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Article

Dispersion of SH and Love Waves

1Institute for Problems in Mechanics, Prosp. Vernadskogo, Moscow, Russia


International Journal of Physics. 2014, 2(5), 170-180
DOI: 10.12691/ijp-2-5-7
Copyright © 2014 Science and Education Publishing

Cite this paper:
Sergey V. Kuznetsov. Dispersion of SH and Love Waves. International Journal of Physics. 2014; 2(5):170-180. doi: 10.12691/ijp-2-5-7.

Correspondence to: Sergey  V. Kuznetsov, Institute for Problems in Mechanics, Prosp. Vernadskogo, Moscow, Russia. Email: kuzn-sergey@yandex.ru

Abstract

A mathematical model for analyzing both Love waves and horizontally polarized shear surface waves (SH-waves) propagating in stratified media with monoclinic symmetry is worked out. Analytic and numerical solutions for SH and Love waves obtained by applying the Modified Transfer Matrix (MTM) method and a special complex formalism, are presented. Displacement fields, specific energy, phase, ray, and group velocities, and dispersion curves for SH and Love waves are compared and analyzed. Plates with different types of boundary conditions imposed on the outer surfaces are considered. Behavior of the leakage Love waves and anomalous SH-waves is discussed.

Keywords

References

[1]  A.E.H. Love, Some Problems of Geodynamics. Cambridge University Press, London (1911).
 
[2]  E. Dieulesaint and D. Royer, Elastic Waves in Solids. Wiley, N.Y. (1980).
 
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[4]  S.V. Kuznetsov, Subsonic Lamb waves in anisotropic plates. Quart. Appl. Math. 60 (2002) 577-587.
 
[5]  S.V. Kuznetsov, Love waves in stratified monoclinic media. Quart. Appl. Math. 62 (2004) 749-766.
 
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[6]  S.V. Kuznetsov, SH-waves in multilayered plates. Quart. Appl. Math. 64 (2006) 153-165.
 
[7]  S.V. Kuznetsov, Love waves in non-destructive diagnostics of layered composites, Acoustical Physics, 56 (2010) 877-892.
 
[8]  M.J.S. Lowe, Matrix techniques for modeling ultrasonic waves in multilayered media. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 42 (1995) 525-542.
 
[9]  D. Lévesque and L. Piché, A robust transfer matrix formulation for the ultrasonic response of multilayered absorbing media. J. Acoust. Soc. 92 (1992) 452-467.
 
[10]  M. Castaings and B. Hosten, Transfer matrix of multilayered absorbing and anisotropic media. Measurments and simulations of ultrasonic wave propagation through composite materials. J. Acoust. Soc. Am. 94 (1993) 1488-1495.
 
[11]  P. Michaels and V. Gottumukkula, Theory of viscoelastic Love waves and their potential application to near-surface sensing to permeability. In: Advances in near-surface seismology and ground-penetrating radar. Geophysical Developments Series. (2010) 263-278.
 
[12]  D. Restrepo, J.D. Gomez, and J.D. Jaramillo, SH wave number Green’s function for a layered, elastic half-space. Part I: Theory and dynamic canyon response by the discrete wave number boundary element method. Pure Appl. Geophys. (2014) 1-14.
 
[13]  M. Behm and R. Snieder, Love waves from local traffic noise interferometry. The Leading Edge. 32 (2013) 628-632.
 
[14]  J. Xia, X. Yin, and Y. Xu, Feasibility of determining Q of near-surface materials from Love waves. J. Appl. Geophysics. 95 (2013) 47-52.
 
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Article

To Principles of Quantum Theory Construction

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

2M.V.Lomonosov Moscow State University, Moscow


International Journal of Physics. 2014, 2(6), 181-188
DOI: 10.12691/ijp-2-6-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Dmitri Yerchuck, Alla Dovlatova, Andrey Alexandrov. To Principles of Quantum Theory Construction. International Journal of Physics. 2014; 2(6):181-188. doi: 10.12691/ijp-2-6-1.

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

Abstract

New insight to the principles of the quantum theory construction is given. It is based on the symmetry study of main differential equations of mechanics and electrodynamics. It has been shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered within the frames of the number theory) determine the mathematical nature of the quantities, incoming in given equations. The substantial consequence of the given consideration is the proof of the main postulate of quantum mechanics, that is, the proof of the statement, that to any quantum mechanical quantity can be set up into the correspondence the Hermitian matrix. It is shown, that a non-abelian character of the multiplicative group of the quaternion ring leads to the nonapplicability of the quaternion calculus for the construction of new versions of quantum mechanics directly. The given conclusion seems to be actual, since there is a number of modern publications with the development of the quantum mechanics theory using the quaternions with the standard basis {e, i, j, k}. The correct way for the construction of new versions of quantum mechanics on the quaternion base is discussed in the paper presented. It is realized by means of the representation of the quaternions through the basis of the linear space of complex numbers over the field of real numbers, under the multiplicative group of which the equations of the dynamics of mechanical systems are invariant. At the same time the quaternion calculus is applicable in electrodynamics, at that the new versions of quantum electrodynamics can be constructed by an infinite number of the ways corresponding to an infinite number of the matrix representations of the standard quaternion basis {e, i, j, k}. The given conclusion is the consequence of the high symmetry of Maxwell equations.

Keywords

References

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[2]  Kramers H A, Quantum Mechanics, North-Holland, Am- sterdam, 1958.
 
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[6]  Born M, Jordan P, Zur Quantenmechanik, Zeitschrift fu¨r Physik, 34 (1925) 858-888.
 
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[11]  Dmitri Yerchuck, Alla Dovlatova, Andrey Alexandrov, Symmetry of Differential Equations and Quantum The- ory, 2nd International Conference on Mathematical Mod- eling in Physical Sciences, 1-5 September, 2013, Prague, Czechia, Journal of Physics: Conference Series, 490 (2014) 012233-7.
 
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[14]  A.Dovlatova and D.Yerchuck, Concept of Fully Du- ally Symmetric Electrodynamics, 7th International Con- ference on Quantum Theory and Symmetries (QTS7), J.Physics: Conference Series, 343 (2012) 012133, 23 pp.
 
[15]  D.Yearchuck, A.Alexandrov and A.Dovlatova, To Nature of Electromagnetic Field, Appl. Math. Comput. Sci., 3, N 2 (2011) 169-200.
 
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[26]  Dmitri Yerchuck, Alla Dovlatova, Felix Borovik, Yauhen Yerchak, Vyacheslav Stelmakh, To Principles of Quan- tum Mechanics Development, International Journal of Physics, 2, N 5 (2014) 129-145.
 
[27]  V.N. Mishra, K. Khatri, L.N. Mishra, On SimultaneousApproximation for Baskakov-Durrmeyer-Stancu type op- erators, Journal of Ultra Scientist of Physical Sciences, 24, N (3)A, (2012) 567-577.
 
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Article

The Wave Properties of Matter: The Physical Aspect

1The State University of Management, Moscow, Russia


International Journal of Physics. 2014, 2(6), 189-196
DOI: 10.12691/ijp-2-6-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Liudmila B. Boldyreva. The Wave Properties of Matter: The Physical Aspect. International Journal of Physics. 2014; 2(6):189-196. doi: 10.12691/ijp-2-6-2.

Correspondence to: Liudmila  B. Boldyreva, The State University of Management, Moscow, Russia. Email: boldyrev-m@yandex.ru

Abstract

The aim of the paper is to show that there is a physical process which could underlie the wave properties of matter. A comparison has been drawn between the properties of a pair of electrically unlike virtual particles created by a quantum entity in the physical vacuum and the characteristics of the quantum entity wave function. Analogies were revealed between the spin precession frequency of pair of virtual particles and the wave function frequency, between the size of the electric dipole produced by a pair of virtual particles and the wave function wavelength, and also between the angle of spin precession of pair of virtual particles and the wave function phase. It is shown that quantum correlations of quantum entities may be caused by spin correlations (by spin supercurrents) between virtual particles created by the quantum entities in the physical vacuum. It is shown that the wave properties of a quantum entity are due to precession of spin of pair of virtual particles created by the quantum entity in the physical vacuum.

Keywords

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Article

The Critical Error in the Formulation of the Special Relativity

1Mechanical Department, DAH (S & P), Beirut, Lebanon


International Journal of Physics. 2014, 2(6), 197-201
DOI: 10.12691/ijp-2-6-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
Radwan M. Kassir. The Critical Error in the Formulation of the Special Relativity. International Journal of Physics. 2014; 2(6):197-201. doi: 10.12691/ijp-2-6-3.

Correspondence to: Radwan  M. Kassir, Mechanical Department, DAH (S & P), Beirut, Lebanon. Email: radwan.elkassir@dargroup.com

Abstract

The perception of events in two inertial reference frames in relative motion was analyzed from the perspective of the Special Relativity postulates, leading to the Lorentz transformation equations for the time and space coordinate in the relative motion direction. Yet, straightforward inconsistencies were identified upon examining the conversion of the time interval between two co-local events in the traveling reference frame. The approach used in the Special Relativity formulation to get around the identified inconsistencies was revealed. Subsequent mathematical contradictions in the Lorentz transformation equations, disproving the Special Relativity predictions, were shown.

Keywords

References

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Article

Concept of Scalar-Vector Potential in the Contemporary Electrodynamic, Problem of Homopolar Induction and Its Solution

1B.I. Verkin Institute for Low Temperature Physics and Engineering NAS, Ukraine, 47 Lenin Ave., Kharkov, Ukraine


International Journal of Physics. 2014, 2(6), 202-210
DOI: 10.12691/ijp-2-6-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
F.F. Mende. Concept of Scalar-Vector Potential in the Contemporary Electrodynamic, Problem of Homopolar Induction and Its Solution. International Journal of Physics. 2014; 2(6):202-210. doi: 10.12691/ijp-2-6-4.

Correspondence to: F.F.  Mende, B.I. Verkin Institute for Low Temperature Physics and Engineering NAS, Ukraine, 47 Lenin Ave., Kharkov, Ukraine. Email: mende_fedor@mail.ru

Abstract

At present classical electrodynamics consists of two not connected together parts. From one side this of Maxwell equations, which determine wave phenomena in the material media, from other side the Lorentz force, which determines power interaction between the moving charges. Still from the times of Lorenz and Poincare this force is introduced as experimental postulate. And as yet there is no that united basis, which connected together these two odd parts of the electrodynamics. Present article solves this problem on the basis of introduction the concept of scalar-vector potential, which assumes the dependence of the scalar potential of charge on its relative speed. In the article is carried out the analysis of the work of different of the schematics of the unipolar generators, among which there are diagrams, the principle of operation of which, until now, did not yield to explanation. The number of such diagrams includes the construction of the generator, whose cylindrical magnet, magnetized in the end direction, revolves together with the conducting disk. Postulate about the Lorentz force, whom is used for explaining the work of unipolar generators, does not give the possibility to explain the operating principle of this generator. It is shown that the concept of scalar- vector potential, developed by the author, gives the possibility to explain the operating principle of all existing types of unipolar generators. Physical explanation of Lorentz force in the concept of scalar- vector potential is given.

Keywords

References

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[4]  F.F. Mende, On refinement of equations of electromagnetic induction, Kharkov, deposited in VINITI, No 774 - B88 Dep., 1988.
 
[5]  F.F. Mende, On refinement of certain laws of classical electrodynamics, arXiv.org/abs/physics/0402084.
 
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[9]  F.F. Mende, Experimental corroboration and theoretical interpretation of dependence of charge velocity on DC flow velocity through superconductors, Proceedings International Conference “Physics in Ukraine”, Kiev 22-27 June, 1993.
 
[10]  F. F. Mende, A New Tipe of Contact Potential Difference and Electrification of Superconducting Coils and Tori, American Journal of Electrical and Electronic Engineering, Vol. 2, No. 5, (2014), 146-151.
 
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Article

Problems of Lorentz Force and Its Solution

1B.I. Verkin Institute for Low Temperature Physics and Engineering NAS, Ukraine, 47 Lenin Ave., Kharkov, Ukraine


International Journal of Physics. 2014, 2(6), 211-216
DOI: 10.12691/ijp-2-6-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
F.F. Mende. Problems of Lorentz Force and Its Solution. International Journal of Physics. 2014; 2(6):211-216. doi: 10.12691/ijp-2-6-5.

Correspondence to: F.F.  Mende, B.I. Verkin Institute for Low Temperature Physics and Engineering NAS, Ukraine, 47 Lenin Ave., Kharkov, Ukraine. Email: mende_fedor@mail.ru

Abstract

In the article is proven that the Lorentz force is the consequence of the dependence of the scalar potential of charge on the speed. It is shown that the dependence of Lorentz force on the speed is nonlinear, as previously supposed. It is shown also, that the forces of interaction of conductors, along which flows the current, are not symmetrical. When the direction of the motion of charges in the conductors they coincide, the force of their interaction occurs less than when directions of motion are different.

Keywords

References

[1]  V.V.Nicolsky, T.I. Nicolskaya, Electrodynamics and propagation of radio waves, Moscow, Nauka, 1989.
 
[2]  R. Feynman, R. Leighton, M. Sends, Feynman lectures on physics, –М. Mir, Vol. 6 (1977).
 
[3]  J.Jackson, Classical Electrodynamics, Mir, Moscow, 1965, 702.
 
[4]  F.F. Mende, On refinement of equations of electromagnetic induction,- Kharkov, deposited in VINITI, No 774-B88 Dep. (1988).
 
[5]  F. F.Mende, Are thereerrorsin modern physics. Kharkov, Constant, 2003.
 
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[6]  F.F. Mende, On refinement of certain laws of classical electrodynamics, arXiv.org/abs/physics/0402084
 
[7]  F. F. MendeNew electrodynamics.Revolution in the modern physics.Kharkov, NTMT, 2012.
 
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Article

Multistability in a Single System with Hidden Attractors- Theory and Experiment

1Department of Physics, B.P. Poddar Institute of Management & Technology, VIP Road, Kolkata, India

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


International Journal of Physics. 2014, 2(6), 217-225
DOI: 10.12691/ijp-2-6-6
Copyright © 2014 Science and Education Publishing

Cite this paper:
Papri Saha, Dolonchampa Saha Anirban Ray, A. Roy Chowdhury. Multistability in a Single System with Hidden Attractors- Theory and Experiment. International Journal of Physics. 2014; 2(6):217-225. doi: 10.12691/ijp-2-6-6.

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

Abstract

Existence of more than one attractor for a single nonlinear system and the corresponding generation of multistability is investigated both from the point of view of theory and experiment. The system under consideration is relatively a new one which possess a single stable fixed point but shows many characteristic features of attractors in phase space. It is shown that the change in the initial condition triggers a host of phenomena not observed before in any dynamical system. Change in the initial conditions enables a switch over from one attractor to the other. Our analysis clearly shows the changes in the Poincaré section and the mechanism of formation of unstable periodic orbits. We point out that in spite of these peculiarities, the model does not possess any standard route to bifurcation but one can visualize the change in the periodicity with respect to the parameters and its dependence on the initial conditions. In the next half of our paper we have constructed analogue electric circuit for the equation and have introduced a mechanism for the choice of initial condition with the help of relay in the circuit. These modified circuits were then used to simulate experimentally the sensitivity on the initial conditions and the transition from one to the other attractor.

Keywords

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Article

Non-Relativistic Weibel Instability Due to Inverse Bremsstrahlung Absorption in Laser Fusion Plasma

1Laboratoire de Physique des Rayonnements et de leurs Interactions avec la Matière (PRIMALAB), département des sciences de la matière, faculté des sciences,université de Batna, Algeria

2Laboratoire Electronique Quantique, faculté des sciences, université (USTHB), Alger, Algeria


International Journal of Physics. 2014, 2(6), 226-230
DOI: 10.12691/ijp-2-6-7
Copyright © 2014 Science and Education Publishing

Cite this paper:
S. Belghit, A. Sid, K. Bendib. Non-Relativistic Weibel Instability Due to Inverse Bremsstrahlung Absorption in Laser Fusion Plasma. International Journal of Physics. 2014; 2(6):226-230. doi: 10.12691/ijp-2-6-7.

Correspondence to: S.  Belghit, Laboratoire de Physique des Rayonnements et de leurs Interactions avec la Matière (PRIMALAB), département des sciences de la matière, faculté des sciences,université de Batna, Algeria. Email: Belghit.slimen@gmail.com

Abstract

The present work has the aim to investigate the Weibel instability induced by inverse bremsstrahlung in laser fusion plasma, where the effect of the self-generated magnetic field is induced. Specifically, we have considered the generated static magnetic field effect on the inverse bremsstrahlung absorption. For this, we consider a homogeneous under dense plasma in interaction with a high-frequency and low-magnitude laser electric field. In our investigation, the unperturbed anisotropic distribution function which takes into account the plasma heating due to inverse bremsstrahlung absorption of laser energy is calculated from the Fokker-Planck equation. By using this distribution function, we have established the dispersion relation of the Weibel modes taking into account the coupling term of quasi-static magnetic fields with high frequency fields of the laser wave. The main obtained result is that the inclusion of the self-generated magnetic field in the inverse bremsstrahlung absorption causes a decrease of the spectral range of the Weibel unstable modes and a reduction of the growth rate of the instability by two orders. This result shows clearly that the previous analyses of the Weibel instability due to inverse bremsstrahlung have an over estimated for the values of the generated static magnetic fields. Therefore, inverse bremsstrahlung overestimated the values of the generated static magnetic fields should not affect the experiences of inertial confinement fusion.

Keywords

References

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Article

Consideration and the Refinement of Some Laws and Concepts of Classical Electrodynamics and New Ideas in Modern Electrodynamics

1B.I. Verkin Institute for Low Temperature Physics and Engineering, NAS Ukraine, 47 Lenin Ave., Kharkov, 61164, Ukraine


International Journal of Physics. 2014, 2(6), 231-263
DOI: 10.12691/ijp-2-6-8
Copyright © 2014 Science and Education Publishing

Cite this paper:
F.F. Mende. Consideration and the Refinement of Some Laws and Concepts of Classical Electrodynamics and New Ideas in Modern Electrodynamics. International Journal of Physics. 2014; 2(6):231-263. doi: 10.12691/ijp-2-6-8.

Correspondence to: F.F.  Mende, B.I. Verkin Institute for Low Temperature Physics and Engineering, NAS Ukraine, 47 Lenin Ave., Kharkov, 61164, Ukraine. Email: mende_fedor@mail.ru

Abstract

The problems considered refer to the material equations of electromagnetic and magnetoelectric induction and physical interpretation of the parameters ε(ω) and μ(ω). Some contradictions found in fundamental studies on classical electrodynamics have been explained. The notion magnetoelectric induction has been introduced, which permits symmetrical writing of the induction laws. It is shown that the results of the special theory of relativity can be obtained from these laws through the Galileo conversions with the accuracy to the v2/c2 terms. The permittivity and permeability of materials media are shown to be independent of frequency. The notions magnetoelectrokinetic and electromagnetopotential waves and kinetic capacity have been introduced. It is shown that along with the longitudinal Langmuir resonance, the transverse resonance is possible in nonmagnetized plasma, and both the resonances are degenerate. A new notion scalar-vector potential is introduced, which permits solution of all present-day problems of classical electrodynamics. The use of the scalar-vector potential makes the magnetic field notion unnecessary.

Keywords

References

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[5]  F. F. Mende, On refinement of equations of electromagnetic induction, – Kharkov, deposited in VINITI, No 774-B88 Dep., 1988.
 
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[12]  F. F. Mende, Transverse Plasma Resonans Mode in an Nonmagnetized Plasma and Its Practical Applications, American Journal of Electrical and Electronic Engineering, Vol. 2, No. 5, (2014), 152-158 .
 
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[16]  F. F. Mende, Transversal plasma resonance in a nonmagnetized plasma and possibilities of practical employment of it, arXiv.org/abs/physics/0506081.
 
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[19]  F. F. Mende, Electric kinetic capacity. Engineering Physics, №3, 2013.
 
[20]  V. V.Nicolsky, T. I. Nicolskaya, Electrodynamics and propagation of radio waves, Moscow, Nauka, 1989.
 
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Article

Carl Sagan’s Conjecture of a Message in π

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


International Journal of Physics. 2014, 2(6), 264-266
DOI: 10.12691/ijp-2-6-9
Copyright © 2014 Science and Education Publishing

Cite this paper:
Arne Bergstrom. Carl Sagan’s Conjecture of a Message in π. International Journal of Physics. 2014; 2(6):264-266. doi: 10.12691/ijp-2-6-9.

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

Abstract

In his novel Contact, the astrophysicist Carl Sagan hypothesized an alien message to be buried somewhere deep inside the numerical representation of the transcendental number π. The present article looks for markers that might possibly support such a hypothesis, and surprisingly finds a sequence of seven successive zeros (actually seven successive nines rounded off) at a depth of 3256 digits into the representation of 2π in the special case of base ten. Finding such a sequence of zeros within the first 1000 digits has a probability of 1 in 10000. No such occurrences happen even remotely for 2π at any base other than ten, nor even remotely in corresponding representations of other common transcendental numbers, such as e, which appear in physical applications. In π, this occurrence thus also remarkably appears at a depth that is a multiple of the same power of two as bits in a computer byte, which thus makes it even more enigmatic. Still, these effects are most probably just numerical coincidences without physical relevance.

Keywords

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[1]  C. Sagan, Contact, (Century Hutchinson Ltd, 1986).
 
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[7]  U.-G. Meissner et al., “Life on earth – An accident? Chiral symmetry and the anthropic principle”, International Journal of Modern Physics E 23, 1461005 (2014).
 
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