary propagation of the front is accompanied by formation of a non-stationary oscillatory tail with complicated internal structure. We demonstrate that the structure of the oscillatory tail is related to a relationship between phase and group velocities of the oscillations. We suggest also an approximate analytic procedure, which allows one to determine all basic characteristics of the propagation process: velocity and width of the front, frequency and amplitude of the after-front oscillations, as well as the structure of the oscillatory tail. As an example, we consider a simple case of biharmonic double-well on-site potential. Numeric results nicely conform to the analytic predictions.

Cite as:
arXiv:1310.0637 [nlin.PS]
(or arXiv:1310.0637v1 [nlin.PS] for this version)

Integrable multi-component Camassa-Holm system

Baoqiang Xia, Zhijun Qiao

Description:

In this paper, we propose a multi-component system of Camassa-Holm equation, denoted by CH( , ) with 2N components and an arbitrary smooth function  . This system is proven integrable in the sense of Lax pair and infinitely many conservation laws. We particularly study the case of N=2 and derive the peaked soliton (peakon) solutions.

Cite as:
  arXiv:1310.0268 [nlin.SI]
  (or arXiv:1310.0268v1 [nlin.SI] for this version)
   

Monte Carlo simulation of classical spin models with chaotic billiards

Hideyuki Suzuki

Description

It has recently been shown that the computing abilities of Boltzmann machines, or Ising spin-glass models, can be implemented by chaotic billiard dynamics without any use of random numbers. In this paper, we further numerically investigate the capabilities of the chaotic billiard dynamics as a deterministic alternative to random Monte Carlo methods by applying it to classical spin models in statistical physics. First, we verify that the billiard dynamics can yield samples that converge to the true distribution of the Ising model on a small lattice, and we show that it appears to have the same convergence rate as random Monte Carlo sampling. Second, we apply the billiard dynamics to finite-size scaling analysis of the critical behavior of the Ising model and show that the phase transition point and the critical exponents are correctly obtained. Third, we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the Potts model. We also discuss the possibility of extensions to continuous-valued models such as the XY model.

Cite as:

arXiv:1308.0660 [cond-mat.stat-mech]
 

 

 

 

 

(or arXiv:1308.0660v1 [cond-mat.stat-mech] for this version)

 

 

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