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Comparing trunk/openmdDocs/openmdDoc.tex (file contents):
Revision 3791 by kstocke1, Wed May 11 15:22:29 2011 UTC vs.
Revision 3792 by gezelter, Thu Aug 9 18:48:23 2012 UTC

+\newcolumntype{H}{p{0.75in}}
+\newcolumntype{I}{p{5in}}
-+
-+
+\newcolumntype{J}{p{1.5in}}
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+\newcolumntype{K}{p{1.2in}}
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+\newcolumntype{L}{p{1.5in}}
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+\newcolumntype{M}{p{1.55in}}
+\title{{\sc OpenMD}: Molecular Dynamics in the Open}
+\label{table:zconParams}
+\end{longtable}
-<
+\chapter{\label{section:restraints}Restraints}
-<
+Restraints are external potentials that are added to a system to keep
-<
+particular molecules or collections of particles close to some
-<
+reference structure.  A restraint can be a collective
->
+% \chapter{\label{section:restraints}Restraints}
->
+% Restraints are external potentials that are added to a system to keep
->
+% particular molecules or collections of particles close to some
->
+% reference structure.  A restraint can be a collective
+\chapter{\label{section:thermInt}Thermodynamic Integration}
+Einstein crystal
+\label{table:thermIntParams}
+\end{longtable}
-+
-+
+\chapter{\label{section:rnemd}RNEMD}
-+
-+
+There are many ways to compute transport properties from molecular
-+
+dynamic simulations.  Equilibrium Molecular Dynamics (EMD) simulations
-+
+can be used by computing relevant time correlation functions and
-+
+assuming linear response theory holds.  These approaches are generally
-+
+subject to noise and poor convergence of the relevant correlation
-+
+functions. Traditional Non-equilibrium Molecular Dynamics (NEMD)
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+methods impose a gradient (e.g. thermal or momentum) on a simulation.
-+
+However, the resulting flux is often difficult to
-+
+measure. Furthermore, problems arise for NEMD simulations of
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+heterogeneous systems, such as phase-phase boundaries or interfaces,
-+
+where the type of gradient to enforce at the boundary between
-+
+materials is unclear.
-+
-+
+{\it Reverse} Non-Equilibrium Molecular Dynamics (RNEMD) methods adopt a
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+different approach in that an unphysical {\it flux} is imposed between
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+different regions or ``slabs'' of the simulation box.  The response of
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+the system is to develop a temperature or momentum {\it gradient}
-+
+between the two regions. Since the amount of the applied flux is known
-+
+exactly, and the measurement of gradient is generally less
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+complicated, imposed-flux methods typically take shorter simulation
-+
+times to obtain converged results for transport properties.
-+
-+
+%RNEMD figure
-+
-+
-+
+RNEMD methods further its advantages by utilizing momentum- and
-+
+energy-conserving approaches to apply fluxes. The original
-+
+``swapping'' approach by Muller-Plathe {\it et al.} %CITATIONS
-+
+can be seen as an imaginary elastic collision between selected
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+particles for each momentum exchange. This simple to implement
-+
+algorithm turned out to be quite useful in many simulations. However,
-+
+the approach inherently perturbs the ideal Maxwell-Boltzmann
-+
+distributions, which leads to undesirable side-effects when the
-+
+applied exchanged flux becomes quite large. %CITATION
-+
+This limits the range of flux available to the method, and also its
-+
+applications.
-+
+In OpenMD, we improve the above method by introducing two alternative
-+
+approaches:
-+
+Non-Isotropic Velocity Scaling (NIVS): %CITATION
-+
+Instead of have two individual particles involved in momentum
-+
+exchange, this algorithm applies scaling to all the particles in
-+
+particular regions:
-+
-+
+%NIVS equations
-+
-+
+Although the above matrices can be diagonal as shown, these
-+
+coefficients cannot be always the same, in order to satisfy the linear
-+
+momentum and kinetic energy conservation constraints:
-+
-+
+%Conservation equations
-+
-+
+And to apply a kinetic energy exchange between the two regions, the
-+
+following should be satisfied as well:
-+
-+
+%Flux equations
-+
-+
+Mathematically, any points in the 3-dimensional space of the solution
-+
+set would satisfy the equations. However, to avoid solving an
-+
+ill-conditioned high-order polynomial in actual practice, another
-+
+constraint, ${x_c=y_c}$, is applied, taking into consideration of its
-+
+physical relevance. Therefore, a quartic equation is solved in actual
-+
+practice to determine the sets of possible coefficients. To determine
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+which set is actually used to perform the scaling, two criteria are
-+
+mainly considered: 1. ${x,y,z\rightarrow 1}$ so that the perturbation
-+
+could be as gentle as possible. 2. ${K^x, K^y, K^z}$ have minimal
-+
+difference among each other, so that the anisotropy introduced by the
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+algorithm can be offset to some extend. One set of scaling
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+coefficients is chosen against these criteria, and the best one is
-+
+used to perform the scaling for that particular step. However, if no
-+
+solution found, the NIVS move is not performed in that step.
-+
-+
+Although the NIVS algorithm can also be applied to impose a
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+directional momentum flux, thermal anisotropy was observed in
-+
+relatively high flux simulations. %This is because...
-+
+However, the gentleness and ability to apply a wide range of kinetic
-+
+energy flux makes the method useful in thermal transport simulations,
-+
+particularly for complex and heterogeneous systems including
-+
+interfaces. %CITATION
-+
-+
+Velocity Shearing and Scaling (VSS): %CITATION
-+
+Learning from NIVS that imposing directional momentum flux by velocity
-+
+scaling could cause problem, we shift the approach to combine the move
-+
+of velocity shearing and scaling:
-+
-+
+%VSS equations
-+
-+
+It turned out that this approach results in a set of simpler-to-solve
-+
+equations for conservation and to satisfy momentum exchange:
-+
-+
+%conservation equations
-+
-+
+Furthermore, isotropic scaling is now possible, with the presence of
-+
+velocity shearing quantities. Only a set of simple quadratic equations
-+
+need to be solved, and the positive set of coefficients are chosen, in
-+
+order to reach minimal perturbations. Similar to the NIVS method, no
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+VSS is performed in a step given that no solution can be found.
-+
-+
+The VSS approach turned out to be versatile in both thermal and
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+directional momentum transport simulations. It is found that the
-+
+perturbation is minimal and undesired side-effects like thermal
-+
+anisotropy can be avoided. Another nice feature of VSS is its ability
-+
+to combine a thermal and a directional momentum flux. This feature has
-+
+been utilized to map out the shear viscosity of SPC/E water in a wide
-+
+range of temperature (90~K) just with one single simulation. Possible
-+
+applications may also include the studies of thermal-momentum coupled
-+
+transport phenomena. VSS also allows the directional momentum flux to
-+
+have quite arbitary directions, which could benefit researches of
-+
+anisotropic systems.
-+
-+
+Table \ref{table:rnemd} summarizes the parameters used in RNEMD
-+
+simulations.
-+
-+
+\begin{longtable}[c]{JKLM}
-+
+\caption{The following keywords must be enclosed inside a {\tt RNEMD\{\}} block}
-+
+\\
-+
+{\bf keyword} & {\bf units} & {\bf use} & {\bf remarks}  \\ \hline
-+
+\endhead
-+
+\hline
-+
+\endfoot
-+
+{\tt useRNEMD} & logical & perform RNEMD? & default is ``false'' \\
-+
+{\tt objectSelection} & string & see section \ref{section:syntax}
-+
+for selection syntax & default is ``select all'' \\
-+
+{\tt method} & string & exchange method & one of the following:
-+
+{\tt Swap, NIVS,} or {\tt VSS}  (default is {\tt VSS}) \\
-+
+{\tt fluxType} & string & what is being exchanged between slabs? & one
-+
+of the following: {\tt KE, Px, Py, Pz, Pvector, KE+Px, KE+Py, KE+Pvector} \\
-+
+{\tt kineticFlux} & kcal mol$^{-1}$ \AA$^{-2}$ fs$^{-1}$ & specify the kinetic energy flux &  \\
-+
+{\tt momentumFlux} & amu \AA$^{-1}$ fs$^{-2}$ & specify the momentum flux & \\
-+
+{\tt momentumFluxVector} & amu \AA$^{-1}$ fs$^{-2}$ & specify the momentum flux when
-+
+{\tt Pvector} is part of the exchange & Vector3d input\\
-+
+{\tt exchangeTime} & fs & how often to perform the exchange & default is 100 fs\\
-+
-+
+{\tt slabWidth} & $\mbox{\AA}$ & width of the two exchange slabs & default is $\mathsf{H}_{zz} / 10.0$ \\
-+
+{\tt slabAcenter} & $\mbox{\AA}$ & center of the end slab & default is 0 \\
-+
+{\tt slabBcenter} & $\mbox{\AA}$ & center of the middle slab & default is $\mathsf{H}_{zz} / 2$ \\
-+
+{\tt outputFileName} & string & file name for output histograms & default is the same prefix as the
-+
+.md file, but with the {\tt .rnemd} extension \\
-+
+{\tt outputBins} & int & number of $z$-bins in the output histogram &
-+
+default is 20 \\
-+
+{\tt outputFields} & string & columns to print in the {\tt .rnemd}
-+
+file where each column is separated by a pipe ($\mid$) symbol. & Allowed column names are: {\sc z, temperature, velocity, density}} \\
-+
+\label{table:rnemd}
-+
+\end{longtable}
-+
-+
+\chapter{\label{section:minimizer}Energy Minimization}
+As one of the basic procedures of molecular modeling, energy

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Comparing trunk/openmdDocs/openmdDoc.tex (file contents): Revision 3791 by kstocke1, Wed May 11 15:22:29 2011 UTC vs. Revision 3792 by gezelter, Thu Aug 9 18:48:23 2012 UTC

Diff Legend

Comparing trunk/openmdDocs/openmdDoc.tex (file contents):
Revision 3791 by kstocke1, Wed May 11 15:22:29 2011 UTC vs.
Revision 3792 by gezelter, Thu Aug 9 18:48:23 2012 UTC