**International Journal of Physics:**Latest Articles More >>

## Article

# Study of Electrocapillarity in Dielectrics Using Palm Oil

^{1}Department. of Physics, Federal University, Ndufu-Alike – Ikwo,

^{2}Department of Industrial Physics, Ebonyi State University, P.B.M 53, Abakaliki, Nigeria

*International Journal of Physics*.

**2014**, 2(3), 83-85

**DOI:**10.12691/ijp-2-3-3

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Nwodo A. N, Ugwu E.I. Study of Electrocapillarity in Dielectrics Using Palm Oil.

*International Journal of Physics*. 2014; 2(3):83-85. doi: 10.12691/ijp-2-3-3.

Correspondence to: Ugwu E.I, Department of Industrial Physics, Ebonyi State University, P.B.M 53, Abakaliki, Nigeria. Email: ugwuei@yahoo.com

## Abstract

## Keywords

## References

[1] | E Colgate; H.Matsumoto; J Vac Sci. Technol., (1990), An investigation of ectrowetting- based microstructure J.Voc. Sci. Technol. A8, 3625-3633 | ||

[2] | Berge, B (1993) Electrocapilarity and wetting of insulator film by water, C.R Acad. Sci. Paris Ser II., (1993), 317, 157-163 | ||

[3] | Pollack; M.G and Fair R.B.,; A.D Shenderov, (2000), Electrowetting –based actuation of Liquid droplet for microfluidic application, Appl. Phys. let. 77, 1725-1726. | ||

[4] | Prins, M.; Welters W.J and Weekamp W.J. (2001), Fluid controlling multichannel structures by electrocapillarity pressure, Science 291, 277-280. | ||

[5] | Lienemann J, Greiner A.; Korvink J.G., (2006), Modeling Simulation, and optimization of Electrowetting, IEEE, Tran. Comp-Aided Des Intgr. Cir. Syst., 25, 234-247. | ||

[6] | P.Zhou; C.W.Wu, Micro and Nanosystem, (2009), 1, 57-62 | ||

[7] | X.Shan; H. (1993), Lattice Boltzmann simulating flows with multiple phase and components Phys. Rev. E, 47, 1815-1819 | ||

[8] | Asberg, A. J, Kponen, A, Merikoski, D and Timnen, J, (2002),lattice Boltzmann simulation of Capillary rise dynamics, J.Stat.Phys 107, 143-153 | ||

[9] | H.Li; J.Li; Y. Chen; H.Fang, Comput. Phys. (2007),Lattice Boltzmann model simulation of elrctrowetting-on- dielectric in a rough wall channel. Compt. Science, http://arcxiv.org/abs/0708.4182v | ||

[10] | Haung,H, Thome D.T, Schaap, M.G and Sukop M.C, (2007), Propsed approximation for contact angles in Shan-and Shen-typemulticomponet multiphase lattice Boltzmann models, Phys. Rev E, 76, 066701 | ||

[11] | Lin, P, (1978), “Some Electrocapiillary-Type Behaviour of Gold Electrode, J. Electrochem. Soc; 194, pp 1077-1098 | ||

[12] | Kata, E (1991). Electrocapillarity in dielectrics, MacMillan, India Press, Madras. | ||

[13] | Chen, J.H and Hsieh, W.H,. (2006), Electrowetting-induced capillary flow in a parallel-plate Channel, J. Colloid. Interface Sci., (2006), 296, 276-283. | ||

[14] | Kang K.H.; Kangn I.S and Lee,C.M, (2003), Wetting Tension Due to Coulombic Interaction in Charge- Related Wetting phenomena Langmuir Vol. 19, No. 13, 2003, 548-513. | ||

## Article

# The Rest Mass of a Particle in a Field and a General Mass Equation

^{1}Department of Mathematics, Faculty of Science, Ain-Shams University, Cairo, Egypt

*International Journal of Physics*.

**2014**, 2(3), 86-95

**DOI:**10.12691/ijp-2-3-4

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Mohamed Ahmed Hassan. The Rest Mass of a Particle in a Field and a General Mass Equation.

*International Journal of Physics*. 2014; 2(3):86-95. doi: 10.12691/ijp-2-3-4.

Correspondence to: Mohamed Ahmed Hassan, Department of Mathematics, Faculty of Science, Ain-Shams University, Cairo, Egypt. Email: el_hmam.1113@Yahoo.com

## Abstract

## Keywords

## References

[1] | Hassan, M. A., “A vector analog for the mass- Model and predictions,” Proc INSA, A63 (6). 437-456. Jul. 1997. | ||

[2] | Thomson, J. J., “On the Electric and Magnetic Effects produced by the Motion of Electrified Bodies,” Philosophical Magazine, 5 11 (68). 229-249. 1881 | ||

[3] | Waghmare, Y. R., Introductory Nuclear Physics, Oxford &IBH publishing Co, New Delhi, 1981. | ||

[4] | Griffiths, D., Introduction to Elementary Particles, Harper &Row, New York, 1987. | ||

[5] | ATLAS Collaboration, “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC”, Phys. Lett., B716 (1). 1-29. Sep. 2012. | ||

[6] | Biswas, S., Roy, P., and Dutt-Mazumder, A. K., “ρ-ω mixing and spin dependent CSV potential”, Indian J. Phys, 85(7). 1185-1189. Jul. 2011. | ||

[7] | Clemmow P. C., An Introduction To Electromagnetic Theory, Cambridge University Press, Cambridge, 1973. | ||

## Article

# A Functional Model of Measurement in Quantum Theory

^{1}Diel Software Beratung und Entwicklung, Seestr. 102, 71067 Sindelfingen, Germany

*International Journal of Physics*.

**2014**, 2(4), 96-104

**DOI:**10.12691/ijp-2-4-1

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Hans H. Diel. A Functional Model of Measurement in Quantum Theory.

*International Journal of Physics*. 2014; 2(4):96-104. doi: 10.12691/ijp-2-4-1.

Correspondence to: Hans H. Diel, Diel Software Beratung und Entwicklung, Seestr. 102, 71067 Sindelfingen, Germany. Email: diel@netic.de

## Abstract

## Keywords

## References

[1] | Baumann, K., Sexl, R., Die Deutungen der Quantentheorie, Vieweg Verlag, Braunschweig/Wiesbaden, 1984. | ||

[2] | Cramer, J., “The Transactional Interpretation of Quantum Mechanics”, Rev Mod Phys 58, 647-688, 1986. | ||

[3] | Wikipedia on Measurement Problem, http://en.wikipedia.org/w/index.php?title=Measurement problem. | ||

[4] | Maudlin, T., “Three Measurement Problems”, Topoi-Int Rev Philos 14, 1995. | ||

[5] | Everett III, H., “Relative State' formulation of Quantum Mechanics”, Rev Mod Phys 29, 454, 1957. | ||

[6] | Feynman, R.P., QED: The Strange Theory of Light and Matter, Princeton University Press, Princeton, 1985. | ||

[7] | Diel, H., “The Formulation of Temporal Relationships with Physics Theories”, Pensee Journal, Vol 75, No. 12; Dec 2013. | ||

[8] | Wikipedia on Objective collapse theory, 2014. | ||

[9] | Feynman, R.P., Hibbs, A.R., Quantum Mechanics and Path Integrals, McGraw Hill, New York, 2005. | ||

[10] | Diel, H., “A Functional Interpretation of Quantum Theory”, in Proceedings of ICCQMNP Barcelona, 2013. | ||

[11] | Dyson, F. J., Advanced Quantum Mechanics, arXiv:quant-ph/0608140v1, 2006. | ||

[12] | Ryder, L.H., Quantum Field Theory, Cambridge University Press, Cambridge, 1985. | ||

[13] | Griffiths, D., Einfuehrung in die Elementarteilchenphysik. | ||

[14] | Mandl, F., Shaw, G., Quantenfeldtheorie, AULA Verlag, Wiesbaden, 1993. | ||

## Article

# Analysis of the Performances of Sealed Timing Resistive Plate Chambers (tRPCs)

^{1}Max-Planck Institute for Nuclear Physics, Heidelberg, Germany

*International Journal of Physics*.

**2014**, 2(4), 105-108

**DOI:**10.12691/ijp-2-4-2

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Khokon Hossen. Analysis of the Performances of Sealed Timing Resistive Plate Chambers (tRPCs).

*International Journal of Physics*. 2014; 2(4):105-108. doi: 10.12691/ijp-2-4-2.

Correspondence to: Khokon Hossen, Max-Planck Institute for Nuclear Physics, Heidelberg, Germany. Email: hossen@mpi-hd.mpg.de

## Abstract

## Keywords

## References

[1] | P.Fonte, A. Smirnitsky and M.C.S Williams, NIM, A 443, (2000), 201. | ||

[2] | Oxford Physics, C4: Particle Physics Major Option Particle Detectors. | ||

[3] | William R. Leo, Techniques for Nuclear and Particle Physics Experiments. | ||

[4] | http://consult.cern.ch/writeup/magboltz/. | ||

[5] | P. Fonte, V. Peskov, B.D. Ramsey, “Streamers in MSGC's and other gaseous detectors” 1-13. | ||

[6] | Nicholas Tsoulfanidis, Measurement and Detection of Radiation, Second Edition. | ||

[7] | http://root.cern.ch/drupal/. | ||

## Article

# Optical Transitions in Quantum Dots

^{1}Faculty of the Sciences, FUNDAPL Laboratory, University of Blida.1, Algeria

^{2}Faculty of the technology, LATSI Laboratory, University of Blida.1, Algeria

*International Journal of Physics*.

**2014**, 2(4), 109-111

**DOI:**10.12691/ijp-2-4-3

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

A. Benahmed, A. Aissat, M. A. Benammar. Optical Transitions in Quantum Dots.

*International Journal of Physics*. 2014; 2(4):109-111. doi: 10.12691/ijp-2-4-3.

Correspondence to: A. Benahmed, Faculty of the Sciences, FUNDAPL Laboratory, University of Blida.1, Algeria. Email: moumenephysique@yahoo.fr

## Abstract

## Keywords

## References

[1] | H. Mathieu :« Physique des Semiconducteurs et des Composants Electronique», 6eme édition, pp (616-62 Paris, 2009). | ||

[2] | COMSOL Multiphysics Model Library copyright 1998-2008 by COMSOL AB. | ||

[3] | RF Module User’s Guide. 1998-2012 COMSOL-Protected by U.S. Patents 7, 519, 518; 7, 596, 474; and 7, 623, 991. Patents pending. | ||

[4] | R. Chau, B. Doyle, S. Datta, J. Kavalieros and K. Zhang, Integrated nanoelectronics for the future, Nature Materials 6 (2007) 810. | ||

[5] | A. Abdelali: «Rôle du rayonnement dans l’élaboration et l’étude nanoagrégats semi-conducteur de ZnS », mémoire de magister, université de Mentouri Constantine. | ||

[6] | P. M. Petroff, K. H. Schmidt, G. Medeiros-Ribeiro, A et J. Kotthaus, Size quantization and zero dimensional e in self assembled semiconductor quantum dots,Jpn. Jl. Appl Phys. 36, Part 1, 4068 (1997). | ||

[7] | C. Charles: «Propriétés électroniques, optiques et dynamiques de boites quantiques auto-organisées et couplées sur substrat InP », thèse doctorat, Institut National des Sciences Appliquées de Rennes, 27 juin 2006. | ||

[8] | U. Banin, Y. Cao, D. Katz et O. Millo, Identification of atomic-like electronic states inindium arsenide nanocrystal quantum dots, Nature 400, 542 (1999). | ||

## Article

# Dark Energy, Exponential Expansion, CMB, Wave/Particle Duality All Result from Lorentz-Covariance of Boltzmann’s Transport Equation

^{1}B&E Scientific Ltd, Seaford BN25 4PA, UK

*International Journal of Physics*.

**2014**, 2(4), 112-117

**DOI:**10.12691/ijp-2-4-4

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Arne Bergstrom. Dark Energy, Exponential Expansion, CMB, Wave/Particle Duality All Result from Lorentz-Covariance of Boltzmann’s Transport Equation.

*International Journal of Physics*. 2014; 2(4):112-117. doi: 10.12691/ijp-2-4-4.

Correspondence to: Arne Bergstrom, B&E Scientific Ltd, Seaford BN25 4PA, UK. Email: arne.bergstrom@physics.org

## Abstract

*f*(

**r**,

*t*,

**v**) of photons at positions

**r**, time

*t*, moving in direction

**v**, and interacting with a surrounding medium by localized collisions. This equation is not necessarily Lorentz-covariant, but can be specialized to a Lorentz-covariant equation describing the propagation of a photon distribution through space. However, this requirement of Lorentz-covariance of the Boltzmann transport equation then leads to a wave-particle duality, in which an ensemble of photons behave as waves, but in which each individual photon interferes only with itself. Applied on cosmological scales, this requirement of Lorentz-covariance of the Boltzmann transport equation also leads to an apparent quantum multiplication, which could explain the existence of the huge amounts of the mysterious “dark energy” that appears to permeate the universe. In addition, it also requires the universe to appear subjected to an exponential expansion as observed, similar to a perspective distortion in time, and then also as a consequence to appear surrounded by a cosmic microwave background radiation (CMB) with an exact Planck spectrum, as observed.

## Keywords

## References

[1] | F. Zwicky, “Die Rotverschiebung von extragalaktischen Nebeln”, Helvetica Physica Acta 6, 110 (1933). F. Zwicky, “On the Masses of Nebulae and of Clusters of Nebulae”, Astrophys. J. 86, 217 (1937). | ||

[2] | V. Rubin, D. Burstein, W. K. Ford, and N. Thonnard, “Rotation velocities of 16 SA galaxies and a comparison of Sa, Sb, and SC rotation properties”, Astrophys. J. 289, 81 (1985). | ||

[3] | S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, et al., “Measurements of Ω and Λ from 42 High-Redshift Supernovae”, Astrophys. J. 517, 565 (1999). | ||

[4] | A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, et al., “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant”, Astron. J. 116, 1009 (1998). | ||

[5] | http://en.wikipedia.org/wiki/Planck_(spacecraft) retrieved 2014-06-16. | ||

[6] | A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors (Univ. of Chicago Press, 1958), pp. 223, 232. | ||

[7] | A. Bergstrom, “Relativistic invariance and the expansion of the universe”, Nuovo Cimento 27B, 145 (1975). | ||

[8] | A. Bergstrom, “Lorentz-covariant quantum transport and the origin of dark energy”, Phys. Scr. 83, 055901 (2011). | ||

[9] | A. Bergstrom, “Is CMB just an observational effect of a universe in accelerated expansion?”, International Journal of Physics 1, 133 (2013). | ||

[10] | A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors (Univ. of Chicago Press, 1958), p. 235. | ||

[11] | J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), p. 550. | ||

[12] | A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors (Univ. of Chicago Press, 1958), p. 236. | ||

[13] | R. Feynman, R. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 1965), Vol III, pp. 1.1-1.9. | ||

[14] | P. A. M. Dirac, The Principles of Quantum Mechanics (Clarendon Press, 1991), p 9. | ||

[15] | J. Frieman, M. Turner, and D. Huterer, “Dark Energy and the Accelerating Universe”, Ann. Rev. Astron. Astrophys. 46 385 (2008). | ||

[16] | M. Kemp, The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat (Yale University Press, 1990). | ||

[17] | P. S. Wesson, “Olbers's paradox and the spectral intensity of the extragalactic background light”, Astrophys. J. 367, 399 (1991). | ||

[18] | G. D. Starkman and D. J. Schwarz, “Is the universe out of tune?”, Sci. Am. 293(2), 48 (2005). | ||

[19] | D. J. Fixsen, E. S. Gheng, J. M. Gales, J. C. Mather, R. A. Shafer, and E. L. Wright, “The cosmic microwave background spectrum from the full COBE FIRAS data set”, Astrophys. J. 473, 576 (1996). | ||

[20] | M. Brooks, “13 things that do not make sense”, NewScientist, 19 March 2005. | ||

## Article

# The Magnetism as an Electric Angle-effect

^{1}Donaustr. 22, 30519 Hannover

*International Journal of Physics*.

**2014**, 2(4), 118-123

**DOI:**10.12691/ijp-2-4-5

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Hans-Joerg Hochecker. The Magnetism as an Electric Angle-effect.

*International Journal of Physics*. 2014; 2(4):118-123. doi: 10.12691/ijp-2-4-5.

Correspondence to: Hans-Joerg Hochecker, Donaustr. 22, 30519 Hannover. Email: jo.hoer@yahoo.de

## Abstract

## Keywords

## References

[1] | A. Einstein, Zur Elektrodynamik bewegter Körper Annalen der Physik 17, 891-921 (1905). | ||

[2] | Dieter Meschede: Gerthsen Physik. 23. Auflage, Springer, Berlin/Heidelberg/New York 2006. | ||

[3] | PAM Dirac: The Quantum Theory of the Electron. In: Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. A, Nr. 778, 1928, S. 610-624. | ||

[4] | James Clerk Maxwell, A Dynamical Theory of the Electromagnetic Field, Royal Society Transactions 155, 1865, Seiten 459-512. | ||

## Article

# Electronic Circuit Simulation of the Lorenz Model With General Circulation

^{1}Department of Physics, Prabhu Jagatbandhu College, Andul Howrah, India

^{2}High Energy Physics Division, Department of Physics, Jadavpur University, Kolkata, India

*International Journal of Physics*.

**2014**, 2(5), 124-128

**DOI:**10.12691/ijp-2-5-1

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

D. C. Saha, Anirban Ray, A. Roy Chowdhury. Electronic Circuit Simulation of the Lorenz Model With General Circulation.

*International Journal of Physics*. 2014; 2(5):124-128. doi: 10.12691/ijp-2-5-1.

Correspondence to: A. Roy Chowdhury, High Energy Physics Division, Department of Physics, Jadavpur University, Kolkata, India. Email: asesh_r@yahoo.com

## Abstract

## Keywords

## References

[1] | S. H. Strogatz, Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity), 1st Edition, Studies in nonlinearity, Westview Press, 2001. | ||

[2] | T.Matsumoto, A chaotic attractor from chua’s circuit, Circuits and Systems, IEEE Transactions on 31 (12) (1984) 1055-1058. | ||

[3] | L. O. CHUA, Chua’s circuit: An overview ten years later, Journal of Circuits, Systems and Computers 04 (02) (1994) 117-159. | ||

[4] | R. Madan, Chua’s Circuit: A Paradigm for Chaos, Journal of circuits, systems, and computers, World Scientific, 1993. | ||

[5] | T. Carroll, L. M. Pecora, Synchronizing chaotic circuits, Circuits and Systems, IEEE Transactions on 38 (4) (1991) 453-456. | ||

[6] | L. M. Pecora, T. L. Carroll, Driving systems with chaotic signals, Phys. Rev. A 44 (1991) 2374-2383. URL http://link.aps.org/doi/10.1103/PhysRevA.44.2374 | ||

[7] | L. M. Pecora, T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990) 821-824. URL http://link.aps.org/doi/10.1103/PhysRevLett.64.821 | ||

[8] | K. Cuomo, A. Oppenheim, S. H. Strogatz, Synchronization of lorenz-based chaotic circuits with applications to communications, Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on 40 (10) (1993) 626-633. | ||

[9] | K. M. Cuomo, A. V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications, Phys. Rev. Lett. 71 (1993) 65-68. URL http://link.aps.org/doi/10.1103/PhysRevLett.71.65 | ||

[10] | E. M. Bollt, Review of chaos communication by feedback control of symbolic dynamics, International Journal of Bifurcation and Chaos 13 (02) (2003) 269-285. | ||

[11] | E. S´anchez, M. A. Mat´ıas, Experimental observation of a periodic rotating wave in rings of unidirectionally coupled analog lorenz oscillators, Phys. Rev. E 57 (1998) 6184-6186. URL http://link.aps.org/doi/10.1103/PhysRevE.57.6184 | ||

[12] | O. Gonzales, G. Han, J. de Gyvez, E. Sinencio, Lorenz-based chaotic cryptosystem: a monolithic implementation, Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on 47 (8) (2000) 1243-1247. | ||

[13] | E. N. Lorenz, Irregularity: a fundamental property of the atmosphere*, Tellus A 36A (2) (1984) 98-110. URL http://dx.doi.org/10.1111/j.1600-0870.1984.tb00230.x | ||

[14] | H. Broer, C. S. A, R. Vitolo, Bifurcations and strange attractors in the lorenz-84 climate model with seasonal forcing, Nonlinearity 15 (4) (2002) 1205. | ||

[15] | L. van Veen, Baroclinic flow and the lorenz-84 model, International Journal of Bifurcation and Chaos 13 (08) (2003) 2117-2139. | ||

[16] | E. N. Lorenz, Compound windows of the hnon-map, Physica D: Nonlinear Phenomena 237 (13) (2008) 1689-1704. URL http://www.sciencedirect.com/science/article/pii/S0167278907004198. | ||

[17] | J. A. C. Gallas, Structure of the parameter space of the h´enon map, Phys. Rev. Lett. 70 (1993) 2714-2717. URL http://link.aps.org/doi/10.1103/PhysRevLett.70.2714 | ||

[18] | C. Masoller, A. Schifino, L. Romanelli, Regular and chaotic behavior in the new lorenz system, Physics Letters A 167 (2) (1992) 185-190. | ||

[19] | C. Masoller, A. S. Schifino, L. Romanelli, Characterization of strange attractors of lorenz model of general circulation of the atmosphere, Chaos, Solitons & Fractals 6 (0) (1995) 357-366, complex Systems in Computational Physics. | ||

[20] | A. Schifino, C. Masoller, Analitical study of the codimension two bifurcations of the new Lorenz system, in: E. Tirapegui,W. Zeller (Eds.), Instabilities and Nonequilibrium Structures V, Vol. 1 of Nonlinear Phenomena and Complex Systems, Springer Netherlands, 1996, pp. 345-348. | ||

[21] | R. Gilmore, M. Lefranc, The Topology of Chaos: Alice in Stretch and Squeezeland, Wiley, 2008. URL http://books.google.co.in/books?id=XuXDrtthXHcC | ||

## Article

# To Principles of Quantum Mechanics Development

^{1}Heat-Mass Transfer Institute of National Academy of Sciences of RB, Brovka Str.15, Minsk, 220072

^{2}M.V.Lomonosov Moscow State University, Moscow, 119899, RF

^{3}Belarusian State University, Nezavisimosti Ave., 4, Minsk, 220030, RB

*International Journal of Physics*.

**2014**, 2(5), 129-145

**DOI:**10.12691/ijp-2-5-2

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Dmitri Yerchuck, Alla Dovlatova, Felix Borovik, Yauhen Yerchak, Vyacheslav Stelmakh. To Principles of Quantum Mechanics Development.

*International Journal of Physics*. 2014; 2(5):129-145. doi: 10.12691/ijp-2-5-2.

Correspondence to: Dmitri Yerchuck, Heat-Mass Transfer Institute of National Academy of Sciences of RB, Brovka Str.15, Minsk, 220072. Email: dpy@tut.by

## Abstract

## Keywords

## References

[1] | Landau L.D, Lifshitz E.M, Quantum Mechanics, Moscow, Nauka, 1989, 768 pp. | ||

[2] | Kramers H A, Quantum Mechanics, North-Holland, Amsterdam, 1958 | ||

[3] | Bohm A, Quantum Mechanics: Foundations and Applications, Springer-Verlag, N.-Y., Berlin, Heidelberg, Tokyo, 1986, M., Mir, 1990, 720 pp. | ||

[4] | Davydov A.S, Quantum Mechanics, Moscow, Nauka, 1973, 703 pp. | ||

[5] | Dmitri Yerchuck, Alla Dovlatova, Andrey Alexandrov, Symmetry of Differential Equations and Quantum Theory, 2nd International Conference on Mathematical Modeling in Physical Sciences, 1-5 September, 2013, Prague, Czechia, Journal of Physics: Conference Series, 490. | ||

[6] | R.Feynman, R.Leyton, M.Sands, Feynman Lections on Physics, V.8, Quantum Mechanics (I), M., 1966, 269 pp. | ||

[7] | E.Vichman, Berklee Course of Physics, V.4, Quantum Physics, p.263, M., 391 pp. | ||

[8] | Dmitry Yearchuck, Yauhen Yerchak, Alla Dovlatova, Quantum-mechanical and Quantum-electrodynamic Equations for Spectroscopic Transitions, Optics Communications, 2010; 283: 3448-3458. | ||

[9] | Yearchuck D, Yerchak Y, Red'kov V, Quantum Mechanical Analogue of Landau{Lifshitz Equation, Doklady NANB, 2007; 51 (N 5): 57-64. | ||

[10] | SchrÄodinger E, Quantisierung als Eigenwertproblem (Erste Mitteilung), Annalen der Physik (Fierte Folge), 79 (1926) 361. | ||

[11] | SchrÄodinger E, Quantisierung als Eigenwertproblem (Zweite Mitteilung), Annalen der Physik (Fierte Folge), 79 (1926) 489. | ||

[12] | SchrÄodinger E, Quantisierung als Eigenwertproblem (Dritte Mitteilung), Annalen der Physik (Fierte Folge), 80 (1926) 437-490. | ||

[13] | SchrÄodinger E, Quantisierung als Eigenwertproblem (Vierte Mitteilung), Annalen der Physik (Fierte Folge), 81 (1926) 109-139. | ||

[14] | SchrÄodinger E, Die Naturwissenschaften, 14 (1926) 664. | ||

[15] | SchrÄodinger E, ÄUber das VerhÄaltnis der Heisenberg-Born-Jordanschen Quantenmechanick zu der meinen, Annalender Physik (Fierte Folge), 79 (1926) 734-756. | ||

[16] | SchrÄodinger E, An Undulatory Theory of the Mechanics of Atoms and Molecules, Physical Review, 28, N 6 (1926) 1049-1070. | ||

[17] | A.Dovlatova and D.Yerchuck, Concept of Fully Dually Symmetric Electrodynamics, 7th International Conference on Quantum Theory and Symmetries (QTS7), J.Physics: Conference Series, 343 (2012) 012133, 23 pp. | ||

[18] | Dirac P.A.M, Quelques Problemes de Mecanique Quantique, Ann.Inst. Henri Poincare, 1931, T.1, fase 4, pp 357-400. | ||

[19] | Rainich G Y, Electrodynamics in the General Relativity Theory, Trans.Am.Math.Soc., 27 (1925) 106-136. | ||

[20] | Heaviside Oliver, Electrical Papers, V.1, Macmillan and Co., London, New York, 1892; 594 pp, Heaviside Oliver, Some Properties of Maxwell Equations, Phil.Trans.Roy.Soc.A, 1893; 183:423-430, Heaviside Oliver, Electromagnetic Theory, London, The Electrician Printing and Publishing Company Limited, 1893; 466 pp. | ||

[21] | Dmitri Yerchuck, Alla Dovlatova, Andrey Alexandrov, To Principles of Quantum Theory Construction, to be published. | ||

[22] | Dmitri Yerchuck, Alla Dovlatova, Andrey Alexandrov, "Boson Model of Quantized EM-Field and Nature of Photons", 2nd International Conference on Mathematical Modeling in Physical Sciences, 1-5 September, 2013, Prague, Czechia, Journal of Physics: Conference Series, 490 (2014). | ||

[23] | Abdelhak Djouadi, The Higgs mechanism and the origin of mass, The 8-th Int.Conf. on Progress in Theor.Phys., AIP Conf.Proc., 1444 (2012) 45-57. | ||

[24] | D.Yearchuck, A.Alexandrov and A.Dovlatova, To Nature of Electromagnetic Field, Appl.Math.Comput.Sci., 3, N 2 (2011) 169-200. | ||

[25] | Born M, Z.f.Phys. 38 (1926) 803; 40 (1926) 167; Experiment and Theory in Physics, Cambridge University Press, 1943, p.23. | ||

[26] | Dirac P.A.M, On the Theory of Quantum Mechanics, Proc.Roy.Soc.A, 112 (1926) 661-677. | ||

[27] | Dirac P.A M, The Quantum Theory of Emission and Absorption of Radiation, Proc.Roy.Soc.,A, 114 (1927) 243-265. | ||

[28] | SchrÄodinger E, Die gegenwÄartige Situation in der Quantenmechanik, Die Naturwissenschaften, 50 (1935) 844-849. | ||

[29] | SchrÄodinger E, Berl.Ber., I6.April I93I. | ||

[30] | SchrÄodinger E, Annales de l'Institut H. Poincare, 269 (Paris, 1931). | ||

[31] | SchrÄodinger E, Cursos de la universidad internacional de verano en Santander, I, 6o (Madrid, Signo, I935). | ||

[32] | Dirac P.A.M, The Physical Interpretation of the Quantum Dynamics, Proc.Roy.Soc.A, 113 (1927) 621-641. | ||

[33] | Dmitri Yerchuck, Yauhen Yerchak, Alla Dovlatova, Vyacheslav Stelmakh, Felix Borovik, The Photon Concept and the Physics of Quantum Absorption Process, in press. | ||

[34] | Misochko O V, Nonclassical states of lattice excitations: squeezed and entangled phonons, Phys.-Usp., 56 (2013) 868. | ||

[35] | Lee K. C., Sprague M R, Sussman B J, Nunn J, Langford N K, Jin X.-M., Champion T, Michelberger P, Reim K F, England D, Jaksch D, Walmsley I A, Entangling Macroscopic Diamonds at Room Temperature, Science, 334 (2011) 1253-1256. | ||

[36] | Dempster A J, Batho H F, Phys.Rev.,30 (1927) 644. | ||

[37] | Scully M O, Zubairy M S, Quantum Optics, Cambridge University Press, 1997, 650 pp. | ||

[38] | Dmitri Yerchuck, Felix Borovik, Alla Dovlatova, Andrey Alexandrov, Concept of Free Acoustic Field, British Journal of Applied Science and Technology, 4, N 15 (2014) 2169-2180. | ||

[39] | Su W.-P., Schrie®er J.R, Heeger A.J, Soliton Excitations in Polyacetylene, Phys.Rev.B, 1980; 22: 2099-2111. | ||

[40] | Lee K. C., Sussman B J, Sprague M R, Michelberger P, Reim K F, Nunn J, Langford N K, Bustard P J, Jaksch D and Walmsley I A, Macroscopic Non-Classical States and Terahertz Quantum Processing in Room-Temperature Diamond, Nature Photonics, 6 (2012) 41-44. | ||

[41] | Dodin I.Y, Geometric view on noneikonal waves, Physics Letters A 378 (2014) 1598-1621. | ||

[42] | Born M, Jordan P, Zur Quantenmechanik, Zeitschrift fÄur Physik, 34 (1925) 858-888. | ||

[43] | Born M, Heisenberg W, Jordan P, Zur Quantenmechanik II, Zeitschrift fÄur Physik, 35 (1926) 557-615. | ||

## Article

# Big Crunch, Big Rip – or a Self-Similar Expansion Replenished by Dark Matter and Dark Energy?

^{1}B&E Scientific Ltd, Seaford BN25 4PA, United Kingdom

*International Journal of Physics*.

**2014**, 2(5), 146-150

**DOI:**10.12691/ijp-2-5-3

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Arne Bergstrom. Big Crunch, Big Rip – or a Self-Similar Expansion Replenished by Dark Matter and Dark Energy?.

*International Journal of Physics*. 2014; 2(5):146-150. doi: 10.12691/ijp-2-5-3.

Correspondence to: Arne Bergstrom, B&E Scientific Ltd, Seaford BN25 4PA, United Kingdom. Email: arne.bergstrom@physics.org

## Abstract

## Keywords

## References

[1] | A. Koestler, The sleepwalkers: A history of man’s changing vision of the universe (Penguin, 1964; also in Kindle 2013). | ||

[2] | http://en.wikipedia.org/wiki/Planck_(spacecraft) retrieved 2014-08-17. | ||

[3] | G. Ellis, R. Maartens, and M. MacCallum, Relativistic Cosmology. (Cambridge, 2012), pp 146-47. | ||

[4] | R. Caldwell, M. Kamionkowski, and N. Weinberg, “Phantom Energy and Cosmic Doomsday”. Phys. Rev. Lett. 91, 7 (2003). | ||

[5] | A. Bergstrom, “Relativistic invariance and the expansion of the universe”, Nuovo Cimento 27B, 145-160 (1975). | ||

[6] | F. Zwicky, “Die Rotverschiebung von extragalaktischen Nebeln”, Helvetica Physica Acta 6, 110 (1933). F. Zwicky, “On the Masses of Nebulae and of Clusters of Nebulae”, Astrophys. J. 86, 217 (1937). | ||

[7] | A. Bergstrom, “Dark energy, exponential expansion, CMB, wave-particle duality all result from Lorentz-covariance of Boltzmann’s transport equation”, International Journal of Physics 2, 112-117 (2014). | ||

[8] | A. Bergstrom, “Lorentz-covariant quantum transport and the origin of dark energy”, Phys. Scr. 83, 055901 (2011). | ||

[9] | A. Bergstrom, “Is CMB just an observational effect of a universe in accelerated expansion?”, International Journal of Physics 1, 133-137 (2013). | ||

[10] | A. Bergstrom, “An element in a paradigm shift? – Could Population II stars actually be younger than Population I stars?”, International Journal of Physics 2, 78-82 (2014). | ||

[11] | A. Bergstrom, “Why galaxies look like islands in the universe – and on the origin of dark matter and energy” (to be published). | ||

[12] | A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors (Univ. of Chicago Press, 1958), p. 232. | ||

[13] | J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), p. 550. | ||

[14] | A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors (Univ. of Chicago Press, 1958), p. 235. | ||

[15] | G. I. Bell and S. Glasstone, Nuclear Reactor Theory (Van Nostrand, 1970), p 54. | ||

[16] | N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions. Vol 1, Ch 20, Sec 12 (Wiley, 1994). | ||

[17] | http://en.wikipedia.org/wiki/Generalized_Pareto_Distribution retrieved 2014-08-17. | ||