trunk/tengDissertation/Appendix.tex

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

The absence of modern software development practices has been a
bottleneck limiting progress in the Scientific Computing
community\cite{Wilson2006}. In the last 20 years , a large number of
few MD packages\cite{Brooks1983, Vincent1995, Kale1999} were
developed to solve common MD problems and perform robust simulations
. Most of these are commercial programs that are either poorly
written or extremely complicated to use correctly. This situation
prevents researchers from reusing or extending those packages to do
cutting-edge research effectively. In the process of studying
structural and dynamic processes in condensed phase systems like
biological membranes and nanoparticles, we developed an open source
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 C++ and Fortran90, {\sc OOPSE} uses C++ Standard
Template Library (STL) and fortran modules as a 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 and 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 provided by the third layer which
contains Input/Output, Molecular Mechanics and Structure modules.
The 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 parser for
meta-data files, which has been implemented using the 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:DynamicProps}), \texttt{Dump2XYZ} (see
Sec.~\ref{appendixSection:Dump2XYZ}), \texttt{Hydro} (see
Sec.~\ref{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 Patterns}

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. As one of the latest advanced
techniques to emerge from object-oriented community, design patterns
were applied in some of the modern scientific software applications,
such as JMol, {\sc OOPSE}\cite{Meineke2005} and
PROTOMOL\cite{Matthey2004} \textit{etc}. The following sections
enumerates some of the patterns used in {\sc OOPSE}.

\subsection{\label{appendixSection:singleton}Singletons}

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. 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}. The declaration and
implementation of IntegratorFactory class are given by declared in
List.~\ref{appendixScheme:singletonDeclaration} and
Scheme.~\ref{appendixScheme:singletonImplementation} respectively.
Since the constructor is declared as protected, a client can not
instantiate IntegratorFactory directly. Moreover, since the member
function getInstance serves as the only entry of access to
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 Methods}

The Factory Method pattern is a creational pattern and 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.
One of the most popular Factory pattern is Parameterized Factory
pattern which creates products based on their identifiers (see
Scheme.~\ref{appendixScheme:factoryDeclaration}). If the identifier
has been already registered, the factory method will invoke the
corresponding creator (see
Scheme.~\ref{appendixScheme:integratorCreator}) which utilizes the
modern C++ template technique to avoid excess subclassing.

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

The visitor pattern is designed to decouple the data structure and
algorithms used upon them by collecting related operation from
element classes into other visitor classes, which is equivalent to
adding virtual functions into a set of classes without modifying
their interfaces. Fig.~\ref{appendixFig:visitorUML} demonstrates the
structure of a Visitor pattern which is used extensively in {\tt
Dump2XYZ}. In order to convert an OOPSE dump file, a series of
distinct operations are performed on different StuntDoubles (See the
class hierarchy in Fig.~\ref{oopseFig:hierarchy} and the declaration
in Scheme.~\ref{appendixScheme:element}). Since the hierarchies
remain stable, it is easy to define a visit operation (see
Scheme.~\ref{appendixScheme:visitor}) for each class of StuntDouble.
Note that using Composite pattern\cite{Gamma1994}, CompositeVisitor
manages a priority visitor list and handles the execution of every
visitor in the priority list on different StuntDoubles.

\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}

\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}

\begin{lstlisting}[float,caption={[The implementation of Parameterized Factory pattern (I)]Source code of 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}

\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}

\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);
};

class CompositeVisitor: public BaseVisitor {
  public:
  typedef list<pair<BaseVisitor*, int> > VistorListType;
  typedef VistorListType::iterator VisitorListIterator;
  virtual void visit(Atom* atom) {
    VisitorListIterator i;
    BaseVisitor* curVisitor;
    for(i = visitorScheme.begin();i != visitorScheme.end();++i) {
      atom->accept(*i);
    }
  }

  virtual void visit(DirectionalAtom* datom) {
    VisitorListIterator i;
    BaseVisitor* curVisitor;
    for(i = visitorScheme.begin();i != visitorScheme.end();++i) {
      atom->accept(*i);
    }
  }

  virtual void visit(RigidBody* rb) {
    VisitorListIterator i;
    std::vector<Atom*> myAtoms;
    std::vector<Atom*>::iterator ai;
    myAtoms = rb->getAtoms();
    for(i = visitorScheme.begin();i != visitorScheme.end();++i) {
      rb->accept(*i);
      for(ai = myAtoms.begin(); ai != myAtoms.end(); ++ai){
        (*ai)->accept(*i);
      }
    }

  void addVisitor(BaseVisitor* v, int priority);
  protected:
    VistorListType visitorList;
};
\end{lstlisting}

\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{figure}
\centering
\includegraphics[width=\linewidth]{hierarchy.eps}
\caption[Class hierarchy for ojects in {\sc OOPSE}]{ A diagram of
the class hierarchy. Objects below others on the diagram inherit
data structures and functions from their parent classes above them.}
\label{oopseFig:hierarchy}
\end{figure}

\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 hierarchy is illustrated in
Fig.~\ref{oopseFig:hierarchy}. Every Molecule, Atom and
DirectionalAtom in {\sc OOPSE} have their own names which are
specified in the meta data 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{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}

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

{\sc OOPSE} provides a powerful selection utility to select
StuntDoubles. 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. 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}

\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}

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
Fig.~\ref{oopseFig:gofr}.

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 prevent a
situation where the program runs out of memory due to large
trajectories, \texttt{dynamicProps} will first estimate the size of
free memory, and determine the number of frames in each block, which
will allow 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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