P. Ošmera- Vortex-ring Modeling of Complex Systems and Mendeleev’s Table

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  Proceedings of the World Congress on Engineering and Computer Science 2007 WCECS 2007, October 24-26, 2007, San Francisco, USA Vortex-ring Modeling of Complex Systems and Mendeleev’s Table P. Ošmera Institute of Automation and Computer Science Brno University of Technology Technicka 2, 616 69 Brno, Czech Republic Tel.: +420 541 142 294, Fax:+420 541 142 490 osmera @fme.vutbr.cz Abstract-This paper is an attempt to attain a new and profound model of the nature’s structure using a vortex-fractal
  Vortex-ring Modeling of Complex Systems and Mendeleev’s Table P. OšmeraInstitute of Automation and Computer ScienceBrno University of TechnologyTechnicka 2, 616 69 Brno, Czech RepublicTel.: +420 541 142 294, Fax:+420 541 142 490osmera @fme.vutbr.cz  Abstract  - This paper is an attempt to attain a newand profound model of the nature’s structureusing a vortex-fractal theory (VFT). Scientists tryto explain some phenomena in Nature that havenot been explained so far. The aim of this paper isthe vortex-fractal modeling of vortex-ring fractalstructure of atoms, molecules, and a creation of elements in the Mendeleev’s periodic table withvortex-ring particles which is not in contradictionto the known laws of nature.  Index Terms   - periodic table, vortex-fractal structures I. I NTRODUCTION Matter is composed of tiny atoms. All the atoms of any elements are identical: they have the same massand the same chemical properties. They differ fromthe atoms of all other elements. Twenties-century X-ray work has shown that the diameters of atoms areof the order 0.2 nm (2x10 -10 m). The mass and thepositive charge are concentrated in a tiny fraction of the atom, called nucleus. The nucleus consists of protons (  p) and neutrons ( n) . Protons and neutronsare made up of smaller subatomic particles, such asquarks. Both protons and neutrons have a massapproximately 1840 times greater than an electron( e) . The more energy an electron has, the further itcan escape the pull of the positively charged nucleus.Electrons are arranged in shells at fixed distancesfrom nucleus, depending on their energy. The mostshells an atom can have is 7, and each shell can onlysupport a certain number of electrons. Givensufficient energy, an electron can jump from oneshell to higher shell. When it falls back to a lowershell, it emits radiation in the form of a photon. Theelectron belongs to the lepton class of particles, itsantiparticle is the positron. Because protons arepositively charged and neutrons are neutral, thenucleus of an atom is always positively charged. Thenumber of proton is called the atomic number  Z  orproton number P . Protons and neutrons are bothnucleons. The number of protons P and neutrons  N  iscalled the nucleon number, or, alternatively, the massnumber  A (A = Z + N). The atomic number Zdetermines the chemical properties of an element andits position in the periodic table. Isotopes of anelement all have the same atomic number  Z  but adifferent mass number  A because they have differentnumber of neutrons. When an element has a relativeatomic mass, which is not a whole number, it isbecause it consists of a mixer of isotopes. Isotopesare nuclides of the same element.The theory of vortex-fractal structures of elements like the theory of black holes was developedbefore there was any indication that they actuallyexist in micro-world. It shows the remarkable powerand depth of fractal-vortex theory [2-6], [9-13], [17].Matter has an innate tendency to self-organizingand generating complexity from a chaos [2],[7],[8].This tendency has been at work since the birth of theuniverse, when a pinpoint of featureless matterbudded from “nothing” at all. Irreversibility andnonlinearity characterize phenomena in every field of complexity. Nonlinearity causes small changes onone level of organization to produce large effects(anomalies) at the same or higher levels. The smallestof events can lead to the most massive consequences.We can see an emergent property, which manifests asthe result of positive and negative feedback. Butglobal features of the system cannot be understoodonly by analyzing the parts separately. Deterministicchaos arises from the infinitely complex fractalstructure.A fractal’s form is the same no matter whatlength scale we use. By using the techniques of parallelism and massive parallelism in computersimulations we come a little closer to explainingbasic principles of complex systems. Chaotic systemsare exquisitely sensitive to initial conditions, andtheir future behavior can only be reliably predictedover a short time period. Moreover, the more chaoticsystem, the less compressible its algorithmicrepresentation is. In essence, the common underlyingtheme linking complexity of nature with computermodels depends on the emergence of a complexorganized behavior. Emergency comes from manysimpler cooperative and conflicting interactionsbetween microscopic components, such as spinningelectrons, atoms etc.Fractals seem to be very powerful in describingnatural objects on all scales. Fractal dimension andfractal measure are crucial parameters for suchdescription [12], [13]. Many natural objects haveself-similarity or partial-self-similarity of the wholeobject and its part. Different physical quantitiesdescribing properties of fractal objects in E-dimensional Euclidean space with a fractal dimensionD were described in [12]. Fractal dimension Ddepends on the inter-relation between the number of repetition and reduction of individual object. There isa relationship between the dimensionality and fractalproperties of matter, which contains the constant of  Proceedings of the World Congress on Engineering and Computer Science 2007WCECS 2007, October 24-26, 2007, San Francisco, USAISBN:978-988-98671-6-4WCECS 2007  golden mean: φ = ( √ 5 – 1)/2 = 0.618.Constant φ is a special case of fractal dimension D defined by thecondition D (D – E + 2) = 1 for E = 3 [12]. Linksbetween inverse coupling constants of variousinteractions (gravitational, electromagnetic, weak andstrong) in the three-dimensional Euclidean space arediscussed in [13]. Different properties of particles(and interactions between them) correspond to thespecific values of a fractal dimension. Followingvalues (D = 0, E – 2, E – 1, E) play the mostimportant role in such analysis [13].Naturalistic explanations of the universe’s srcinare speculative [1],[2],[7]. But does this mean suchinquiries are impotent or without value? The samecriticism can be made of any attempt to reconstructunique events in the past. We cannot complete ourknowledge without answering some of thefundamental question about nature. How does theuniverse begin? What is turbulence? Above all, in auniverse ruled by entropy, drawing inexorably towardgreater and greater disorder, how does order arise?Although the various speculative srcin scenariosmay be tested against data collected in laboratoryexperiments, these models cannot be tested againstthe actual events in question, i.e., the srcin of complex structures. Such scenarios, then, must everremain speculation, not knowledge. There is no wayto know whether the results from these experimentstell anything about the way universe itself evolved. Ina strict sense, these speculative reconstructions arenot falsifiable; they may only be judged plausible orimplausible. In the familiar Popper sense of whatscience is, a theory is deemed scientific if it can bechecked or tested by experiment against observable,repeatable phenomena. The chaos began to unite thestudy of different systems. A simulation brings itsown problem: the tiny imprecision built into eachcalculation rapidly takes over, because this is asystem with sensitive dependence on initialconditions. But people have to know about disorder if they are going to deal with it. Classical scientistswant to discover regularities. It is not easy to find thegrail of science, the Grand Unified Theory or “theoryof everything”. On the other hand, there is a trend inscience toward reductionism, the analysis of systemonly in terms of their constituent parts: quarks,chromosomes, or neuron. Some scientists believe thatthey are looking for the whole.Just as an electron’s random degeneracy motionsbecome more vigorous when one confines theelectron to smaller and smaller region [16], so alsogravitational vacuum fluctuations are more vigorousin small regions than in large, that is, for smallwavelengths rather than for large. In 1955, JohnWheeler, by combining the laws of quantummechanics and the laws of general relativity in atentative and crude way deduced, that in a region thesize of the Planck-Wheeler length (1.62 x 10 -33 centimeter) or smaller. The vacuum fluctuations arethere so huge that space as we know it “boils” andbecomes a froth of quantum foam – the same sort of quantum foam as makes up the core of space timesingularity [16]. How the electron can be createdfrom quantum foam is illustrated on Fig.1 and thefinal vortex-ring electron structure is on Fig.2. Fig. 1 Quantum foam with vortex-rings (basic partsof the electron structure) and vortex-coils (basicparts of the proton and the neutron structure) Fig. 2 The vortex-fractal structure model of twoelectrons (in the electron ray [11]) II. A TOMIC SPECTRA Hydrogen is the lightest and simplest element. In1885, J.J.Balmer, a Swiss high school teacher, found WKDWWKHZDYHOHQJWKV    RIWKHIRXUYLVLEOHOLQHV  produced by hydrogen are described by: 1/  λ = R (1/2 2 – 1/n 2 ), n = 3, 4. 5. 6 with R = 1.097 x 10 7 m -1 . Itcan be generalized to 1/  λ = R(1/ n 2   2 – 1/n 1   2 ), n 2 =1,2,3; n 1 = (n 2 + 1), (n 2 + 2), …… Any detailedmodel of the atom’s structure ought to be able topredict these wavelengths of the light given off byhydrogen, the simplest atom.Absorption of photons is the reverse process of emission. If a photon with energy equal to thedifference in energy of two states of an atom passedby, that photon may be absorbed and its energy willput the atom into a higher energy state. The photon’senergy equals the change in energy of the atombecause energy is conserved. If the photon’s energyis not equal to the difference in energy of two states Proceedings of the World Congress on Engineering and Computer Science 2007WCECS 2007, October 24-26, 2007, San Francisco, USAISBN:978-988-98671-6-4WCECS 2007  of the atom, the photon will not be absorbed. Thisexplains the line spectra observed in absorptionspectra. In continuous or white light, photons of allwavelengths are present. Only those with particularenergies (or wavelengths) corresponding todifferences in energy will be absorbed; all others passby untouched. III. A TOMIC STRUCTURE IN QUANTUMMECHANICS Energy is quantized. The n in E n is called theprincipal quantum number. There are other quantities.Angular momentum L:L = √ (l (l + 1)) h/ (2 π ) l = 0, 1,….., n-1 , l iscalled the orbital quantum numberz-component of angular momnentum L z L z = m l h/ (2 π ) m l = - l,........., -1, 0, 1, ........., l –1, l where m l is called the magnetic quantumnumber.The intrinsic angular momentum of the electron,often called the electron’s spin S:S = √ ((1/2)(1/2+ 1)) h/ (2 π )z-component S z of the spin of the electron isS z = m s h/ (2 π ) m s = -1/2,+1/2 IV. C OMPLEX ATOMS As with hydrogen-like atoms, the same quantumnumbers describe states that may be filled byelectrons in more complex atom ( He has Z=2):Principal quantum number n=1electron number Znlm l m s 1100+1/22100-1/2Principal quantum number n=2electron number Znlm l m s 1200+1/22200-1/2321-1+1/2421-1-1/25210+1/26210-1/27211+1/28211-1/2The same information can be stated with anothernotation.The principle quantum number n is explicitly statedas 1, 2, 3,….,7.The orbital quantum number l is given by a letter: l = 0 is an s -state l = 1 is an p -state l = 2 is an d -state l = 3 is an f  -stateThe number of electrons in a particular “orbital” isdescribed with an exponent. Here are a few atomsshowing which states are filled with electrons:Element Z configuration H 11s He 21s 2 Li 31s 2 2s Be 41s 2 2s 2 B 51s 2 2s 2 2p C 61s 2 2s 2 2p 2 N 71s 2 2s 2 2p 3 O 81s 2 2s 2 2p 4 F 91s 2 2s 2 2p 5 Ne 101s 2 2s 2 2p 6 The Pauli exclusion principle requires that no twoelectrons may have the same four quantum numbers.It follows that, if two electrons in an atom have thesame values of n, l and m l they must have differentvalues of m s . Their spins must be opposed (theelectrons have opposite vortex-ring orientation [10]).Each orbital can hold two electrons with oppositespins. The term shell is used for a group of orbitalswith the same principal quantum number. A subshellis a group of orbitals with the same principal andsecond quantum numbers, e.g. the 3p subshell [14].An electron moving in an orbit can have only certainamount of energy, not an infinitive number of values:its energy is quantized. It is due to minimum energyto create vortex-photon structure that translatesenergy to the electron [10,11]. If the energy of theelectron is quatized, the radius of the orbit also mustbe quantized. There is a restricted number of orbitswith certain radii, not an infinite number of orbits.The wave theory of the electron replaces the idea of finding the electron in a certain position in its orbitwith the idea of the probability of finding the electronin a certain volume: the orbital. The volume of spacein which there is a 95% chance of finding the electronis called the atomic orbital. There is 5% probabilitythat the electron will be outside this volume of spaceat a given instant. Fig. 3 The vortex-ring structure of the nucleus of thehelium 24 He (alpha particle) and its orbital 1s Proceedings of the World Congress on Engineering and Computer Science 2007WCECS 2007, October 24-26, 2007, San Francisco, USAISBN:978-988-98671-6-4WCECS 2007  Atoms combine to form a molecule. Theirshared air of electrons is called a covalent bond. Theyoccupy the same orbital with opposite spins. The H 2 molecule atoms H share electrons. Each hydrogenatom shares its electron with another hydrogen atomto gain a full outer s shell of 2 electrons. Covalentbonding is important in carbon compounds. Thebonds in methane CH 4 are such to carbon hascompleted its octet. In carbon dioxide, the carbonatom shares two electrons with each of two oxygenatoms, in order to give all three atoms a full octet of valence electrons. In CH 4 and NH 4+ all the bonds arethe same. The structures are perfect tetrahedra with WKHWHWUDKHGUDODQJOH  .    o . In NH 3 the bondangle is 107 o , and in a molecule of water H 2 O it is104.5 o . Diamond is the hardest naturally occurringsubstance. The extraordinary properties of diamondarise from its structure (see Fig.5). Fig. 4 The vortex-ring structure of the atom 37 LiFig. 5 The vortex-ring structure of the atom 612 CFig.6 The vortex-ring structure of the atom 816 O Intermolecular forces and bonds are of a number of types: dipole-dipole interactions, van der Waalsforces and the hydrogen bond. Polar molecules havea dipole. Dipole consists of two electric charges of equal magnitude and opposite signs separated by asmall distance. Water molecules are attracted to ionsin the crystal. In a snowflake the hydrated ions aresurrounded with six water molecules.There are three simple rules how to create atoms:1) Only two protons can be on one rotational axis2) Two protons cannot be connected directly withvortex nuclear bond (only the proton with theneutron can be nuclear bond)3) Two protons can levitate each other on onerotational axis (see p 2 and p 4 in Fig.5) Fig.7 The classical structure model of the molecule H 2 O (compare with   structure model on Fig.6) Fig. 8 The vortex-ring structure model of the benzenemolecule Fig. 9 The vortex-ring structure of the atom 614 C Proceedings of the World Congress on Engineering and Computer Science 2007WCECS 2007, October 24-26, 2007, San Francisco, USAISBN:978-988-98671-6-4WCECS 2007
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