<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2018-9-3-319-322</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-774</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МАТЕМАТИКА</subject></subj-group></article-categories><title-group><article-title>Method of application three-dimensional billiard systems in passive heating systems</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Rakhimov</surname><given-names>E. Yu.</given-names></name></name-alternatives><bio xml:lang="en"><p>Tashkent</p></bio><email xlink:type="simple">rey_86@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Physical-Technical Institute, SPA “Physics-Sun”, Uzbek Academy of Sciences</institution><country>Uzbekistan</country></aff><pub-date pub-type="collection"><year>2018</year></pub-date><pub-date pub-type="epub"><day>14</day><month>08</month><year>2025</year></pub-date><volume>9</volume><issue>3</issue><fpage>319</fpage><lpage>322</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Rakhimov E.Y., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Rakhimov E.Y.</copyright-holder><copyright-holder xml:lang="en">Rakhimov E.Y.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/774">https://nanojournal.ifmo.ru/jour/article/view/774</self-uri><abstract><p>In this article, the method of determining ray absorption ability by premises with insolation passive heating system by numerical experiments was studied. A heated premise (HP), having a translucent enclosure (TE), walls covered with a special smooth enclosure, was chosen as the object of study. The dynamics of the solar rays were studied as a billiard system and the reflection equations are given. Verification of result reliability was performed.</p></abstract><kwd-group xml:lang="en"><kwd>ray absorption ability</kwd><kwd>insolation passive heating systems</kwd><kwd>3D billiard systems</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Creagh S.C. Directional emission from weakly eccentric resonators. Phys Rev Lett., 2007, 98(15), P. 153901.</mixed-citation><mixed-citation xml:lang="en">Creagh S.C. Directional emission from weakly eccentric resonators. Phys Rev Lett., 2007, 98(15), P. 153901.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Dembowski C., Gr¨af H-D., Heine A, Hesse T., Rehfeld H., Richter A. First experimental test of a trace formula for billiard systems showing mixed dynamics. Phys Rev Lett., 2001, 86(15), P. 3284-7.</mixed-citation><mixed-citation xml:lang="en">Dembowski C., Gr¨af H-D., Heine A, Hesse T., Rehfeld H., Richter A. First experimental test of a trace formula for billiard systems showing mixed dynamics. Phys Rev Lett., 2001, 86(15), P. 3284-7.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Abdullaev S.S. and Zaslavskii G.M. Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media. Sov. Phys. Usp., 1991, 34(8), P. 645.</mixed-citation><mixed-citation xml:lang="en">Abdullaev S.S. and Zaslavskii G.M. Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media. Sov. Phys. Usp., 1991, 34(8), P. 645.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Loskutov A.Yu., Ryabov A.B., Akinshin L.G. Mechanism of Fermi acceleration in dispersing billiards with time-dependent boundaries. Journal of Experimental and Theoretical Physics, 1999, 89(2), P. 966–974.</mixed-citation><mixed-citation xml:lang="en">Loskutov A.Yu., Ryabov A.B., Akinshin L.G. Mechanism of Fermi acceleration in dispersing billiards with time-dependent boundaries. Journal of Experimental and Theoretical Physics, 1999, 89(2), P. 966–974.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Eckmann J.P., Mejı´a-Monasterio C. Thermal Rectification in Billiardlike Systems. Phys Rev Lett., 2006, 97(9), P. 094301.</mixed-citation><mixed-citation xml:lang="en">Eckmann J.P., Mejı´a-Monasterio C. Thermal Rectification in Billiardlike Systems. Phys Rev Lett., 2006, 97(9), P. 094301.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Lee K.Y., Chi D.Y., Kim S.H., Seo K.W., and Yoon J. Passive residual heat removal system of an open-pool type research reactor using gravity core cooling tank, in Proceedings of the European Research Reactor Conference (RRFM ’14), Ljubljana, Slovenia, March-April, 2014, P. 593–599.</mixed-citation><mixed-citation xml:lang="en">Lee K.Y., Chi D.Y., Kim S.H., Seo K.W., and Yoon J. Passive residual heat removal system of an open-pool type research reactor using gravity core cooling tank, in Proceedings of the European Research Reactor Conference (RRFM ’14), Ljubljana, Slovenia, March-April, 2014, P. 593–599.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Weiss D., Roukes M.L. and et al. Electron pinball and commensurate orbits in a periodic array of scatterers. Phys. Rev. Lett., 1991, 66, P. 2790.</mixed-citation><mixed-citation xml:lang="en">Weiss D., Roukes M.L. and et al. Electron pinball and commensurate orbits in a periodic array of scatterers. Phys. Rev. Lett., 1991, 66, P. 2790.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Markarian R., Kamphorst S.O., de Carvalho S.P. Chaotic Properties of the Elliptical Stadium. Commun. Math. Phys. 1996, 174, P. 661–679.</mixed-citation><mixed-citation xml:lang="en">Markarian R., Kamphorst S.O., de Carvalho S.P. Chaotic Properties of the Elliptical Stadium. Commun. Math. Phys. 1996, 174, P. 661–679.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Berry M.V. Regularity and chaos in classical mechanics, illustrated by three deformations of a circular billiard. Eur. J. Phys. 1981, 2, P. 91–102.</mixed-citation><mixed-citation xml:lang="en">Berry M.V. Regularity and chaos in classical mechanics, illustrated by three deformations of a circular billiard. Eur. J. Phys. 1981, 2, P. 91–102.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Edson D.L., Carl P.D. Recurrence of particles in static and time varying oval billiards. Physics Letters A, 2012, 376 (20), P. 1669–1674.</mixed-citation><mixed-citation xml:lang="en">Edson D.L., Carl P.D. Recurrence of particles in static and time varying oval billiards. Physics Letters A, 2012, 376 (20), P. 1669–1674.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Akhmadjanov T., Rakhimov E. and Otajanov D. Particle dynamics in corrugated rectangular billiard. Nanosystems: Phys., Chem., Math., 2015, 6(2), P. 262–267.</mixed-citation><mixed-citation xml:lang="en">Akhmadjanov T., Rakhimov E. and Otajanov D. Particle dynamics in corrugated rectangular billiard. Nanosystems: Phys., Chem., Math., 2015, 6(2), P. 262–267.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Duffie J.A., Beckman W.A. Solar Engineer of Thermal Processes. Fourth Solution. Hoboven New Jersey: John Wiley Sons. Inc., 2013, 910 p.</mixed-citation><mixed-citation xml:lang="en">Duffie J.A., Beckman W.A. Solar Engineer of Thermal Processes. Fourth Solution. Hoboven New Jersey: John Wiley Sons. Inc., 2013, 910 p.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Avezov R.R., Avezova N.R. and et al. Ray absorption ability capacity by premises with insolation passive heating system. Alternative Energy and Ecology, 2017, 07-09, P. 034–042.</mixed-citation><mixed-citation xml:lang="en">Avezov R.R., Avezova N.R. and et al. Ray absorption ability capacity by premises with insolation passive heating system. Alternative Energy and Ecology, 2017, 07-09, P. 034–042.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
