http://tm.spbstu.ru/api.php?action=feedcontributions&user=%D0%94%D0%B5%D0%BD%D0%B8%D1%81&feedformat=atomDepartment of Theoretical and Applied Mechanics - User contributions [en]2024-03-29T15:00:08ZUser contributionsMediaWiki 1.27.3http://tm.spbstu.ru/?title=File:20170819_URTEC-2688826-MS.pdf&diff=10095File:20170819 URTEC-2688826-MS.pdf2017-09-20T09:35:33Z<p>Денис: </p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=File:Balls_test_0.png&diff=8490File:Balls test 0.png2016-09-03T09:26:29Z<p>Денис: </p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=File:Htmlets_folder.png&diff=8411File:Htmlets folder.png2016-06-28T05:39:44Z<p>Денис: </p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=Displacement_variance_in_one-dimensional_crystal&diff=6991Displacement variance in one-dimensional crystal2016-02-01T11:16:29Z<p>Денис: </p>
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<div>[[ru:Дисперсия перемещений в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[The movements dispersion of one-dimensional crystal]] <HR><br />
<br />
Developers : [[D.V. Tsvetkov]], [[A.M. Krivtsov]]<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Chain/One_dim_crystal_1.4.1/Equations_en.html |width=1020 |height=550 |border=0 }}</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=6971Virtual laboratory2016-01-29T16:27:10Z<p>Денис: /* Physics */</p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
{{DISPLAYTITLE:<span style="display:none">{{FULLPAGENAME}}</span>}}<br />
<center><h1>Welcome to the Virtual laboratory page!</h1></center><br />
<br />
<br />
Here you can see computer experiments in interactive online format. Various systems can be investigated: mathematical, mechanical, physical, biological, etc. Also, you can learn online programming and visualization. More experiments are available on the Russian page (see the link at the left panel).<br />
__NOTOC__<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Игра "Жизнь" | Conway's Game of Life]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/CelAut_v2_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program, representing a classic [https://en.wikipedia.org/wiki/Conway's_Game_of_Life "Conway's Game of Life"]. The cells can be drawn on the field by cursor.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование Солнечной системы|Solar System model]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Solar_System_v1_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
This model demonstrates the real attitude of the orbital periods of the planets. The radiuses of the planet orbits, as well as the sizes of the planets and the Sun are shown in a logarithmic scale.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Движение материальной точки в центральном поле | Dynamics of a particle in a central field]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/FC_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The application allows you to study a particle trajectory in a central power-law potential field.<br />
</td></tr><br />
</table><br />
}}</div><br />
<!-- СЛЕДУЮЩАЯ СТРОКА --><br />
<br style="clear: both" /><br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика взаимодействующих частиц | Dynamics of interacting particles]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Balls_v6_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates dynamics of interacting particles. Each particle represents a viscoelastic sphere.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика одномерного кристалла|Chain]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Chain_v3_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates dynamics of a 1D harmonic crystal.<br />
See also [[Heat transfer in a 1D harmonic crystal]].<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование структуры кристаллических решеток | Periodic vacancies in a crystal lattice]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Lattice_v8_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program demontrates different crystal lattice structures.<br />
</td></tr><br />
</table><br />
}}</div><br />
<br style="clear: both" /><br />
<br />
<center><h1> Some other virtual stands arranged by topic </h1></center><br />
<br />
<br />
== Physics ==<br />
<br />
* [[Energy fluctuations in one-dimensional crystal]]<br />
* [[Heat transfer in a 1D harmonic crystal]]<br />
* [[Nosé–Hoover thermostat]]<br />
<br />
* [[The movements dispersion of one-dimensional crystal]]<br />
<br />
== Links ==<br />
* [[Main_Page | Department "Theoretical Mechanics"]]</div>Денисhttp://tm.spbstu.ru/?title=Displacement_variance_in_one-dimensional_crystal&diff=6967Displacement variance in one-dimensional crystal2016-01-29T16:06:57Z<p>Денис: Created page with "ru:Дисперсия перемещений в одномерном кристалле Virtual laboratory > The movements dispersion of one-dimensional crystal <H..."</p>
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<div>[[ru:Дисперсия перемещений в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[The movements dispersion of one-dimensional crystal]] <HR><br />
<br />
Developers : [[D.V. Tsvetkov]], [[A.M. Krivtsov]]<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Chain/One_dim_crystal_1.4/Equations_en.html |width=1020 |height=550 |border=0 }}</div>Денисhttp://tm.spbstu.ru/?title=File:Tcvet_masters_Theme3_Temperature_long.png&diff=6756File:Tcvet masters Theme3 Temperature long.png2016-01-13T17:07:25Z<p>Денис: Денис uploaded a new version of &quot;File:Tcvet masters Theme3 Temperature long.png&quot;</p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=File:Tcvet_masters_Theme3_Temperature_short.png&diff=6755File:Tcvet masters Theme3 Temperature short.png2016-01-13T17:06:58Z<p>Денис: Денис uploaded a new version of &quot;File:Tcvet masters Theme3 Temperature short.png&quot;</p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=File:Tsvetkov_Master%27s_graduation_work.pdf&diff=6213File:Tsvetkov Master's graduation work.pdf2015-10-22T11:18:59Z<p>Денис: </p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=File:Tsvetkov_Master%27s_poster.png&diff=6212File:Tsvetkov Master's poster.png2015-10-22T11:12:20Z<p>Денис: </p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=File:Tsvetkov_Master%27s_presentation.pdf&diff=6211File:Tsvetkov Master's presentation.pdf2015-10-22T11:07:54Z<p>Денис: </p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=File:Bessel_fluctuations_v3.0.zip&diff=6190File:Bessel fluctuations v3.0.zip2015-10-20T21:12:55Z<p>Денис: </p>
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<div></div>Денисhttp://tm.spbstu.ru/?title=Energy_fluctuations_in_one-dimensional_crystal&diff=6189Energy fluctuations in one-dimensional crystal2015-10-20T21:11:05Z<p>Денис: </p>
<hr />
<div>[[ru:Колебания энергий в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Energy fluctuations in one-dimensional crystal]] <HR><br />
[[D.V. Tsvetkov]] (programming), [[A.M. Krivtsov]] (analytical silution) <HR><br />
<br />
This program demonstrates the fluctuations in the kinetic, potential, and full energy in the one-dimensional crystal.<br />
Fluctuations of the kinetic energy described by the following equation:<br />
<br />
:<math><br />
K_J(t) = \frac{E}{2} \left(1 + J_0(4 \omega_0 )\right)<br />
,\qquad \omega_0 = \sqrt{C/m},<br />
</math><br />
where<br />
<math>J_0</math> — Bessel function of the first kind at 0,<br />
<math>C</math> — is the stiffness of the interparticle bond,<br />
<math>m</math> — is the particle mass.<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Bessel_fluctuations/Bessel_fluctuations_v3.0/Bessel_fluctuations_en.html |width=1055 |height=675 |border=0 }}<br />
<br />
Download program: [[Media:Bessel_fluctuations_v3.0.zip|Bessel_fluctuations_v3.0.zip]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Energy_fluctuations_in_one-dimensional_crystal&diff=6183Energy fluctuations in one-dimensional crystal2015-10-20T17:51:27Z<p>Денис: </p>
<hr />
<div>[[ru:Колебания энергий в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Energy fluctuations in one-dimensional crystal]] <HR><br />
This program demonstrates the fluctuations in the kinetic, potential, and full energy in the one-dimensional crystal.<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Bessel_fluctuations/Bessel_fluctuations_v2.5_no_realiz/Bessel_fluctuations_en.html |width=1055 |height=650 |border=0 }}<br />
<br />
Download program: [[Media:Bessel_fluctuations_v2.5_no_realiz.zip|Bessel_fluctuations_v2.5_no_realiz.zip]]<br />
<br />
Programmed by [[D.V. Tsvetkov]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Energy_fluctuations_in_one-dimensional_crystal&diff=6182Energy fluctuations in one-dimensional crystal2015-10-20T17:50:28Z<p>Денис: </p>
<hr />
<div>[[ru:Колебания энергий в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Energy fluctuations in one-dimensional crystal]] <HR><br />
This program demonstrates the fluctuations in the kinetic, potential, and full energy in the one-dimensional crystal.<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Bessel_fluctuations/Bessel_fluctuations_v2.5_no_realiz/Bessel_fluctuations_en.html |width=1055 |height=640 |border=0 }}<br />
<br />
Download program: [[Media:Bessel_fluctuations_v2.5_no_realiz.zip|Bessel_fluctuations_v2.5_no_realiz.zip]]<br />
<br />
Programmed by [[D.V. Tsvetkov]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=File:Bessel_fluctuations_v2.5_no_realiz.zip&diff=6181File:Bessel fluctuations v2.5 no realiz.zip2015-10-20T17:48:43Z<p>Денис: </p>
<hr />
<div></div>Денисhttp://tm.spbstu.ru/?title=Energy_fluctuations_in_one-dimensional_crystal&diff=6164Energy fluctuations in one-dimensional crystal2015-10-18T21:39:44Z<p>Денис: </p>
<hr />
<div>[[ru:Колебания энергий в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Energy fluctuations in one-dimensional crystal]] <HR><br />
This program demonstrates the fluctuations in the kinetic, potential, and full energy in the one-dimensional crystal.<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Bessel_fluctuations/Bessel_fluctuations_v2.4_no_realiz/Bessel_fluctuations_en.html |width=1030 |height=640 |border=0 }}<br />
<br />
Download program: [[Media:Bessel_fluctuations_v2.4_no_realiz.zip|Bessel_fluctuations_v2.4_no_realiz.zip]]<br />
<br />
Programmed by [[D.V. Tsvetkov]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Energy_fluctuations_in_one-dimensional_crystal&diff=6163Energy fluctuations in one-dimensional crystal2015-10-18T21:39:05Z<p>Денис: </p>
<hr />
<div>[[ru:Колебания энергий в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Energy fluctuations in one-dimensional crystal]] <HR><br />
This program demonstrates the fluctuations in the kinetic, potential, and full energy in the one-dimensional crystal.<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Bessel_fluctuations/Bessel_fluctuations_v2.4_no_realiz/Bessel_fluctuations_en.html |width=1030 |height=640 |border=0 }}<br />
<br />
Download program: [[Media:Bessel_fluctuations_v2.3_no_realiz.zip|Bessel_fluctuations_v2.3_no_realiz.zip]]<br />
<br />
Programmed by [[D.V. Tsvetkov]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Energy_fluctuations_in_one-dimensional_crystal&diff=6162Energy fluctuations in one-dimensional crystal2015-10-18T21:38:23Z<p>Денис: </p>
<hr />
<div>[[ru:Колебания энергий в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Energy fluctuations in one-dimensional crystal]] <HR><br />
This program demonstrates the fluctuations in the kinetic, potential, and full energy in the one-dimensional crystal.<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Bessel_fluctuations/Bessel_fluctuations_v2.3_no_realiz/Bessel_fluctuations_en.html |width=1030 |height=640 |border=0 }}<br />
<br />
Download program: [[Media:Bessel_fluctuations_v2.3_no_realiz.zip|Bessel_fluctuations_v2.3_no_realiz.zip]]<br />
Programmed by [[D.V. Tsvetkov]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Fluctuations_in_energy-dimensional_crystal&diff=6161Fluctuations in energy-dimensional crystal2015-10-18T14:07:43Z<p>Денис: Blanked the page</p>
<hr />
<div></div>Денисhttp://tm.spbstu.ru/?title=Energy_fluctuations_in_one-dimensional_crystal&diff=6160Energy fluctuations in one-dimensional crystal2015-10-18T14:07:24Z<p>Денис: Created page with "ru:Колебания энергий в одномерном кристалле Virtual laboratory > Heat transfer in a 1D harmonic crystal <HR> This program demon..."</p>
<hr />
<div>[[ru:Колебания энергий в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] <HR><br />
This program demonstrates the fluctuations in the kinetic, potential, and full energy in the one-dimensional crystal.<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Bessel_fluctuations/Bessel_fluctuations_v2.3_no_realiz/Bessel_fluctuations_en.html |width=1030 |height=640 |border=0 }}<br />
<br />
Download program: [[Media:Bessel_fluctuations_v2.3_no_realiz.zip|Bessel_fluctuations_v2.3_no_realiz.zip]]<br />
Programmed by [[D.V. Tsvetkov]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=6159Virtual laboratory2015-10-18T14:06:57Z<p>Денис: </p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
{{DISPLAYTITLE:<span style="display:none">{{FULLPAGENAME}}</span>}}<br />
<center><h1>Welcome to the Virtual laboratory page!</h1></center><br />
<br />
<br />
Here you can see computer experiments in interactive online format. Various systems can be investigated: mathematical, mechanical, physical, biological, etc. Also, you can learn online programming and visualization. More experiments are available on the Russian page (see the link at the left panel).<br />
__NOTOC__<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Игра "Жизнь" | Conway's Game of Life]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/CelAut_v2_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program, representing a classic [https://en.wikipedia.org/wiki/Conway's_Game_of_Life "Conway's Game of Life"]. The cells can be drawn on the field by cursor.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование Солнечной системы|Solar System model]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Solar_System_v1_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
This model demonstrates the real attitude of the orbital periods of the planets. The radiuses of the planet orbits, as well as the sizes of the planets and the Sun are shown in a logarithmic scale.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Движение материальной точки в центральном поле | Dynamics of a particle in a central field]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/FC_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The application allows you to study a particle trajectory in a central power-law potential field.<br />
</td></tr><br />
</table><br />
}}</div><br />
<!-- СЛЕДУЮЩАЯ СТРОКА --><br />
<br style="clear: both" /><br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика взаимодействующих частиц | Dynamics of interacting particles]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Balls_v6_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates dynamics of interacting particles. Each particle represents a viscoelastic sphere.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика одномерного кристалла|Chain]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Chain_v3_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates dynamics of a 1D harmonic crystal.<br />
See also [[Heat transfer in a 1D harmonic crystal]].<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование структуры кристаллических решеток | Periodic vacancies in a crystal lattice]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Lattice_v8_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program demontrates different crystal lattice structures.<br />
</td></tr><br />
</table><br />
}}</div><br />
<br style="clear: both" /><br />
<br />
[[Energy fluctuations in one-dimensional crystal]]</div>Денисhttp://tm.spbstu.ru/?title=Fluctuations_in_energy-dimensional_crystal&diff=6158Fluctuations in energy-dimensional crystal2015-10-18T14:04:37Z<p>Денис: Created page with "ru:Колебания энергий в одномерном кристалле Virtual laboratory > Heat transfer in a 1D harmonic crystal <HR> This program demon..."</p>
<hr />
<div>[[ru:Колебания энергий в одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] <HR><br />
This program demonstrates the fluctuations in the kinetic, potential, and full energy in the one-dimensional crystal.<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Bessel_fluctuations/Bessel_fluctuations_v2.3_no_realiz/Bessel_fluctuations_en.html |width=1030 |height=640 |border=0 }}<br />
<br />
Download program: [[Media:Bessel_fluctuations_v2.3_no_realiz.zip|Bessel_fluctuations_v2.3_no_realiz.zip]]<br />
Programmed by [[D.V. Tsvetkov]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=6157Virtual laboratory2015-10-18T13:59:43Z<p>Денис: </p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
{{DISPLAYTITLE:<span style="display:none">{{FULLPAGENAME}}</span>}}<br />
<center><h1>Welcome to the Virtual laboratory page!</h1></center><br />
<br />
<br />
Here you can see computer experiments in interactive online format. Various systems can be investigated: mathematical, mechanical, physical, biological, etc. Also, you can learn online programming and visualization. More experiments are available on the Russian page (see the link at the left panel).<br />
__NOTOC__<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Игра "Жизнь" | Conway's Game of Life]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/CelAut_v2_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program, representing a classic [https://en.wikipedia.org/wiki/Conway's_Game_of_Life "Conway's Game of Life"]. The cells can be drawn on the field by cursor.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование Солнечной системы|Solar System model]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Solar_System_v1_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
This model demonstrates the real attitude of the orbital periods of the planets. The radiuses of the planet orbits, as well as the sizes of the planets and the Sun are shown in a logarithmic scale.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Движение материальной точки в центральном поле | Dynamics of a particle in a central field]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/FC_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The application allows you to study a particle trajectory in a central power-law potential field.<br />
</td></tr><br />
</table><br />
}}</div><br />
<!-- СЛЕДУЮЩАЯ СТРОКА --><br />
<br style="clear: both" /><br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика взаимодействующих частиц | Dynamics of interacting particles]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Balls_v6_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates dynamics of interacting particles. Each particle represents a viscoelastic sphere.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика одномерного кристалла|Chain]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Chain_v3_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates dynamics of a 1D harmonic crystal.<br />
See also [[Heat transfer in a 1D harmonic crystal]].<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование структуры кристаллических решеток | Periodic vacancies in a crystal lattice]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Lattice_v8_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program demontrates different crystal lattice structures.<br />
</td></tr><br />
</table><br />
}}</div><br />
<br style="clear: both" /><br />
<br />
[[Fluctuations in energy-dimensional crystal]]</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=6156Virtual laboratory2015-10-18T13:59:33Z<p>Денис: </p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
{{DISPLAYTITLE:<span style="display:none">{{FULLPAGENAME}}</span>}}<br />
<center><h1>Welcome to the Virtual laboratory page!</h1></center><br />
<br />
<br />
Here you can see computer experiments in interactive online format. Various systems can be investigated: mathematical, mechanical, physical, biological, etc. Also, you can learn online programming and visualization. More experiments are available on the Russian page (see the link at the left panel).<br />
__NOTOC__<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Игра "Жизнь" | Conway's Game of Life]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/CelAut_v2_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program, representing a classic [https://en.wikipedia.org/wiki/Conway's_Game_of_Life "Conway's Game of Life"]. The cells can be drawn on the field by cursor.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование Солнечной системы|Solar System model]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Solar_System_v1_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
This model demonstrates the real attitude of the orbital periods of the planets. The radiuses of the planet orbits, as well as the sizes of the planets and the Sun are shown in a logarithmic scale.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Движение материальной точки в центральном поле | Dynamics of a particle in a central field]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/FC_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The application allows you to study a particle trajectory in a central power-law potential field.<br />
</td></tr><br />
</table><br />
}}</div><br />
<!-- СЛЕДУЮЩАЯ СТРОКА --><br />
<br style="clear: both" /><br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика взаимодействующих частиц | Dynamics of interacting particles]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Balls_v6_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates dynamics of interacting particles. Each particle represents a viscoelastic sphere.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика одномерного кристалла|Chain]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Chain_v3_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates dynamics of a 1D harmonic crystal.<br />
See also [[Heat transfer in a 1D harmonic crystal]].<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование структуры кристаллических решеток | Periodic vacancies in a crystal lattice]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Lattice_v8_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program demontrates different crystal lattice structures.<br />
</td></tr><br />
</table><br />
}}</div><br />
<br style="clear: both" /><br />
<br />
[[fluctuations in energy-dimensional crystal]]</div>Денисhttp://tm.spbstu.ru/?title=Tsvetkov_Denis&diff=6002Tsvetkov Denis2015-10-10T17:55:08Z<p>Денис: </p>
<hr />
<div>[[ru:Цветков Денис Валерьевич]]<br />
[[File: IMG 0782.JPG|right|400px]]<br />
<br />
== Education ==<br />
* School №455<br />
* SPbSTU, Department "Theoretical Mechanics"<br />
<br />
== Research interests ==<br />
* Programming (Java, C++, Python, JavaScript)<br />
* Graphics library [http://en.wikipedia.org/wiki/OpenGL OpenGL]<br />
* The molecular dynamics method<br />
<br />
== Research projects ==<br />
* [[:ru:VirtLab | VirtLab]]<br />
* [[:ru:Моделирование динамики толпы в областях со сложной геометрией | Crowd dynamics modelling in complicated geometry area ]]<br />
* [[:ru:JavaScript-программирование | JavaScript-programming]]<br />
* Working with a3r files (department extension)<br />
<!--[[File:A3r-viewer.gif|a3r viewer]]--><br />
* Crystal lattices modeling <br />
<!--[[File:Crystal-lattice.gif|Crystal lattice]]<br />
* Gravitational forces modeling ([http://tm.spbstu.ru/images/9/9c/Gravit.gif gif])--><br />
* Perfectly elastic collision modeling<br />
[[File:5.gif]]<br />
* Particle interactions modeling<br />
<!--[[File:7.gif]]--><br />
* [[:ru:Съемки в фотолаборатории| High speed camera shooting]]<br />
<gallery widths=350px heights=250px perrow=3><br />
File:Bottle0000004078.jpg|Balloon with water<br />
File:Sphere0000002845.jpg|Soapbubble<br />
</gallery><br />
<!--{{#widget:YouTube|id=T2aFye6sYMo}} {{#widget:YouTube|id=Ls3qp3aU6ew}}--><br />
<br />
== Personal projects ==<br />
* 2D engine ([http://tm.spbstu.ru/images/a/ab/2D-Engine.gif gif])<br />
* Minicraft-clone<br />
<!--[[File:Myminicraft.gif]]--><br />
* Game TAL<br />
[[File:TAL.gif]]<br />
<br />
== Virtual laboratory projects ==<br />
<br />
* [[Heat transfer in a 1D harmonic crystal]]<br />
* [[Heat transfer in a 1D harmonic crystal: periodic temperature]]<br />
* [[Heat transfer in a 1D harmonic crystal: regular temperature]]<br />
<br />
== Contacts ==<br />
[[File:TM-Animation cropped.gif|thumb|TM]]<br />
Phone: +7-911-948-8429<br />
<br />
E-mail: DVTsvetkov@ya.ru<br />
<br />
== Interesting links ==<br />
[http://codepen.io/stuffit/pen/KrAwx Cloth simulation]<br />
<br />
[http://workshop.chromeexperiments.com/stars/ WebGL - interactive space]<br />
<br />
[http://alteredqualia.com/three/examples/materials_shaders_fresnel.html WebGL - soapbubbles] <br />
<br />
[http://mrdoob.com/projects/harmony/ JavaScript - drawing tool]<br />
<br />
[http://acko.net/ Hackery, Math & Design]</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=5994Virtual laboratory2015-10-10T17:45:02Z<p>Денис: </p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
{{DISPLAYTITLE:<span style="display:none">{{FULLPAGENAME}}</span>}}<br />
<center><h1>Welcome to Virtual laboratory page!</h1></center><br />
<br />
Here you can see projects, that allow you to conduct experiments online in an interactive mode. You can investigate all possible systems: mathematical, mechanical, physical, biological, etc. Also, you can learn online programming and visualization.<br />
__NOTOC__<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Игра "Жизнь" | Conway's Game of Life]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/CelAut_v2_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program, representing a classic game [https://en.wikipedia.org/wiki/Conway's_Game_of_Life "Conway's Game of Life"] with the ability to draw cells on the field by cursor.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование Солнечной системы|Solar System model]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Solar_System_v1_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
This model demonstrates the real attitude of the orbital periods of the planets. The radiuses of the planet orbits, as well as the sizes of the planets and the sun are shown in a logarithmic scale.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Движение материальной точки в центральном поле | The motion of a particle in a central field]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/FC_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
That application allows you to study the trajectory of a particle in a central power-law gravitational field.<br />
</td></tr><br />
</table><br />
}}</div><br />
<!-- СЛЕДУЮЩАЯ СТРОКА --><br />
<br style="clear: both" /><br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика взаимодействующих частиц | The dynamics of interacting particles]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Balls_v6_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates the dynamics of interacting particles. Each particle represents a viscoelastic sphere.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Динамика одномерного кристалла|Chain]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Chain_v3_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates the dynamics of one-dimensional crystal.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[:ru:Моделирование структуры кристаллических решеток | The crystal lattices structure modeling]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Lattice_v8_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates different crystal lattice structures.<br />
</td></tr><br />
</table><br />
}}</div><br />
<br style="clear: both" /><br />
<br />
* [[Heat transfer in a 1D harmonic crystal]]</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=5987Virtual laboratory2015-10-10T17:36:58Z<p>Денис: </p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
{{DISPLAYTITLE:<span style="display:none">{{FULLPAGENAME}}</span>}}<br />
<center><h1>Welcome to Virtual laboratory page!</h1></center><br />
<br />
Here you can see projects, that allow you to conduct experiments online in an interactive mode. You can investigate all possible systems: mathematical, mechanical, physical, biological, etc. Also, you can learn online programming and visualization.<br />
__NOTOC__<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Conway's Game of Life]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/CelAut_v2_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program, representing a classic game [https://en.wikipedia.org/wiki/Conway's_Game_of_Life "Conway's Game of Life"] with the ability to draw cells on the field by cursor.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Моделирование Солнечной системы|Solar System model]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Solar_System_v1_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
This model demonstrates the real attitude of the orbital periods of the planets. The radiuses of the planet orbits, as well as the sizes of the planets and the sun are shown in a logarithmic scale.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[The motion of a particle in a central field]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/FC_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
That application allows you to study the trajectory of a particle in a central power-law gravitational field.<br />
</td></tr><br />
</table><br />
}}</div><br />
<!-- СЛЕДУЮЩАЯ СТРОКА --><br />
<br style="clear: both" /><br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[The dynamics of interacting particles]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Balls_v6_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates the dynamics of interacting particles. Each particle represents a viscoelastic sphere.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Динамика одномерного кристалла|Chain]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Chain_v3_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates the dynamics of one-dimensional crystal.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[The Crystal lattices structure modeling]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Lattice_v8_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
The program simulates different crystal lattice structures.<br />
</td></tr><br />
</table><br />
}}</div><br />
<br style="clear: both" /><br />
<br />
* [[Heat transfer in a 1D harmonic crystal]]</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=5986Virtual laboratory2015-10-10T17:18:12Z<p>Денис: </p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
{{DISPLAYTITLE:<span style="display:none">{{FULLPAGENAME}}</span>}}<br />
<center><h1>Welcome to Virtual laboratory page!</h1></center><br />
<br />
Here you can see projects, that allow you to conduct experiments online in an interactive mode. You can investigate all possible systems: mathematical, mechanical, physical, biological, etc. Also, you can learn online programming and visualization.<br />
__NOTOC__<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Conway's Game of Life]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/CelAut_v2_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Программа, представляющая из себя классическую игру [http://ru.wikipedia.org/wiki/Жизнь_(игра) "Жизнь"] Джона Конвея с возможностью рисовать курсором клетки на поле.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Моделирование Солнечной системы|Solar System model]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Solar_System_v1_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Данная модель демонстрирует реальное соотношение периодов обращения планет.<br />
Радиусы орбит планет, а также размеры планет и Солнца показаны в логарифмическом масштабе.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[The motion of a particle in a central field]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/FC_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Интерактивное приложение позволяет изучать траектории материальной точки в центральном степенном поле притяжения.<br />
</td></tr><br />
</table><br />
}}</div><br />
<!-- СЛЕДУЮЩАЯ СТРОКА --><br />
<br style="clear: both" /><br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[The dynamics of interacting particles]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Balls_v6_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Программа моделирует динамику взаимодуйствующих частиц. Каждая частица представляет из себя вязкоупругий шар.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Динамика одномерного кристалла|Chain]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Chain_v3_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Программа, моделирующая динамику одномерного кристалла.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[The Crystal lattices structure modeling]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Lattice_v8_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Программа, моделирующая различные структуры кристаллических решеток.<br />
</td></tr><br />
</table><br />
}}</div><br />
<br style="clear: both" /><br />
<br />
* [[Heat transfer in a 1D harmonic crystal]]</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=5985Virtual laboratory2015-10-10T17:13:38Z<p>Денис: </p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
{{DISPLAYTITLE:<span style="display:none">{{FULLPAGENAME}}</span>}}<br />
<center><h1>Welcome to Virtual laboratory page!</h1></center><br />
<br />
Here you can see projects, that allow you to conduct experiments online in an interactive mode. You can investigate all possible systems: mathematical, mechanical, physical, biological, etc. Also, you can learn online programming and visualization.<br />
__NOTOC__<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Игра "Жизнь"]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/CelAut_v2_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Программа, представляющая из себя классическую игру [http://ru.wikipedia.org/wiki/Жизнь_(игра) "Жизнь"] Джона Конвея с возможностью рисовать курсором клетки на поле.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Моделирование Солнечной системы|Модель Солнечной системы]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Solar_System_v1_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Данная модель демонстрирует реальное соотношение периодов обращения планет.<br />
Радиусы орбит планет, а также размеры планет и Солнца показаны в логарифмическом масштабе.<br />
</td></tr><br />
</table><br />
}}<br />
</div><br />
<br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Движение материальной точки в центральном поле]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/FC_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Интерактивное приложение позволяет изучать траектории материальной точки в центральном степенном поле притяжения.<br />
</td></tr><br />
</table><br />
}}</div><br />
<!-- СЛЕДУЮЩАЯ СТРОКА --><br />
<br style="clear: both" /><br />
<div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Динамика взаимодействующих частиц]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Balls_v6_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Программа моделирует динамику взаимодуйствующих частиц. Каждая частица представляет из себя вязкоупругий шар.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Динамика одномерного кристалла|Цепь]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Chain_v3_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Программа, моделирующая динамику одномерного кристалла.<br />
</td></tr><br />
</table><br />
}}<br />
<br />
</div><div style="float:left; width:33%"><br />
{{Раздел заглавной страницы | x = 0 | Содержание = <br />
<table><br />
<tr><td style="height:40px;"><br />
<div style="font-size:135%; text-align:center; font-weight:bold">[[Моделирование структуры кристаллических решеток]]</div><br />
</td></tr><br />
<tr><td style="height:260px; background-color:#F8F8F8; text-align:center"><br />
<htmlet nocache="yes">Tcvetkov/Mini_Demos/Lattice_v8_mini</htmlet><br />
</td></tr><br />
<tr><td style="height:100px; text-align:center"><br />
Программа, моделирующая различные структуры кристаллических решеток.<br />
</td></tr><br />
</table><br />
}}</div><br />
<br style="clear: both" /><br />
<br />
* [[Heat transfer in a 1D harmonic crystal]]</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal&diff=5983Heat transfer in a 1D harmonic crystal2015-10-10T13:26:10Z<p>Денис: </p>
<hr />
<div>[[ru:Распространение тепла в гармоническом одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] <HR><br />
[[A.M. Krivtsov]] (analytical silution, simulation algorithms), [[D.V. Tsvetkov]] (programming, calculation algorithms).<HR><br />
__NOEDITSECTION__<br />
__NOTOC__<br />
<br />
Heat transfer in the simplest discrete systems doesn’t obey common macroscopic laws. Recently experimentalists have observed the similar behavior at nanolevel, in molecular and atomic systems. The simulation below demonstrates heat transfer process in a 1D harmonic crystal. Two graphs are shown: results of molecular dynamics simulation and corresponding continuum solution. You can also compare the results with predictions of other continuum models. The analysis of the system and derivation of the continuum solution are presented in paper: [[A.M. Krivtsov]], '''On unsteady heat conduction in a harmonic crystal'''. 2015, ArXiv:1509.02506 ([http://arxiv.org/abs/1509.02506 abstract], [http://arxiv.org/pdf/1509.02506v2.pdf pdf]). <br />
<br />
{{oncolor|yellow|black|Use the '''Restart''' button to see the process from the beginning.}}<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20v8b-10%20debug%20random/Equations.html |width=1030 |height=745 |border=0 }}<br />
<br />
== Discrete model (microlevel) ==<br />
<br />
We consider a one-dimensional crystal, described by the following equations of motion:<br />
:<math><br />
\ddot{u}_i = \omega_0^2(u_{i-1}-2u_i+u_{i+1})<br />
,\qquad \omega_0 = \sqrt{C/m},<br />
</math><br />
where<br />
<math>u_i</math> is the displacement of the <math>i</math>th particle,<br />
<math>m</math> is the particle mass,<br />
<math>C</math> is the stiffness of the interparticle bond.<br />
The crystal is infinite: the index <math>i</math> is an arbitrary integer.<br />
The initial conditions are<br />
:<math><br />
u_i|_{t=0} = 0<br />
,\qquad<br />
\dot u_i|_{t=0} = \sigma(x)\varrho_i<br />
,<br />
</math><br />
where <math>\varrho_i</math> are independent random values with zero expectation and unit variance; <math>\sigma</math> is variance of the initial velocities of the particles, which is a slowly varying function of the spatial coordinate <math>x=ia</math>, where <math>a</math> is the lattice constant. These initial conditions correspond to an instantaneous temperature perturbation, which can be induced in crystals, for example, by an ultrashort laser pulse. Periodic conditions are used at the boundaries.<br />
<br />
== Kinetic temperature (link between micro and macro) ==<br />
<br />
The kinetic temperature <math>T</math> is defined as <br />
:<math><br />
T(x) = \frac m{k_{B}}\langle\dot u_i^2\rangle,<br />
</math><br />
where <br />
<math>k_{B}</math> is the Boltzmann constant,<br />
<math>i=x/a</math>, <br />
angle brackets stand for mathematical expectation.<br />
<br />
== Continuum description (macrolevel) ==<br />
<br />
{{oncolor||blue|—}} Reversible heat equation (Krivtsov): <math>\ddot T +\frac1t\dot T = c^2 T''</math> — the equation derived as direct consequence of the discrete microscopic equations [http://arxiv.org/abs/1509.02506]<br />
<br />
Notations:<br />
<math>t</math> is time (variable),<br />
<math>c</math> is the sound speed.<br />
<br />
== Classic continuum equations ==<br />
<br />
{{oncolor||red|—}} Heat (Fourier): <math>\dot T = \beta T''</math> [https://en.wikipedia.org/wiki/Heat_equation]<br />
<br />
{{oncolor||#008888|—}} Heat wave (MCV): <math>\ddot T +\frac1\tau\dot T = \frac\beta\tau T''</math><br />
<br />
{{oncolor||#00ff00|—}} Wave (d’Alembert): <math>\ddot T = c^2 T''</math> [https://en.wikipedia.org/wiki/Wave_equation]<br />
<br />
Notations:<br />
<math>\tau</math> is the relaxation time (constant),<br />
<math>\beta</math> is the thermal diffusivity,<br />
<math>\kappa</math> is the thermal conductivity,<br />
<math>\rho</math> is the density,<br />
MCV stands for Maxwell-Cattaneo-Vernotte.<br />
<br />
== Related publications ==<br />
<br />
* [[A.M. Krivtsov]]. '''On unsteady heat conduction in a harmonic crystal.''' 2015, ArXiv:1509.02506 ([http://arxiv.org/abs/1509.02506 abstract], [http://arxiv.org/pdf/1509.02506v2.pdf pdf]) <br />
<br />
* [[A.M. Krivtsov]]. '''Energy oscillations in a one-dimensional crystal.''' Doklady Physics, 2014, Vol. 59, No. 9, pp. 427–430 (pdf: [[Media: Krivtsov_2014_DAN_eng_corrected.pdf| 162 Kb]])<br />
<!--<br />
* [[A.A. Le-Zakharov]], [[A.M. Krivtsov]]. '''Molecular dynamics investigation of heat conduction in crystals with defects.''' Doklady Physics, 2008, Vol. 53, No. 5, pp. 261–264 (pdf: [http://www.ipme.ru/ipme/labs/msm/Pub/Le_2008_DAN_eng.pdf 196 Kb])<br />
<br />
* [[A.M. Krivtsov]] '''From nonlinear oscillations to equation of state in simple discrete systems.''' Chaos, Solitons & Fractals, 2003, 17(1), 79-87. (pdf: [http://www.ipme.ru/ipme/labs/msm/Pub/Krivtsov_2003_CSF.pdf 117 Kb])<br />
--><br />
<br />
== Presentations ==<br />
<br />
* [[A.M. Krivtsov]]. '''One-dimensional crystals and heat superconductivity.''' [http://www.apm-conf.spb.ru International Summer School-Conference “Advanced Problems in Mechanics”], 2015, St. Petersburg, Russia. ''Plenary lecture:'' [[Media: Krivtsov_2015_06_22_APM_09-02_modified_151010_.pdf|pdf 1913 Kb]]. <br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal:_regular_temperature&diff=5894Heat transfer in a 1D harmonic crystal: regular temperature2015-10-07T22:50:54Z<p>Денис: </p>
<hr />
<div>[[ru:Распространение тепла в гармоническом одномерном кристалле: регулярная температура]]<br />
<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] > [[Heat transfer in a 1D harmonic crystal: regular temperature|regular temperature]] <HR><br />
<br />
== Describtion ==<br />
<br />
This page is an extension of the page [[Heat transfer in a 1D harmonic crystal]].<br />
The program below demonstrates an attempt to set the initial temperature in a regular way, in order to answer the question: ''Isn't there some way to choose the initial conditions that makes all of the averaging unnecessary?''<br />
<br />
The idea is to set the initial velocities randomly, but then the displacements are chosen in a way that the total energy (sum of kinetic and potential energies) associated with particles is a regular (not random) function of the particle number. The simulation below shows evolution of the spatial profiles of the total, kinetic and potential energies.<br />
<br />
== Simulation: evolution of the spatial distribution of the energies ==<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20test_prog2_4/Equations.html |width=1030 |height=885 |border=0 }}<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal:_periodic_temperature&diff=5893Heat transfer in a 1D harmonic crystal: periodic temperature2015-10-07T22:50:47Z<p>Денис: </p>
<hr />
<div>[[ru:Распространение тепла в гармоническом одномерном кристалле: периодическая температура]]<br />
<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] > [[Heat transfer in a 1D harmonic crystal: periodic temperature|periodic temperature]] <HR><br />
<br />
== Describtion ==<br />
<br />
This page is an extension of the page [[Heat transfer in a 1D harmonic crystal]].<br />
The program below allows two possibilities to set the initial temperature:<br />
* random: the initial particle velocities are set by a random number generator;<br />
* periodic: the initial particle velocities are set as a short-period sinusoidal wave.<br />
<br />
== Simulation: evolution of the spatial distribution of the kinetic temperature ==<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20v8b-10%20debug%20period/Equations.html |width=1030 |height=785 |border=0 }}<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal&diff=5892Heat transfer in a 1D harmonic crystal2015-10-07T22:50:12Z<p>Денис: </p>
<hr />
<div>[[ru:Распространение тепла в гармоническом одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] <HR><br />
<br />
Theory: [[А.М. Кривцов|A.M. Krivtsov]], published at [http://arxiv.org/abs/1509.02506 arXiv:1509.02506 (cond-mat.stat-mech)]<br />
<br />
Programming: D.V. Tsvetkov<br />
<br />
== Microscopic model ==<br />
<br />
We consider a one-dimensional crystal, described by the following equations of motion:<br />
:<math><br />
\ddot{u}_i = \omega_0^2(u_{i-1}-2u_i+u_{i+1})<br />
,\qquad \omega_0 = \sqrt{C/m},<br />
</math><br />
where<br />
<math>u_i</math> is the displacement of the <math>i</math>th particle,<br />
<math>m</math> is the particle mass,<br />
<math>C</math> is the stiffness of the interparticle bond.<br />
The crystal is infinite: the index <math>i</math> is an arbitrary integer.<br />
The initial conditions are<br />
:<math><br />
u_i|_{t=0} = 0<br />
,\qquad<br />
\dot u_i|_{t=0} = \sigma(x)\varrho_i<br />
,<br />
</math><br />
where <math>\varrho_i</math> are independent random values with zero expectation and unit variance; <math>\sigma</math> is variance of the initial velocities of the particles, which is a slowly varying function of the spatial coordinate <math>x=ia</math>, where <math>a</math> is the lattice constant. These initial conditions correspond to an instantaneous temperature perturbation, which can be induced in crystals, for example, by an ultrashort laser pulse.<br />
<br />
== Simulation: evolution of the spatial distribution of the kinetic temperature ==<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20v8b-10%20debug%20random/Equations.html |width=1030 |height=785 |border=0 }}<br />
<br />
== Kinetic temperature: link between micro and macro ==<br />
<br />
The kinetic temperature <math>T</math> is defined as <br />
:<math><br />
T(x) = \frac m{k_{B}}\langle\dot u_i^2\rangle,<br />
</math><br />
where <br />
<math>k_{B}</math> is the Boltzmann constant,<br />
<math>i=x/a</math>, <br />
angle brackets stand for mathematical expectation.<br />
<br />
== Macroscopic equations ==<br />
<br />
{{oncolor||red|—}} Heat (Fourier): <math>\dot T = \beta T''</math> [https://en.wikipedia.org/wiki/Heat_equation]<br />
<br />
{{oncolor||#008888|—}} Heat wave (MCV): <math>\ddot T +\frac1\tau\dot T = \frac\beta\tau T''</math><br />
<br />
{{oncolor||#00ff00|—}} Wave (d’Alembert): <math>\ddot T = c^2 T''</math> [https://en.wikipedia.org/wiki/Wave_equation]<br />
<br />
{{oncolor||blue|—}} Reversible (Krivtsov): <math>\ddot T +\frac1t\dot T = c^2 T''</math> [http://arxiv.org/abs/1509.02506]<br />
<br />
Notations:<br />
<math>t</math> is time (variable),<br />
<math>\tau</math> is the relaxation time (constant),<br />
<math>\beta</math> is the thermal diffusivity,<br />
<math>\kappa</math> is the thermal conductivity,<br />
<math>c</math> is the sound speed,<br />
<math>\rho</math> is the density,<br />
MCV stands for Maxwell-Cattaneo-Vernotte.<br />
<br />
<br />
<br />
== See also ==<br />
<br />
* [[Heat transfer in a 1D harmonic crystal: periodic temperature]]<br />
* [[Heat transfer in a 1D harmonic crystal: regular temperature]]<br />
<br />
[[Category: Virtual laboratory]]</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal&diff=5891Heat transfer in a 1D harmonic crystal2015-10-07T22:44:32Z<p>Денис: </p>
<hr />
<div>[[ru:Распространение тепла в гармоническом одномерном кристалле]]<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] <HR><br />
<br />
Theory: [[А.М. Кривцов|A.M. Krivtsov]], published at [http://arxiv.org/abs/1509.02506 arXiv:1509.02506 (cond-mat.stat-mech)]<br />
<br />
Programming: D.V. Tsvetkov<br />
<br />
== Microscopic model ==<br />
<br />
We consider a one-dimensional crystal, described by the following equations of motion:<br />
:<math><br />
\ddot{u}_i = \omega_0^2(u_{i-1}-2u_i+u_{i+1})<br />
,\qquad \omega_0 = \sqrt{C/m},<br />
</math><br />
where<br />
<math>u_i</math> is the displacement of the <math>i</math>th particle,<br />
<math>m</math> is the particle mass,<br />
<math>C</math> is the stiffness of the interparticle bond.<br />
The crystal is infinite: the index <math>i</math> is an arbitrary integer.<br />
The initial conditions are<br />
:<math><br />
u_i|_{t=0} = 0<br />
,\qquad<br />
\dot u_i|_{t=0} = \sigma(x)\varrho_i<br />
,<br />
</math><br />
where <math>\varrho_i</math> are independent random values with zero expectation and unit variance; <math>\sigma</math> is variance of the initial velocities of the particles, which is a slowly varying function of the spatial coordinate <math>x=ia</math>, where <math>a</math> is the lattice constant. These initial conditions correspond to an instantaneous temperature perturbation, which can be induced in crystals, for example, by an ultrashort laser pulse.<br />
<br />
== Simulation: evolution of the spatial distribution of the kinetic temperature ==<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20v8b-10%20debug%20random/Equations.html |width=1030 |height=785 |border=0 }}<br />
<br />
== Kinetic temperature: link between micro and macro ==<br />
<br />
The kinetic temperature <math>T</math> is defined as <br />
:<math><br />
T(x) = \frac m{k_{B}}\langle\dot u_i^2\rangle,<br />
</math><br />
where <br />
<math>k_{B}</math> is the Boltzmann constant,<br />
<math>i=x/a</math>, <br />
angle brackets stand for mathematical expectation.<br />
<br />
== Macroscopic equations ==<br />
<br />
{{oncolor||red|—}} Heat (Fourier): <math>\dot T = \beta T''</math> [https://en.wikipedia.org/wiki/Heat_equation]<br />
<br />
{{oncolor||#008888|—}} Heat wave (MCV): <math>\ddot T +\frac1\tau\dot T = \frac\beta\tau T''</math><br />
<br />
{{oncolor||#00ff00|—}} Wave (d’Alembert): <math>\ddot T = c^2 T''</math> [https://en.wikipedia.org/wiki/Wave_equation]<br />
<br />
{{oncolor||blue|—}} Reversible (Krivtsov): <math>\ddot T +\frac1t\dot T = c^2 T''</math> [http://arxiv.org/abs/1509.02506]<br />
<br />
Notations:<br />
<math>t</math> is time (variable),<br />
<math>\tau</math> is the relaxation time (constant),<br />
<math>\beta</math> is the thermal diffusivity,<br />
<math>\kappa</math> is the thermal conductivity,<br />
<math>c</math> is the sound speed,<br />
<math>\rho</math> is the density,<br />
MCV stands for Maxwell-Cattaneo-Vernotte.<br />
<br />
<br />
<br />
== See also ==<br />
<br />
* [[Heat transfer in a 1D harmonic crystal: periodic temperature]]<br />
* [[Heat transfer in a 1D harmonic crystal: regular temperature]]</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal:_regular_temperature&diff=5890Heat transfer in a 1D harmonic crystal: regular temperature2015-10-07T22:43:33Z<p>Денис: </p>
<hr />
<div>[[ru:Распространение тепла в гармоническом одномерном кристалле: регулярная температура]]<br />
<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] > [[Heat transfer in a 1D harmonic crystal: regular temperature|regular temperature]] <HR><br />
<br />
== Describtion ==<br />
<br />
This page is an extension of the page [[Heat transfer in a 1D harmonic crystal]].<br />
The program below demonstrates an attempt to set the initial temperature in a regular way, in order to answer the question: ''Isn't there some way to choose the initial conditions that makes all of the averaging unnecessary?''<br />
<br />
The idea is to set the initial velocities randomly, but then the displacements are chosen in a way that the total energy (sum of kinetic and potential energies) associated with particles is a regular (not random) function of the particle number. The simulation below shows evolution of the spatial profiles of the total, kinetic and potential energies.<br />
<br />
== Simulation: evolution of the spatial distribution of the energies ==<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20test_prog2_4/Equations.html |width=1030 |height=885 |border=0 }}</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal:_regular_temperature&diff=5889Heat transfer in a 1D harmonic crystal: regular temperature2015-10-07T22:42:58Z<p>Денис: Created page with "Virtual laborotory > Heat transfer in a 1D harmonic crystal > regular temperature <HR> == Describtion..."</p>
<hr />
<div>[[Virtual laborotory]] > [[Heat transfer in a 1D harmonic crystal]] > [[Heat transfer in a 1D harmonic crystal: regular temperature|regular temperature]] <HR><br />
<br />
== Describtion ==<br />
<br />
This page is an extension of the page [[Heat transfer in a 1D harmonic crystal]].<br />
The program below demonstrates an attempt to set the initial temperature in a regular way, in order to answer the question: ''Isn't there some way to choose the initial conditions that makes all of the averaging unnecessary?''<br />
<br />
The idea is to set the initial velocities randomly, but then the displacements are chosen in a way that the total energy (sum of kinetic and potential energies) associated with particles is a regular (not random) function of the particle number. The simulation below shows evolution of the spatial profiles of the total, kinetic and potential energies.<br />
<br />
== Simulation: evolution of the spatial distribution of the energies ==<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20test_prog2_4/Equations.html |width=1030 |height=885 |border=0 }}</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal&diff=5888Heat transfer in a 1D harmonic crystal2015-10-07T22:38:38Z<p>Денис: </p>
<hr />
<div>[[ru:Распространение тепла в гармоническом одномерном кристалле]]<br />
[[Anton Krivtsov]] > [[Heat transfer in a 1D harmonic crystal]] <HR><br />
<br />
Theory: [[А.М. Кривцов|A.M. Krivtsov]], published at [http://arxiv.org/abs/1509.02506 arXiv:1509.02506 (cond-mat.stat-mech)]<br />
<br />
Programming: D.V. Tsvetkov<br />
<br />
== Microscopic model ==<br />
<br />
We consider a one-dimensional crystal, described by the following equations of motion:<br />
:<math><br />
\ddot{u}_i = \omega_0^2(u_{i-1}-2u_i+u_{i+1})<br />
,\qquad \omega_0 = \sqrt{C/m},<br />
</math><br />
where<br />
<math>u_i</math> is the displacement of the <math>i</math>th particle,<br />
<math>m</math> is the particle mass,<br />
<math>C</math> is the stiffness of the interparticle bond.<br />
The crystal is infinite: the index <math>i</math> is an arbitrary integer.<br />
The initial conditions are<br />
:<math><br />
u_i|_{t=0} = 0<br />
,\qquad<br />
\dot u_i|_{t=0} = \sigma(x)\varrho_i<br />
,<br />
</math><br />
where <math>\varrho_i</math> are independent random values with zero expectation and unit variance; <math>\sigma</math> is variance of the initial velocities of the particles, which is a slowly varying function of the spatial coordinate <math>x=ia</math>, where <math>a</math> is the lattice constant. These initial conditions correspond to an instantaneous temperature perturbation, which can be induced in crystals, for example, by an ultrashort laser pulse.<br />
<br />
== Simulation: evolution of the spatial distribution of the kinetic temperature ==<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20v8b-10%20debug%20random/Equations.html |width=1030 |height=785 |border=0 }}<br />
<br />
== Kinetic temperature: link between micro and macro ==<br />
<br />
The kinetic temperature <math>T</math> is defined as <br />
:<math><br />
T(x) = \frac m{k_{B}}\langle\dot u_i^2\rangle,<br />
</math><br />
where <br />
<math>k_{B}</math> is the Boltzmann constant,<br />
<math>i=x/a</math>, <br />
angle brackets stand for mathematical expectation.<br />
<br />
== Macroscopic equations ==<br />
<br />
{{oncolor||red|—}} Heat (Fourier): <math>\dot T = \beta T''</math> [https://en.wikipedia.org/wiki/Heat_equation]<br />
<br />
{{oncolor||#008888|—}} Heat wave (MCV): <math>\ddot T +\frac1\tau\dot T = \frac\beta\tau T''</math><br />
<br />
{{oncolor||#00ff00|—}} Wave (d’Alembert): <math>\ddot T = c^2 T''</math> [https://en.wikipedia.org/wiki/Wave_equation]<br />
<br />
{{oncolor||blue|—}} Reversible (Krivtsov): <math>\ddot T +\frac1t\dot T = c^2 T''</math> [http://arxiv.org/abs/1509.02506]<br />
<br />
Notations:<br />
<math>t</math> is time (variable),<br />
<math>\tau</math> is the relaxation time (constant),<br />
<math>\beta</math> is the thermal diffusivity,<br />
<math>\kappa</math> is the thermal conductivity,<br />
<math>c</math> is the sound speed,<br />
<math>\rho</math> is the density,<br />
MCV stands for Maxwell-Cattaneo-Vernotte.<br />
<br />
<br />
<br />
== See also ==<br />
<br />
* [[Heat transfer in a 1D harmonic crystal: periodic temperature]]<br />
* [[Heat transfer in a 1D harmonic crystal: regular temperature]]</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal:_periodic_temperature&diff=5887Heat transfer in a 1D harmonic crystal: periodic temperature2015-10-07T22:37:06Z<p>Денис: </p>
<hr />
<div>[[ru:Распространение тепла в гармоническом одномерном кристалле: периодическая температура]]<br />
<br />
[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] > [[Heat transfer in a 1D harmonic crystal: periodic temperature|periodic temperature]] <HR><br />
<br />
== Describtion ==<br />
<br />
This page is an extension of the page [[Heat transfer in a 1D harmonic crystal]].<br />
The program below allows two possibilities to set the initial temperature:<br />
* random: the initial particle velocities are set by a random number generator;<br />
* periodic: the initial particle velocities are set as a short-period sinusoidal wave.<br />
<br />
== Simulation: evolution of the spatial distribution of the kinetic temperature ==<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20v8b-10%20debug%20period/Equations.html |width=1030 |height=785 |border=0 }}</div>Денисhttp://tm.spbstu.ru/?title=Heat_transfer_in_a_1D_harmonic_crystal:_periodic_temperature&diff=5886Heat transfer in a 1D harmonic crystal: periodic temperature2015-10-07T22:33:53Z<p>Денис: Created page with "Virtual laboratory > Heat transfer in a 1D harmonic crystal > periodic temperature <HR> == Describtio..."</p>
<hr />
<div>[[Virtual laboratory]] > [[Heat transfer in a 1D harmonic crystal]] > [[Heat transfer in a 1D harmonic crystal: periodic temperature|periodic temperature]] <HR><br />
<br />
== Describtion ==<br />
<br />
This page is an extension of the page [[Heat transfer in a 1D harmonic crystal]].<br />
The program below allows two possibilities to set the initial temperature:<br />
* random: the initial particle velocities are set by a random number generator;<br />
* periodic: the initial particle velocities are set as a short-period sinusoidal wave.<br />
<br />
== Simulation: evolution of the spatial distribution of the kinetic temperature ==<br />
<br />
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Equations/Equation%20v8b-10%20debug%20period/Equations.html |width=1030 |height=785 |border=0 }}</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=5879Virtual laboratory2015-10-07T22:24:01Z<p>Денис: </p>
<hr />
<div>[[ru:Виртуальная лаборатория]]<br />
<br />
* [[Heat transfer in a 1D harmonic crystal]]</div>Денисhttp://tm.spbstu.ru/?title=Virtual_laboratory&diff=5869Virtual laboratory2015-10-07T21:35:48Z<p>Денис: Created page with "ru:Виртуальная лаборатория"</p>
<hr />
<div>[[ru:Виртуальная лаборатория]]</div>Денисhttp://tm.spbstu.ru/?title=User:%D0%94%D0%B5%D0%BD%D0%B8%D1%81&diff=5868User:Денис2015-10-07T21:35:11Z<p>Денис: </p>
<hr />
<div>[[Tsvetkov_Denis]]<br />
<br />
[http://tm.spbstu.ru/Цветков_Денис_Валерьевич Цветков Денис Валерьевич]</div>Денисhttp://tm.spbstu.ru/?title=Tsvetkov_Denis&diff=5859Tsvetkov Denis2015-10-07T21:21:23Z<p>Денис: Created page with "ru:Цветков Денис Валерьевич 400px == Education == * School №455 * SPbSTU, Department "Theoretical Mechanics" == Rese..."</p>
<hr />
<div>[[ru:Цветков Денис Валерьевич]]<br />
[[File: IMG 0782.JPG|right|400px]]<br />
<br />
== Education ==<br />
* School №455<br />
* SPbSTU, Department "Theoretical Mechanics"<br />
<br />
== Research interests ==<br />
* Programming (Java, C++, Python, JavaScript)<br />
* Graphics library [http://en.wikipedia.org/wiki/OpenGL OpenGL]<br />
* The molecular dynamics method<br />
<br />
== Research projects ==<br />
* [[:ru:VirtLab | VirtLab]]<br />
* [[:ru:Моделирование динамики толпы в областях со сложной геометрией | Crowd dynamics modelling in complicated geometry area ]]<br />
* [[:ru:JavaScript-программирование | JavaScript-programming]]<br />
* Working with a3r files (department extension)<br />
[[File:A3r-viewer.gif|a3r viewer]]<br />
* Crystal lattice modeling <br />
[[File:Crystal-lattice.gif|Crystal lattice]]<br />
* Gravitational forces modeling ([http://tm.spbstu.ru/images/9/9c/Gravit.gif gif])<br />
* Perfectly elastic collision modeling<br />
[[File:5.gif]]<br />
* Particle interactions modeling<br />
[[File:7.gif]]<br />
* [[:ru:Съемки в фотолаборатории| High speed camera shooting]]<br />
<gallery widths=350px heights=250px perrow=3><br />
File:Bottle0000004078.jpg|Balloon with water<br />
File:Sphere0000002845.jpg|Soapbubble<br />
</gallery><br />
{{#widget:YouTube|id=T2aFye6sYMo}} {{#widget:YouTube|id=Ls3qp3aU6ew}}<br />
<br />
== Personal projects ==<br />
* 2D engine ([http://tm.spbstu.ru/images/a/ab/2D-Engine.gif gif])<br />
* Minicraft-clone<br />
[[File:Myminicraft.gif]]<br />
* Game TAL<br />
[[File:TAL.gif]]<br />
<br />
== Contacts ==<br />
[[File:TM-Animation cropped.gif|thumb|TM]]<br />
Phone: +7-911-948-8429<br />
<br />
E-mail: DVTsvetkov@ya.ru<br />
<br />
== Interesting links ==<br />
[http://codepen.io/stuffit/pen/KrAwx Cloth simulation]<br />
<br />
[http://workshop.chromeexperiments.com/stars/ WebGL - interactive space]<br />
<br />
[http://alteredqualia.com/three/examples/materials_shaders_fresnel.html WebGL - soapbubbles] <br />
<br />
[http://mrdoob.com/projects/harmony/ JavaScript - drawing tool]<br />
<br />
[http://acko.net/ Hackery, Math & Design]</div>Денисhttp://tm.spbstu.ru/?title=File:Tcvet_masters_Theme3_time_reverse(N,A)_6_lines.png&diff=5526File:Tcvet masters Theme3 time reverse(N,A) 6 lines.png2015-06-14T10:50:59Z<p>Денис: </p>
<hr />
<div></div>Денисhttp://tm.spbstu.ru/?title=File:Tcvet_masters_Theme3_Temperature_short.png&diff=5525File:Tcvet masters Theme3 Temperature short.png2015-06-14T10:50:52Z<p>Денис: </p>
<hr />
<div></div>Денисhttp://tm.spbstu.ru/?title=File:Tcvet_masters_Theme3_Temperature_long.png&diff=5524File:Tcvet masters Theme3 Temperature long.png2015-06-14T10:50:46Z<p>Денис: </p>
<hr />
<div></div>Денисhttp://tm.spbstu.ru/?title=File:Tcvet_masters_Theme3_sin_trans_T36035.png&diff=5523File:Tcvet masters Theme3 sin trans T36035.png2015-06-14T10:50:35Z<p>Денис: </p>
<hr />
<div></div>Денисhttp://tm.spbstu.ru/?title=File:Tcvet_masters_Theme3_sin_trans_T18000.png&diff=5522File:Tcvet masters Theme3 sin trans T18000.png2015-06-14T10:50:27Z<p>Денис: </p>
<hr />
<div></div>Денис