Special Issue No. – 1, March, 2019

Abstract:

Taking into account the 2 sp -hybridization effect for valence electrons in carbon atoms, we introduce a unitary matrix U as an order parameter and suggest a scalar chiral model of graphene for the description of carbon nanotubes. We consider both single-walled and two-walled carbon nanotubes, analyze corresponding solutions to the model equations and estimate the Young’s modulus. We discuss also the possible extension of the model in question to describe fullerenes as three-dimensional hedgehog structures (skyrmions). We find the corresponding Lagrangian density for the spherirically-symmetric chiral angle. The other extension of the model concerns spin and magnetic excitations of graphene-based configurations. To this end, the 8- spinor field should be introduced as a new order parameter (Rybakov, 2015).

Keywords:

Chiral Model,Chiral Current ,Grapheme ,Young’s Modulus ,CarbonNanotubes,

Refference:

I.Bolotin K.I., Sikes K.J., Jiang Z., Klima M., Fudenberg G., Hone J., Kim P., Stormer H.L.(2008). Ultrahigh electron mobility in suspended graphene. Solid State Communications, 146(9-10): 351-355.Available online: https://www.sciencedirect.com/science/article/pii/S0038109808001178

II.Derrick G.H. (1964). Comments on nonlinear wave equations as a model for elementary particles. Journal of Mathematical Physics, 5(9): 1252-1254.Available online: http://aip.scitation.org/doi/abs/10.1063/1.1704233

III.Geim A.K. (2009). Graphene: status and prospects. Science, 324: 1530-1534.Available online: http://science.sciencemag.org/content/324/5934/1530

IV.Hobart R.H. (1963). On the instability of a class of unitary field models. Proceedings of the Physical Society, 82(2): 201-203.Available online: http://iopscience.iop.org/article/10.1088/0370-1328/82/2/306

V.Lee C., Wei X., Kysar J.W., Hone J.(2008). Measurement of elastic properties and intrinsic strength of monolayer graphene. Science, 321(5887): 385-388.Available online: https://www.ncbi.nlm.nih.gov/pubmed/18635798

VI.Lu X., Chen Z. (2005). Curved pi-conjugation aromaticity, and the related chemistry of small fullerenes (<C60)and single-walled carbon nanotubes. Chemical Review, 105(10): 3643-3696.Available online: https://pubs.acs.org/doi/abs/10.1021/cr030093d

VII.Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A.(2004). Electric field effect in atomically thin carbon films. Science, 306(5696): 666-669.Available online: http://science.sciencemag.org/content/306/5696/666

VIII.Rybakov Yu.P. (2012). On chiral model of graphene. Solid State Phenomena, 190: 59-62.Available online: https://www.scientific.net/SSP.190.59

IX.Rybakov Yu.P. (2015). Spin excitations in chiral model of graphene. Solid State Phenomena, 233-234: 16-19.Available online: https://www.scientific.net/SSP.233-234.16

X.Semenoff G.W. (1984). Condensed-matter simulation of a three-dimensional anomaly. Physical Review Letters, 53: 2449-2452.Available online: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.53.2449

XI.Skyrme T.H.R. (1962). A unified field theory of mesons and baryons. Nuclear Physics, 31(4): 556-569.Available online: https://www.sciencedirect.com/science/article/pii/0029558262907757

XII.Terrones M. (2003). Science and technology of the twenty-first century: synthesis, properties, and applications of carbon nanotubes. Annual Review of Materials Research, 33: 419-501.Available online: http://www.annualreviews.org/doi/abs/10.1146/annurev.matsci.33.012802.100255

XIII.Yu M.F., Files B.S., Arepalli S., Ruoff R.S. (2000). Tensile loading of ropes of single wallcarbon nanotubes and their mechanical properties. Physical Review Letters, 84(24): 5552-5555.Available online: https://www.ncbi.nlm.nih.gov/pubmed/10990992

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Abstract:

It is shown that the Maxwell’s equations for surface electromagnetic TM waves, propagating along the plane boundary between two nonlinear dielectrics with arbitrary diagonal tensor of dielectric permittivity, depending on 2 | | E  , can be integrated in quadratures. For the TM plane wave the magnetic intensity has only the transverse component, but the electric intensity has both transverse and longitudinal ones. This fact permits one to find the first integral of the Maxwell’s equations and eliminate the magnetic intensity. The resulting equations for the electric intensity can be simplified and integrated, if one uses the transverse permittivity as the independent variable. Finally, we consider the Kerr dielectrics, with the permittivity being a quadratic function of the electric intensity. In this case the quadratures can be reduced to the elliptical integrals.

Keywords:

Maxwell’s Equations,Surface Waves,Dielectric Permittivity ,KerrDielectrics,

Refference:

I.Abdulhalim I., Zourob M., Lakhtakia A. (2008). Surface plasmon resonance for bio-sensing:a mini-review. Electromagnetism, 28: 214-242.Available online: http://www.tandfonline.com/doi/abs/10.1080/02726340801921650

II.Agranovich V.M., Chernyak V.Y. (1982). Perturbation theory for weakly nonlinear P-polarized surface polaritons. Solid State Communications, 44(8): 1309-1311.Available online: https://www.sciencedirect.com/science/article/pii/0038109882911115

III.Agranovich V.M., Darmanyan S.A., Dubovsky O.A., Kamchatnov A.M., Ogievetsky E.I., Reineker P. (1996). Fermi resonance solitary wave on the interface between two layers of organic semiconductors. Physical Review B: Condensed Matter, 53(23): 15451-15454.Available online: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.53.15451

IV.Agranovich V.M., Darmanyan S.A., Kamchatnov A.M., Leskova T.A., Boardman A.D. (1997). Variational approach to solitons in systems with cascaded 2xnonlinearity. Physical Review E –Statistical, Nonlinear, and Soft Matter Physics, 55(2): 1894-1898.Available online: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.55.1894

V.Agranovich V.M., Mills D.L. (1985). Surface polaritons -Electromagnetic waveson interface surfaces and boundaries. NASA STI/Recon Technical Report A86:36694.Available online: https://www.researchgate.net/publication/238534155_Surface_polaritons_-_Electromagnetic_waves_on_interface_surfaces_and_boundaries

VI.Boardman A.D. (1982). Electromagnetic Surface Modes. John Wiley & Sons Ltd, New York.

VII.Fedyanin V.K., Minalache D. (1982). P-polarized nonlinear surface polaritons in layered structures. Zeitschrift für Physik. B: Condensed Matter, 47(2): 167-173.Available online: https://link.springer.com/article/10.1007/BF01441299

VIII.Gaspar-Armenta J.A., Villa-Villa F. (2013). Electromagnetic surface waves at a metal 2D photonic crystal interface. Journal of the Optical Society of America, 30B(8): 2271-2276.Available online: https://www.osapublishing.org/josab/abstract.cfm?uri=josab-30-8-2271

IX.Mackay T.G., Lakhtakia A. (2010). Electromagnetic Anisotropy and Bi-anisotropy: AField Guide. World Scientific, Singapore.

X.Minalache D., Mazilu D., Bertolotti M., Sibila C., Fedyanin V.K. (1988). Nonlinear TE-polarized surface guided waves in a dielectric “anti-waveguide”. Solid State Communications, 66(5): 517-520.Available online: https://www.sciencedirect.com/science/article/pii/0038109888909726

XI.Minalache D., Nazmitdinov R.G., Fedyanin V.K. (1984). P-polarized nonlinear surface waves insymmetric layered structures. Physica Scripta, 29(3): 269-274.Available online: http://iopscience.iop.org/article/10.1088/0031-8949/29/3/014

XII.Minalache D., Nazmitdinov R.G., Fedyanin V.K. (1989). Nonlinear optical waves in layered structures. Soviet Journal of Particles and Nuclei, 20(1): 86-93.Available online: https://elibrary.ru/title_about.asp?id=25707

XIII.Neidlinger Th., Reineker P., Agranovich V.M. (1997). Influence of static disorder on the dynamics of Fermi resonance solitary waves at the interface between two molecular layers. Journal of Luminescence, 72-74: 804-805.Available online: https://www.sciencedirect.com/science/article/pii/S0022231396003377

XIV.Polo J., Mackay T., Lakhtakia A. (2013). Electromagnetic Surface Waves: AModern Perspective. Elsevier Inc., New York.

XV.Sarid D., Challener W. (2010). Modern Introduction to Surface Plasmons: Theory, Mathematical Modeling and Applications. Cambridge University Press, London.

XVI.Strashko A.A., Agranovich V.M. (2011). To the theory of surface plasmon-polaritons on metals covered with resonant thin films. Optics Communications, 332: 201-205.Available online: https://docslide.com.br/documents/to-the-theory-of-surface-plasmon-polaritons-on-metals-covered-with-resonant.html

XVII.Uvarova L.A., Fedyanin V.K. (1996). Asymptotic solutions for electromagnetic waves in a nonlinear optical cylinder. Theoretical and Mathematical Physics, 106(1): 68-75.Available online: https://link.springer.com/article/10.1007/BF02070764

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Abstract:

The Kerr-Newman, Schwarzschild, Reissner-Nordström, Kerr and Lense-Thirring metrics have been presented. The deflection of light by Kerr–Newman’s black hole has been evaluated. Expressions for the law of motion and trajectory of light have been obtained. The black hole is assumed to be slowly rotating. The light impact parameter is considered to be much superior to the gravitational radius and classical radius of the black hole. The deflection of light is both due to attraction by the black hole mass and due to repulsion by its charge and specific angular momentum.

Keywords:

Kerr–Newman Black Holes ,Relativistic Deflection of Light,

Refference:

I.Chandrasekhar S. (1983).The Mathematical Theory of Black Holes. Clarendon Press, Oxford.

II.EddingtonA. (1923). The Mathematical Theory of Relativity. University Press, Cambridge.

III.Fil’chenkov M., Laptev Yu. (2017). Evolution of two-horizon metrics revisited. Grav. Cosmol. 23(4): 381.

IV.Fil’chenkov M., Laptev Yu. (2016). Quantum Gravity. Lenand, Moscow (in Russian).

V.Hawking S. (1975). Particle creation by black holes. Comm. Math. Phys. 43: 199.

VI.Kerr R. (1963). Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11: 237.

VII.Lense J., Thirring H. (1918).Überden Einfluss des Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der EinsteinischenGravitationstheorie. Phys. Zs. 19: 156.

VIII.Misner C., Thorne K., Wheeler J. (1973). Gravitation. W.H. Freeman and Co., San Francisco.

IX.NewmanE. et al. (1965). Metric of a rotating, charged mass. J. Math. Phys., 6: 918.

X.Nordström G. (1918). On the energy of the gravitational field in Einstein’s theory. Proc. Kon. Ned. Akad. Wt., 20: 1238.

XI.Novikov I., Frolov V. (1998).Black Hole Physics: Basic Concepts and New Developments, Springer.Dordrecht.

XII.Penrose R. (1969). Sources of the ultra-high energy cosmic rays. NuovoCimento,1: 252.

XIII.Reissner H. (1916). Über die Eigengravitation des elektrischenFeldesnach der EinsteinischenTheorie. Ann. Phys., 50: 106.

XIV.Schwarzschild K. (1916). Über das GravitationsfeldeinesMassenpunktesnachEinsteinischenTheorie. Sitz. Preuss. Akad. Wiss., 1: 189.

XV.Weinberg S.(1972).Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. J. Wiley and Sons, Inc., N. Y.

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Abstract:

Quantum key distribution protocols and the questions of their protection were studied. There were estimated mutual influences between legitimate users and for any types of cracker attack. For example, BB84 protocol is shown to be unconditional security protocols using photon polarization between outlying channels. Secret keys share between spatially separated (removed or remote) legitimate users. A simple method of generating a dichotomy signal has also been accomplished. In fact, this method can open the way of probabilistic quantum states. We argue that quantum cryptographic systems can be partially simulate on a classical computer with finite degrees of freedom. Quantum entanglement is a basic tool of communication and processing of the information.

Keywords:

Quantum Cryptography ,Entangled State,

Refference:

I.Avila Aoki M. (2011). A Simulation of a Virtual Q-bit on a Classical Computer has been developed recently. Universidad Autonomadel Estado de Mexico,18(2): 173-174.

II.Bennett C., Bessette F., Brassard G., Salvail L. and Smolin J. (1992). Experimental quantum cryptography. J. Cryptology, 5(1): 3-28.

III.Bennett C.H. (1992), Experimental Quantum Cryptography. Journal of Cryptography, 5(1): 3-28.

IV.Bennett C.H. (1992), Quantum Cryptography Using Any Two NonorthogonalStates. Phys. Rev. Letters, 68(21), 3121-3124.

V.Bennett C.H. and Brassard G. (1984). Quantum cryptography: public-key distribution and coin tossing. in Proc. Of IEEE Intern. Conf. On Computers Systems and Signal Processing, Bangalore, India, December1948, New York: IEEE Press, 560: 175.

VI.Bennett C.H., Brassard G. (1984). Quantum cryptography: Public key distribution and coin tossing. Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, 175-179.

VII.Breguest J., Muller A. and Gisin N. (1994). Quantum cryptography with polarized photons in optical fibers: experimental and practical limits. Journal of Modern Optics, 41(12): 2405-2412.

VIII.Clepov N. (2006). Quantum cryptography: the transmission of quantum key. Electronics: Science, Technology, Business, 54-56.

IX.Diffie W. and Hellman M. (1976). New directions in cryptography. IEEE Trans. Inform. Theory IT, 22(6): 644.

X.Einstein A., Podolsky B. and Rosen N. (1935). Quantum-Mechanical Description of Physical Reality be Considered Complete?” Physical Review, 47(10): 777–780.

XI.Goby C., Yuan Z. and A. Shied (2004). Quantum key distribution over 122 km of standard telecom fiber. Appl. Phys. Lett, 84: 3762-3764.

XII.Golubchikov D.M. and Rumiantsev K.E.(2015), “Quantum Cryptography: principles, protocols, systems”, MSU Press, 315.

XIII.Hiskett P.A., Bonfrate G., Buller G.S. and Townsend P.D. (2001). Eighty Kilometer transmission experiment using an SPAD-based quantum cryptography receiver operating at 1.55 ^m. Journal Modern Optics, 48(13): 1957-1966.

XIV.Hiskett P.A., Rosenberg D., Peterson G., Hughes R.J., Nam S., Lita A.E., Miller A.J. and Northolt J.E. (2006). Long-distance quantum key distribution in optical fiber. New J. Phys. 8: 193.

XV.Hughes R., Morgan G. and Peterson C. (2000). Practical quantum key distribution over a 48-km optical fiber network. Journal. Modern. Optics, 47(2-3): 533-547.

XVI.Kamalov T.F. (2001). Hidden Variables and theNature of Quantum Statistics. J. of Russian Laser Research, 22(5): 475-479.

XVII.Kamalov T.F. (2009). Quantum computers and its Quasi-classical model. Nanotechnologies and Nanomaterials, MSOU Press, Moscow, 324-327.

XVIII.Kamalov T.F. and Rybakov Y.P. (2006). Probabilistic simulation of quantum computation. Quantum Computers and Computing, 6(1):125-136.

XIX.Kimura T., Nambu Y., Hatanaka T., Tomita A., Kosaka H. and Nakamura K. (2004). Single-photon interference over 150km transmission using silica-based integrated optic interferometers for quantum cryptography. Japan J. Appl. Phys, 43(9): 1217-1219.

XX.Kotel’nikov V. A.(1959). The Theory of Optimum Noise Immunity, Mc. Grow-Hill Book Co.

XXI.Marand C. and Townsend P. (1995). Quantum key distribution over distances as long as 30 km. Opt. Lett, 20(16): 1695-1697.

XXII.Muller A. and Gisin N. (1996). Quantum cryptography over 23 km in installed under-lake telecom fiber. EurophysLett, 33(5):335-339.

XXIII.Muller A., Breguet J. and Gisin N. (1993). Experimental demonstration of quantum cryptography using polarized photons in optical fiber over more than 1 km. EurophysicsLett, 23(6): 383-388.

XXIV.Muller A., Zbinden H. and Gisin N. (1995). Underwater quantum coding. Nature 378: 449-449.XXV.Revert R.L., Shamir A. and Adelman L. (1978). A method for obtaining digital signatures and public-key cryptosystems. Common. ACM,21(2): 120-126.

XXVI.RybakovYu.P. andKamalov T.F. (2016). Bell’s Theorem and Entangled Solitons. International Journal of Theoretical Physics, 55(9):4075-4080.

XXVII.Shannon C.E. (1949). Communication theory of secretsystems. Bell Syst. Technol. J, 28(4): 656-715.

XXVIII.Shor P.W. (1994). Algorithms for quantum computation: discrete logarithms and factoring. Proceedings of the 35th Symposium on Foundations of Computer Science, Los Alamitos, ed. by Sh. Goldwasser (IEEE Computer Society Press), 124-134.

XXIX.Takesue H., Diamante E., Honjo T., Langrock C., Fejer M., Inouse K. and Yamamoto Y. (2005). Differential phase shift quantum key distribution experiment over 105km fiber. New J. Phys. 7: 232.

XXX.Townsend P.D. (1995). Quantum cryptography on multiuser optical fiber networks. Nature 385: 47-49.

XXXI.Townsend P.D. (1997). Simultaneous quantum cryptographic key distribution and conventional data transmission over installed fiber using wavelength-division multiplexing. Electronics Lett, 33(3): 188-190.

XXXII.Townsend P.D. (1998). Quantum cryptography on optical fiber networks. Opt. Fiber Tech. 4(4): 345-370.

XXXIII.Wisner S. (1983). Conjugate coding. SIGACT News, 15(1): 78.

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Abstract:

The work is devoted to the study of Abrikosov vortices using the superconductivity model at the twin boundaries (MSC-TB) proposed in the works of V.А. Chizhov. The new model allows a deeper understanding of the mechanism of formation, evolution, and destruction of Abrikosov vortices and associated creep currents. A quantitative comparison of theoretical estimates of MSC-TB with experimental data is carried out. A good correspondence is shown. Methods of fighting with the creep current are sug-gested. Materials are described, including new ones, which, in accordance with the theory of MSC-TB, should have improved properties of superconductivity of the second kind. Perspective directions of further research are formulated.

Keywords:

Superconductivity,Abrikosov Vortices,Fluxoids,Twin Boundaries,

Refference:

I.Abrikosov A.A. (1957). On the magnetic properties of superconductors of the second group. JETP, 32: 1442.

II.Chizhov V.A. (2015).Again about superconductivity, or experiments are waiting for an answer.Publishing house “Sputnik +”, Moscow, Russia.

III.Chizhov V.A. (2017).Again about superconductivity, or experiments are waiting for an answer. Part II. Publishing house “Sputnik +”, Moscow, Russia.

IV.Essmann U. and Trauble H. (1967).The direct observation of individual flux lines in type II superconductors. Physical Letters, 24A: 526.

V.URL http://fiz.1september.ru/2003/43/no43_1.htm

VI.URL https://42.tut.by/552232?utm_campaign=news-feed&utm_medium=rss&utm_source=rss-news

VII.URL http://planet-today.ru/novosti/nauka/item/57546-fiziki-slozhili-vikhri-abrikosova-v-bukvy-s-pomoshchyu-lazernogo-pintseta.

VIII.URL http: //www.medcryoservice.ru/s_conduct.htm

IX.Kortnev A.V., Rublev Yu.V., Kutsenko A.N. (1965). Workshop on physics. Publishing house”High School”, Moscow, Russia.

X.Kozlov V.A., Samokhvalov A.V. (1991) Closed Abrikosov vortices in superconductors of the second kind. Letters to JETP, 53: 150-153.

XI.Kozlov V.A., Samokhvalov A.V. (1993) Stabilization of Toroidal Abrikosov Vortex in a Non-uniform Superconductor J. Superconductivity. 6(2): 63–68.

XII.Physical encyclopedia (1988). Abrikosov vortex lattice. Ch. Ed. A.M. Prokhorov. Moscow: Soviet Encyclopedia. 1: 389.

XIII.Tikhomirov I.V., Yugay K.N. (2008) Dynamics of closed Dynamics of closed Abrikosov vortices in superconductors of the second kind. Vestnik NSU. Series: Physics. 3: 105-108.

XIV.Zakharov M.S. (2015) Suppression of magnetic relaxation in massive high-temperature superconductors. Thesis for a candidate ‘s degree Ph.D. sciences. Ekaterinburg, 2015, 100 p. URL http: //elar.urfu.ru/ bit-stream/10995/34475/1/urgu1476_d.pdf

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Abstract:

We study the processes typical for liquids under the influence of powerful impulses of electric current. The maximum temperature and pressure arising in cavitation bubbles at such processes are calculated. To this aim, the main equation of cavitation (Rayleigh - Plisset's equation) is solved numerically. The maximum amplitudes of fluctuations of temperature and pressure in a cavity are calculated during a collapse. The analysis of the process shows the existence of the extreme value of pressure above which the cavitation is not observed. Before the limiting pressure being achieved, the cavity increases several times, collapses and comes back to the initial radius, oscillating near it. The increasing of the maximum value of the bubble radius yields, therefore, the increasing of the extreme values of temperature and pressure in a bubble at a collapse. It is established that the maximum amplitude of a bubble during spark cavitation can reach values of the order 200. This fact gives the evidence of large local pressure and temperature in the cavity at the time of a collapse. These temperature and pressure have been calculated in this work. The main conclusion is made that in a liquid metal's phase the intensive cavitation, with local increasing temperature and pressure in a cavity, is possible. Therefore, the process in question can initiate reactions of nuclear fusion in a liquid metal's phase.

Keywords:

Spark Cavitation ,Rayleigh's Equation,Cavity,

Refference:

I.Martynyuk M.M. (1999). Phase transitions at pulse heating.RUDNUniversity,Moscow.

II.TaleyarkhanR.P., WestC.D., ChoJ.S., Lahey R.T.Jr., NigmatulinR.I. et al.(2002). BlockEvidence for Nuclear Emissions During Acoustic Cavitation.Science. 8(295): 1868-1873.

III.Takahashi A.(1993). Cold Fusion Research: Present Research. V. 19: 179-185.

IV.Martynyuk M.M.(1980). Radio technician and electronic engineer. 1: 157.

V.Bulls S. P., Litvinov U.A., Month G.A., Proskurovsky D.I.(1975). UFN. 115(1): 101.

VI.Klimkin I.F., Ponomarenko V.V.(1979). Journal of technical physics. 49(9): 1893.

VII.Martynyuk M.M., Kravchenko N.Yu.(1998).Limit of thermodynamic stability of a liquid phase in the field of negative pressure. Journal of physical chemistry. 72(6): 998-1001.

VIII.Martynyuk M.M., Tamanga P.A., Kravchenko N.Yu.(2002). The chart of conditions of the titan in the field of phase transition liquid –steam. RUDNBulletin. Series “‘Physics”‘. 10(1): 5–8.

IX.Martynyuk M.M., Kravchenko N.Yu.(2003). Nuclear fusion reaction in metaphase substance in the process of electrical explosion. Applied Physics. 1: 79.

X.Furthis G.N., Zhukov V.M., Baskin L.M.(1984). Issue silnotochnyelectronics.Edition. Month G.A. –Novosibirsk: Science:24.

XI.Martynyuk M.M., Kravchenko N.Yu. (2000). Reaktsii yadernogo sinteza v mezofaznom vechsestve v processe electricheskogo vzriva. Prikladnayafizika. 1: 79 –90.

XII.Tamanga P.A., Martynyuk M.M., Kravchenko N.Yu.(2001).Spinodal of a liquid phase on the generalized Bertelo’s equation. Messenger of RUDN. Series: Mathematics, informatics, physics. 9: 56 –58.

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Abstract:

The use of variational methods for the construction of sufficiently accurate approximate solutions of a given system requires the existence of the correspondent variational principle - a solution of the inverse problem of the calculus of variations. In the frame of the Euler’s functionals there may not exist variational principles. But if we extend the class of functionals then it could allow to get the variational formulations of the given problems. There naturally arises the problem of the constructive determination of the corresponding functionals – in general non-classical Hamiltonian actions – and their applications for the search of approximate solutions of the given boundary value problems. Its solution may not be unique. In particular, there can exists a bi-variational system, i.e. generated by two different Hamiltonian actions. The main aim of the paper is to present a scheme for the construction of indirect variational formulations for given evolutionary problems and to demonstrate the effective use of the non-classical Hamiltonian actions for the construction of approximate solutions with the high accuracy for the given dissipative problem. In the paper there are used notions and methods of nonlinear functional analysis and of modern calculus of variations.

Keywords:

Bi-Variationality,Potentiality ,Hamiltonian Action,Dissipative Systems,Approximate solutions,

Refference:

I.Budochkina S., Savchin V.(2012).On direct variational formulations for second order evolutionary equations. Eurasian Mathematical Journal, 3(4):23–34.

II.Budotchkina S., Savchin V.(2007).On indirect variational formulations for operatorequations. Journalof Function Spaces and Applications, 5(3): 231–242.

III.Filippov V., Savchin V., Shorokhov S. (1994). Variational principles for non-potential operators.Journal of Mathematical Sciences, 68(3): 275–398.

IV.Mikhlin S. (1971).Numerical performance of variational methods. Wolters-Noordhoff publishing,Groningen, the Netherlands.

V.Morse P., Feshbach H. (1953).Methods of Theoretical Physics. McGraw-Hill Book Company INC, New York, Toronto, London.

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Abstract:

The accumulation of photo-sensitizer (PS) mainly in tumor cells (TC) is a necessary condition for the effectiveness of photodynamic therapy (PDT). The purpose of this work is the modeling of the accumulation kinetics of anionic PS in TC differing in energy metabolism and trans-membrane potentials (TMP). The kinetic model (KM) including a system of linear differential equations describing the accumulation of PS in some model system based on Nernst theory, is suggested. This system consists of four parallel-sequential compartments separated by permeable membranes with different electric field gradients. These potentials include negative plasma and the mitochondrial TMP as well as energy-dependent positive TMP of the nuclear membranes. The model in question accounts for the phenomenon of reduction of plasma and mitochondrial TMP in TC due to their more rapid division in comparison with normal cells. The KM is constructed for TC of tumor areas sites under hypoxic or oxygen conditions. We conclude that the accumulation kinetics of anionic PS (chlorin E6) in the tumor cells mainly depends on the relationship between the transfer rate constants through their plasma and mitochondrial membranes, these constants being functions of TMP.

Keywords:

Photodynamic Therapy,Kinetic Model,Photo-Sensitizers-Anions,Tumor Cells,Trans-Membrane Potential,

Refference:

I.Allison RR, Sibata CH. (2010). Oncologic photodynamic therapy photo-sensitizers: a clinical review.Photo-diagnosis and Photodynamic Therapy,7: 61–75.

II.Araujo R. P., McElwain D. L. S. (2004). A History of the Study of Solid Tumor Growth: The Contribution of Mathematical Modeling. Bulletin of Mathematical Biology, 66: 1039–1091.

III.Askarova K. Z., Morozova, G. I., Anoshin, A. A. (2016) Prediction of the efficiencyof PDT on the basis of kinetic model of the distribution of photo-sensitizer in the cells of malignant tumors with different levels of trans-membrane potentials.Mathematics. Computer. Education. Proceedings of the 23rd International Symposium. Section: Biophysics of complex biological systems,Joint Institute for NuclearResearch, Dubna, January, p.92.See also URL http://www.mce.su

IV.Astanin S. A., Kolobov A.V., Lobanov A. I., Pimenova T. P., Polezhaev A. A., Solyanik G. I. (2008). Influence of spatial heterogeneity of the medium on tumorgrowth and invasion. Analysis by methods of mathematical modeling. Medicine in the Mirror of Computer Science. Moscow, p.p.188-223.

V.Borisov V.A., Guseva O. A., Grigoryan S. S., (2009). The use of selective chrono-phototherapyimmunity, the head and neck: features of cellular immunity, Journal of Oncosurgery, 1(2): 86.

VI.Byrne H. M., King J. R., McElwain D. L. S., Preziosi L. (2003). Atwo-phase model of solid tumor growth.Applied Mathematics Letters, 16: 567–573.

VII.Castano A.P, Demidova T.N, Hamblin M.R. (2005). Mechanisms in photodynamic therapy: part three: photo-sensitizer pharmacokinetics, bio-distribution, tumor localization and modes of tumor destruction.Photo-diagnosisandPhotodynamic Therapy,2: 91–106.

VIII.Chin W. W., Heng P.W., Bhuvaneswari R, Lau W.K., Olivo M. (2006). The potential application of chlorinE6-polyvinylpyrrolidone formulation in photodynamic therapy.Photochemical & Photo-biological Sciences,5:1031–1037.

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Abstract:

The discharge curve Q=f (H) is a complex characteristic of run-of-river mode, which takes into consideration both: peculiar properties of the river bed and peculiar properties of the riverbed-forming activity. The discharge curve Q=f (H) is on the one hand the basis for the transition from levels to discharges and calculation with the help of them of all flow characteristics, on the other hand a kind of integral characteristic of the river channel mode. This article deals with the actual issue of constructing a curve, establishing relation between discharges and levels for shots of rivers when there aren`t or there are few hydrological field observations. The article analyses the peculiarities of the hydrological and run-of-river mode of Russian rivers and are defined the generalized characteristics for construction of discharge curves. The relation of the generalized indicator αF/αM with the type of river channel regime is established.

Keywords:

Discharge Curve ,Run-Of-River Mode,Riverbed-Forming Process ,

Refference:

I.Rzhanitsyn N.A. (1960). Morphological and hydrological patterns of river network structure.Publishing House “Gidrometeoizdat”, Leningrad, USSR.Available online at: https://www.twirpx.com/look/37152/

II.Rzhanitsyn N.A. (1985). River bed forming processes of rivers. Publishing House “Gidrometeoizdat”, Leningrad, USSR. Available online at: http://urss.ru/cgibin/db.pl?lang=Ru&blang=ru&page=Book&id=106878

III.Sinichenko E.K. (2003). Extrapolation of the relationship curve of costs and levels Q = f (H). Vestnik of thePeoples’ Friendship University of Russia,2:62-66. Available online at: https://elibrary.ru/item.asp?id=9911911

IV.Tarbeyeva A.M.,ChalovR.S.(2009). Characteristics ofchannelprocessesin brooks and the smallest plain rivers. Geography and Natural Resources,30(4):388-392.Available online at:https://www.sciencedirect.com/science/article/pii/ S1875372809000896

V.Saleh Yousefi, Somayeh Mirzaee, Saskia Keesstra, Nicola Surian, Hamid Reza Pourghasemi, Hamid Reza Zakizadehf, Sahar Tabibian (2018). Effects of an extreme flood on river morphology (case study: Karoon River, Iran). Geomorphology, 304: 30-39.

VI.P. Cienciala,G.B. Pasternack (2017). Floodplain inundation response to climate, valleyform, and flow regulation on a gravel-bedriverin a Mediterranean-climate region. Geomorphology,282: 1-17.

VII.Oliver T. Coomes, Michel Lapointe, Michael Templeton, Geneva List (2016). Amazon river flow regime and flood recessional agriculture: Flood stage reversals and risk of annual crop loss. Journal of Hydrology, 539: 214-222.

VIII.Cuan Petheram,Thomas A McMahon,Murray C Peel (2008). Flow characteristics ofriversin northern Australia: Implications for development. Journal of Hydrology,357(1–2):93-111.

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Abstract:

The article presents researches of the thinking activity of project schematization. Often, work on the project is done without understanding the problem. The solution appears accidentally and unconsciously. The quality of the result depends on the algorithm of conscious plans. Techniques of thought schematization allow us to more consciously approach design. This technique has been tested in design practice by three project teams. We investigated the technique of schematization of thought on five educational projects. The research was carried out in three project groups using the example of training projects. The results of the research showed the best effectiveness in the group, which conducted a reflexive analysis and worked with the technique of the schematization described in the article. The results of the group that worked on this technique were better than the rest. One of the basic concepts is reflexive analysis, which allows both identifying and mastering the actualization of the design process. The group that made the reflexive analysis also showed better results. This is part of the methodology of schematization, which is described in the article. The algorithm of thought activity and the actualization of the techniques of schematization in project thinking are disclosed.

Keywords:

Scheme,Schematization,Project Thinking, Reflection,

Refference:

I.GraaflandAd. (2000). The Socius of Architecture: Amsterdam, Tokyo, New York / Arie Graafland. 010 Publishers, Rotterdam, Netherlands.

II.Anisimov O.S. (2009). Methodology of safety. RAMiAPublishers. Moscow, Russia.

III.Bernstein R.J. (1967). John Dewey. Washingtone square press, New York, USA.

IV.Bogin G.I. (1986). Typology of understanding the text.KGU Publishers. Kalinin, Russia.Available online at: http://linguistics-online.narod.ru/index/0-240

V.Bouryak A.P. (1998).Architecture and methodological movement(Архитектура и методологическое движение). Traditions and Innovations in Higher Architectural and Artistic Education(Традиціїтановаціїувищійархітектурно-художнійосвіті), 23 (3): 32-35. Available online at: http://www.alexander-bouryak.com/page-pub.html

VI.Charles Jencks, (1987). Post-Modernism and Electric Continuity. Rizzoli Publishers, New York, USA.

VII.Erofalov B.L. (2002) Post-Soviet city(Постсоветскийгород). NIITIAG Publishers. Tolyatti, Russia.

VIII.Gamezo M.V., Domashenko I.A. (1999). Atlas on psychology-information and methodical manual on the course of human psychology (Атласпопсихологии; информационно-методическоепособиепокурсупсихологиячеловека). The Pedagogical Society of Russia (Педагогическое общество России), Moscow, Russia. Available online at:https://studfiles.net/preview/1843321/

IX.Kotarbinsky T.(1975). Treatise on Good Work (Traktat o dobrej robocie). Prague, Czech Republic, Available online at: https://ru.scribd.com/document/293431892/prof-TADEUSZ-KOTARBIN-SKI-Traktat-o-dobrej-robocie

X.Partlett W. (2004).Breaching Cultural Worlds with the Village School: Educational Visions, Local Initiative, and Rural Experience at S.T. Shatsky’s Kaluga School System, 1919-1931. Proquest Academic Research Library Publishers, USA,vol 82, chapter 4,pp. 847-885.Available online at: https://www.revolvy.com/main/index.php?s=Stanislav%20Shatsky

XI.Polat E.S. (2000).New information technologies in the education system.Education Publishers. Moscow, Russia

XII.Rappaport. A.G. (1987). Architecture and ontology. Available online at: http://papardes.blogspot.ru/2011/11/1985.html

XIII.Schedrovitsky G.P. (1971).Configuration as a method of construction of complex knowledge. Systematics,8(4).Available online at: http://www.fondgp.ru/gp/biblio/eng/3

XIV.Schedrovitsky G.P. (1986). Schemesofthoughtactivity(Схемы мыследеятельности –системно-структурное строение, смысл и содержаниe). System research (Cистемные исследования). Moscow, Russia.Available online at: http://www.fondgp.ru/gp/biblio/rus/57

XV.Tietz J.,Hoffman W., MeuserP.(1999).The Story of Architecture of the 20thcentury. Konemann Publisher,Konemann, Germany.

XVI.Wiseman, Carter (2007). Louis I. Kahn: Beyond Time and Style: A Life in Architecture. W.W. Norton Publishers,New York, US.Available online at: https://books.google.ru/books/about/Louis_I_Kahn.html?id=WLGNrcU8VJYC&redir_esc=y

XVII.Zinchenko A.P. (2016).Technology of system thinking: Experience in applying and translating technologies of system thinking(Технологиясистемногомышления: Опытпримененияитрансляциитехнологийсистемногомышления). Alpina Publisher, Moscow, Russia.

XVIII.Zinchenko A.P. (1944). The technology of schematization in the SMD methodology. Centaur Publishers,Moscow, Russia. Available online at: http://priss-laboratory.net.ru/T.E.X.T.S.-/epistem_1993_2-5_zinchenko.htm

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