--- trunk/oopseDocs/oopseDoc.tex 2008/05/30 15:58:01 3402 +++ trunk/oopseDocs/oopseDoc.tex 2008/05/30 18:16:59 3403 @@ -498,7 +498,7 @@ are SD and CG. Either {\tt ensemble} or {\tt minimizer {\tt minimizer} & string & Chooses a minimizer & Possible minimizers are SD and CG. Either {\tt ensemble} or {\tt minimizer} must be specified. \\ {\tt ensemble} & string & Sets the ensemble. & Possible ensembles are -NVE, NVT, NPTi, NPAT, NPTf, and NPTxyz. Either {\tt ensemble} +NVE, NVT, NPTi, NPAT, NPTf, NPTxyz, and LD. Either {\tt ensemble} or {\tt minimizer} must be specified. \\ {\tt dt} & fs & Sets the time step. & Selection of {\tt dt} should be small enough to sample the fastest motion of the simulation. ({\tt @@ -1905,6 +1905,8 @@ NPTxyz & approximate isobaric-isothermal & {\tt ensemb & (with changes to box shape) & \\ NPTxyz & approximate isobaric-isothermal & {\tt ensemble = NPTxyz;} \\ & (with separate barostats on each box dimension) & \\ +LD & Langevin Dynamics & {\tt ensemble = LD;} \\ + & (approximates the effects of an implicit solvent) & \\ \end{tabular} \end{center} @@ -2370,15 +2372,14 @@ simulations). orientational anisotropy in the system (i.e. in lipid bilayer simulations). -\section{Langevin Dynamics (LANGEVINDYNAMICS)\label{LDRB}} +\section{Langevin Dynamics (LD)\label{LDRB}} -{\sc oopse} implements a Langevin dynamics integrator in order to -perform molecular dynamics simulations in implicit solvent -environments. This results in substantial performance gains when the -detailed dynamics of the solvent is not important. Since {\sc oopse} -also handles rigid bodies of arbitrary composition and shape, the -Langevin integrator is somewhat more complex than in other simulation -packages. +{\sc oopse} implements a Langevin integrator in order to perform +molecular dynamics simulations in implicit solvent environments. This +can result in substantial performance gains when the detailed dynamics +of the solvent is not important. Since {\sc oopse} also handles rigid +bodies of arbitrary composition and shape, the Langevin integrator is +by necessity somewhat more complex than in other simulation packages. Consider the Langevin equations of motion in generalized coordinates \begin{equation} @@ -2435,11 +2436,19 @@ $\Xi_R$ is the $6\times6$ resistance tensor at the cen 2 k_B T \Xi_R \delta(t - t'). \label{eq:randomForce} \end{equation} $\Xi_R$ is the $6\times6$ resistance tensor at the center of -resistance. Once this tensor is known for a given rigid body (as -described in the previous section) obtaining a stochastic vector that -has the properties in Eq. (\ref{eq:randomForce}) can be done -efficiently by carrying out a one-time Cholesky decomposition to -obtain the square root matrix of the resistance tensor, +resistance. + +For atoms and ellipsoids, there are good approximations for this +tensor that are based on Stokes' law. For arbitrary rigid bodies, the +resistance tensor must be pre-computed before Langevin dynamics can be +used. The {\sc oopse} distribution contains a utitilty program called +Hydro that performs this computation. + +Once this tensor is known for a given {\tt integrableObject}, +obtaining a stochastic vector that has the properties in +Eq. (\ref{eq:randomForce}) can be done efficiently by carrying out a +one-time Cholesky decomposition to obtain the square root matrix of +the resistance tensor, \begin{equation} \Xi_R = {\bf S} {\bf S}^{T}, \label{eq:Cholesky} @@ -2477,10 +2486,10 @@ frame, we consider the equation of motion for the angu \begin{equation} \frac{\partial}{\partial t}{\bf j}(t) = \tau^{~b}(t) \end{equation} -Embedding the friction and random forces into the the total force and -torque, one can integrate the Langevin equations of motion for a rigid -body of arbitrary shape in a velocity-Verlet style 2-part algorithm, -where $h = \delta t$: +By embedding the friction and random forces into the the total force +and torque, {\sc oopse} integrates the Langevin equations of motion +for a rigid body of arbitrary shape in a velocity-Verlet style 2-part +algorithm, where $h = \delta t$: {\tt move A:} \begin{align*} @@ -2585,35 +2594,40 @@ the velocities can be advanced to the same time value. + \frac{h}{2} {\bf \tau}^{~b}(t + h) . \end{align*} -The viscosity of the implicit of solvents must be specified using {\tt -viscosity} keywords in the meta-data file to use langevin dynamics -integrator. For simple shaped particles (spheres and ellipsoids), no -further parameters are necessary. However, there are no analytical -solutions for composite shaped particles, the approximate methods have -to be applied to get the resistance tensor. The file which contains -the information about hydro properties is indicated by {\tt -HydroPropFile} keyword in meta-data file. The {\tt HydroPropFile} is -precalculated by {\tt Hydro}. - -\begin{longtable}[c]{ABCD} -\caption{Meta-data Keywords: Langevin Dynamics Parameters} +The viscosity of the implicit solvent must be specified using the {\tt +viscosity} keyword in the meta-data file if the Langevin integrator is +selected. For simple particles (spheres and ellipsoids), no further +parameters are necessary. Since there are no analytic solutions for +the resistance tensors for composite rigid bodies, the approximate +tensors for these objects must also be specified in order to use +Langevin dynamics. The meta-data file must therefore point to another +file which contains the information about the hydrodynamic properties +of all complex rigid bodies being used during the simulation. The +{\tt HydroPropFile} keyword is used to specify the name of this +file. A {\tt HydroPropFile} should be precalculated using the Hydro +program that is included in the {\sc oopse} distribution. + +\begin{longtable}[c]{ABG} +\caption{Meta-data Keywords: Required parameters for the Langevin integrator} \\ -{\bf keyword} & {\bf units} & {\bf use} & {\bf remarks} \\ \hline +{\bf keyword} & {\bf units} & {\bf use} \\ \hline \endhead \hline \endfoot -{\tt viscosity} & centipoise & Sets the value of viscosity of implicit -solvents & \\ {\tt HydroPropFile} & string & specifies the resistance -tensor file & usually a {\tt .diff} file which is precalculated by -{\sc Hydro}. Not necessory for simple shaped particles (spheres and -ellipsoids) \\ -{\tt beadSize} & $\mbox{\AA}$ & Sets the diameters of -beads when {\sc Rough Shell Model} is used to generate the resistance -tensor file. \\ +{\tt viscosity} & centipoise & Sets the value of viscosity of the implicit +solvent \\ +{\tt targetTemp} & K & Sets the target temperature of the system. +This parameter must be specified to use Langevin dynamics. \\ +{\tt HydroPropFile} & string & Specifies the name of the resistance +tensor (usually a {\tt .diff} file) which is precalculated by {\tt +Hydro}. This keyworkd is not necessary if the simulation contains only +simple bodies (spheres and ellipsoids). \\ +{\tt beadSize} & $\mbox{\AA}$ & Sets the diameter of the beads to use +when the {\tt RoughShell} model is used to approximate the resistance +tensor. \label{table:ldParameters} \end{longtable} - \section{\label{sec:constraints}Constraint Methods} \subsection{\label{oopseSec:rattle}The {\sc rattle} Method for Bond @@ -3459,14 +3473,18 @@ The options available for SimpleBuilder are as follows \end{longtable} \section{\label{oopseSec:Hydro}Hydro} -{\tt Hydro} generates {\tt .diff} file which is required when a Langevin -Dynamics simulation using approximate models (supports Bead Model and -Rough Shell Model) is performed. To generate the {\tt }.diff file, the -meta-data file is needed as the input file. The viscosity of the fluid -flow (solvent) and the temperature of the system have to be defined in -meta-data file. If the approximate model is {\tt Rough Shell Model}, -the {\tt beadSize} which is the diameter of every beads must be -specified in meta-data file. +{\tt Hydro} generates resistance tensor ({\tt .diff}) files which are +required when using the Langevin integrator using complex rigid +bodies. {\tt Hydro} supports two approximate models: the {\tt +BeadModel} and {\tt RoughShell}. Additionally, {\tt Hydro} can +generate resistance tensor files using analytic solutions for simple +shapes. To generate a {\tt }.diff file, a meta-data file is needed as +the input file. Since the resistance tensor depends on these +quantities, the {\tt viscosity} of the solvent and the temperature +({\tt targetTemp}) of the system must be defined in meta-data file. If +the approximate model in use is the {\tt RoughShell} model the {\tt +beadSize} (the diameter of the small beads used to approximate the +surface of the body) must also be specified. The options available for Hydro are as follows: \begin{longtable}[c]{|EFG|} @@ -3480,10 +3498,10 @@ The options available for Hydro are as follows: -V& {\tt -{}-version} & Print version and exit\\ -i& {\tt -{}-input=filename} & input MetaData (md) file\\ -o& {\tt -{}-output=STRING} & Output file name\\ - & {\tt -{}-model=STRING} & hydrodynamics model (supports -RoughShell and BeadModel)\\ + & {\tt -{}-model=STRING} & hydrodynamics model (supports both +{\tt RoughShell} and {\tt BeadModel})\\ -b& {\tt -{}-beads} & generate the beads only, -hydrodynamics will be performed (default=off)\\ +hydrodynamic calculations will not be performed (default=off)\\ \end{longtable}