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1 tim 2805 \appendix
2 tim 2815 \chapter{\label{chapt:oopse}Object-Oriented Parallel Simulation Engine}
3 tim 2685
4 tim 2840 Absence of applying modern software development practices is the
5     bottleneck of Scientific Computing community\cite{Wilson2006}. In
6 tim 2841 the last 20 years , there are quite a few MD
7     packages\cite{Brooks1983, Vincent1995, Kale1999} that were developed
8     to solve common MD problems and perform robust simulations .
9     Unfortunately, most of them are commercial programs that are either
10     poorly written or extremely complicate. Consequently, it prevents
11     the researchers to reuse or extend those packages to do cutting-edge
12     research effectively. Along the way of studying structural and
13     dynamic processes in condensed phase systems like biological
14     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 tim 2815 \begin{enumerate}
18     \item {\sc OOPSE} performs Molecular Dynamics (MD) simulations on non-standard
19     atom types (transition metals, point dipoles, sticky potentials,
20     Gay-Berne ellipsoids, or other "lumpy"atoms with orientational
21     degrees of freedom), as well as rigid bodies.
22     \item {\sc OOPSE} uses a force-based decomposition algorithm using MPI on cheap
23     Beowulf clusters to obtain very efficient parallelism.
24     \item {\sc OOPSE} integrates the equations of motion using advanced methods for
25     orientational dynamics in NVE, NVT, NPT, NPAT, and NP$\gamma$T
26     ensembles.
27     \item {\sc OOPSE} can carry out simulations on metallic systems using the
28     Embedded Atom Method (EAM) as well as the Sutton-Chen potential.
29     \item {\sc OOPSE} can perform simulations on Gay-Berne liquid crystals.
30     \item {\sc OOPSE} can simulate systems containing the extremely efficient
31     extended-Soft Sticky Dipole (SSD/E) model for water.
32     \end{enumerate}
33 tim 2688
34 tim 2812 \section{\label{appendixSection:architecture }Architecture}
35    
36 tim 2815 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 tim 2840 \texttt{DynamicProps} (see Sec.~\ref{appendixSection:DynamicProps}),
63     \texttt{Dump2XYZ} (see Sec.~\ref{appendixSection:Dump2XYZ}),
64     \texttt{Hydro} (see Sec.~\ref{appendixSection:hydrodynamics})
65 tim 2815 \textit{etc}.
66    
67 tim 2812 \begin{figure}
68     \centering
69 tim 2813 \includegraphics[width=\linewidth]{architecture.eps}
70 tim 2815 \caption[The architecture of {\sc OOPSE}] {Overview of the structure
71     of {\sc OOPSE}} \label{appendixFig:architecture}
72 tim 2812 \end{figure}
73    
74 tim 2685 \section{\label{appendixSection:desginPattern}Design Pattern}
75    
76 tim 2688 Design patterns are optimal solutions to commonly-occurring problems
77     in software design. Although originated as an architectural concept
78 tim 2807 for buildings and towns by Christopher Alexander
79     \cite{Alexander1987}, software patterns first became popular with
80     the wide acceptance of the book, Design Patterns: Elements of
81     Reusable Object-Oriented Software \cite{Gamma1994}. Patterns reflect
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.
88 tim 2685
89 tim 2688 Patterns are usually described using a format that includes the
90     following information:
91     \begin{enumerate}
92     \item The \emph{name} that is commonly used for the pattern. Good pattern names form a vocabulary for
93     discussing conceptual abstractions. a pattern may have more than one commonly used or recognizable name
94     in the literature. In this case it is common practice to document these nicknames or synonyms under
95     the heading of \emph{Aliases} or \emph{Also Known As}.
96     \item The \emph{motivation} or \emph{context} that this pattern applies
97     to. Sometimes, it will include some prerequisites that should be satisfied before deciding to use a pattern
98     \item The \emph{solution} to the problem that the pattern
99     addresses. It describes how to construct the necessary work products. The description may include
100     pictures, diagrams and prose which identify the pattern's structure, its participants, and their
101     collaborations, to show how the problem is solved.
102     \item The \emph{consequences} of using the given solution to solve a
103     problem, both positive and negative.
104     \end{enumerate}
105 tim 2685
106 tim 2688 As one of the latest advanced techniques emerged from
107     object-oriented community, design patterns were applied in some of
108 tim 2815 the modern scientific software applications, such as JMol, {\sc
109 tim 2839 OOPSE}\cite{Meineke2005} and PROTOMOL\cite{Matthey2005}
110     \textit{etc}. The following sections enumerates some of the patterns
111     used in {\sc OOPSE}.
112 tim 2685
113 tim 2693 \subsection{\label{appendixSection:singleton}Singleton}
114 tim 2836
115 tim 2821 The Singleton pattern not only provides a mechanism to restrict
116     instantiation of a class to one object, but also provides a global
117     point of access to the object. Currently implemented as a global
118     variable, the logging utility which reports error and warning
119     messages to the console in {\sc OOPSE} is a good candidate for
120     applying the Singleton pattern to avoid the global namespace
121     pollution.Although the singleton pattern can be implemented in
122     various ways to account for different aspects of the software
123     designs, such as lifespan control \textit{etc}, we only use the
124 tim 2836 static data approach in {\sc OOPSE}. IntegratorFactory class is
125     declared as
126    
127 tim 2835 \begin{lstlisting}[float,caption={[A classic Singleton design pattern implementation(I)] The declaration of of simple Singleton pattern.},label={appendixScheme:singletonDeclaration}]
128 tim 2693
129 tim 2825 class IntegratorFactory {
130 tim 2832 public:
131     static IntegratorFactory*
132     getInstance();
133     protected:
134     IntegratorFactory();
135     private:
136     static IntegratorFactory* instance_;
137 tim 2825 };
138    
139 tim 2821 \end{lstlisting}
140 tim 2836
141 tim 2821 The corresponding implementation is
142 tim 2836
143 tim 2835 \begin{lstlisting}[float,caption={[A classic implementation of Singleton design pattern (II)] The implementation of simple Singleton pattern.},label={appendixScheme:singletonImplementation}]
144 tim 2821
145     IntegratorFactory::instance_ = NULL;
146    
147     IntegratorFactory* getInstance() {
148     if (instance_ == NULL){
149     instance_ = new IntegratorFactory;
150     }
151     return instance_;
152     }
153 tim 2825
154 tim 2821 \end{lstlisting}
155    
156 tim 2836 Since constructor is declared as protected, a client can not
157     instantiate IntegratorFactory directly. Moreover, since the member
158     function getInstance serves as the only entry of access to
159     IntegratorFactory, this approach fulfills the basic requirement, a
160     single instance. Another consequence of this approach is the
161     automatic destruction since static data are destroyed upon program
162     termination.
163    
164 tim 2688 \subsection{\label{appendixSection:factoryMethod}Factory Method}
165 tim 2685
166 tim 2821 Categoried as a creational pattern, the Factory Method pattern deals
167     with the problem of creating objects without specifying the exact
168     class of object that will be created. Factory Method is typically
169     implemented by delegating the creation operation to the subclasses.
170 tim 2836 Parameterized Factory pattern where factory method (
171     createIntegrator member function) creates products based on the
172     identifier (see List.~\ref{appendixScheme:factoryDeclaration}). If
173     the identifier has been already registered, the factory method will
174     invoke the corresponding creator (see List.~\ref{integratorCreator})
175     which utilizes the modern C++ template technique to avoid excess
176     subclassing.
177 tim 2822
178 tim 2836 \begin{lstlisting}[float,caption={[The implementation of Parameterized Factory pattern (I)]Source code of IntegratorFactory class.},label={appendixScheme:factoryDeclaration}]
179    
180 tim 2825 class IntegratorFactory {
181 tim 2832 public:
182     typedef std::map<string, IntegratorCreator*> CreatorMapType;
183 tim 2821
184 tim 2832 bool registerIntegrator(IntegratorCreator* creator) {
185     return creatorMap_.insert(creator->getIdent(), creator).second;
186     }
187 tim 2821
188 tim 2832 Integrator* createIntegrator(const string& id, SimInfo* info) {
189     Integrator* result = NULL;
190     CreatorMapType::iterator i = creatorMap_.find(id);
191     if (i != creatorMap_.end()) {
192     result = (i->second)->create(info);
193 tim 2831 }
194 tim 2832 return result;
195     }
196 tim 2825
197 tim 2832 private:
198     CreatorMapType creatorMap_;
199 tim 2825 };
200 tim 2821 \end{lstlisting}
201 tim 2836
202 tim 2835 \begin{lstlisting}[float,caption={[The implementation of Parameterized Factory pattern (III)]Source code of creator classes.},label={appendixScheme:integratorCreator}]
203 tim 2821
204 tim 2825 class IntegratorCreator {
205 tim 2832 public:
206 tim 2823 IntegratorCreator(const string& ident) : ident_(ident) {}
207 tim 2822
208 tim 2823 const string& getIdent() const { return ident_; }
209 tim 2821
210     virtual Integrator* create(SimInfo* info) const = 0;
211    
212 tim 2832 private:
213 tim 2823 string ident_;
214 tim 2825 };
215 tim 2821
216 tim 2833 template<class ConcreteIntegrator>
217     class IntegratorBuilder : public IntegratorCreator {
218 tim 2832 public:
219     IntegratorBuilder(const string& ident)
220 tim 2833 : IntegratorCreator(ident) {}
221 tim 2832 virtual Integrator* create(SimInfo* info) const {
222     return new ConcreteIntegrator(info);
223     }
224 tim 2825 };
225 tim 2821 \end{lstlisting}
226    
227 tim 2688 \subsection{\label{appendixSection:visitorPattern}Visitor}
228 tim 2821
229 tim 2836 The visitor pattern is designed to decouple the data structure and
230     algorithms used upon them by collecting related operation from
231     element classes into other visitor classes, which is equivalent to
232     adding virtual functions into a set of classes without modifying
233     their interfaces. Fig.~\ref{appendixFig:visitorUML} demonstrates the
234     structure of Visitor pattern which is used extensively in {\tt
235     Dump2XYZ}. In order to convert an OOPSE dump file, a series of
236     distinct operations are performed on different StuntDoubles (See the
237     class hierarchy in Fig.~\ref{oopseFig:hierarchy} and the declaration
238     in List.~\ref{appendixScheme:element}). Since the hierarchies
239     remains stable, it is easy to define a visit operation (see
240     List.~\ref{appendixScheme:visitor}) for each class of StuntDouble.
241     Note that using Composite pattern\cite{Gamma1994}, CompositVisitor
242     manages a priority visitor list and handles the execution of every
243     visitor in the priority list on different StuntDoubles.
244 tim 2685
245 tim 2824 \begin{figure}
246     \centering
247 tim 2826 \includegraphics[width=\linewidth]{visitor.eps}
248 tim 2835 \caption[The UML class diagram of Visitor patten] {The UML class
249     diagram of Visitor patten.} \label{appendixFig:visitorUML}
250 tim 2824 \end{figure}
251    
252 tim 2838 \begin{figure}
253     \centering
254     \includegraphics[width=\linewidth]{hierarchy.eps}
255     \caption[Class hierarchy for ojects in {\sc OOPSE}]{ A diagram of
256     the class hierarchy. } \label{oopseFig:hierarchy}
257     \end{figure}
258 tim 2836
259     \begin{lstlisting}[float,caption={[The implementation of Visitor pattern (II)]Source code of the element classes.},label={appendixScheme:element}]
260    
261     class StuntDouble { public:
262     virtual void accept(BaseVisitor* v) = 0;
263     };
264    
265     class Atom: public StuntDouble { public:
266     virtual void accept{BaseVisitor* v*} {
267     v->visit(this);
268     }
269     };
270    
271     class DirectionalAtom: public Atom { public:
272     virtual void accept{BaseVisitor* v*} {
273     v->visit(this);
274     }
275     };
276    
277     class RigidBody: public StuntDouble { public:
278     virtual void accept{BaseVisitor* v*} {
279     v->visit(this);
280     }
281     };
282    
283     \end{lstlisting}
284    
285 tim 2824 \begin{lstlisting}[float,caption={[The implementation of Visitor pattern (I)]Source code of the visitor classes.},label={appendixScheme:visitor}]
286 tim 2825
287     class BaseVisitor{
288 tim 2832 public:
289     virtual void visit(Atom* atom);
290     virtual void visit(DirectionalAtom* datom);
291     virtual void visit(RigidBody* rb);
292 tim 2825 };
293    
294 tim 2835 class BaseAtomVisitor:public BaseVisitor{ public:
295     virtual void visit(Atom* atom);
296     virtual void visit(DirectionalAtom* datom);
297     virtual void visit(RigidBody* rb);
298     };
299    
300 tim 2836 class SSDAtomVisitor:public BaseAtomVisitor{ public:
301     virtual void visit(Atom* atom);
302     virtual void visit(DirectionalAtom* datom);
303     virtual void visit(RigidBody* rb);
304     };
305 tim 2824
306 tim 2836 class CompositeVisitor: public BaseVisitor {
307 tim 2832 public:
308 tim 2821
309 tim 2836 typedef list<pair<BaseVisitor*, int> > VistorListType;
310     typedef VistorListType::iterator VisitorListIterator;
311     virtual void visit(Atom* atom) {
312     VisitorListIterator i;
313     BaseVisitor* curVisitor;
314     for(i = visitorList.begin();i != visitorList.end();++i) {
315     atom->accept(*i);
316     }
317 tim 2832 }
318 tim 2821
319 tim 2836 virtual void visit(DirectionalAtom* datom) {
320     VisitorListIterator i;
321     BaseVisitor* curVisitor;
322     for(i = visitorList.begin();i != visitorList.end();++i) {
323     atom->accept(*i);
324     }
325 tim 2832 }
326 tim 2821
327 tim 2836 virtual void visit(RigidBody* rb) {
328     VisitorListIterator i;
329     std::vector<Atom*> myAtoms;
330     std::vector<Atom*>::iterator ai;
331     myAtoms = rb->getAtoms();
332     for(i = visitorList.begin();i != visitorList.end();++i) {{
333     rb->accept(*i);
334     for(ai = myAtoms.begin(); ai != myAtoms.end(); ++ai){
335     (*ai)->accept(*i);
336     }
337 tim 2832 }
338 tim 2836
339     void addVisitor(BaseVisitor* v, int priority);
340    
341     protected:
342     VistorListType visitorList;
343 tim 2825 };
344    
345 tim 2821 \end{lstlisting}
346 tim 2829
347 tim 2730 \section{\label{appendixSection:concepts}Concepts}
348 tim 2685
349 tim 2829 OOPSE manipulates both traditional atoms as well as some objects
350     that {\it behave like atoms}. These objects can be rigid
351     collections of atoms or atoms which have orientational degrees of
352 tim 2836 freedom. A diagram of the class hierarchy is illustrated in
353     Fig.~\ref{oopseFig:hierarchy}. Every Molecule, Atom and
354 tim 2829 DirectionalAtom in {\sc OOPSE} have their own names which are
355     specified in the {\tt .md} file. In contrast, RigidBodies are
356     denoted by their membership and index inside a particular molecule:
357     [MoleculeName]\_RB\_[index] (the contents inside the brackets depend
358     on the specifics of the simulation). The names of rigid bodies are
359     generated automatically. For example, the name of the first rigid
360     body in a DMPC molecule is DMPC\_RB\_0.
361 tim 2838 \begin{itemize}
362     \item A {\bf StuntDouble} is {\it any} object that can be manipulated by the
363     integrators and minimizers.
364     \item An {\bf Atom} is a fundamental point-particle that can be moved around during a simulation.
365     \item A {\bf DirectionalAtom} is an atom which has {\it orientational} as well as translational degrees of freedom.
366     \item A {\bf RigidBody} is a collection of {\bf Atom}s or {\bf
367     DirectionalAtom}s which behaves as a single unit.
368     \end{itemize}
369 tim 2688
370 tim 2730 \section{\label{appendixSection:syntax}Syntax of the Select Command}
371    
372 tim 2837 {\sc OOPSE} provides a powerful selection utility to select
373     StuntDoubles. The most general form of the select command is:
374 tim 2730
375 tim 2837 {\tt select {\it expression}}.
376    
377     This expression represents an arbitrary set of StuntDoubles (Atoms
378     or RigidBodies) in {\sc OOPSE}. Expressions are composed of either
379     name expressions, index expressions, predefined sets, user-defined
380     expressions, comparison operators, within expressions, or logical
381     combinations of the above expression types. Expressions can be
382     combined using parentheses and the Boolean operators.
383    
384 tim 2730 \subsection{\label{appendixSection:logical}Logical expressions}
385    
386     The logical operators allow complex queries to be constructed out of
387     simpler ones using the standard boolean connectives {\bf and}, {\bf
388     or}, {\bf not}. Parentheses can be used to alter the precedence of
389     the operators.
390    
391     \begin{center}
392     \begin{tabular}{|ll|}
393     \hline
394     {\bf logical operator} & {\bf equivalent operator} \\
395     \hline
396     and & ``\&'', ``\&\&'' \\
397     or & ``$|$'', ``$||$'', ``,'' \\
398     not & ``!'' \\
399     \hline
400     \end{tabular}
401     \end{center}
402    
403     \subsection{\label{appendixSection:name}Name expressions}
404    
405     \begin{center}
406 tim 2805 \begin{tabular}{|llp{2in}|}
407 tim 2730 \hline {\bf type of expression} & {\bf examples} & {\bf translation
408     of
409     examples} \\
410     \hline expression without ``.'' & select DMPC & select all
411     StuntDoubles
412     belonging to all DMPC molecules \\
413     & select C* & select all atoms which have atom types beginning with C
414     \\
415     & select DMPC\_RB\_* & select all RigidBodies in DMPC molecules (but
416     only select the rigid bodies, and not the atoms belonging to them). \\
417     \hline expression has one ``.'' & select TIP3P.O\_TIP3P & select the
418     O\_TIP3P
419     atoms belonging to TIP3P molecules \\
420     & select DMPC\_RB\_O.PO4 & select the PO4 atoms belonging to
421     the first
422     RigidBody in each DMPC molecule \\
423     & select DMPC.20 & select the twentieth StuntDouble in each DMPC
424     molecule \\
425     \hline expression has two ``.''s & select DMPC.DMPC\_RB\_?.* &
426     select all atoms
427     belonging to all rigid bodies within all DMPC molecules \\
428     \hline
429     \end{tabular}
430     \end{center}
431    
432     \subsection{\label{appendixSection:index}Index expressions}
433    
434     \begin{center}
435     \begin{tabular}{|lp{4in}|}
436     \hline
437     {\bf examples} & {\bf translation of examples} \\
438     \hline
439     select 20 & select all of the StuntDoubles belonging to Molecule 20 \\
440     select 20 to 30 & select all of the StuntDoubles belonging to
441     molecules which have global indices between 20 (inclusive) and 30
442     (exclusive) \\
443     \hline
444     \end{tabular}
445     \end{center}
446    
447     \subsection{\label{appendixSection:predefined}Predefined sets}
448    
449     \begin{center}
450     \begin{tabular}{|ll|}
451     \hline
452     {\bf keyword} & {\bf description} \\
453     \hline
454     all & select all StuntDoubles \\
455     none & select none of the StuntDoubles \\
456     \hline
457     \end{tabular}
458     \end{center}
459    
460     \subsection{\label{appendixSection:userdefined}User-defined expressions}
461    
462     Users can define arbitrary terms to represent groups of
463     StuntDoubles, and then use the define terms in select commands. The
464     general form for the define command is: {\bf define {\it term
465 tim 2815 expression}}. Once defined, the user can specify such terms in
466     boolean expressions
467 tim 2730
468     {\tt define SSDWATER SSD or SSD1 or SSDRF}
469    
470     {\tt select SSDWATER}
471    
472     \subsection{\label{appendixSection:comparison}Comparison expressions}
473    
474     StuntDoubles can be selected by using comparision operators on their
475     properties. The general form for the comparison command is: a
476     property name, followed by a comparision operator and then a number.
477    
478     \begin{center}
479     \begin{tabular}{|l|l|}
480     \hline
481     {\bf property} & mass, charge \\
482     {\bf comparison operator} & ``$>$'', ``$<$'', ``$=$'', ``$>=$'',
483     ``$<=$'', ``$!=$'' \\
484     \hline
485     \end{tabular}
486     \end{center}
487    
488     For example, the phrase {\tt select mass > 16.0 and charge < -2}
489 tim 2805 would select StuntDoubles which have mass greater than 16.0 and
490 tim 2730 charges less than -2.
491    
492     \subsection{\label{appendixSection:within}Within expressions}
493    
494     The ``within'' keyword allows the user to select all StuntDoubles
495     within the specified distance (in Angstroms) from a selection,
496     including the selected atom itself. The general form for within
497     selection is: {\tt select within(distance, expression)}
498    
499     For example, the phrase {\tt select within(2.5, PO4 or NC4)} would
500     select all StuntDoubles which are within 2.5 angstroms of PO4 or NC4
501     atoms.
502    
503    
504 tim 2811 \section{\label{appendixSection:analysisFramework}Analysis Framework}
505 tim 2730
506     \subsection{\label{appendixSection:StaticProps}StaticProps}
507    
508     {\tt StaticProps} can compute properties which are averaged over
509     some or all of the configurations that are contained within a dump
510     file. The most common example of a static property that can be
511     computed is the pair distribution function between atoms of type $A$
512 tim 2815 and other atoms of type $B$, $g_{AB}(r)$. {\tt StaticProps} can
513     also be used to compute the density distributions of other molecules
514     in a reference frame {\it fixed to the body-fixed reference frame}
515     of a selected atom or rigid body.
516 tim 2730
517     There are five seperate radial distribution functions availiable in
518     OOPSE. Since every radial distrbution function invlove the
519     calculation between pairs of bodies, {\tt -{}-sele1} and {\tt
520     -{}-sele2} must be specified to tell StaticProps which bodies to
521     include in the calculation.
522    
523     \begin{description}
524     \item[{\tt -{}-gofr}] Computes the pair distribution function,
525     \begin{equation*}
526     g_{AB}(r) = \frac{1}{\rho_B}\frac{1}{N_A} \langle \sum_{i \in A}
527     \sum_{j \in B} \delta(r - r_{ij}) \rangle
528     \end{equation*}
529     \item[{\tt -{}-r\_theta}] Computes the angle-dependent pair distribution
530     function. The angle is defined by the intermolecular vector
531     $\vec{r}$ and $z$-axis of DirectionalAtom A,
532     \begin{equation*}
533     g_{AB}(r, \cos \theta) = \frac{1}{\rho_B}\frac{1}{N_A} \langle
534     \sum_{i \in A} \sum_{j \in B} \delta(r - r_{ij}) \delta(\cos
535     \theta_{ij} - \cos \theta)\rangle
536     \end{equation*}
537     \item[{\tt -{}-r\_omega}] Computes the angle-dependent pair distribution
538     function. The angle is defined by the $z$-axes of the two
539     DirectionalAtoms A and B.
540     \begin{equation*}
541     g_{AB}(r, \cos \omega) = \frac{1}{\rho_B}\frac{1}{N_A} \langle
542     \sum_{i \in A} \sum_{j \in B} \delta(r - r_{ij}) \delta(\cos
543     \omega_{ij} - \cos \omega)\rangle
544     \end{equation*}
545     \item[{\tt -{}-theta\_omega}] Computes the pair distribution in the angular
546     space $\theta, \omega$ defined by the two angles mentioned above.
547     \begin{equation*}
548     g_{AB}(\cos\theta, \cos \omega) = \frac{1}{\rho_B}\frac{1}{N_A}
549     \langle \sum_{i \in A} \sum_{j \in B} \langle \delta(\cos
550     \theta_{ij} - \cos \theta) \delta(\cos \omega_{ij} - \cos
551     \omega)\rangle
552     \end{equation*}
553     \item[{\tt -{}-gxyz}] Calculates the density distribution of particles of type
554     B in the body frame of particle A. Therefore, {\tt -{}-originsele}
555     and {\tt -{}-refsele} must be given to define A's internal
556     coordinate set as the reference frame for the calculation.
557     \end{description}
558    
559     The vectors (and angles) associated with these angular pair
560     distribution functions are most easily seen in the figure below:
561    
562     \begin{figure}
563     \centering
564 tim 2805 \includegraphics[width=3in]{definition.eps}
565 tim 2730 \caption[Definitions of the angles between directional objects]{ \\
566     Any two directional objects (DirectionalAtoms and RigidBodies) have
567     a set of two angles ($\theta$, and $\omega$) between the z-axes of
568     their body-fixed frames.} \label{oopseFig:gofr}
569     \end{figure}
570    
571 tim 2815 Due to the fact that the selected StuntDoubles from two selections
572     may be overlapped, {\tt StaticProps} performs the calculation in
573     three stages which are illustrated in
574     Fig.~\ref{oopseFig:staticPropsProcess}.
575    
576     \begin{figure}
577     \centering
578     \includegraphics[width=\linewidth]{staticPropsProcess.eps}
579     \caption[A representation of the three-stage correlations in
580 tim 2816 \texttt{StaticProps}]{This diagram illustrates three-stage
581     processing used by \texttt{StaticProps}. $S_1$ and $S_2$ are the
582     numbers of selected stuntdobules from {\tt -{}-sele1} and {\tt
583     -{}-sele2} respectively, while $C$ is the number of stuntdobules
584     appearing at both sets. The first stage($S_1-C$ and $S_2$) and
585     second stages ($S_1$ and $S_2-C$) are completely non-overlapping. On
586     the contrary, the third stage($C$ and $C$) are completely
587     overlapping} \label{oopseFig:staticPropsProcess}
588 tim 2815 \end{figure}
589    
590 tim 2730 The options available for {\tt StaticProps} are as follows:
591     \begin{longtable}[c]{|EFG|}
592     \caption{StaticProps Command-line Options}
593     \\ \hline
594     {\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline
595     \endhead
596     \hline
597     \endfoot
598     -h& {\tt -{}-help} & Print help and exit \\
599     -V& {\tt -{}-version} & Print version and exit \\
600 tim 2809 -i& {\tt -{}-input} & input dump file \\
601     -o& {\tt -{}-output} & output file name \\
602     -n& {\tt -{}-step} & process every n frame (default=`1') \\
603     -r& {\tt -{}-nrbins} & number of bins for distance (default=`100') \\
604     -a& {\tt -{}-nanglebins} & number of bins for cos(angle) (default= `50') \\
605     -l& {\tt -{}-length} & maximum length (Defaults to 1/2 smallest length of first frame) \\
606     & {\tt -{}-sele1} & select the first StuntDouble set \\
607     & {\tt -{}-sele2} & select the second StuntDouble set \\
608     & {\tt -{}-sele3} & select the third StuntDouble set \\
609     & {\tt -{}-refsele} & select reference (can only be used with {\tt -{}-gxyz}) \\
610     & {\tt -{}-molname} & molecule name \\
611     & {\tt -{}-begin} & begin internal index \\
612     & {\tt -{}-end} & end internal index \\
613 tim 2730 \hline
614     \multicolumn{3}{|l|}{One option from the following group of options is required:} \\
615     \hline
616     & {\tt -{}-gofr} & $g(r)$ \\
617     & {\tt -{}-r\_theta} & $g(r, \cos(\theta))$ \\
618     & {\tt -{}-r\_omega} & $g(r, \cos(\omega))$ \\
619     & {\tt -{}-theta\_omega} & $g(\cos(\theta), \cos(\omega))$ \\
620     & {\tt -{}-gxyz} & $g(x, y, z)$ \\
621     & {\tt -{}-p2} & $P_2$ order parameter ({\tt -{}-sele1} and {\tt -{}-sele2} must be specified) \\
622     & {\tt -{}-scd} & $S_{CD}$ order parameter(either {\tt -{}-sele1}, {\tt -{}-sele2}, {\tt -{}-sele3} are specified or {\tt -{}-molname}, {\tt -{}-begin}, {\tt -{}-end} are specified) \\
623     & {\tt -{}-density} & density plot ({\tt -{}-sele1} must be specified) \\
624     & {\tt -{}-slab\_density} & slab density ({\tt -{}-sele1} must be specified)
625     \end{longtable}
626    
627     \subsection{\label{appendixSection:DynamicProps}DynamicProps}
628    
629     {\tt DynamicProps} computes time correlation functions from the
630     configurations stored in a dump file. Typical examples of time
631     correlation functions are the mean square displacement and the
632     velocity autocorrelation functions. Once again, the selection
633     syntax can be used to specify the StuntDoubles that will be used for
634     the calculation. A general time correlation function can be thought
635     of as:
636     \begin{equation}
637     C_{AB}(t) = \langle \vec{u}_A(t) \cdot \vec{v}_B(0) \rangle
638     \end{equation}
639     where $\vec{u}_A(t)$ is a vector property associated with an atom of
640     type $A$ at time $t$, and $\vec{v}_B(t^{\prime})$ is a different
641     vector property associated with an atom of type $B$ at a different
642     time $t^{\prime}$. In most autocorrelation functions, the vector
643     properties ($\vec{v}$ and $\vec{u}$) and the types of atoms ($A$ and
644     $B$) are identical, and the three calculations built in to {\tt
645     DynamicProps} make these assumptions. It is possible, however, to
646     make simple modifications to the {\tt DynamicProps} code to allow
647     the use of {\it cross} time correlation functions (i.e. with
648     different vectors). The ability to use two selection scripts to
649     select different types of atoms is already present in the code.
650    
651 tim 2815 For large simulations, the trajectory files can sometimes reach
652     sizes in excess of several gigabytes. In order to effectively
653     analyze that amount of data. In order to prevent a situation where
654     the program runs out of memory due to large trajectories,
655     \texttt{dynamicProps} will estimate the size of free memory at
656     first, and determine the number of frames in each block, which
657     allows the operating system to load two blocks of data
658     simultaneously without swapping. Upon reading two blocks of the
659     trajectory, \texttt{dynamicProps} will calculate the time
660     correlation within the first block and the cross correlations
661     between the two blocks. This second block is then freed and then
662     incremented and the process repeated until the end of the
663     trajectory. Once the end is reached, the first block is freed then
664     incremented, until all frame pairs have been correlated in time.
665 tim 2816 This process is illustrated in
666     Fig.~\ref{oopseFig:dynamicPropsProcess}.
667 tim 2815
668 tim 2816 \begin{figure}
669     \centering
670     \includegraphics[width=\linewidth]{dynamicPropsProcess.eps}
671     \caption[A representation of the block correlations in
672     \texttt{dynamicProps}]{This diagram illustrates block correlations
673     processing in \texttt{dynamicProps}. The shaded region represents
674     the self correlation of the block, and the open blocks are read one
675     at a time and the cross correlations between blocks are calculated.}
676     \label{oopseFig:dynamicPropsProcess}
677     \end{figure}
678    
679 tim 2730 The options available for DynamicProps are as follows:
680     \begin{longtable}[c]{|EFG|}
681     \caption{DynamicProps Command-line Options}
682     \\ \hline
683     {\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline
684     \endhead
685     \hline
686     \endfoot
687     -h& {\tt -{}-help} & Print help and exit \\
688     -V& {\tt -{}-version} & Print version and exit \\
689 tim 2809 -i& {\tt -{}-input} & input dump file \\
690     -o& {\tt -{}-output} & output file name \\
691     & {\tt -{}-sele1} & select first StuntDouble set \\
692     & {\tt -{}-sele2} & select second StuntDouble set (if sele2 is not set, use script from sele1) \\
693 tim 2730 \hline
694     \multicolumn{3}{|l|}{One option from the following group of options is required:} \\
695     \hline
696     -r& {\tt -{}-rcorr} & compute mean square displacement \\
697     -v& {\tt -{}-vcorr} & compute velocity correlation function \\
698     -d& {\tt -{}-dcorr} & compute dipole correlation function
699     \end{longtable}
700    
701 tim 2811 \section{\label{appendixSection:tools}Other Useful Utilities}
702    
703     \subsection{\label{appendixSection:Dump2XYZ}Dump2XYZ}
704    
705 tim 2821 {\tt Dump2XYZ} can transform an OOPSE dump file into a xyz file
706     which can be opened by other molecular dynamics viewers such as Jmol
707     and VMD\cite{Humphrey1996}. The options available for Dump2XYZ are
708     as follows:
709 tim 2811
710    
711     \begin{longtable}[c]{|EFG|}
712     \caption{Dump2XYZ Command-line Options}
713     \\ \hline
714     {\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline
715     \endhead
716     \hline
717     \endfoot
718     -h & {\tt -{}-help} & Print help and exit \\
719     -V & {\tt -{}-version} & Print version and exit \\
720     -i & {\tt -{}-input} & input dump file \\
721     -o & {\tt -{}-output} & output file name \\
722     -n & {\tt -{}-frame} & print every n frame (default=`1') \\
723     -w & {\tt -{}-water} & skip the the waters (default=off) \\
724     -m & {\tt -{}-periodicBox} & map to the periodic box (default=off)\\
725     -z & {\tt -{}-zconstraint} & replace the atom types of zconstraint molecules (default=off) \\
726     -r & {\tt -{}-rigidbody} & add a pseudo COM atom to rigidbody (default=off) \\
727     -t & {\tt -{}-watertype} & replace the atom type of water model (default=on) \\
728     -b & {\tt -{}-basetype} & using base atom type (default=off) \\
729     & {\tt -{}-repeatX} & The number of images to repeat in the x direction (default=`0') \\
730     & {\tt -{}-repeatY} & The number of images to repeat in the y direction (default=`0') \\
731     & {\tt -{}-repeatZ} & The number of images to repeat in the z direction (default=`0') \\
732     -s & {\tt -{}-selection} & By specifying {\tt -{}-selection}=``selection command'' with Dump2XYZ, the user can select an arbitrary set of StuntDoubles to be
733     converted. \\
734     & {\tt -{}-originsele} & By specifying {\tt -{}-originsele}=``selection command'' with Dump2XYZ, the user can re-center the origin of the system around a specific StuntDouble \\
735     & {\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}.
736     \end{longtable}
737    
738 tim 2815 \subsection{\label{appendixSection:hydrodynamics}Hydro}
739 tim 2821
740     {\tt Hydro} can calculate resistance and diffusion tensors at the
741     center of resistance. Both tensors at the center of diffusion can
742     also be reported from the program, as well as the coordinates for
743     the beads which are used to approximate the arbitrary shapes. The
744     options available for Hydro are as follows:
745 tim 2811 \begin{longtable}[c]{|EFG|}
746     \caption{Hydrodynamics Command-line Options}
747     \\ \hline
748     {\bf option} & {\bf verbose option} & {\bf behavior} \\ \hline
749     \endhead
750     \hline
751     \endfoot
752     -h & {\tt -{}-help} & Print help and exit \\
753     -V & {\tt -{}-version} & Print version and exit \\
754     -i & {\tt -{}-input} & input dump file \\
755     -o & {\tt -{}-output} & output file prefix (default=`hydro') \\
756     -b & {\tt -{}-beads} & generate the beads only, hydrodynamics calculation will not be performed (default=off)\\
757 tim 2815 & {\tt -{}-model} & hydrodynamics model (supports ``AnalyticalModel'', ``RoughShell'' and ``BeadModel'') \\
758 tim 2811 \end{longtable}