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[[Department of TM]] > [[Project "Termokristall"]] > [[Fluctuations in energy in the one-dimensional crystal with a substrate]] <HR>
[[Virtual Laboratory]] > [[Fluctuations in energy in the one-dimensional crystal with a substrate]] <HR>
<math>
\def\be#1{\begin{equation}\label{#1}}
\def\ee{\end{equation}}
\def\({\left(}
\def\){\right)}
\let\eps=\varepsilon
\let\w=\omega
\let\al=\alpha
\renewcommand {\=}{\mathrel{\stackrel{\rm def}=}}
</math>
Examines the chain consisting of identical masses <math>m</math>, connected by springs stiffness <math>C_0</math>. The chain is on an elastic foundation stiffness <math>C_1</math>. Then the equation of the dynamics of the chain of particles is of the form:
::<math>
\be{1Delta}
\ddot{u}_n
    =\(\w^2_0 \Delta^2_n-\w^2_1\) u_n
,\qquad
    \w_0\=\sqrt{C_0/m}
,\qquad
    \w_1\=\sqrt{C_1/m}
,\ee
</math>
where <math>u_n</math> — moving the <math>n</math>-th particle;
<math>\Delta^2_n</math> — difference operator of second order:
::<math>
\be{delta2}
    \Delta^2_n u_n \= u_{n-1}-2u_{n}+u_{n+1},
\ee
</math>
<math>n</math> — an index that takes arbitrary integer.

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Developers: [[Tsvetkov Denis]], [[Krivtsov Anton]]



[[Category: Virtual Laboratory]]
[[Category: Programming]]
[[Category: Project "Termokristall"]]