Trying to draw the images

Former-commit-id: 25bf663661f3428ea2a9d7ea0558a479c2a3f50b
This commit is contained in:
Marek Nečada 2020-06-05 16:43:16 +03:00
parent b80e7607f8
commit 6648e926db
4 changed files with 1657 additions and 12 deletions

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@ -469,9 +469,7 @@ sideways false
status open status open
\begin_layout Plain Layout \begin_layout Plain Layout
\begin_inset Caption Standard \align center
\begin_layout Plain Layout
\begin_inset Graphics \begin_inset Graphics
filename figs/beyn_lMax_cutoff_Au_sphere.pdf filename figs/beyn_lMax_cutoff_Au_sphere.pdf
width 100text% width 100text%
@ -479,10 +477,9 @@ status open
\end_inset \end_inset
\end_layout \begin_inset Caption Standard
\end_inset
\begin_layout Plain Layout
Consequences of multipole degree cutoff: Eigenfrequencies found with Beyn's Consequences of multipole degree cutoff: Eigenfrequencies found with Beyn's
algorithm for an infinite square lattice of golden spherical nanoparticles algorithm for an infinite square lattice of golden spherical nanoparticles
with varying particle size. with varying particle size.
@ -498,8 +495,13 @@ name "square lattice var lMax, r at gamma point Au"
\end_inset \end_inset
\end_layout
\end_inset
\begin_inset Note Note \begin_inset Note Note
status open status collapsed
\begin_layout Plain Layout \begin_layout Plain Layout
\begin_inset Float figure \begin_inset Float figure

1629
lepaper/figs/hex/pokus.svg Normal file

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@ -768,6 +768,15 @@ empty
\begin_inset Formula $\gamma(z)$ \begin_inset Formula $\gamma(z)$
\end_inset \end_inset
if the branch is selected to be continuous for
\begin_inset Formula $-3\pi/2<\arg\left(z-1\right)<\pi/2$
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
as defined in as defined in
\begin_inset CommandInset ref \begin_inset CommandInset ref
LatexCommand eqref LatexCommand eqref
@ -776,6 +785,11 @@ plural "false"
caps "false" caps "false"
noprefix "false" noprefix "false"
\end_inset
\end_layout
\end_inset \end_inset
(blue, circular shape). (blue, circular shape).
@ -1415,11 +1429,11 @@ FP: check sign of
\begin{multline} \begin{multline}
\sigma_{l,m}^{\left(\mathrm{L},\eta\right)}\left(\vect k,\vect s\right)=-\frac{i^{l+1}}{\kappa^{2}\mathcal{A}}\pi^{3/2}2\left(\left(l-m\right)/2\right)!\left(\left(l+m\right)/2\right)!\times\\ \sigma_{l,m}^{\left(\mathrm{L},\eta\right)}\left(\vect k,\vect s\right)=-\frac{i^{l+1}}{\kappa^{2}\mathcal{A}}\pi^{3/2}2\left(\left(l-m\right)/2\right)!\left(\left(l+m\right)/2\right)!\times\\
\times\sum_{\vect K\in\Lambda^{*}}\underbrace{e^{i\vect K\cdot\vect s}}_{\text{nemá tu být \ensuremath{\vect{k\cdot s}?}}}\ush lm\left(\vect k+\vect K\right)\sum_{j=0}^{l-\left|m\right|}\left(-1\right)^{j}\left(\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)\right)^{2j+1}\Delta_{j}\left(\frac{\kappa^{2}\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)^{2}}{4\eta^{2}},-i\kappa\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)s_{\perp}\right)\times\\ \times\sum_{\vect K\in\Lambda^{*}}\underbrace{e^{i\vect K\cdot\vect s}}_{\text{nemá tu být \ensuremath{\vect{k\cdot s}?}}}\ush lm\left(\vect k+\vect K\right)\sum_{j=0}^{l-\left|m\right|}\left(-1\right)^{j}\left(\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)\right)^{2j+1}\Delta_{j}\left(\frac{\kappa^{2}\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)^{2}}{4\eta^{2}},-i\kappa\gamma\left(\left|\vect k+\vect K\right|/\kappa\right)s_{\perp}\right)\times\\
\times\sum_{\begin{array}{c} \times\sum_{\substack{s\\
s\\
j\le s\le\min\left(2j,l-\left|m\right|\right)\\ j\le s\le\min\left(2j,l-\left|m\right|\right)\\
l-n+\left|m\right|\,\mathrm{even} l-n+\left|m\right|\,\mathrm{even}
\end{array}}\frac{1}{\left(2j-s\right)!\left(s-j\right)!}\frac{\left(-\kappa s_{\perp}\right)^{2j-s}\left(\left|\vect k+\vect K\right|/\kappa\right)^{l-s}}{\left(\frac{1}{2}\left(l-m-s\right)\right)!\left(\frac{1}{2}\left(l+m-s\right)\right)!}\label{eq:Ewald in 3D long-range part 1D 2D} }
}\frac{1}{\left(2j-s\right)!\left(s-j\right)!}\frac{\left(-\kappa s_{\perp}\right)^{2j-s}\left(\left|\vect k+\vect K\right|/\kappa\right)^{l-s}}{\left(\frac{1}{2}\left(l-m-s\right)\right)!\left(\frac{1}{2}\left(l+m-s\right)\right)!}\label{eq:Ewald in 3D long-range part 1D 2D}
\end{multline} \end{multline}
\end_inset \end_inset