Implement some Päivi's comments.

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Marek Nečada 2019-11-12 12:23:46 +02:00
parent 21a1313a55
commit 3b6dedf4a2
3 changed files with 77 additions and 32 deletions

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@ -597,11 +597,11 @@ Category: Methods and Algorithms for Scientific Computing?
\end_layout
\begin_layout Abstract
The (somewhat underrated) T-matrix multiple scattering method (TMMSM) can
be used to solve the electromagnetic response of systems consisting of
many compact scatterers, retaining a good level of accuracy while using
relatively few of degrees of freedom, largely surpassing other methods
in the number of scatterers it can deal with.
The T-matrix multiple scattering method (TMMSM) can be used to solve the
electromagnetic response of systems consisting of many compact scatterers,
retaining a good level of accuracy while using relatively few degrees of
freedom, largely surpassing other methods in the number of scatterers it
can deal with.
\end_layout
\begin_layout Abstract

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@ -488,7 +488,7 @@ noprefix "false"
around the origin (typically due to presence of a scatterer), one has to
add the outgoing VSWFs
\begin_inset Formula $\vswfrtlm{\tau}lm\left(\kappa\vect r\right)$
\begin_inset Formula $\vswfouttlm{\tau}lm\left(\kappa\vect r\right)$
\end_inset
to have a complete basis of the solutions in the volume
@ -608,7 +608,7 @@ transition matrix,
\begin_inset Formula $T$
\end_inset
-matrix we can solve the single-patricle scatering prroblem simply by substituti
-matrix we can solve the single-particle scattering problem simply by substituti
ng appropriate expansion coefficients
\begin_inset Formula $\rcoefftlm{\tau'}{l'}{m'}$
\end_inset
@ -680,12 +680,12 @@ literal "false"
, but in general one can find them numerically by simulating scattering
of a regular spherical wave
\begin_inset Formula $\vswfouttlm{\tau}lm$
\begin_inset Formula $\vswfrtlm{\tau}lm$
\end_inset
and projecting the scattered fields (or induced currents, depending on
the method) onto the outgoing VSWFs
\begin_inset Formula $\vswfrtlm{\tau}{'l'}{m'}$
\begin_inset Formula $\vswfouttlm{\tau'}{l'}{m'}$
\end_inset
.
@ -974,15 +974,67 @@ noprefix "false"
\begin_inset Formula $\mezikuli{R^{<}}{R^{>}}{\vect 0}$
\end_inset
via by electromagnetic radiation is
by electromagnetic radiation is
\begin_inset Formula
\begin{equation}
P=\frac{1}{2\kappa^{2}\eta_{0}\eta}\left(\Re\left(\rcoeffp{}^{\dagger}\outcoeffp{}\right)+\left\Vert \outcoeffp{}\right\Vert ^{2}\right)=\frac{1}{2\kappa^{2}\eta_{0}\eta}\rcoeffp{}^{\dagger}\left(\Tp{}^{\dagger}\Tp{}+\frac{\Tp{}^{\dagger}+\Tp{}}{2}\right)\rcoeffp{}.\label{eq:Power transport}
P=\frac{1}{2\kappa^{2}\eta_{0}\eta}\left(\Re\left(\rcoeffp{}^{\dagger}\outcoeffp{}\right)+\left\Vert \outcoeffp{}\right\Vert ^{2}\right)=\frac{1}{2\kappa^{2}\eta_{0}\eta}\rcoeffp{}^{\dagger}\left(\Tp{}^{\dagger}\Tp{}+\frac{\Tp{}^{\dagger}+\Tp{}}{2}\right)\rcoeffp{},\label{eq:Power transport}
\end{equation}
\end_inset
where
\begin_inset Formula $\eta_{0}=\sqrt{\mu_{0}/\varepsilon_{0}}$
\end_inset
and
\begin_inset Formula $\eta=\sqrt{\mu/\varepsilon}$
\end_inset
are wave impedance of vacuum and relative wave impedance of the medium
in
\begin_inset Formula $\mezikuli{R^{<}}{R^{>}}{\vect 0}$
\end_inset
, respectively.
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\shape up
\size normal
\emph off
\nospellcheck off
\bar no
\strikeout off
\xout off
\uuline off
\uwave off
\noun off
\color none
\begin_inset Formula $P$
\end_inset
is well-defined only when
\begin_inset Formula $\eta$
\end_inset
is real.
\family default
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\size default
\emph default
\nospellcheck default
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\color inherit
In realistic scattering setups, power is transferred by radiation into
\begin_inset Formula $\openball{R^{<}}{\vect 0}$
\end_inset
@ -1357,8 +1409,11 @@ In practice, the multiple-scattering problem is solved in its truncated
\begin_inset Formula $\tau lm$
\end_inset
-multiindices left.
-multi-indices left.
The truncation degree can vary for different scatterers (e.g.
\begin_inset space \space{}
\end_inset
due to different physical sizes), so the truncated block
\begin_inset Formula $\left[\tropsp pq\right]_{l_{q}\le L_{q};l_{p}\le L_{q}}$
\end_inset
@ -1394,7 +1449,7 @@ If no other type of truncation is done, there remain
\begin_inset Formula $\tau lm$
\end_inset
-multiindices for
-multi-indices for the
\begin_inset Formula $p$
\end_inset

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@ -117,7 +117,7 @@ Some refs here?
\end_inset
The most commonly used general approaches used in computational electrodynamics
The most common general approaches used in computational electrodynamics
are often unsuitable for simulating systems with larger number of scatterers
due to their computational complexity: differential methods such as the
finite difference time domain (FDTD) method or the finite element method
@ -159,8 +159,8 @@ literal "false"
\begin_layout Standard
The natural way to overcome both limitations of CDA mentioned above is to
include higher multipoles into account.
Instead of polarisability tensor, the scattering properties of an individual
take higher multipoles into account.
Instead of a polarisability tensor, the scattering properties of an individual
particle are then described with more general
\begin_inset Formula $T$
\end_inset
@ -280,20 +280,10 @@ TODO refs to the code repositories once it is published.
The features include computations of electromagnetic response to external
driving, the related cross sections, and finding resonances of finite structure
s.
Moreover, it includes the improvements covered in this paper, enabling
Moreover, it includes the improvements covered in this article, enabling
to simulate even larger systems and also infinite structures with periodicity
in one, two or three dimensions, which can be used e.g.
for quickly evaluating dispersions of such structures
\begin_inset Marginal
status open
\begin_layout Plain Layout
And also their topological invariants (TODO)?
\end_layout
\end_inset
.
in one or two or three dimensions, which can be used e.g.
for quickly evaluating dispersions of such structures.
The QPMS suite contains a core C library, Python bindings and several utilities
for routine computations.
\begin_inset Marginal