trunk/tengDissertation/Appendix.tex

\appendix
\chapter{\label{chapt:oopse}Object-Oriented Parallel Simulation Engine}

Designing object-oriented software is hard, and designing reusable
object-oriented scientific software is even harder. Absence of
applying modern software development practices is the bottleneck of
Scientific Computing community\cite{Wilson2006}. For instance, in
the last 20 years , there are quite a few MD packages that were
developed to solve common MD problems and perform robust simulations
. However, many of the codes are legacy programs that are either
poorly organized or extremely complex. Usually, these packages were
contributed by scientists without official computer science
training. The development of most MD applications are lack of strong
coordination to enforce design and programming guidelines. Moreover,
most MD programs also suffer from missing design and implement
documents which is crucial to the maintenance and extensibility.
Along the way of studying structural and dynamic processes in
condensed phase systems like biological membranes and nanoparticles,
we developed and maintained an Object-Oriented Parallel Simulation
Engine ({\sc OOPSE}). This new molecular dynamics package has some
unique features
\begin{enumerate}
  \item {\sc OOPSE} performs Molecular Dynamics (MD) simulations on non-standard
atom types (transition metals, point dipoles, sticky potentials,
Gay-Berne ellipsoids, or other "lumpy"atoms with orientational
degrees of freedom), as well as rigid bodies.
  \item {\sc OOPSE} uses a force-based decomposition algorithm using MPI on cheap
Beowulf clusters to obtain very efficient parallelism.
  \item {\sc OOPSE} integrates the equations of motion using advanced methods for
orientational dynamics in NVE, NVT, NPT, NPAT, and NP$\gamma$T
ensembles.
  \item {\sc OOPSE} can carry out simulations on metallic systems using the
Embedded Atom Method (EAM) as well as the Sutton-Chen potential.
  \item {\sc OOPSE} can perform simulations on Gay-Berne liquid crystals.
  \item  {\sc OOPSE} can simulate systems containing the extremely efficient
extended-Soft Sticky Dipole (SSD/E) model for water.
\end{enumerate}

\section{\label{appendixSection:architecture }Architecture}

Mainly written by \texttt{C/C++} and \texttt{Fortran90}, {\sc OOPSE}
uses C++ Standard Template Library (STL) and fortran modules as the
foundation. As an extensive set of the STL and Fortran90 modules,
{\sc Base Classes} provide generic implementations of mathematical
objects (e.g., matrices, vectors, polynomials, random number
generators) and advanced data structures and algorithms(e.g., tuple,
bitset, generic data, string manipulation). The molecular data
structures for the representation of atoms, bonds, bends, torsions,
rigid bodies and molecules \textit{etc} are contained in the {\sc
Kernel} which is implemented with {\sc Base Classes} and are
carefully designed to provide maximum extensibility and flexibility.
The functionality required for applications is provide by the third
layer which contains Input/Output, Molecular Mechanics and Structure
modules. Input/Output module not only implements general methods for
file handling, but also defines a generic force field interface.
Another important component of Input/Output module is the meta-data
file parser, which is rewritten using ANother Tool for Language
Recognition(ANTLR)\cite{Parr1995, Schaps1999} syntax. The Molecular
Mechanics module consists of energy minimization and a wide
varieties of integration methods(see Chap.~\ref{chapt:methodology}).
The structure module contains a flexible and powerful selection
library which syntax is elaborated in
Sec.~\ref{appendixSection:syntax}. The top layer is made of the main
program of the package, \texttt{oopse} and it corresponding parallel
version \texttt{oopse\_MPI}, as well as other useful utilities, such
as \texttt{StatProps} (see Sec.~\ref{appendixSection:StaticProps}),
\texttt{DynamicProps} (see
Sec.~\ref{appendixSection:appendixSection:DynamicProps}),
\texttt{Dump2XYZ} (see
Sec.~\ref{appendixSection:appendixSection:Dump2XYZ}), \texttt{Hydro}
(see Sec.~\ref{appendixSection:appendixSection:hydrodynamics})
\textit{etc}.

\begin{figure}
\centering
\includegraphics[width=\linewidth]{architecture.eps}
\caption[The architecture of {\sc OOPSE}] {Overview of the structure
of {\sc OOPSE}} \label{appendixFig:architecture}
\end{figure}

\section{\label{appendixSection:desginPattern}Design Pattern}

Design patterns are optimal solutions to commonly-occurring problems
in software design. Although originated as an architectural concept
for buildings and towns by Christopher Alexander
\cite{Alexander1987}, software patterns first became popular with
the wide acceptance of the book, Design Patterns: Elements of
Reusable Object-Oriented Software \cite{Gamma1994}. Patterns reflect
the experience, knowledge and insights of developers who have
successfully used these patterns in their own work. Patterns are
reusable. They provide a ready-made solution that can be adapted to
different problems as necessary. Pattern are expressive. they
provide a common vocabulary of solutions that can express large
solutions succinctly.

Patterns are usually described using a format that includes the
following information:
\begin{enumerate}
  \item The \emph{name} that is commonly used for the pattern. Good pattern names form a vocabulary for
  discussing conceptual abstractions. a pattern may have more than one commonly used or recognizable name
  in the literature. In this case it is common practice to document these nicknames or synonyms under
  the heading of \emph{Aliases} or \emph{Also Known As}.
  \item The \emph{motivation} or \emph{context} that this pattern applies
  to. Sometimes, it will include some prerequisites that should be satisfied before deciding to use a pattern
  \item The \emph{solution} to the problem that the pattern
  addresses. It describes how to construct the necessary work products. The description may include
  pictures, diagrams and prose which identify the pattern's structure, its participants, and their
  collaborations, to show how the problem is solved.
  \item The \emph{consequences} of using the given solution to solve a
  problem, both positive and negative.
\end{enumerate}

As one of the latest advanced techniques emerged from
object-oriented community, design patterns were applied in some of
the modern scientific software applications, such as JMol, {\sc
OOPSE}\cite{Meineke05} and PROTOMOL\cite{Matthey05} \textit{etc}.
The following sections enumerates some of the patterns used in {\sc
OOPSE}.

\subsection{\label{appendixSection:singleton}Singleton}
The Singleton pattern not only provides a mechanism to restrict
instantiation of a class to one object, but also provides a global
point of access to the object. Currently implemented as a global
variable, the logging utility which reports error and warning
messages to the console in {\sc OOPSE} is a good candidate for
applying the Singleton pattern to avoid the global namespace
pollution.Although the singleton pattern can be implemented in
various ways  to account for different aspects of the software
designs, such as lifespan control \textit{etc}, we only use the
static data approach in {\sc OOPSE}. {\tt IntegratorFactory} class
is declared as
\begin{lstlisting}[float,caption={[A classic Singleton design pattern implementation(I)] The declaration of of simple Singleton pattern.},label={appendixScheme:singletonDeclaration}]

class IntegratorFactory {
public:
  static IntegratorFactory*
  getInstance();
protected:
  IntegratorFactory();
private:
  static IntegratorFactory* instance_;
};

\end{lstlisting}
The corresponding implementation is
\begin{lstlisting}[float,caption={[A classic implementation of Singleton design pattern (II)] The implementation of simple Singleton pattern.},label={appendixScheme:singletonImplementation}]

IntegratorFactory::instance_ = NULL;

IntegratorFactory* getInstance() {
  if (instance_ == NULL){
    instance_ = new IntegratorFactory;
  }
  return instance_;
}

\end{lstlisting}
Since constructor is declared as {\tt protected}, a client can not
instantiate {\tt IntegratorFactory} directly. Moreover, since the
member function {\tt getInstance} serves as the only entry of access
to {\tt IntegratorFactory}, this approach fulfills the basic
requirement, a single instance. Another consequence of this approach
is the automatic destruction since static data are destroyed upon
program termination.

\subsection{\label{appendixSection:factoryMethod}Factory Method}

Categoried as a creational pattern, the Factory Method pattern deals
with the problem of creating objects without specifying the exact
class of object that will be created. Factory Method is typically
implemented by delegating the creation operation to the subclasses.
{\tt Integrator} class Parameterized Factory pattern where factory
method ({\tt createIntegrator} member function) creates products
based on the identifier (see
List.~\ref{appendixScheme:factoryDeclaration}). If the identifier
has been already registered, the factory method will invoke the
corresponding creator (see List.~\ref{integratorCreator}) which
utilizes the modern C++ template technique to avoid subclassing.
\begin{lstlisting}[float,caption={[The implementation of Parameterized Factory pattern (I)]Source code of {\tt IntegratorFactory} class.},label={appendixScheme:factoryDeclaration}]

class IntegratorFactory {
public:
  typedef std::map<string, IntegratorCreator*> CreatorMapType;

  bool registerIntegrator(IntegratorCreator* creator) {
    return creatorMap_.insert(creator->getIdent(), creator).second;
  }

  Integrator* createIntegrator(const string& id, SimInfo* info) {
    Integrator* result = NULL;
    CreatorMapType::iterator i = creatorMap_.find(id);
    if (i != creatorMap_.end()) {
      result = (i->second)->create(info);
    }
    return result;
  }

private:
  CreatorMapType creatorMap_;
};
\end{lstlisting}
\begin{lstlisting}[float,caption={[The implementation of Parameterized Factory pattern (III)]Source code of creator classes.},label={appendixScheme:integratorCreator}]

class IntegratorCreator {
public:
    IntegratorCreator(const string& ident) : ident_(ident) {}

    const string& getIdent() const { return ident_; }

    virtual Integrator* create(SimInfo* info) const = 0;

private:
    string ident_;
};

template<class ConcreteIntegrator>
class IntegratorBuilder : public IntegratorCreator {
public:
  IntegratorBuilder(const string& ident)
                   : IntegratorCreator(ident) {}
  virtual  Integrator* create(SimInfo* info) const {
    return new ConcreteIntegrator(info);
  }
};
\end{lstlisting}

\subsection{\label{appendixSection:visitorPattern}Visitor}

The purpose of the Visitor Pattern is to encapsulate an operation
that you want to perform on the elements. The operation being
performed on a structure can be switched without changing the
interfaces of the elements. In other words, one can add virtual
functions into a set of classes without modifying their interfaces.
Fig.~\ref{appendixFig:visitorUML} demonstrates the structure of
Visitor pattern which is used extensively in {\tt Dump2XYZ}. In
order to convert an OOPSE dump file, a series of distinct and
unrelated operations are performed on different StuntDoubles.
Visitor allows one to keep related operations together by packing
them into one class. {\tt BaseAtomVisitor} is a typical example of
visitor in {\tt Dump2XYZ} program{see
List.~\ref{appendixScheme:visitor}}. In contrast to the operations,
the object structure or element classes rarely change(See
Fig.~\ref{oopseFig:heirarchy} and
List.~\ref{appendixScheme:element}).


\begin{figure}
\centering
\includegraphics[width=\linewidth]{visitor.eps}
\caption[The UML class diagram of Visitor patten] {The UML class
diagram of Visitor patten.} \label{appendixFig:visitorUML}
\end{figure}

\begin{lstlisting}[float,caption={[The implementation of Visitor pattern (I)]Source code of the visitor classes.},label={appendixScheme:visitor}]

class BaseVisitor{
public:
  virtual void visit(Atom* atom);
  virtual void visit(DirectionalAtom* datom);
  virtual void visit(RigidBody* rb);
};

class BaseAtomVisitor:public BaseVisitor{ public:
  virtual void visit(Atom* atom);
  virtual void visit(DirectionalAtom* datom);
  virtual void visit(RigidBody* rb);
};

\end{lstlisting}

\begin{lstlisting}[float,caption={[The implementation of Visitor pattern (II)]Source code of the element classes.},label={appendixScheme:element}]

class StuntDouble {
public:
  virtual void accept(BaseVisitor* v) = 0;
};

class Atom: public StuntDouble {
public:
  virtual void accept{BaseVisitor* v*} {
    v->visit(this);
  }
};

class DirectionalAtom: public Atom {
public:
  virtual void accept{BaseVisitor* v*} {
    v->visit(this);
  }
};

class RigidBody: public StuntDouble {
public:
  virtual void accept{BaseVisitor* v*} {
    v->visit(this);
  }
};

\end{lstlisting}

\section{\label{appendixSection:concepts}Concepts}

OOPSE manipulates both traditional atoms as well as some objects
that {\it behave like atoms}.  These objects can be rigid
collections of atoms or atoms which have orientational degrees of
freedom.  A diagram of the class heirarchy is illustrated in
Fig.~\ref{oopseFig:heirarchy}. Every Molecule, Atom and
DirectionalAtom in {\sc OOPSE} have their own names which are
specified in the {\tt .md} file. In contrast, RigidBodies are
denoted by their membership and index inside a particular molecule:
[MoleculeName]\_RB\_[index] (the contents inside the brackets depend
on the specifics of the simulation). The names of rigid bodies are
generated automatically. For example, the name of the first rigid
body in a DMPC molecule is DMPC\_RB\_0.
%\begin{figure}
%\centering
%\includegraphics[width=\linewidth]{heirarchy.eps}
%\caption[Class heirarchy for ojects in {\sc OOPSE}]{ A diagram of
%the class heirarchy.
%\begin{itemize}
%\item A {\bf StuntDouble} is {\it any} object that can be manipulated by the
%integrators and minimizers.
%\item An {\bf Atom} is a fundamental point-particle that can be moved around during a simulation.
%\item A {\bf DirectionalAtom} is an atom which has {\it orientational} as well as translational degrees of freedom.
%\item A {\bf RigidBody} is a collection of {\bf Atom}s or {\bf
%DirectionalAtom}s which behaves as a single unit.
%\end{itemize}
%} \label{oopseFig:heirarchy}
%\end{figure}

\section{\label{appendixSection:syntax}Syntax of the Select Command}

The most general form of the select command is: {\tt select {\it
expression}}. This expression represents an arbitrary set of
StuntDoubles (Atoms or RigidBodies) in {\sc OOPSE}. Expressions are
composed of either name expressions, index expressions, predefined
sets, user-defined expressions, comparison operators, within
expressions, or logical combinations of the above expression types.
Expressions can be combined using parentheses and the Boolean
operators.

\subsection{\label{appendixSection:logical}Logical expressions}

The logical operators allow complex queries to be constructed out of
simpler ones using the standard boolean connectives {\bf and}, {\bf
or}, {\bf not}. Parentheses can be used to alter the precedence of
the operators.

\begin{center}
\begin{tabular}{|ll|}
\hline
{\bf logical operator} & {\bf equivalent operator}  \\
\hline
and & ``\&'', ``\&\&'' \\
or & ``$|$'', ``$||$'', ``,'' \\
not & ``!''  \\
\hline
\end{tabular}
\end{center}

\subsection{\label{appendixSection:name}Name expressions}

\begin{center}
\begin{tabular}{|llp{2in}|}
\hline {\bf type of expression} & {\bf examples} & {\bf translation
of
examples} \\
\hline expression without ``.'' & select DMPC & select all
StuntDoubles
belonging to all DMPC molecules \\
 & select C* & select all atoms which have atom types beginning with C
\\
 & select DMPC\_RB\_* & select all RigidBodies in DMPC molecules (but
only select the rigid bodies, and not the atoms belonging to them). \\
\hline expression has one ``.'' & select TIP3P.O\_TIP3P & select the
O\_TIP3P
atoms belonging to TIP3P molecules \\
 & select DMPC\_RB\_O.PO4 & select the PO4 atoms belonging to
the first
RigidBody in each DMPC molecule \\
 & select DMPC.20 & select the twentieth StuntDouble in each DMPC
molecule \\
\hline expression has two ``.''s & select DMPC.DMPC\_RB\_?.* &
select all atoms
belonging to all rigid bodies within all DMPC molecules \\
\hline
\end{tabular}
\end{center}

\subsection{\label{appendixSection:index}Index expressions}

\begin{center}
\begin{tabular}{|lp{4in}|}
\hline
{\bf examples} & {\bf translation of examples} \\
\hline
select 20 & select all of the StuntDoubles belonging to Molecule 20 \\
select 20 to 30 & select all of the StuntDoubles belonging to
molecules which have global indices between 20 (inclusive) and 30
(exclusive) \\
\hline
\end{tabular}
\end{center}

\subsection{\label{appendixSection:predefined}Predefined sets}

\begin{center}
\begin{tabular}{|ll|}
\hline
{\bf keyword} & {\bf description} \\
\hline
all & select all StuntDoubles \\
none & select none of the StuntDoubles \\
\hline
\end{tabular}
\end{center}

\subsection{\label{appendixSection:userdefined}User-defined expressions}

Users can define arbitrary terms to represent groups of
StuntDoubles, and then use the define terms in select commands. The
general form for the define command is: {\bf define {\it term
expression}}. Once defined, the user can specify such terms in
boolean expressions

{\tt define SSDWATER SSD or SSD1 or SSDRF}

{\tt select SSDWATER}

\subsection{\label{appendixSection:comparison}Comparison expressions}

StuntDoubles can be selected by using comparision operators on their
properties. The general form for the comparison command is: a
property name, followed by a comparision operator and then a number.

\begin{center}
\begin{tabular}{|l|l|}
\hline
{\bf property} & mass, charge \\
{\bf comparison operator} & ``$>$'', ``$<$'', ``$=$'', ``$>=$'',
``$<=$'', ``$!=$'' \\
\hline
\end{tabular}
\end{center}

For example, the phrase {\tt select mass > 16.0 and charge < -2}
would select StuntDoubles which have mass greater than 16.0 and
charges less than -2.

\subsection{\label{appendixSection:within}Within expressions}

The ``within'' keyword allows the user to select all StuntDoubles
within the specified distance (in Angstroms) from a selection,
including the selected atom itself. The general form for within
selection is: {\tt select within(distance, expression)}

For example, the phrase {\tt select within(2.5, PO4 or NC4)} would
select all StuntDoubles which are within 2.5 angstroms of PO4 or NC4
atoms.


\section{\label{appendixSection:analysisFramework}Analysis Framework}

\subsection{\label{appendixSection:StaticProps}StaticProps}

{\tt StaticProps} can compute properties which are averaged over
some or all of the configurations that are contained within a dump
file. The most common example of a static property that can be
computed is the pair distribution function between atoms of type $A$
and other atoms of type $B$, $g_{AB}(r)$.  {\tt StaticProps} can
also be used to compute the density distributions of other molecules
in a reference frame {\it fixed to the body-fixed reference frame}
of a selected atom or rigid body.

There are five seperate radial distribution functions availiable in
OOPSE. Since every radial distrbution function invlove the
calculation between pairs of bodies, {\tt -{}-sele1} and {\tt
-{}-sele2} must be specified to tell StaticProps which bodies to
include in the calculation.

\begin{description}
\item[{\tt -{}-gofr}] Computes the pair distribution function,
\begin{equation*}
g_{AB}(r) = \frac{1}{\rho_B}\frac{1}{N_A} \langle \sum_{i \in A}
\sum_{j \in B} \delta(r - r_{ij}) \rangle
\end{equation*}
\item[{\tt -{}-r\_theta}] Computes the angle-dependent pair distribution
function. The angle is defined by the intermolecular vector
$\vec{r}$ and $z$-axis of DirectionalAtom A,
\begin{equation*}
g_{AB}(r, \cos \theta) = \frac{1}{\rho_B}\frac{1}{N_A} \langle
\sum_{i \in A} \sum_{j \in B} \delta(r - r_{ij}) \delta(\cos
\theta_{ij} - \cos \theta)\rangle
\end{equation*}
\item[{\tt -{}-r\_omega}] Computes the angle-dependent pair distribution
function. The angle is defined by the $z$-axes of the two
DirectionalAtoms A and B.
\begin{equation*}
g_{AB}(r, \cos \omega) = \frac{1}{\rho_B}\frac{1}{N_A} \langle
\sum_{i \in A} \sum_{j \in B} \delta(r - r_{ij}) \delta(\cos
\omega_{ij} - \cos \omega)\rangle
\end{equation*}
\item[{\tt -{}-theta\_omega}] Computes the pair distribution in the angular
space $\theta, \omega$ defined by the two angles mentioned above.
\begin{equation*}
g_{AB}(\cos\theta, \cos \omega) = \frac{1}{\rho_B}\frac{1}{N_A}
\langle \sum_{i \in A} \sum_{j \in B} \langle \delta(\cos
\theta_{ij} - \cos \theta) \delta(\cos \omega_{ij} - \cos
\omega)\rangle
\end{equation*}
\item[{\tt -{}-gxyz}] Calculates the density distribution of particles of type
B in the body frame of particle A. Therefore, {\tt -{}-originsele}
and {\tt -{}-refsele} must be given to define A's internal
coordinate set as the reference frame for the calculation.
\end{description}

The vectors (and angles) associated with these angular pair
distribution functions are most easily seen in the figure below:

\begin{figure}
\centering
\includegraphics[width=3in]{definition.eps}
\caption[Definitions of the angles between directional objects]{ \\
Any two directional objects (DirectionalAtoms and RigidBodies) have
a set of two angles ($\theta$, and $\omega$) between the z-axes of
their body-fixed frames.} \label{oopseFig:gofr}
\end{figure}

Due to the fact that the selected StuntDoubles from two selections
may be overlapped, {\tt StaticProps} performs the calculation in
three stages which are illustrated in
Fig.~\ref{oopseFig:staticPropsProcess}.

\begin{figure}
\centering
\includegraphics[width=\linewidth]{staticPropsProcess.eps}
\caption[A representation of the three-stage correlations in
\texttt{StaticProps}]{This diagram illustrates three-stage
processing used by \texttt{StaticProps}. $S_1$ and $S_2$ are the
numbers of selected stuntdobules from {\tt -{}-sele1} and {\tt
-{}-sele2} respectively, while $C$ is the number of stuntdobules
appearing at both sets. The first stage($S_1-C$ and $S_2$) and
second stages ($S_1$ and $S_2-C$) are completely non-overlapping. On
the contrary, the third stage($C$ and $C$) are completely
overlapping} \label{oopseFig:staticPropsProcess}
\end{figure}

The options available for {\tt StaticProps} are as follows:
\begin{longtable}[c]{|EFG|}
\caption{StaticProps Command-line Options}
\\ \hline
{\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline
\endhead
\hline
\endfoot
  -h& {\tt -{}-help}                    &  Print help and exit \\
  -V& {\tt -{}-version}                 &  Print version and exit \\
  -i& {\tt -{}-input}          &  input dump file \\
  -o& {\tt -{}-output}         &  output file name \\
  -n& {\tt -{}-step}                &  process every n frame  (default=`1') \\
  -r& {\tt -{}-nrbins}              &  number of bins for distance  (default=`100') \\
  -a& {\tt -{}-nanglebins}          &  number of bins for cos(angle)  (default= `50') \\
  -l& {\tt -{}-length}           &  maximum length (Defaults to 1/2 smallest length of first frame) \\
    & {\tt -{}-sele1}   & select the first StuntDouble set \\
    & {\tt -{}-sele2}   & select the second StuntDouble set \\
    & {\tt -{}-sele3}   & select the third StuntDouble set \\
    & {\tt -{}-refsele} & select reference (can only be used with {\tt -{}-gxyz}) \\
    & {\tt -{}-molname}           & molecule name \\
    & {\tt -{}-begin}                & begin internal index \\
    & {\tt -{}-end}                  & end internal index \\
\hline
\multicolumn{3}{|l|}{One option from the following group of options is required:} \\
\hline
    &  {\tt -{}-gofr}                    &  $g(r)$ \\
    &  {\tt -{}-r\_theta}                 &  $g(r, \cos(\theta))$ \\
    &  {\tt -{}-r\_omega}                 &  $g(r, \cos(\omega))$ \\
    &  {\tt -{}-theta\_omega}             &  $g(\cos(\theta), \cos(\omega))$ \\
    &  {\tt -{}-gxyz}                    &  $g(x, y, z)$ \\
    &  {\tt -{}-p2}                      &  $P_2$ order parameter ({\tt -{}-sele1} and {\tt -{}-sele2} must be specified) \\
    &  {\tt -{}-scd}                     &  $S_{CD}$ order parameter(either {\tt -{}-sele1}, {\tt -{}-sele2}, {\tt -{}-sele3} are specified or {\tt -{}-molname}, {\tt -{}-begin}, {\tt -{}-end} are specified) \\
    &  {\tt -{}-density}                 &  density plot ({\tt -{}-sele1} must be specified) \\
    &  {\tt -{}-slab\_density}           &  slab density ({\tt -{}-sele1} must be specified)
\end{longtable}

\subsection{\label{appendixSection:DynamicProps}DynamicProps}

{\tt DynamicProps} computes time correlation functions from the
configurations stored in a dump file.  Typical examples of time
correlation functions are the mean square displacement and the
velocity autocorrelation functions.   Once again, the selection
syntax can be used to specify the StuntDoubles that will be used for
the calculation.  A general time correlation function can be thought
of as:
\begin{equation}
C_{AB}(t) = \langle \vec{u}_A(t) \cdot \vec{v}_B(0) \rangle
\end{equation}
where $\vec{u}_A(t)$ is a vector property associated with an atom of
type $A$ at time $t$, and $\vec{v}_B(t^{\prime})$ is a different
vector property associated with an atom of type $B$ at a different
time $t^{\prime}$.  In most autocorrelation functions, the vector
properties ($\vec{v}$ and $\vec{u}$) and the types of atoms ($A$ and
$B$) are identical, and the three calculations built in to {\tt
DynamicProps} make these assumptions.  It is possible, however, to
make simple modifications to the {\tt DynamicProps} code to allow
the use of {\it cross} time correlation functions (i.e. with
different vectors).  The ability to use two selection scripts to
select different types of atoms is already present in the code.

For large simulations, the trajectory files can sometimes reach
sizes in excess of several gigabytes. In order to effectively
analyze that amount of data. In order to prevent a situation where
the program runs out of memory due to large trajectories,
\texttt{dynamicProps} will estimate the size of free memory at
first, and determine the number of frames in each block, which
allows the operating system to load two blocks of data
simultaneously without swapping. Upon reading two blocks of the
trajectory, \texttt{dynamicProps} will calculate the time
correlation within the first block and the cross correlations
between the two blocks. This second block is then freed and then
incremented and the process repeated until the end of the
trajectory. Once the end is reached, the first block is freed then
incremented, until all frame pairs have been correlated in time.
This process is illustrated in
Fig.~\ref{oopseFig:dynamicPropsProcess}.

\begin{figure}
\centering
\includegraphics[width=\linewidth]{dynamicPropsProcess.eps}
\caption[A representation of the block correlations in
\texttt{dynamicProps}]{This diagram illustrates block correlations
processing in \texttt{dynamicProps}. The shaded region represents
the self correlation of the block, and the open blocks are read one
at a time and the cross correlations between blocks are calculated.}
\label{oopseFig:dynamicPropsProcess}
\end{figure}

The options available for DynamicProps are as follows:
\begin{longtable}[c]{|EFG|}
\caption{DynamicProps Command-line Options}
\\ \hline
{\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline
\endhead
\hline
\endfoot
  -h& {\tt -{}-help}                   & Print help and exit \\
  -V& {\tt -{}-version}                & Print version and exit \\
  -i& {\tt -{}-input}         & input dump file \\
  -o& {\tt -{}-output}        & output file name \\
    & {\tt -{}-sele1} & select first StuntDouble set \\
    & {\tt -{}-sele2} & select second StuntDouble set (if sele2 is not set, use script from sele1) \\
\hline
\multicolumn{3}{|l|}{One option from the following group of options is required:} \\
\hline
  -r& {\tt -{}-rcorr}                  & compute mean square displacement \\
  -v& {\tt -{}-vcorr}                  & compute velocity correlation function \\
  -d& {\tt -{}-dcorr}                  & compute dipole correlation function
\end{longtable}

\section{\label{appendixSection:tools}Other Useful Utilities}

\subsection{\label{appendixSection:Dump2XYZ}Dump2XYZ}

{\tt Dump2XYZ} can transform an OOPSE dump file into a xyz file
which can be opened by other molecular dynamics viewers such as Jmol
and VMD\cite{Humphrey1996}. The options available for Dump2XYZ are
as follows:


\begin{longtable}[c]{|EFG|}
\caption{Dump2XYZ Command-line Options}
\\ \hline
{\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline
\endhead
\hline
\endfoot
  -h & {\tt -{}-help} &                        Print help and exit \\
  -V & {\tt -{}-version} &                     Print version and exit \\
  -i & {\tt -{}-input}  &             input dump file \\
  -o & {\tt -{}-output} &             output file name \\
  -n & {\tt -{}-frame}   &                 print every n frame  (default=`1') \\
  -w & {\tt -{}-water}       &                 skip the the waters  (default=off) \\
  -m & {\tt -{}-periodicBox} &                 map to the periodic box  (default=off)\\
  -z & {\tt -{}-zconstraint}  &                replace the atom types of zconstraint molecules  (default=off) \\
  -r & {\tt -{}-rigidbody}  &                  add a pseudo COM atom to rigidbody  (default=off) \\
  -t & {\tt -{}-watertype} &                   replace the atom type of water model (default=on) \\
  -b & {\tt -{}-basetype}  &                   using base atom type  (default=off) \\
     & {\tt -{}-repeatX}  &                 The number of images to repeat in the x direction  (default=`0') \\
     & {\tt -{}-repeatY} &                 The number of images to repeat in the y direction  (default=`0') \\
     &  {\tt -{}-repeatZ}  &                The number of images to repeat in the z direction  (default=`0') \\
  -s & {\tt -{}-selection} & By specifying {\tt -{}-selection}=``selection command'' with Dump2XYZ, the user can select an arbitrary set of StuntDoubles to be
converted. \\
     & {\tt -{}-originsele} & By specifying {\tt -{}-originsele}=``selection command'' with Dump2XYZ, the user can re-center the origin of the system around a specific StuntDouble \\
     & {\tt -{}-refsele} &  In order to rotate the system, {\tt -{}-originsele} and {\tt -{}-refsele} must be given to define the new coordinate set. A StuntDouble which contains a dipole (the direction of the dipole is always (0, 0, 1) in body frame) is specified by {\tt -{}-originsele}. The new x-z plane is defined by the direction of the dipole and the StuntDouble is specified by {\tt -{}-refsele}.
\end{longtable}

\subsection{\label{appendixSection:hydrodynamics}Hydro}

{\tt Hydro} can calculate resistance and diffusion tensors at the
center of resistance. Both tensors at the center of diffusion can
also be reported from the program, as well as the coordinates for
the beads which are used to approximate the arbitrary shapes. The
options available for Hydro are as follows:
\begin{longtable}[c]{|EFG|}
\caption{Hydrodynamics Command-line Options}
\\ \hline
{\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline
\endhead
\hline
\endfoot
  -h & {\tt -{}-help} &                        Print help and exit \\
  -V & {\tt -{}-version} &                     Print version and exit \\
  -i & {\tt -{}-input}  &             input dump file \\
  -o & {\tt -{}-output} &             output file prefix  (default=`hydro') \\
  -b & {\tt -{}-beads}  &                   generate the beads only, hydrodynamics calculation will not be performed (default=off)\\
     & {\tt -{}-model}  &                 hydrodynamics model (supports ``AnalyticalModel'', ``RoughShell'' and ``BeadModel'') \\
\end{longtable}
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