--- trunk/tengDissertation/Methodology.tex	2006/06/06 20:49:05	2806
+++ trunk/tengDissertation/Methodology.tex	2006/06/07 01:49:15	2807
@@ -139,7 +139,7 @@ in Fig.~\ref{timestep}.
 average 7\% increase in computation time using the DLM method in
 place of quaternions. This cost is more than justified when
 comparing the energy conservation of the two methods as illustrated
-in Fig.~\ref{timestep}.
+in Fig.~\ref{methodFig:timestep}.
 
 \begin{figure}
 \centering
@@ -474,8 +474,7 @@ Bond constraints are applied at the end of both the {\
 \end{equation}
 
 Bond constraints are applied at the end of both the {\tt moveA} and
-{\tt moveB} portions of the algorithm.  Details on the constraint
-algorithms are given in section \ref{oopseSec:rattle}.
+{\tt moveB} portions of the algorithm.
 
 \subsection{\label{methodSection:NPTf}Constant-pressure integration with a
 flexible box (NPTf)}
@@ -793,24 +792,23 @@ systems\cite{Garcia-Palacios1998,Berkov2002,Denisov200
 between the native and denatured states. Because of its stability
 against noise, Langevin dynamics is very suitable for studying
 remagnetization processes in various
-systems\cite{Garcia-Palacios1998,Berkov2002,Denisov2003}. For
-instance, the oscillation power spectrum of nanoparticles from
-Langevin dynamics simulation has the same peak frequencies for
-different wave vectors,which recovers the property of magnetic
-excitations in small finite structures\cite{Berkov2005a}. In an
-attempt to reduce the computational cost of simulation, multiple
-time stepping (MTS) methods have been introduced and have been of
-great interest to macromolecule and protein
-community\cite{Tuckerman1992}. Relying on the observation that
-forces between distant atoms generally demonstrate slower
-fluctuations than forces between close atoms, MTS method are
-generally implemented by evaluating the slowly fluctuating forces
-less frequently than the fast ones. Unfortunately, nonlinear
-instability resulting from increasing timestep in MTS simulation
-have became a critical obstruction preventing the long time
-simulation. Due to the coupling to the heat bath, Langevin dynamics
-has been shown to be able to damp out the resonance artifact more
-efficiently\cite{Sandu1999}.
+systems\cite{Palacios1998,Berkov2002,Denisov2003}. For instance, the
+oscillation power spectrum of nanoparticles from Langevin dynamics
+simulation has the same peak frequencies for different wave
+vectors,which recovers the property of magnetic excitations in small
+finite structures\cite{Berkov2005a}. In an attempt to reduce the
+computational cost of simulation, multiple time stepping (MTS)
+methods have been introduced and have been of great interest to
+macromolecule and protein community\cite{Tuckerman1992}. Relying on
+the observation that forces between distant atoms generally
+demonstrate slower fluctuations than forces between close atoms, MTS
+method are generally implemented by evaluating the slowly
+fluctuating forces less frequently than the fast ones.
+Unfortunately, nonlinear instability resulting from increasing
+timestep in MTS simulation have became a critical obstruction
+preventing the long time simulation. Due to the coupling to the heat
+bath, Langevin dynamics has been shown to be able to damp out the
+resonance artifact more efficiently\cite{Sandu1999}.
 
 %review rigid body dynamics
 Rigid bodies are frequently involved in the modeling of different
@@ -898,7 +896,7 @@ term\cite{Beard2001}. As a complement to IBD which has
 average acceleration is not always true for cooperative motion which
 is common in protein motion. An inertial Brownian dynamics (IBD) was
 proposed to address this issue by adding an inertial correction
-term\cite{Beard2001}. As a complement to IBD which has a lower bound
+term\cite{Beard2003}. As a complement to IBD which has a lower bound
 in time step because of the inertial relaxation time, long-time-step
 inertial dynamics (LTID) can be used to investigate the inertial
 behavior of the polymer segments in low friction
