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  JOURNAL "NP" ISSUES

"Nauchnoe Priborostroenie", 2016, Vol. 26, no. 4. ISSN 2312-2951. DOI: 10.18358/np-26-4-699

"NP" 2016 year Vol. 26 no. 4.,   ABSTRACTS

ABSTRACTS, REFERENCES

A. V. Kovalchuk1, A. A. Mitina1, E. A. Polushkin1, E. I. Galperin2,
T. G. Dyuzheva2, I. A. Semenenko2, A. I. Semenenko1, S. Yu. Shapoval1

POTENTIALITY AND PECULIARITY OF ELLIPSOMETRY IN THE SURFACE STUDIES OF LIQUIDS

"Nauchnoe priborostroenie", 2016, vol. 26, no. 4, pp. 3—12.
doi: 10.18358/np-26-4-i312
 

This paper is reported on the procedure of solving the inverse problem of ellipsometry respectively to all the parameters of the surface structure and volume of liquids. The inverse problem is mathematically incorrect due to a weak optical contrast between surface and volume of a liquid. In order to solve the problem, a trial function is introduced. The most general expression for the function is obtained. The optimal solution of the inverse problem is found through an analysis of the trial function peculiarities appearing along the trajectory of the movement of the functional of the inverse problem to the point of the absolute (the deepest) minimum. The stability of the functional movement trajectory is achieved by a specific selection of the starting point on the trajectory. General patterns of the trial function's behavior are found for an ideal situation, as well as for a real situation through a numerical simulation. It is shown that the optimal solution obtained with the trial function is highly accurate.
 

Keywords: ellipsometry, polarization angles, mathematically incorrect inverse problem, criterion, optimum solution, numerical experiment, ground, optical constants

Author affiliations:

1Institute of Microelectronics Technology and High Purity Materials RAS, Chernogolovka,
Moscow Reg., Russia
2I.M. Sechenov First Moscow State Medical University, Russia

 
Contacts: Semenenko Al'bert Ivanovich, sem199@mail.ru
Article received in edition: 5.08.2016
Full text (In Russ.) >>

REFERENCES

  1. Kovalchuk A.V., Mitina A.A., Polushkin E.A., Galperin E.I., Dyuzheva T.G., Semenenko I.A., Semenenko A.I., Shapoval S.Yu. [Potential of spectral ellipsometry in studying the blood serum of chronic pancreatitis patients. Full factorial experiment]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2014, vol. 24, no. 2, pp. 104—117. URL: http://213.170.69.26/en/mag/2014/full2/Art14.pdf. (In Russ.).
  2. Semenenko A.I., Semenenko I.A. [On the new potentials of ellipsometry arising from the null optical circuit. Ellipsometry of real surface structures. 19. Optimal solution choice of inverse problem in studying of ultra thin superficial films]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2010, vol. 20, no. 4, pp. 132—142. URL: http://213.170.69.26/en/mag/2010/full4/Art16.pdf. (In Russ.).
  3. Box M.J. A new method of constrained optimization and a comparison with other methods. Comp. Journ., 1965, vol. 8, no. 1, pp. 42—51. Doi: 10.1093/comjnl/8.1.42.
  4. Semenenko A.I., Semenenko I.A. [Solid body and liquid superficial structure study by ellipsometry considering mathematical inverse problem incorrectness. Part 6. On stability of the inverse problem solution. Box method modification]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2012, vol. 22, no. 3, pp. 69—77. URL: http://213.170.69.26/en/mag/2012/full3/Art11.pdf. (In Russ.).
 

A. S. Berdnikov1, I. A. Averin1,2, N. K. Krasnova2, K. V. Solovyev2

UNIVERSAL EXPRESSIONS FOR 3D ELECTRIC AND MAGNETIC POTENTIALS WHICH ARE UNIFORM IN EULER TERMS

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 13—30.
doi: 10.18358/np-26-4-i1330
 

Electric and magnetic fields which are uniform in Euler terms are a useful instrument to design the systems of charge particle optics. The similarity principle for charged particle trajectories in these fields which was realized by Yu.K. Golikov for the first time enables to create spectrographic charge particle optical systems in a more systematic and intelligence way by using the fields which are uniform in Euler terms. As a result the analytical expressions for the Laplace potentials which are uniform in Euler terms are a useful tool to design optical systems of this type. This paper considers general expressions of an algebraic-differential type which produces 3D harmonic functions which are uniform in Euler’ terms and can be used as potentials of corresponding electric and magnetic fields.
 

Keywords: electric fields, magnetic fields, uniform in Euler’ terms functions, similarity principle for charged particle trajectories, analytical solutions of Laplace equation

Author affiliations:

1Institute for Analytical Instrumentation of RAS, Saint - Petersburg , Russia
2Peter The Great Saint-Petersburg Polytechnic University, Russia

 
Contacts: Berdnikov Alexander Sergeevich, asberd@yandex.ru
Article received in edition: 28.07.2016
Full text (In Russ.) >>

REFERENCES

  1. Fihtengolc G.M. Kurs differencial'nogo i integral'nogo ischisleniya [Course of differential and integral calculus], vol. 1. Moscow, Fizmatlit Publ., 2001. 616 p. (In Russ.).
  2. Smirnov V.I. Kurs vysshej matematiki [Course of the higher mathematics], vol. 1. Moscow, Nauka Publ., 1974. 480 p. (In Russ.).
  3. Golikov Yu.K., Krasnova N.K. [The electric fields uniform in Euler, for electronic spectrography]. Zhurnal tekhnicheskoj fiziki [Journal of technical physics], 2011, vol. 81, no. 2, pp. 9—15. (In Russ.).
  4. Golikov Yu.K., Krasnova N.K. Teoriya sinteza ehlektrostaticheskih ehnergoanalizatorov [Theory of synthesis of electrostatic power analyzers]. Saint-Petersburg, Polytechnical university Publ., 2010. 409 p. (In Russ.).
  5. Krasnova N.K. Teoriya i sintez dispergiruyushchih i fokusiruyushchih ehlektronno-opticheskih sred. Diss. dokt. fiz.-mat. nauk [The theory and synthesis of the dispersing and focusing electron-optical environments. Dr. phys. and math. sci. diss.]. Saint-Petersburg, 2013. 259 p. (In Russ.).
  6. Golikov Yu.K., Krasnova N.K. [The generalized principle of similarity and its application in electronic spectrography]. Prikladnaya fizika [Applied physics], 2007, no. 2, pp. 5—11. (In Russ.).
  7. Golikov Yu.K., Krasnova N.K. [Analytical structures of electric spectrographs the fields of which are expressed in a uniform generalized form]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2014, vol. 24, no. 1, pp. 50—58. URL: http://213.170.69.26/mag/2014/full1/Art6.pdf. (In Russ.).
  8. Averin I.A., Berdnikov A.S., Gall N.R. [The principle of similarity of trajectories at the movement of charged particles with a different masses in electric and magnetic fields, uniform in Euler]. Pis'ma v ZhTF [Letters in ZhTF], 2016, vol. 42, no. 23—24. (In Russ.).
  9. Berdnikov A.S., Averin I.A., Golikov Yu.K. [The static mass spectrographs of new type using the electric and magnetic fields uniform in Euler. I]. Mass-spektrometriya [Mass-spectrometry], 2015, vol. 12, no. 4, pp. 272—281. (In Russ.).
  10. Krasnova N.K. [Two-dimensional sedate electronic spectrographs with the symmetry plane]. Zhurnal tekhnicheskoj fiziki [Journal of technical physics], 2011, vol. 81, no. 6, pp. 97—103. (In Russ.).
  11. Averin I.A. [The axisymmetric electrostatic electronic spectrographs using potentials, uniform in Euler, with nonintegral orders of uniformity]. Tez. dokl. VIII S’ezda VMSO i VIII Vserossijskoj konferencii [Theses reports VIII Congress of VMSO and VIII All-Russian conference]. 02—17 october 2015, Moscow, VMSO "Trovant" Publ. 132 p. (In Russ.).
  12. Averin I.A. [Electrostatic and magnetostatic electron spectrographs based on Euler’ homogeneous potentials with non-integer orders]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2015, vol. 25, no. 3, pp. 35—44. Doi: 10.18358/np-25-3-i3544 .
  13. Averin I.A., Berdnikov A.S. [Regional fields the bessetochnykh of electronic spectrographs with electrostatic fields, uniform in Euler]. Uspekhi prikladnoj fiziki [Achievements of applied physics], 2016, vol. 4, no. 1,
    pp. 5—8. (In Russ.).
  14. Berdnikov A.S., Averin I.A., Golikov Yu.K. [The static mass spectrographs of new type using the electric and magnetic fields uniform in Euler. II]. Mass-spektrometriya [Mass-spectrometry], 2016, vol. 13, no. 1, pp. 11—20. (In Russ.).
  15. Berdnikov A.S., Averin I.A. [New approach to development of ion-optical schemes of static mass spectrographs on the basis of the non-uniform magnetic fields uniform in Euler]. Uspekhi prikladnoj fiziki [Achievements of applied physics], 2016, vol. 4, no. 1, pp. 89—95. (In Russ.).
  16. Gabdullin P.G., Golikov Yu.K., Krasnova N.K., Davydov S.N. [Application of a formula of Donkin in the theory of power-analyzers. I]. Zhurnal tekhnicheskoj fiziki [Journal of technical physics], 2000, vol. 70, no. 2, pp. 91—94. (In Russ.).
  17. Gabdullin P.G., Golikov Yu.K., Krasnova N.K., Davydov S.N. [Application of a formula of Donkin in the theory of power-analyzers. II]. Zhurnal tekhnicheskoj fiziki [Journal of technical physics], 2000, vol. 70, no. 3, pp. 44—47. (In Russ.).
  18. Berdnikov A.S., Averin I.A. [About impossibility of double focusing in the combined electric and magnetic fields uniform in Euler]. Mass-spektrometriya [Mass-spectrometry], 2016, vol. 13, no. 1, pp. 62—65. (In Russ.).
  19. Golikov Yu.K., Utkin K.G., Cheparuhin V.V. Raschet elementov elektrostaticheskich elektronno-opticheskich system. Uchebnoe posobie [Calculation of elements of electrostatic electron-optical systems. Education book]. Leningrad, LPI Publ., 1984. 79 p. (In Russ.).
  20. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Theorem of uniformity of scalar and vector potentials for the electric and magnetic fields uniform in Euler]. Uspekhi prikladnoj fiziki [Achievements of applied physics], 2016, vol. 4, no. 6. (In Russ.).
  21. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Three-dimensional electric and magnetic potentials uniform in Euler]. Vestnik Aktyubinskogo regional'nogo gosudarstvennogo universiteta im. K. Zhubanova. Fiziko-matematicheskie nauki [Bulletin of the Aktyubinsk regional state university of K. Zhubanov. Physical and mathematical sciences], 2016, no. 2 (44), pp. 147—165. (In Russ.).
  22. Berdnikov A.S., Krasnova N.K. [Sufficient criteria for stability and narrowness of the band-shaped ion beams in 3D electric and magnetic fields with plane of symmetry]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2015, vol. 25, no. 2, pp. 69—90. Doi: 10.18358/np-25-2-i6990. (In Russ.).
  23. Uitteker E.T., Vatson G. Kurs sovremennogo analiza. Ch. 2: Transcendentnye funkcii [Course of the modern analysis. Part 2: Transcendental functions]. Moscow, GIFML Publ., 1963. 516 p. (In Russ.).
  24. Gobson E.V. Teoriya sfericheskih i ehllipsoidal'nyh funkcij [Theory of spherical and ellipsoidal functions]. Moscow, Izdatel'stvo inostrannoj literatury, 1952. 476 p. (In Russ.).
  25. Golikov Yu.K. [The solution of a task of Cauchy for uniform harmonious potentials of zero frequency rate]. Vestnik Aktyubinskogo regional'nogo gosudarstvennogo universiteta im. K. Zhubanova. Fiziko-matematicheskie nauki [Bulletin of the Aktyubinsk regional state university of K. Zhubanov. Physical and mathematical sciences], 2016,
    no. 2(44), pp. 59—62. (In Russ.).
  26. Golikov Yu.K. [Analytical ways of the description of harmonious functions]. Vestnik Aktyubinskogo regional'nogo gosudarstvennogo universiteta im. K. Zhubanova. Fiziko-matematicheskie nauki [Bulletin of the Aktyubinsk regional state university of K. Zhubanov. Physical and mathematical sciences], 2016, no. 2 (44), pp. 165—181. (In Russ.).
  27. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [The elementary analytical electric and magnetic potentials uniform in Euler]. Vestnik Aktyubinskogo regional'nogo gosudarstvennogo universiteta im. K. Zhubanova. Fiziko-matematicheskie nauki [Bulletin of the Aktyubinsk regional state university of K. Zhubanov. Physical and mathematical sciences], 2016, no. 2 (44), pp. 17—32. (In Russ.).
  28. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Quasi-polynomial three-dimensional electric and magnetic potentials uniform in Euler]. Nauchno-tekhnicheskie vedomosti SPbGPU. Fiziko-matematicheskie nauki [Scientific and technical sheets CÏáÃÏÓ. Physical and mathematical sciences], 2016, no. 4. (In Russ.).
  29. Hoks P., Kasper E. Osnovy ehlektronnoj optiki [Fundamentals of electronic optics], vol. 1. Moscow, Mir Publ., 1993. 552 p. (In Russ.).
  30. Donkin W.F. On the Equation of Laplace‘s Functions &c. Philosophical Transactions of the Royal Society of London, 1857, vol. 147, pp. 43—57. Doi: 10.1098/rstl.1857.0005.
  31. Donkin W.F. On the Equation of Laplace‘s Functions &c. Proceedings of the Royal Society of London, 1856-1857, vol. 8, pp. 307—310. Doi: 10.1098/rspl.1856.0075.
  32. Lavrent'ev M.A., Shabat B.V. Metody teorii funkcij kompleksnogo peremennogo [Methods of the theory of functions of complex variable]. Moscow, Nauka Publ., 1965. 716 p. (In Russ.).
  33. Markushevich A.I. Teoriya analiticheskih funkcij [Theory of analytical functions], vol. 1, 2. Moscow, Nauka Publ., 1968. 486 and 624 p. (In Russ.).
  34. Evgrafov M.A. Analiticheskie funkcii [Analytical functions]. Third edition processed and added. Moscow, Nauka Publ., 1991. 448 p. (In Russ.).
  35. Gurvic A., Kurant P. Teoriya funkcij [Function theory]. Moscow, Nauka Publ., 1968. 646 p.  (In Russ.).
  36. Gyunter N.M. Integrirovanie uravnenij v chastnyh proizvodnyh pervogo poryadka [Integration of the equations in private derivatives of the first order]. Leningrad-Moscow, ONTI Publ., 1934. (In Russ.).
  37. Trikomi F. Lekcii po uravneniyam v chastnyh proizvodnyh [Lectures on the equations in private derivatives]. Moscow, Izdatel'stvo inostrannoj literatury, 1957. 443 p. (In Russ.).
  38. Rashevskij P.K. Geometricheskaya teoriya uravnenij s chastnymi proizvodnymi [The geometrical theory of the equations with private derivatives]. Leningrad-Moscow, OGIZ Publ., 1947. 362 c. (In Russ.).
  39. Finikov S.P. Metod vneshnih form Kartana v differencial'noj geometrii [Method of external forms of Cartan in differential geometry]. Leningrad-Moscow, OGIZ Publ., 1948. 432 c. (In Russ.).
  40. Thomson W. Extraits de deux Lettres adressées à M. Liouville. Journal de mathématiques pures et appliquées, 1847, vol. XII, pp. 256—264.
  41. Thomson W. (Lord Kelvin), Teht P.G. Traktat po natural'noj filosofii [The treatise on natural philosophy], part. II. Moscow-Izhevsk, NIC "Regulyarnaya i haoticheskaya dinamika" Publ., 2011. 560 p. (In Russ.).
  42. Sretenskij L.N. Teoriya n'yutonovskogo potenciala [Theory of the Newtonian potential]. Leningrad-Moscow, OGIZ-GITTL Publ., 1946. 318 p. (In Russ.).
  43. Vladimirov V.S. Uravneniya matematicheskoj fiziki [Equations of mathematical physics]. Moscow, Nauka Publ., 1981. 512 p. (In Russ.).
  44. Smirnov V.I. Kurs vysshej matematiki [Course of the higher mathematics], vol. 4, part 2. Moscow, Nauka Publ., 1981. 297 p. (In Russ.).
  45. Thomson W. (Lord Kelvin), Teht P.G. Traktat po natural'noj filosofii [The treatise on natural philosophy], part I. Moscow-Izhevsk, NIC "Regulyarnaya i haoticheskaya dinamika" Publ., 2010. 572 p. (In Russ.).
  46. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Integrated formulas for the three-dimensional electric and magnetic potentials uniform in Euler with nonintegral orders of uniformity]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2016, vol. 26, no. 4. pp. 31—42. URL: http://213.170.69.26/mag/2016/full4/Art3.pdf. (In Russ.).
  47. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Research of the theorem of differentiation and integration of the three-dimensional electric and magnetic potentials uniform in Euler]. Uspekhi prikladnoj fiziki [Achievements of applied physics], 2016, vol. 4, no. 6. (In Russ.).
 

A. S. Berdnikov1, I. A. Averin1,2, N. K. Krasnova2, K. V. Solovyev2

INTEGRAL EXPRESSIONS FOR 3D ELECTRIC AND MAGNETIC POTENTIALS WHICH ARE UNIFORM IN EULER TERMS AND HAVE NON-INTEGER ORDERS OF UNIFORMITY

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 31—42.
doi: 10.18358/np-26-4-i3142
 

In our previous paper "Universal expressions for 3D electric and magnetic potentials which are uniform in Euler terms" (see this issue) we already noted the usefulness of the paradigma of Euler’s uniform fields for designing of electron-optical and ion-optical systems. Non-integer orders of uniformity significantly extends possibilities and flexibility of usage for such fields in charged particle optics. As a result the analytical expressions for the Laplace potentials which are uniform in Euler terms are a useful tool to design optical systems of this type. However, at this moment general theory of harmonic and uniform 3D functions with non-integer order of uniformity is absent. This paper considers particular integral expressions which produces 3D harmonic functions which are uniform in Euler’ terms with non-integer orders of uniformity and can be used as potentials of corresponding electric and magnetic fields.
 

Keywords: electric fields, magnetic fields, uniform in Euler’ terms functions, similarity principle for charged particle trajectories, analytical solutions of Laplace equation

Author affiliations:

1Institute for Analytical Instrumentation of RAS, Saint - Petersburg , Russia
2Peter The Great Saint-Petersburg Polytechnic University, Russia

 
Contacts: Berdnikov Alexander Sergeevich, asberd@yandex.ru
Article received in edition: 28.07.2016
Full text (In Russ.) >>

REFERENCES

  1. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Universal expressions or 3D electric and magnetic potentials which are uniform in Euler terms]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2016, vol. 26, no. 4, pp. 13—30. (In Russ.).
  2. Golikov Yu.K., Krasnova N.K. [The electric fields uniform in Euler, for electronic spectrography]. Zhurnal tekhnicheskoj fiziki [Journal of technical physics], 2011, vol. 81, no. 2, pp. 9—15. (In Russ.).
  3. Golikov Yu.K., Krasnova N.K. Teoriya sinteza ehlektrostaticheskih ehnergoanalizatorov [Theory of synthesis of electrostatic power analyzers]. Saint-Petersburg, Polytechnical university Publ., 2010. 409 p. (In Russ.).
  4. Krasnova N.K. Teoriya i sintez dispergiruyushchih i fokusiruyushchih ehlektronno-opticheskih sred. Diss. dokt. fiz.-mat. nauk [The theory and synthesis of the dispersing and focusing electron-optical environments. Dr. phys. and math. sci. diss.]. Saint-Petersburg, 2013. 259 p. (In Russ.).
  5. Golikov Yu.K., Krasnova N.K. [The generalized principle of similarity and its application in electronic spectrography]. Prikladnaya fizika [Applied physics], 2007, no. 2, pp. 5—11. (In Russ.).
  6. Golikov Yu.K., Krasnova N.K. [Analytical structures of electric spectrographs the fields of which are expressed in a uniform generalized form]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2014, vol. 24, no. 1, pp. 50—58. URL: http://213.170.69.26/mag/2014/full1/Art6.pdf. (In Russ.).
  7. Averin I.A., Berdnikov A.S., Gall N.R. [The principle of similarity of trajectories at the movement of charged particles with a different masses in electric and magnetic fields, uniform in Euler]. Pis'ma v ZhTF [Letters in ZhTF], 2016, vol. 42, no. 23—24. (In Russ.).
  8. Krasnova N.K. [Two-dimensional sedate electronic spectrographs with the symmetry plane]. Zhurnal tekhnicheskoj fiziki [Journal of technical physics], 2011, vol. 81, no. 6, pp. 97—103. (In Russ.).
  9. Averin I.A. [The axisymmetric electrostatic electronic spectrographs using potentials, uniform in Euler, with nonintegral orders of uniformity]. Tez. dokl. VIII S’ezda VMSO i VIII Vserossijskoj konferencii [Theses reports VIII Congress of VMSO and VIII All-Russian conference]. 02—17 october 2015, Moscow, VMSO "Trovant" Publ. 132 p. (In Russ.).
  10. Averin I.A. [Electrostatic and magnetostatic electron spectrographs based on Euler’ homogeneous potentials with non-integer orders]. Nauchnoe Priborostroenie [Scientific Instrumentation], 2015, vol. 25, no. 3, pp. 35—44. Doi: 10.18358/np-25-3-i3544. (In Russ.).
  11. Averin I.A., Berdnikov A.S. [Regional fields the bessetochnykh of electronic spectrographs with electrostatic fields, uniform in Euler]. Uspekhi prikladnoj fiziki [Achievements of applied physics], 2016, vol. 4, no. 1,
    pp. 5—8. (In Russ.).
  12. Berdnikov A.S., Averin I.A., Golikov Yu.K. [The static mass spectrogaphs of new type using the electric and magnetic fields uniform in Euler. I]. Mass-spektrometriya [Mass-spectrometry], 2015, vol. 12, no. 4, pp. 272—281. (In Russ.).
  13. Berdnikov A.S., Averin I.A., Golikov Yu.K. [The static mass spectrogaphs of new type using the electric and magnetic fields uniform in Euler. II]. Mass-spektrometriya [Mass-spectrometry], 2016, vol. 13, no. 1, pp. 11—20. (In Russ.).
  14. Berdnikov A.S., Averin I.A. [New approach to development of ion-optical schemes of static mass spectrographs on the basis of the non-uniform magnetic fields uniform in Euler]. Uspekhi prikladnoj fiziki [Achievements of applied physics], 2016, vol. 4, no. 1, pp. 89—95. (In Russ.).
  15. Berdnikov A.S., Averin I.A. [About impossibility of double focusing in the combined electric and magnetic fields uniform in Euler]. Mass-spektrometriya [Mass-spectrometry], 2016, vol. 13, no. 1, pp. 62—65. (In Russ.).
  16. Gobson E.V. Teoriya sfericheskih i ehllipsoidal'nyh funkcij [Theory of spherical and ellipsoidal functions]. Moscow, Izdatel'stvo inostrannoj literatury, 1952. 476 p. (In Russ.).
  17. Uitteker E.T., Vatson G. Kurs sovremennogo analiza. Ch. 2: Transcendentnye funkcii [Course of the modern analysis. Part 2: Transcendental functions]. Moscow, GIFML Publ., 1963. 516 p. (In Russ.).
  18. Fihtengolc G.M. Kurs differencial'nogo i integral'nogo ischisleniya. Tom 1 [Course of differential and integral calculus. Vol. 1]. Moscow, Fizmatlit Publ., 2001. 616 p. (In Russ.).
  19. Smirnov V.I. Kurs vysshej matematiki. Tom 1 [Course of the higher mathematics. Vol. 1]. Moscow, Nauka Publ., 1974. 480 p. (In Russ.).
  20. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Three-dimensional electric and magnetic potentials uniform in Euler]. Vestnik Aktyubinskogo regional'nogo gosudarstvennogo universiteta im. K. Zhubanova. Fiziko-matematicheskie nauki [Bulletin of the Aktyubinsk regional state university of K. Zhubanov. Physical and mathematical sciences], 2016, no. 2 (44), pp. 147—165. (In Russ.).
  21. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Theorem of uniformity of scalar and vector potentials for the electric and magnetic fields uniform in Euler]. Uspekhi prikladnoj fiziki [Achievements of applied physics], 2016, vol. 4, no. 6. (In Russ.).
  22. Donkin W.F. On the Equation of Laplace‘s Functions &c. Philosophical Transactions of the Royal Society of London, 1857, vol. 147, pp. 43—57.
  23. Donkin W.F. On the Equation of Laplace‘s Functions &c. Proceedings of the Royal Society of London, 1856-1857, vol. 8, pp. 307—310. Doi: 10.1098/rspl.1856.0075.
  24. Gabdullin P.G., Golikov Yu.K., Krasnova N.K., Davydov S.N. [Application of a formula of Donkin in the theory of power-analyzers. I]. Zhurnal tekhnicheskoj fiziki [Journal of technical physics], 2000, vol. 70, no. 2, pp. 91—94. (In Russ.).
  25. Gabdullin P.G., Golikov Yu.K., Krasnova N.K., Davydov S.N. [Application of a formula of Donkin in the theory of power-analyzers. II]. Zhurnal tekhnicheskoj fiziki [Journal of technical physics], 2000, vol. 70, no. 3, pp. 44—47. (In Russ.).
  26. Berdnikov A.S., Averin I.A., Krasnova N.K., Solovyev K.V. [Research of the theorem of differentiation and integration of the three-dimensional electric and magnetic potentials uniform in Euler]. Uspekhi prikladnoj fiziki [Achievements of applied physics], 2016, vol. 4, no. 6. (In Russ.).
  27. Thomson W. Extraits de deux Lettres adressées à M. Liouville. Journal de mathématiques pures et appliquées, 1847, vol. XII, pp. 256—264.
  28. Sretenskij L.N. Teoriya n'yutonovskogo potenciala [Theory of the Newtonian potential]. Leningrad-Moscow, OGIZ-GITTL Publ., 1946. 318 p. (In Russ.).
  29. Vladimirov V.S. Uravneniya matematicheskoj fiziki [Equations of mathematical physics]. Moscow, Nauka Publ., 1981. 512 p. (In Russ.).
  30. Smirnov V.I. Kurs vysshej matematiki [Course of the higher mathematics], vol. 4, part 2. Moscow, Nauka Publ., 1981. 297 p. (In Russ.).
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B. P. Sharfarets

ON THE DYNAMICS OF SHOCK WAVES IN THE LIQUID. OVERVIEW

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 43—54.
doi: 10.18358/np-26-4-i4354
 

We consider the laws of shock compression, the boundary conditions on the front of waves. We show conservation laws at the front of shock wave. Are discussed methods for calculating the dynamics of shock waves and equations of state of the fluid. Provides a simplified formalism, which is the theory of shock waves for the case of plane shock front. Outlines the existing methods of numerical calculation of shock waves. Provides an example of setting a boundary value problem of the propagation of the shock wave.
 

Keywords: shock wave, wave front, equations of state of liquid, shock adiabata

Author affiliations:

Institute for Analytical Instrumentation of RAS, Saint - Petersburg , Russia

 
Contacts: Sharfarets Boris Pinkusovich, sharb@mail.ru
Article received in edition: 10.07.2016
Full text (In Russ.) >>

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A. A. Evstrapov, V. E. Kurochkin, B. P. Sharfarets

THE MODELING OF MICROFLUIDIC PROCESSES. ACCOUNT OF THE SURFACE FORCES

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 55—63.
doi: 10.18358/np-26-4-i5563
 

We consider the features of the surface tension forces in microfluidic. Given boundary conditions on the interfaces between immiscible fluids, and liquids and solids taking into account the surface pressure. We also consider the effect of mass transfer along the interface of two media, arising due to the presence of surface tension gradient (Marangoni effect), take into account the influence of temperature on surface tension forces. The algorithm, allowing estimating the coefficient of surface tension on the boundary solid-liquid with changes in temperature is given. Considered the capillary instability of the Rayleigh–Plateau. Emphasizes the importance of these aspects in the creation of a real microfluidic models using computing packages and physical models in the interests of scientific instrumentation.
 

Keywords: microfluidics, surface forces, surface pressure, Marangoni effect, capillary instability of the Rayleigh–Plateau

Author affiliations:

Institute for Analytical Instrumentation of RAS, Saint - Petersburg , Russia

 
Contacts: Sharfarets Boris Pinkusovich, sharb@mail.ru
Article received in edition: 7.07.2016
Full text (In Russ.) >>

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A. P. Scherbakov

SIMULATION OF ION-MOLECULE COLLISIONS IN INHOMOGENEOUS TIME-DEPENDED ELECTROGASDYNAMIC FIELDS

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 64—76.
doi: 10.18358/np-26-4-i6476
 

Computer based procedures have been developed and tested to simulate the ion motion in inhomogeneous time-depended electrogasdynamic fields. Procedures are based on combined model of ion-molecule collision. This combined approach takes into account both repulsive and attractive region of the interaction potential and correctly describes the ion scattering over a wide range of collision energies. Models and computational procedures developed enable to introduce the anisotropic modes of scattering. Monte Carlo simulation of free path length ore free time is based on time discretization technique, which is well combined with discretization of motion equations.
 

Keywords: collision cross section, mobility, diffusion, polarization potential, hard sphere potential, electrogasdynamic field

Author affiliations:

Institute for Analytical Instrumentation of RAS, Saint - Petersburg , Russia

 
Contacts: Scherbakov Anatoliy Petrovich, anpshch@yandex.ru
Article received in edition: 14.10.2016
Full text (In Russ.) >>

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A. Grigoryev, V. Mamaev

APPLICATION OF ARTIFICIAL NEURAL NETWORKS IN KNOWLEDGE CONTROL

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 77—84.
doi: 10.18358/np-26-4-i7784
 

The task of automatization of knowledge control of a specialist based on the use of artificial neural networks (ANN) is reviewed. The task implies the use of each of commercial and proprietary ANN design software as well as integration of subtask solving software. Open and closed type models of testing and adaptive test activities using fuzzy-logic apparatus are described. On the ground of test activities description the testing algorithm is formed based on the classic and special ANNs. Topology and characteristics of ANN are defined, different neural network training methods are considered. Objectivity and accuracy of control and examinator (instructor, teacher, inspector) relief are provided.
 

Keywords: artificial neural networks, testing of trainee, fuzzy logic, event classification

Author affiliations:

State University of Aerospace Instrumentation, Saint-Petersburg, Russia

 
Contacts: Grigoryev Aleksandr Pavlovich, alexgrig-1986@mail.ru
Article received in edition: 19.09.2016
Full text (In Russ.) >>

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A. Grigoryev, V. Mamaev

EXPERIENCE OF USE OF NEURAL NETWORKS IN THE ANALYSIS AND THE STRUCTURAL RECONSTRUCTION OF SUBJECT KNOWLEDGE OF THE SPECIALIST

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 85—93.
doi: 10.18358/np-26-4-i8593
 

The paper reviews in a specific context of subjective field of knowledge the construction of graphic semantic model of that field. With the use of this model the task of automated analysis of current state of graph of knowledge of examinee (trainee) is considered. The result of analysis is the indication of gaps of knowledge — fell out elements and links of the graphic semantic model, which allows to recover it with additional target-method training. As an instrument of the automatization authors propose to use neural networks of the perceptron type. Monitoring, diagnostics, knowledge recovery and individual learning material studying paths ensuring reliability of error detection, objective knowledge evaluation and adaptivity by means of knowledge recovery procedure are performed based on the results of neural-network testing.
 

Keywords: graphic semantic model, artificial neural networks, knowledge testing

Author affiliations:

State University of Aerospace Instrumentation, Saint-Petersburg, Russia

 
Contacts: Grigoryev Aleksandr Pavlovich, alexgrig-1986@mail.ru
Article received in edition: 19.09.2016
Full text (In Russ.) >>

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FROM EDITION

Volume 26 table of contents

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 99—102.
 

  Full text (In Engl.) >>

 

FROM EDITION

The author's index of volume 26

"Nauchnoe Priborostroenie", 2016, vol. 26, no. 4, pp. 104—104.
 

  Full text (In Engl.) >>

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