# One-Bi=
llion-Particle electromagnetic Scattering Problem

Consider one billion spherical particles (radius *r*) random=
ly located in a finite, spherical medium (radius *R*) in free s=
pace in an incident electromagnetic plane wave field (wavelength =CE=BB, wa=
ve number *k*=3D2=CF=80/=CE=BB). Show the ensemble-averaged 4=C3=974=
Mueller scattering matrix interrelating the four Stokes parameters (~~I~~ =3D (*I*,*Q*,*U*,*V*=
)) of the incident field and the scattered field when the size parameter (<=
em>x=3D*k**r*) and complex refractive index (*m*)=
of the individual spherical particles are *x*=3D1.76 and *m*=
=3D1.50+*i*10^{-4} and when the volume fraction of the spher=
ical particles in the spherical medium is *v*=3D20%.

You may consider an exact or an approximate solution, or a measurement.&=
nbsp;If the one-billion-particle challenge cannot be met, compute or measur=
e the scattering matrix for a finite medium composed of the maximum nu=
mber of spherical particles accessible for your method.

## Workshop

The problem and the solution attempts will be discussed at a one-day wor=
kshop on Friday, August 19th, 2016. The workshop is organized as a part of =
the EMTS 2016 conference and its Multiple Scattering session. The worksh=
op is open and free of charge. If interested to join, please e-mail tentati=
ve registration to Dr. Antti Penttil=C3=A4. The workshop =
will be held at the University of Helsinki and organized by the ERC SAEMPL project.

## Program

Kumpula Campus, Physicum lobby

Kumpula Campus, Physicum, room E207

- 10:00
*Antti Penttil=C3=A4*, Opening
- 10:05
*Daniel Mackowski*, Multi-sphere *T*-matr=
ix method and its capabilities
- 10:20
*Johannes Markkanen*, FMM-accelerated *T*=
-matrix implementation
- 10:35
*Dimitrios Tzarouchis*, TBA=
- 10:50
*Xavier Faget*, TBA
- 11:05
*Jukka R=C3=A4bin=C3=A4*, Exa=
ct solution with the Discrete Exterior Calculus for a limited problem
- 11:20
* Maxim Yurkin*, Exact solutio=
n, capabilities of discrete-dipole approximation code ADDA

- 11:35
*Karri Muinonen*, Radiative-transfer solution with in=
coherent scattering
- 11.50
*Antti Penttil=C3=A4*, Exact solutions for reduced pr=
oblems vs. approximate radiative-transfer solutions=

12.15-13.30, lunch, Kumpula Campus, Dynamicum

- 13:30 Open discussion
- future prospects
- joint article for Radio Science

End by 15:00

## Venue

The Helsinki University Faculty of Science is lo=
cated at the Kumpula Campus. It can be reach=
ed by several bus lines from the Helsinki or Pasila railway stations, by tr=
am lines 6 and 8, or by bus number 506 from Otaniemi. Please see the Journey Planner =
for details, the street address for the campus is "Gustaf H=C3=A4llstr=C3=
=B6min katu 2a"**.**

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