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1   \appendix
2   \chapter{\label{chapt:oopse}Object-Oriented Parallel Simulation Engine}
3  
4 < Designing object-oriented software is hard, and designing reusable
5 < object-oriented scientific software is even harder. Absence of
6 < applying modern software development practices is the bottleneck of
7 < Scientific Computing community\cite{Wilson2006}. For instance, in
8 < the last 20 years , there are quite a few MD packages that were
4 > The absence of modern software development practices has been a
5 > bottleneck limiting progress in the Scientific Computing
6 > community\cite{Wilson2006}. In the last 20 years , a large number of
7 > few MD packages\cite{Brooks1983, Vincent1995, Kale1999} were
8   developed to solve common MD problems and perform robust simulations
9 < . However, many of the codes are legacy programs that are either
10 < poorly organized or extremely complex. Usually, these packages were
11 < contributed by scientists without official computer science
12 < training. The development of most MD applications are lack of strong
13 < coordination to enforce design and programming guidelines. Moreover,
14 < most MD programs also suffer from missing design and implement
15 < documents which is crucial to the maintenance and extensibility.
16 < Along the way of studying structural and dynamic processes in
18 < condensed phase systems like biological membranes and nanoparticles,
19 < we developed and maintained an Object-Oriented Parallel Simulation
20 < Engine ({\sc OOPSE}). This new molecular dynamics package has some
21 < unique features
9 > . Most of these are commercial programs that are either poorly
10 > written or extremely complicated to use correctly. This situation
11 > prevents researchers from reusing or extending those packages to do
12 > cutting-edge research effectively. In the process of studying
13 > structural and dynamic processes in condensed phase systems like
14 > biological membranes and nanoparticles, we developed an open source
15 > Object-Oriented Parallel Simulation Engine ({\sc OOPSE}). This new
16 > molecular dynamics package has some unique features
17   \begin{enumerate}
18    \item {\sc OOPSE} performs Molecular Dynamics (MD) simulations on non-standard
19   atom types (transition metals, point dipoles, sticky potentials,
# Line 38 | Line 33 | Mainly written by \texttt{C/C++} and \texttt{Fortran90
33  
34   \section{\label{appendixSection:architecture }Architecture}
35  
36 < Mainly written by \texttt{C/C++} and \texttt{Fortran90}, {\sc OOPSE}
37 < uses C++ Standard Template Library (STL) and fortran modules as the
38 < foundation. As an extensive set of the STL and Fortran90 modules,
39 < {\sc Base Classes} provide generic implementations of mathematical
40 < objects (e.g., matrices, vectors, polynomials, random number
41 < generators) and advanced data structures and algorithms(e.g., tuple,
42 < bitset, generic data, string manipulation). The molecular data
43 < structures for the representation of atoms, bonds, bends, torsions,
44 < rigid bodies and molecules \textit{etc} are contained in the {\sc
45 < Kernel} which is implemented with {\sc Base Classes} and are
46 < carefully designed to provide maximum extensibility and flexibility.
47 < The functionality required for applications is provide by the third
48 < layer which contains Input/Output, Molecular Mechanics and Structure
49 < modules. Input/Output module not only implements general methods for
50 < file handling, but also defines a generic force field interface.
51 < Another important component of Input/Output module is the meta-data
52 < file parser, which is rewritten using ANother Tool for Language
53 < Recognition(ANTLR)\cite{Parr1995, Schaps1999} syntax. The Molecular
54 < Mechanics module consists of energy minimization and a wide
55 < varieties of integration methods(see Chap.~\ref{chapt:methodology}).
56 < The structure module contains a flexible and powerful selection
57 < library which syntax is elaborated in
58 < Sec.~\ref{appendixSection:syntax}. The top layer is made of the main
59 < program of the package, \texttt{oopse} and it corresponding parallel
60 < version \texttt{oopse\_MPI}, as well as other useful utilities, such
61 < as \texttt{StatProps} (see Sec.~\ref{appendixSection:StaticProps}),
62 < \texttt{DynamicProps} (see
63 < Sec.~\ref{appendixSection:appendixSection:DynamicProps}),
64 < \texttt{Dump2XYZ} (see
65 < Sec.~\ref{appendixSection:appendixSection:Dump2XYZ}), \texttt{Hydro}
71 < (see Sec.~\ref{appendixSection:appendixSection:hydrodynamics})
72 < \textit{etc}.
36 > Mainly written by C++ and Fortran90, {\sc OOPSE} uses C++ Standard
37 > Template Library (STL) and fortran modules as a foundation. As an
38 > extensive set of the STL and Fortran90 modules, {\sc Base Classes}
39 > provide generic implementations of mathematical objects (e.g.,
40 > matrices, vectors, polynomials, random number generators) and
41 > advanced data structures and algorithms(e.g., tuple, bitset, generic
42 > data and string manipulation). The molecular data structures for the
43 > representation of atoms, bonds, bends, torsions, rigid bodies and
44 > molecules \textit{etc} are contained in the {\sc Kernel} which is
45 > implemented with {\sc Base Classes} and are carefully designed to
46 > provide maximum extensibility and flexibility. The functionality
47 > required for applications is provided by the third layer which
48 > contains Input/Output, Molecular Mechanics and Structure modules.
49 > The Input/Output module not only implements general methods for file
50 > handling, but also defines a generic force field interface. Another
51 > important component of Input/Output module is the parser for
52 > meta-data files, which has been implemented using the ANother Tool
53 > for Language Recognition(ANTLR)\cite{Parr1995, Schaps1999} syntax.
54 > The Molecular Mechanics module consists of energy minimization and a
55 > wide varieties of integration methods(see
56 > Chap.~\ref{chapt:methodology}). The structure module contains a
57 > flexible and powerful selection library which syntax is elaborated
58 > in Sec.~\ref{appendixSection:syntax}. The top layer is made of the
59 > main program of the package, \texttt{oopse} and it corresponding
60 > parallel version \texttt{oopse\_MPI}, as well as other useful
61 > utilities, such as \texttt{StatProps} (see
62 > Sec.~\ref{appendixSection:StaticProps}), \texttt{DynamicProps} (see
63 > Sec.~\ref{appendixSection:DynamicProps}), \texttt{Dump2XYZ} (see
64 > Sec.~\ref{appendixSection:Dump2XYZ}), \texttt{Hydro} (see
65 > Sec.~\ref{appendixSection:hydrodynamics}) \textit{etc}.
66  
67   \begin{figure}
68   \centering
# Line 78 | Line 71 | of {\sc OOPSE}} \label{appendixFig:architecture}
71   of {\sc OOPSE}} \label{appendixFig:architecture}
72   \end{figure}
73  
74 < \section{\label{appendixSection:desginPattern}Design Pattern}
74 > \section{\label{appendixSection:desginPattern}Design Patterns}
75  
76   Design patterns are optimal solutions to commonly-occurring problems
77   in software design. Although originated as an architectural concept
# Line 89 | Line 82 | different problems as necessary. Pattern are expressiv
82   the experience, knowledge and insights of developers who have
83   successfully used these patterns in their own work. Patterns are
84   reusable. They provide a ready-made solution that can be adapted to
85 < different problems as necessary. Pattern are expressive. they
86 < provide a common vocabulary of solutions that can express large
87 < solutions succinctly.
85 > different problems as necessary. As one of the latest advanced
86 > techniques to emerge from object-oriented community, design patterns
87 > were applied in some of the modern scientific software applications,
88 > such as JMol, {\sc OOPSE}\cite{Meineke2005} and
89 > PROTOMOL\cite{Matthey2004} \textit{etc}. The following sections
90 > enumerates some of the patterns used in {\sc OOPSE}.
91  
92 < Patterns are usually described using a format that includes the
97 < following information:
98 < \begin{enumerate}
99 <  \item The \emph{name} that is commonly used for the pattern. Good pattern names form a vocabulary for
100 <  discussing conceptual abstractions. a pattern may have more than one commonly used or recognizable name
101 <  in the literature. In this case it is common practice to document these nicknames or synonyms under
102 <  the heading of \emph{Aliases} or \emph{Also Known As}.
103 <  \item The \emph{motivation} or \emph{context} that this pattern applies
104 <  to. Sometimes, it will include some prerequisites that should be satisfied before deciding to use a pattern
105 <  \item The \emph{solution} to the problem that the pattern
106 <  addresses. It describes how to construct the necessary work products. The description may include
107 <  pictures, diagrams and prose which identify the pattern's structure, its participants, and their
108 <  collaborations, to show how the problem is solved.
109 <  \item The \emph{consequences} of using the given solution to solve a
110 <  problem, both positive and negative.
111 < \end{enumerate}
92 > \subsection{\label{appendixSection:singleton}Singletons}
93  
113 – As one of the latest advanced techniques emerged from
114 – object-oriented community, design patterns were applied in some of
115 – the modern scientific software applications, such as JMol, {\sc
116 – OOPSE}\cite{Meineke05} and PROTOMOL\cite{Matthey05} \textit{etc}.
117 – The following sections enumerates some of the patterns used in {\sc
118 – OOPSE}.
119 –
120 – \subsection{\label{appendixSection:singleton}Singleton}
94   The Singleton pattern not only provides a mechanism to restrict
95   instantiation of a class to one object, but also provides a global
96 < point of access to the object. Currently implemented as a global
97 < variable, the logging utility which reports error and warning
98 < messages to the console in {\sc OOPSE} is a good candidate for
99 < applying the Singleton pattern to avoid the global namespace
100 < pollution.Although the singleton pattern can be implemented in
101 < various ways  to account for different aspects of the software
102 < designs, such as lifespan control \textit{etc}, we only use the
103 < static data approach in {\sc OOPSE}. {\tt IntegratorFactory} class
104 < is declared as
105 < \begin{lstlisting}[float,caption={[A classic Singleton design pattern implementation(I)] Declaration of {\tt IntegratorFactory} class.},label={appendixScheme:singletonDeclaration}]
96 > point of access to the object. Although the singleton pattern can be
97 > implemented in various ways  to account for different aspects of the
98 > software designs, such as lifespan control \textit{etc}, we only use
99 > the static data approach in {\sc OOPSE}. The declaration and
100 > implementation of IntegratorFactory class are given by declared in
101 > List.~\ref{appendixScheme:singletonDeclaration} and
102 > Scheme.~\ref{appendixScheme:singletonImplementation} respectively.
103 > Since the constructor is declared as protected, a client can not
104 > instantiate IntegratorFactory directly. Moreover, since the member
105 > function getInstance serves as the only entry of access to
106 > IntegratorFactory, this approach fulfills the basic requirement, a
107 > single instance. Another consequence of this approach is the
108 > automatic destruction since static data are destroyed upon program
109 > termination.
110  
111 < class IntegratorFactory {
112 <  public:
113 <    static IntegratorFactory* getInstance();
114 <    protected:
115 <      IntegratorFactory();
116 <    private:
117 <      static IntegratorFactory* instance_;
111 > \subsection{\label{appendixSection:factoryMethod}Factory Methods}
112 >
113 > The Factory Method pattern is a creational pattern and deals with
114 > the problem of creating objects without specifying the exact class
115 > of object that will be created. Factory method is typically
116 > implemented by delegating the creation operation to the subclasses.
117 > One of the most popular Factory pattern is Parameterized Factory
118 > pattern which creates products based on their identifiers (see
119 > Scheme.~\ref{appendixScheme:factoryDeclaration}). If the identifier
120 > has been already registered, the factory method will invoke the
121 > corresponding creator (see
122 > Scheme.~\ref{appendixScheme:integratorCreator}) which utilizes the
123 > modern C++ template technique to avoid excess subclassing.
124 >
125 > \subsection{\label{appendixSection:visitorPattern}Visitor}
126 >
127 > The visitor pattern is designed to decouple the data structure and
128 > algorithms used upon them by collecting related operation from
129 > element classes into other visitor classes, which is equivalent to
130 > adding virtual functions into a set of classes without modifying
131 > their interfaces. Fig.~\ref{appendixFig:visitorUML} demonstrates the
132 > structure of a Visitor pattern which is used extensively in {\tt
133 > Dump2XYZ}. In order to convert an OOPSE dump file, a series of
134 > distinct operations are performed on different StuntDoubles (See the
135 > class hierarchy in Fig.~\ref{oopseFig:hierarchy} and the declaration
136 > in Scheme.~\ref{appendixScheme:element}). Since the hierarchies
137 > remain stable, it is easy to define a visit operation (see
138 > Scheme.~\ref{appendixScheme:visitor}) for each class of StuntDouble.
139 > Note that using Composite pattern\cite{Gamma1994}, CompositeVisitor
140 > manages a priority visitor list and handles the execution of every
141 > visitor in the priority list on different StuntDoubles.
142 >
143 > \begin{lstlisting}[float,caption={[A classic Singleton design pattern implementation(I)] The declaration of of simple Singleton pattern.},label={appendixScheme:singletonDeclaration}]
144 >
145 > class IntegratorFactory { public:
146 >  static IntegratorFactory* getInstance(); protected:
147 >  IntegratorFactory();
148 > private:
149 >  static IntegratorFactory* instance_;
150   };
151  
152   \end{lstlisting}
144 – The corresponding implementation is
145 – \begin{lstlisting}[float,caption={[A classic implementation of Singleton design pattern (II)] Implementation of {\tt IntegratorFactory} class.},label={appendixScheme:singletonImplementation}]
153  
154 + \begin{lstlisting}[float,caption={[A classic implementation of Singleton design pattern (II)] The implementation of simple Singleton pattern.},label={appendixScheme:singletonImplementation}]
155 +
156   IntegratorFactory::instance_ = NULL;
157  
158   IntegratorFactory* getInstance() {
# Line 154 | Line 163 | Since constructor is declared as {\tt protected}, a cl
163   }
164  
165   \end{lstlisting}
157 – Since constructor is declared as {\tt protected}, a client can not
158 – instantiate {\tt IntegratorFactory} directly. Moreover, since the
159 – member function {\tt getInstance} serves as the only entry of access
160 – to {\tt IntegratorFactory}, this approach fulfills the basic
161 – requirement, a single instance. Another consequence of this approach
162 – is the automatic destruction since static data are destroyed upon
163 – program termination.
166  
167 < \subsection{\label{appendixSection:factoryMethod}Factory Method}
167 > \begin{lstlisting}[float,caption={[The implementation of Parameterized Factory pattern (I)]Source code of IntegratorFactory class.},label={appendixScheme:factoryDeclaration}]
168  
169 < Categoried as a creational pattern, the Factory Method pattern deals
170 < with the problem of creating objects without specifying the exact
169 < class of object that will be created. Factory Method is typically
170 < implemented by delegating the creation operation to the subclasses.
169 > class IntegratorFactory { public:
170 >  typedef std::map<string, IntegratorCreator*> CreatorMapType;
171  
172 < Registers a creator with a type identifier. Looks up the type
173 < identifier in the internal map. If it is found, it invokes the
174 < corresponding creator for the type identifier and returns its
175 < result.
176 < \begin{lstlisting}[float,caption={[The implementation of Factory pattern (I)].},label={appendixScheme:factoryDeclaration}]
172 >  bool registerIntegrator(IntegratorCreator* creator) {
173 >    return creatorMap_.insert(creator->getIdent(), creator).second;
174 >  }
175  
176 < class IntegratorFactory {
177 <  public:
178 <    typedef std::map<string, IntegratorCreator*> CreatorMapType;
176 >  Integrator* createIntegrator(const string& id, SimInfo* info) {
177 >    Integrator* result = NULL;
178 >    CreatorMapType::iterator i = creatorMap_.find(id);
179 >    if (i != creatorMap_.end()) {
180 >      result = (i->second)->create(info);
181 >    }
182 >    return result;
183 >  }
184  
185 <    bool registerIntegrator(IntegratorCreator* creator);
186 <
184 <    Integrator* createIntegrator(const string& id, SimInfo* info);
185 <
186 <  private:
187 <    CreatorMapType creatorMap_;
185 > private:
186 >  CreatorMapType creatorMap_;
187   };
189 –
188   \end{lstlisting}
189  
190 < \begin{lstlisting}[float,caption={[The implementation of Factory pattern (II)].},label={appendixScheme:factoryDeclarationImplementation}]
190 > \begin{lstlisting}[float,caption={[The implementation of Parameterized Factory pattern (III)]Source code of creator classes.},label={appendixScheme:integratorCreator}]
191  
194 – bool IntegratorFactory::unregisterIntegrator(const string& id) {
195 –  return creatorMap_.erase(id) == 1;
196 – }
197 –
198 – Integrator* IntegratorFactory::createIntegrator(const string& id,
199 –                                                SimInfo* info) {
200 –  CreatorMapType::iterator i = creatorMap_.find(id);
201 –  if (i != creatorMap_.end()) {
202 –    return (i->second)->create(info);
203 –  } else {
204 –    return NULL;
205 –  }
206 – }
207 –
208 – \end{lstlisting}
209 –
210 – \begin{lstlisting}[float,caption={[The implementation of Factory pattern (III)].},label={appendixScheme:integratorCreator}]
211 –
192   class IntegratorCreator {
193    public:
194      IntegratorCreator(const string& ident) : ident_(ident) {}
# Line 217 | Line 197 | class IntegratorCreator {
197  
198      virtual Integrator* create(SimInfo* info) const = 0;
199  
200 <  private:
200 > private:
201      string ident_;
202   };
203  
204 < template<class ConcreteIntegrator>
205 < class IntegratorBuilder : public IntegratorCreator {
204 > template<class ConcreteIntegrator> class IntegratorBuilder : public
205 > IntegratorCreator {
206    public:
207 <    IntegratorBuilder(const string& ident) : IntegratorCreator(ident) {}
207 >    IntegratorBuilder(const string& ident)
208 >                     : IntegratorCreator(ident) {}
209      virtual  Integrator* create(SimInfo* info) const {
210        return new ConcreteIntegrator(info);
211      }
212   };
213   \end{lstlisting}
214  
234 – \subsection{\label{appendixSection:visitorPattern}Visitor}
235 –
236 – The purpose of the Visitor Pattern is to encapsulate an operation
237 – that you want to perform on the elements. The operation being
238 – performed on a structure can be switched without changing the
239 – interfaces  of the elements. In other words, one can add virtual
240 – functions into a set of classes without modifying their interfaces.
241 – The UML class diagram of Visitor patten is shown in
242 – Fig.~\ref{appendixFig:visitorUML}. {\tt Dump2XYZ} program in
243 – Sec.~\ref{appendixSection:Dump2XYZ} uses Visitor pattern
244 – extensively.
245 –
246 – \begin{figure}
247 – \centering
248 – \includegraphics[width=\linewidth]{visitor.eps}
249 – \caption[The architecture of {\sc OOPSE}] {Overview of the structure
250 – of {\sc OOPSE}} \label{appendixFig:visitorUML}
251 – \end{figure}
252 –
253 – \begin{lstlisting}[float,caption={[The implementation of Visitor pattern (I)]Source code of the visitor classes.},label={appendixScheme:visitor}]
254 –
255 – class BaseVisitor{
256 –  public:
257 –    virtual void visit(Atom* atom);
258 –    virtual void visit(DirectionalAtom* datom);
259 –    virtual void visit(RigidBody* rb);
260 – };
261 –
262 – \end{lstlisting}
263 –
215   \begin{lstlisting}[float,caption={[The implementation of Visitor pattern (II)]Source code of the element classes.},label={appendixScheme:element}]
216  
217   class StuntDouble {
# Line 291 | Line 242 | class RigidBody: public StuntDouble {
242  
243   \end{lstlisting}
244  
245 + \begin{lstlisting}[float,caption={[The implementation of Visitor pattern (I)]Source code of the visitor classes.},label={appendixScheme:visitor}]
246 +
247 + class BaseVisitor{
248 +  public:
249 +    virtual void visit(Atom* atom);
250 +    virtual void visit(DirectionalAtom* datom);
251 +    virtual void visit(RigidBody* rb);
252 + };
253 +
254 + class BaseAtomVisitor:public BaseVisitor{
255 +  public:
256 +    virtual void visit(Atom* atom);
257 +    virtual void visit(DirectionalAtom* datom);
258 +    virtual void visit(RigidBody* rb);
259 + };
260 +
261 + class CompositeVisitor: public BaseVisitor {
262 +  public:
263 +  typedef list<pair<BaseVisitor*, int> > VistorListType;
264 +  typedef VistorListType::iterator VisitorListIterator;
265 +  virtual void visit(Atom* atom) {
266 +    VisitorListIterator i;
267 +    BaseVisitor* curVisitor;
268 +    for(i = visitorScheme.begin();i != visitorScheme.end();++i) {
269 +      atom->accept(*i);
270 +    }
271 +  }
272 +
273 +  virtual void visit(DirectionalAtom* datom) {
274 +    VisitorListIterator i;
275 +    BaseVisitor* curVisitor;
276 +    for(i = visitorScheme.begin();i != visitorScheme.end();++i) {
277 +      atom->accept(*i);
278 +    }
279 +  }
280 +
281 +  virtual void visit(RigidBody* rb) {
282 +    VisitorListIterator i;
283 +    std::vector<Atom*> myAtoms;
284 +    std::vector<Atom*>::iterator ai;
285 +    myAtoms = rb->getAtoms();
286 +    for(i = visitorScheme.begin();i != visitorScheme.end();++i) {
287 +      rb->accept(*i);
288 +      for(ai = myAtoms.begin(); ai != myAtoms.end(); ++ai){
289 +        (*ai)->accept(*i);
290 +      }
291 +    }
292 +
293 +  void addVisitor(BaseVisitor* v, int priority);
294 +  protected:
295 +    VistorListType visitorList;
296 + };
297 + \end{lstlisting}
298 +
299 + \begin{figure}
300 + \centering
301 + \includegraphics[width=\linewidth]{visitor.eps}
302 + \caption[The UML class diagram of Visitor patten] {The UML class
303 + diagram of Visitor patten.} \label{appendixFig:visitorUML}
304 + \end{figure}
305 +
306 + \begin{figure}
307 + \centering
308 + \includegraphics[width=\linewidth]{hierarchy.eps}
309 + \caption[Class hierarchy for ojects in {\sc OOPSE}]{ A diagram of
310 + the class hierarchy. Objects below others on the diagram inherit
311 + data structures and functions from their parent classes above them.}
312 + \label{oopseFig:hierarchy}
313 + \end{figure}
314 +
315   \section{\label{appendixSection:concepts}Concepts}
316  
317   OOPSE manipulates both traditional atoms as well as some objects
318   that {\it behave like atoms}.  These objects can be rigid
319   collections of atoms or atoms which have orientational degrees of
320 < freedom.  A diagram of the class heirarchy is illustrated in
321 < Fig.~\ref{oopseFig:heirarchy}. Every Molecule, Atom and
320 > freedom.  A diagram of the class hierarchy is illustrated in
321 > Fig.~\ref{oopseFig:hierarchy}. Every Molecule, Atom and
322   DirectionalAtom in {\sc OOPSE} have their own names which are
323 < specified in the {\tt .md} file. In contrast, RigidBodies are
323 > specified in the meta data file. In contrast, RigidBodies are
324   denoted by their membership and index inside a particular molecule:
325   [MoleculeName]\_RB\_[index] (the contents inside the brackets depend
326   on the specifics of the simulation). The names of rigid bodies are
327   generated automatically. For example, the name of the first rigid
328   body in a DMPC molecule is DMPC\_RB\_0.
308 – \begin{figure}
309 – \centering
310 – \includegraphics[width=\linewidth]{heirarchy.eps}
311 – \caption[Class heirarchy for StuntDoubles in {\sc OOPSE}]{ The class
312 – heirarchy of StuntDoubles in {\sc OOPSE}.
329   \begin{itemize}
330   \item A {\bf StuntDouble} is {\it any} object that can be manipulated by the
331   integrators and minimizers.
# Line 318 | Line 334 | DirectionalAtom}s which behaves as a single unit.
334   \item A {\bf RigidBody} is a collection of {\bf Atom}s or {\bf
335   DirectionalAtom}s which behaves as a single unit.
336   \end{itemize}
321 – } \label{oopseFig:heirarchy}
322 – \end{figure}
337  
338   \section{\label{appendixSection:syntax}Syntax of the Select Command}
339  
340 < The most general form of the select command is: {\tt select {\it
341 < expression}}. This expression represents an arbitrary set of
328 < StuntDoubles (Atoms or RigidBodies) in {\sc OOPSE}. Expressions are
329 < composed of either name expressions, index expressions, predefined
330 < sets, user-defined expressions, comparison operators, within
331 < expressions, or logical combinations of the above expression types.
332 < Expressions can be combined using parentheses and the Boolean
333 < operators.
340 > {\sc OOPSE} provides a powerful selection utility to select
341 > StuntDoubles. The most general form of the select command is:
342  
343 + {\tt select {\it expression}}.
344 +
345 + This expression represents an arbitrary set of StuntDoubles (Atoms
346 + or RigidBodies) in {\sc OOPSE}. Expressions are composed of either
347 + name expressions, index expressions, predefined sets, user-defined
348 + expressions, comparison operators, within expressions, or logical
349 + combinations of the above expression types. Expressions can be
350 + combined using parentheses and the Boolean operators.
351 +
352   \subsection{\label{appendixSection:logical}Logical expressions}
353  
354   The logical operators allow complex queries to be constructed out of
# Line 463 | Line 480 | of a selected atom or rigid body.
480   and other atoms of type $B$, $g_{AB}(r)$.  {\tt StaticProps} can
481   also be used to compute the density distributions of other molecules
482   in a reference frame {\it fixed to the body-fixed reference frame}
483 < of a selected atom or rigid body.
483 > of a selected atom or rigid body. Due to the fact that the selected
484 > StuntDoubles from two selections may be overlapped, {\tt
485 > StaticProps} performs the calculation in three stages which are
486 > illustrated in Fig.~\ref{oopseFig:staticPropsProcess}.
487 >
488 > \begin{figure}
489 > \centering
490 > \includegraphics[width=\linewidth]{staticPropsProcess.eps}
491 > \caption[A representation of the three-stage correlations in
492 > \texttt{StaticProps}]{This diagram illustrates three-stage
493 > processing used by \texttt{StaticProps}. $S_1$ and $S_2$ are the
494 > numbers of selected StuntDobules from {\tt -{}-sele1} and {\tt
495 > -{}-sele2} respectively, while $C$ is the number of StuntDobules
496 > appearing at both sets. The first stage($S_1-C$ and $S_2$) and
497 > second stages ($S_1$ and $S_2-C$) are completely non-overlapping. On
498 > the contrary, the third stage($C$ and $C$) are completely
499 > overlapping} \label{oopseFig:staticPropsProcess}
500 > \end{figure}
501  
502 + \begin{figure}
503 + \centering
504 + \includegraphics[width=3in]{definition.eps}
505 + \caption[Definitions of the angles between directional objects]{Any
506 + two directional objects (DirectionalAtoms and RigidBodies) have a
507 + set of two angles ($\theta$, and $\omega$) between the z-axes of
508 + their body-fixed frames.} \label{oopseFig:gofr}
509 + \end{figure}
510 +
511   There are five seperate radial distribution functions availiable in
512   OOPSE. Since every radial distrbution function invlove the
513   calculation between pairs of bodies, {\tt -{}-sele1} and {\tt
# Line 508 | Line 551 | distribution functions are most easily seen in the fig
551   \end{description}
552  
553   The vectors (and angles) associated with these angular pair
554 < distribution functions are most easily seen in the figure below:
554 > distribution functions are most easily seen in
555 > Fig.~\ref{oopseFig:gofr}.
556  
513 – \begin{figure}
514 – \centering
515 – \includegraphics[width=3in]{definition.eps}
516 – \caption[Definitions of the angles between directional objects]{ \\
517 – Any two directional objects (DirectionalAtoms and RigidBodies) have
518 – a set of two angles ($\theta$, and $\omega$) between the z-axes of
519 – their body-fixed frames.} \label{oopseFig:gofr}
520 – \end{figure}
521 –
522 – Due to the fact that the selected StuntDoubles from two selections
523 – may be overlapped, {\tt StaticProps} performs the calculation in
524 – three stages which are illustrated in
525 – Fig.~\ref{oopseFig:staticPropsProcess}.
526 –
527 – \begin{figure}
528 – \centering
529 – \includegraphics[width=\linewidth]{staticPropsProcess.eps}
530 – \caption[A representation of the three-stage correlations in
531 – \texttt{StaticProps}]{This diagram illustrates three-stage
532 – processing used by \texttt{StaticProps}. $S_1$ and $S_2$ are the
533 – numbers of selected stuntdobules from {\tt -{}-sele1} and {\tt
534 – -{}-sele2} respectively, while $C$ is the number of stuntdobules
535 – appearing at both sets. The first stage($S_1-C$ and $S_2$) and
536 – second stages ($S_1$ and $S_2-C$) are completely non-overlapping. On
537 – the contrary, the third stage($C$ and $C$) are completely
538 – overlapping} \label{oopseFig:staticPropsProcess}
539 – \end{figure}
540 –
557   The options available for {\tt StaticProps} are as follows:
558   \begin{longtable}[c]{|EFG|}
559   \caption{StaticProps Command-line Options}
# Line 600 | Line 616 | sizes in excess of several gigabytes. In order to effe
616   select different types of atoms is already present in the code.
617  
618   For large simulations, the trajectory files can sometimes reach
619 < sizes in excess of several gigabytes. In order to effectively
620 < analyze that amount of data. In order to prevent a situation where
621 < the program runs out of memory due to large trajectories,
622 < \texttt{dynamicProps} will estimate the size of free memory at
623 < first, and determine the number of frames in each block, which
608 < allows the operating system to load two blocks of data
619 > sizes in excess of several gigabytes. In order to prevent a
620 > situation where the program runs out of memory due to large
621 > trajectories, \texttt{dynamicProps} will first estimate the size of
622 > free memory, and determine the number of frames in each block, which
623 > will allow the operating system to load two blocks of data
624   simultaneously without swapping. Upon reading two blocks of the
625   trajectory, \texttt{dynamicProps} will calculate the time
626   correlation within the first block and the cross correlations

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