\documentclass{scrartcl}

\begin{document}
%% This is a template for a use case for ESPResSo++.
%% General hints:
%% * Try to be as specific as you can.
%% * If you do specify magnitudes without any units, reduced units are
%%   assumed.
%% * If a section/subsection/minisec does not apply to your use case,
%%   skip it and/or remove it.

% Give the use case a name.
\section{Use Case: Ion distribution around a charged rod}

\minisec{Short description}
% Please provide a short description of the simulated system and the
% purpose of the simulation.
Simulation of a charged cylinder in a salt solution to determine the
distribution of the ions around the cylinder.

\minisec{Reporter}
% Please provide your name.
Olaf Lenz

\minisec{Publications}
% If available, can you provide references to articles where the
% system is used?
\begin{itemize}
\item M.~Deserno. {\em Counterion condensation for rigid linear
    polyelectrolytes}.  PhD thesis, Universit{\"a}t Mainz, February
  2000.
\end{itemize}

\subsection*{Description of the physical system}
% In this subsection, the physical system of the use case should be
% specified.

\minisec{Statistical Ensemble}
% In what physical ensemble does the system live?  
% Examples: NVT, NVE, NpT, \mu pT
NVT

\minisec{Periodic directions}
% In which directions is the system periodic?
% Examples: all, none, x and y
all

\minisec{Unit cell geometry}
% If any of the directions is periodic, please specify the geometry
% and size of the unit cell
% Examples: cubic ($L=100$), rectangular ($L_x=L_y=100$, $L_z=50$)
cubic ($L=100$)

\minisec{Fixed objects and external fields}
% Are there any fixed objects in the system ("constraints" in
% ESPResSo)? Please specify all properties of the object (position,
% direction, charge, ...)!
% Are there any external fields actig in the system?
% Examples: cylinder in z-direction, cylindrical pore in z
% direction, electric field ($E=0.1$) in z-direction
1 charged cylinder (charge: -300), parallel to the z-axis in the
center of the unit cell in x and y, that stretches the whole box

\minisec{Number and types of particles}
% What types of particles do exist in the system?
% How many particles of each type exist?
% Example: 100 ions, 1000 dipoles, 10000 ellipsoids
400 counterions, 100 coions

\minisec{Constant properties of the particles} 
% What properties do the different types of particles have, that do
% not change during the simulation? Please specify their values, if
% possible.  
% Example: dipoles: dipole moment $\mu=1.0$
counterions: charge $q=+1$; coions: charge $q=-1$

\minisec{Variable properties of the particles}
% What properties of the different particle types are variable?
% By default, we assume that the 3D position is variable, please
% specify, if the particles are fixed in any direction.
% Example: direction of the dipole moment, particles are fixed in z

\minisec{Interactions}
% What interactions act between the different objects (particles and
% fixed objects) in the system? Please give the type and the
% parameters of the interactions!
% Please specify explicitly, if there is no interaction between some
% particle types. If the system contains bonds with a fixed length (as
% implemented by Rattle/Shake/LINC), specify them here.
\begin{itemize}
\item purely repulsive core of a LJ interaction ($\sigma=2.0$,
  $\epsilon=1.0$, $r_\mathrm{cut}=1.0$) between all particles and
  between the cylinder and the particles
\item electrostatic interactions between all particles and between
  the cylinder and the particles 
\end{itemize}

\minisec{Non-equilibrium process}
% In the case of an out-of-equilibrium simulation, please describe the
% underlying physical process, i.e. which changes are expected in the
% system.

\minisec{Other comments}
% Are there any additional comments on the physical system?

\subsection*{Description of the simulation}
% In this subsection, the simulation process should be described.
% If you do not feel it is necessary to specify some of the items,
% just skip the section. For example, the setup of some systems might
% be trivial, or the type of analysis is not important.
% Any MD, any thermostat, any barostat, MC single particle moves

\minisec{Molecular dynamics or Monte-Carlo}
% Please specify whether a molecular dynamics (MD) or a Monte-Carlo
% (MC) type of simulation is to be performed.  
% Examples: MD, MC, hybrid (MD plus MC volume moves for contant pressure)
MD

\minisec{System setup and warming up}
% Specify, how the system can can be set up (including "warming up"),
% i.e. how an initial configuration of the system can be created.
% If necessary, specify in which geometry the particles should be
% located initially.
% Example: 
\begin{itemize}
\item Randomly place the ions in the whole system.
\item Warm up by doing a simulation without electrostatic interactions
  and with capped LJ interactions.
\end{itemize}

\minisec{Required simulation algorithms}
% If any specific algorithms are required for the simulation, please
% specify them here.  
% Examples: Lattice-Boltzmann for hydrodynamic interactions

\minisec{Suggested simulation algorithms}
% If you want to suggest algorithms that can be effectively used in
% the simulation, please specify them here. These can encompass:
% thermostats, barostats, algorithms for long-ranged algorithms, etc.
\begin{itemize}
\item P3M for electrostatic interactions
\item Verlet lists for the short-ranged interactions
\end{itemize}

\minisec{Analysis}
% Describe, what analysis are to be done in the system, and, if
% possible, the expected values. If you do averages, specify exactly
% what you average over (e.g. time average, ensemble average, ...). Also,
% specify the statistical methods you use (e.g. histograms).
Compute the radial distribution function of the ion types with respect to
the cylinder:
\begin{itemize}
\item In each timestep, compute density histograms of the ion types
  over the distance to the cylinder.
\item At the end, average the histograms.
\item Compute the radial distribution function by normalising the
  histograms.
\end{itemize}

\subsection*{Further information}

\minisec{Did the use case work with the old ESPResSo program?}
% If this use case did not work with the old ESPResSo code, or only
% insatisfactorily, please specify why it did not work!
yes

\minisec{Bottlenecks and expected problems}
% If you do know of specific problems connected to this use case
% (extensive memory consumption, performance bottlenecks) or things
% that require special attention, please list them here.

\minisec{Expected hardware requirements}
% How many processors do you expect should typically suffice to
% perform a simulation?
One processor.


\clearpage


\section{Use Case: Coalescing Particles}

\minisec{Short description}
% Please provide a short description of the simulated system and the
% purpose of the simulation.
Simulation of a coalescing particles (e.g. liquid droplets [could be
diesel exhaust hydrocarbon droplets]) with the possibility of
specifying the radius of the particle arising from the collision of
two other particles.



\minisec{Reporter}
% Please provide your name.
Lorenzo Isella

\minisec{Publications}
% If available, can you provide references to articles where the
% system is used?
\begin{itemize}
\item M.C Heine \& S.E. Pratsinis. Brownian Coagulation at High
  Concentration.  \emph{Langmuir, 23}, 9882-9890, (2007).
\end{itemize}

\subsection*{Description of the physical system}
% In this subsection, the physical system of the use case should be
% specified.
The physical system in exam consists of Brownian particles whose
dynamics in investigated by solving the 3D Langevin equations.
The most fundamental process to simulate is the case of perfect
coalescence. In this case, the collision of two particles having radia
$r_1$ and $r_2$ leads to a particle with radius
$R=(r_1^3+r_2^3)^{1/3}$.
It would be very desirable to be able to generalise the previous formula to take
into account the fractal nature of the resulting particle by
introducing a fractal dimension $1\le d_f \le 3$ such that:
$R=(r_1^{d_f}+r_2^{d_f})^{1/d_f}$.
Another required feature would be, while keeping the system
temperature fluctuating around the value  $T$ fixed by Langevin
thermostat, to be able to express the friction coefficient of each
particle (here I refer to the particles  generated by the dynamics
from the coalescence of other existing particles) as a function
e.g. of the particle radius 
(as in the paper mentioned above) or the particle mass.

\minisec{Statistical Ensemble}
% In what physical ensemble does the system live?  
% Examples: NVT, NVE, NpT, \mu pT
NVT

\minisec{Periodic directions}
% In which directions is the system periodic?
% Examples: all, none, x and y
all

\minisec{Unit cell geometry}
% If any of the directions is periodic, please specify the geometry
% and size of the unit cell
% Examples: cubic ($L=100$), rectangular ($L_x=L_y=100$, $L_z=50$)
cubic ($L=100$)

\minisec{Fixed objects and external fields}
% Are there any fixed objects in the system ("constraints" in
% ESPResSo)? Please specify all properties of the object (position,
% direction, charge, ...)!
% Are there any external fields actig in the system?
% Examples: cylinder in z-direction, cylindrical pore in z
% direction, electric field ($E=0.1$) in z-direction

No fixed objects and no external fields required, though it would be
very interesting to simulate the system under shear.

\minisec{Number and types of particles}
% What types of particles do exist in the system?
% How many particles of each type exist?
% Example: 100 ions, 1000 dipoles, 10000 ellipsoids

Around $\sim 1000-5000$ particles are required for the simulations, one
particle kind is enough for most applications.


\minisec{Constant properties of the particles} 
% What properties do the different types of particles have, that do
% not change during the simulation? Please specify their values, if
% possible.  
% Example: dipoles: dipole moment $\mu=1.0$
Charge $q=+1$; mass $m=1$ (of the original particles at the beginning of
the simulation)

\minisec{Variable properties of the particles}
% What properties of the different particle types are variable?
% By default, we assume that the 3D position is variable, please
% specify, if the particles are fixed in any direction.
% Example: direction of the dipole moment, particles are fixed in z
mass (of the particles generated by the dynamics of the system). If
Espresso++ can be automatically made aware of the mass of the particle
brought about by two coalescing particles, this would allow to
perhaps tune some mass-dependent properties of the particle (for
instance 
the friction coefficient).


\minisec{Interactions}
% What interactions act between the different objects (particles and
% fixed objects) in the system? Please give the type and the
% parameters of the interactions!
% Please specify explicitly, if there is no interaction between some
% particle types. If the system contains bonds with a fixed length (as
% implemented by Rattle/Shake/LINC), specify them here.
\begin{itemize}
\item the interaction potential will be most likely a tabulated
  interaction. Being this a mesoscopic system, the interaction
  potential can be quite different from those usually used in MD. It
  will probably have a soft repulsive core and an attractive part at
  large particle separations. 
\end{itemize}

\minisec{Non-equilibrium process}
% In the case of an out-of-equilibrium simulation, please describe the
% underlying physical process, i.e. which changes are expected in the
% system.
The physical process we want to simulate is the nanoparticle coalescence.
The introduction of the fractal dimension  $d_f$ to specify the radius
of the particle resulting by two coalescing particles account for
complex phenomena of  mass rearrangement  in the resulting
particle.
While the total mass of the system is conserved, the total number of
particles (counting as one single particle the particle created by two
coalescing particles) decreases as time progresses. 



\minisec{Other comments}
% Are there any additional comments on the physical system?

\subsection*{Description of the simulation}
% In this subsection, the simulation process should be described.
% If you do not feel it is necessary to specify some of the items,
% just skip the section. For example, the setup of some systems might
% be trivial, or the type of analysis is not important.
% Any MD, any thermostat, any barostat, MC single particle moves

\minisec{Molecular dynamics or Monte-Carlo}
% Please specify whether a molecular dynamics (MD) or a Monte-Carlo
% (MC) type of simulation is to be performed.  
% Examples: MD, MC, hybrid (MD plus MC volume moves for contant pressure)
Monte Carlo

\minisec{System setup and warming up}
% Specify, how the system can can be set up (including "warming up"),
% i.e. how an initial configuration of the system can be created.
% If necessary, specify in which geometry the particles should be
% located initially.
% Example: 
\begin{itemize}
\item Randomly place the particles in the whole system.
\item Warm up by doing a simulation without with capped tabulated interactions.
\end{itemize}

\minisec{Required simulation algorithms}
% If any specific algorithms are required for the simulation, please
% specify them here.  
% Examples: Lattice-Boltzmann for hydrodynamic interaction

\minisec{Suggested simulation algorithms}
% If you want to suggest algorithms that can be effectively used in
% the simulation, please specify them here. These can encompass:
% thermostats, barostats, algorithms for long-ranged algorithms, etc.
\begin{itemize}
% \item P3M for electrostatic interactions
\item Verlet lists for the short-ranged interactions
\end{itemize}

\minisec{Analysis}
% Describe, what analysis are to be done in the system, and, if
% possible, the expected values. If you do averages, specify exactly
% what you average over (e.g. time average, ensemble average, ...). Also,
% specify the statistical methods you use (e.g. histograms).
\begin{itemize}
\item Compute the total number of particles as a function of time.
\item Compute some particle mean properties (particle mean diameter,
  mean mass, velocity etc... ) as a function of time.
% \item Compute the radial distribution function by normalising the
%   histograms.
\end{itemize}

\subsection*{Further information}

\minisec{Did the use case work with the old ESPResSo program?}
% If this use case did not work with the old ESPResSo code, or only
% insatisfactorily, please specify why it did not work!
No
\minisec{Bottlenecks and expected problems}
% If you do know of specific problems connected to this use case
% (extensive memory consumption, performance bottlenecks) or things
% that require special attention, please list them here.
The maximum allowed time step decreases dramatically with by
decreasing the range of the attractive part of the interaction potential. 
\minisec{Expected hardware requirements}
% How many processors do you expect should typically suffice to
% perform a simulation?
One processor.



\end{document}



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