Canonical Equations of Optical Hysteresis
The work was carried out within the context of a competitive ideology of creating the element base of digital optical computers (transphasors, optical switches, memory elements) built on a basis other than the Fabry–Perot interferometer. Mathematical models of stationary (problem I) and non-stationa...
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| Veröffentlicht in: | Cybernetics and systems analysis 2022-07, Vol.58 (4), p.660-670 |
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| creator | Starkov, V. M. |
| description | The work was carried out within the context of a competitive ideology of creating the element base of digital optical computers (transphasors, optical switches, memory elements) built on a basis other than the Fabry–Perot interferometer. Mathematical models of stationary (problem I) and non-stationary (problem II) four-beam laser interaction in optically nonlinear media are considered in detail. Problem (I) is the system of ordinary differential equations with specified boundary conditions. Problem (II) is the system of integro-differential equations with boundary conditions. We introduced the original sought-for functions
z
(
x
) and
u
(
z
,
t
)
, υ
(
z
,
t
) (II). As a result, the problem (I) is reduced to solving a simple transcendental equation (canonical equation of optical hysteresis). The problem (II) is reduced to solving a system of two nonlinear integral equations for the amplitudes of interference patterns (the canonical system of equations of non-stationary optical hysteresis). |
| doi_str_mv | 10.1007/s10559-022-00498-3 |
| format | Article |
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z
(
x
) and
u
(
z
,
t
)
, υ
(
z
,
t
) (II). As a result, the problem (I) is reduced to solving a simple transcendental equation (canonical equation of optical hysteresis). The problem (II) is reduced to solving a system of two nonlinear integral equations for the amplitudes of interference patterns (the canonical system of equations of non-stationary optical hysteresis).</description><identifier>ISSN: 1060-0396</identifier><identifier>EISSN: 1573-8337</identifier><identifier>DOI: 10.1007/s10559-022-00498-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Artificial Intelligence ; Boundary conditions ; Control ; Differential equations ; Digital computers ; Hysteresis ; Integral equations ; Mathematics ; Mathematics and Statistics ; Network switches ; Optical computers ; Optical memory (data storage) ; Processor Architectures ; Software Engineering/Programming and Operating Systems ; Switches ; Systems Theory</subject><ispartof>Cybernetics and systems analysis, 2022-07, Vol.58 (4), p.660-670</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><rights>COPYRIGHT 2022 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c343t-b68d82d0a600f9b24da01a9f1bea0943bb64472b50857c21a560b5aa683de5aa3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10559-022-00498-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10559-022-00498-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Starkov, V. M.</creatorcontrib><title>Canonical Equations of Optical Hysteresis</title><title>Cybernetics and systems analysis</title><addtitle>Cybern Syst Anal</addtitle><description>The work was carried out within the context of a competitive ideology of creating the element base of digital optical computers (transphasors, optical switches, memory elements) built on a basis other than the Fabry–Perot interferometer. Mathematical models of stationary (problem I) and non-stationary (problem II) four-beam laser interaction in optically nonlinear media are considered in detail. Problem (I) is the system of ordinary differential equations with specified boundary conditions. Problem (II) is the system of integro-differential equations with boundary conditions. We introduced the original sought-for functions
z
(
x
) and
u
(
z
,
t
)
, υ
(
z
,
t
) (II). As a result, the problem (I) is reduced to solving a simple transcendental equation (canonical equation of optical hysteresis). The problem (II) is reduced to solving a system of two nonlinear integral equations for the amplitudes of interference patterns (the canonical system of equations of non-stationary optical hysteresis).</description><subject>Artificial Intelligence</subject><subject>Boundary conditions</subject><subject>Control</subject><subject>Differential equations</subject><subject>Digital computers</subject><subject>Hysteresis</subject><subject>Integral equations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Network switches</subject><subject>Optical computers</subject><subject>Optical memory (data storage)</subject><subject>Processor Architectures</subject><subject>Software Engineering/Programming and Operating Systems</subject><subject>Switches</subject><subject>Systems Theory</subject><issn>1060-0396</issn><issn>1573-8337</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1rAjEQhkNpodb2D_Qk9OQhdpJsPvYoYmtBEPpxDtndrKzoRpMs1H_f6BaKlzKHGYbnnXd4EXokMCEA8jkQ4DzHQCkGyHKF2RUaEC4ZVozJ6zSDAAwsF7foLoQNADCQaoDGM9O6tinNdjQ_dCY2rg0jV49W-3heLo4hWm9DE-7RTW22wT789iH6epl_zhZ4uXp9m02XuGQZi7gQqlK0AiMA6rygWWWAmLwmhTWQZ6woRJZJWnBQXJaUGC6g4MYIxSqbOhuip_7u3rtDZ0PUG9f5NllqKqnKckYFS9Skp9Zma3XT1i56U6aq7K4pXWvrJu2nkkoO_OQ7ROMLQWKi_Y5r04Wg3z7eL1nas6V3IXhb671vdsYfNQF9ylv3eeuUtz7nrU8fsV4UEtyurf_7-x_VD8lnf_s</recordid><startdate>20220701</startdate><enddate>20220701</enddate><creator>Starkov, V. M.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope><scope>JQ2</scope></search><sort><creationdate>20220701</creationdate><title>Canonical Equations of Optical Hysteresis</title><author>Starkov, V. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c343t-b68d82d0a600f9b24da01a9f1bea0943bb64472b50857c21a560b5aa683de5aa3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Artificial Intelligence</topic><topic>Boundary conditions</topic><topic>Control</topic><topic>Differential equations</topic><topic>Digital computers</topic><topic>Hysteresis</topic><topic>Integral equations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Network switches</topic><topic>Optical computers</topic><topic>Optical memory (data storage)</topic><topic>Processor Architectures</topic><topic>Software Engineering/Programming and Operating Systems</topic><topic>Switches</topic><topic>Systems Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Starkov, V. M.</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Cybernetics and systems analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Starkov, V. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Canonical Equations of Optical Hysteresis</atitle><jtitle>Cybernetics and systems analysis</jtitle><stitle>Cybern Syst Anal</stitle><date>2022-07-01</date><risdate>2022</risdate><volume>58</volume><issue>4</issue><spage>660</spage><epage>670</epage><pages>660-670</pages><issn>1060-0396</issn><eissn>1573-8337</eissn><abstract>The work was carried out within the context of a competitive ideology of creating the element base of digital optical computers (transphasors, optical switches, memory elements) built on a basis other than the Fabry–Perot interferometer. Mathematical models of stationary (problem I) and non-stationary (problem II) four-beam laser interaction in optically nonlinear media are considered in detail. Problem (I) is the system of ordinary differential equations with specified boundary conditions. Problem (II) is the system of integro-differential equations with boundary conditions. We introduced the original sought-for functions
z
(
x
) and
u
(
z
,
t
)
, υ
(
z
,
t
) (II). As a result, the problem (I) is reduced to solving a simple transcendental equation (canonical equation of optical hysteresis). The problem (II) is reduced to solving a system of two nonlinear integral equations for the amplitudes of interference patterns (the canonical system of equations of non-stationary optical hysteresis).</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10559-022-00498-3</doi><tpages>11</tpages></addata></record> |
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| subjects | Artificial Intelligence Boundary conditions Control Differential equations Digital computers Hysteresis Integral equations Mathematics Mathematics and Statistics Network switches Optical computers Optical memory (data storage) Processor Architectures Software Engineering/Programming and Operating Systems Switches Systems Theory |
| title | Canonical Equations of Optical Hysteresis |
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