updates to hyper doc pages

doc/src/fix_hyper_global.txt

@@ -33,9 +33,9 @@ dynamics of the system in a manner that effectively accelerates time.
 This is in contrast to the "fix hyper/local"_fix_hyper_local.html
 command, which can be user to perform a local hyperdynamics (LHD)
 simulation, by adding a local bias potential to multiple pairs of
-atoms at each timestep.  GHD can speed-up a small simulation with up
-to a few 100 atoms.  For larger systems, LHD is needed to achieve good
-speed-ups.
+atoms at each timestep.  GHD can time accelerate a small simulation
+with up to a few 100 atoms.  For larger systems, LHD is needed to
+achieve good time acceleration.
 
 For a system that undergoes rare transition events, where one or more
 atoms move over an energy barrier to a new potential energy basin, the
@@ -43,23 +43,24 @@ effect of the bias potential is to induce more rapid transitions.
 This can lead to a dramatic speed-up in the rate at which events
 occurs, without altering their relative frequencies, thus leading to
 an overall increase in the elapsed real time of the simulation as
-compared to simulating for the same number of timesteps with normal
-MD.  See the "hyper"_hyper.html doc page for a more general discussion
-of hyperdynamics and citations that explain both GHD and LHD.
-
-The equations and logic used by this fix to perform GHD are as
-follows.  This follows the description of GHD given in
-"(Voter2013)"_#Voter2013ghd.  The bond-boost form of a bias potential
-for GHD is due to Miron and Fichthorn as described in
-"(Miron)"_#Mironghd.  Here we use a simplified version of bond-boost
-GHD where a single bond is biased at any one timestep.
-
-Bonds are defined between every pair of I,J atoms whose R0ij distance
+compared to running for the same number of timesteps with normal MD.
+See the "hyper"_hyper.html doc page for a more general discussion of
+hyperdynamics and citations that explain both GHD and LHD.
+
+The equations and logic used by this fix to perform GHD follow the
+description given in "(Voter2013)"_#Voter2013ghd.  The bond-boost form
+of a bias potential for HD is due to Miron and Fichthorn as described
+in "(Miron)"_#Mironghd.  In LAMMPS we use a simplified version of
+bond-boost GHD where a single bond in the system is biased at any one
+timestep.
+
+Bonds are defined between each pair of I,J atoms whose R0ij distance
 is less than {cutbond}, when the system is in a quenched state
 (minimum) energy.  Note that these are not "bonds" in a covalent
 sense.  A bond is simply any pair of atoms that meet the distance
-criterion.  {Cutbond} is an argument to this fix; it is discussed more
-below.
+criterion.  {Cutbond} is an argument to this fix; it is discussed
+below.  A bond is only formed if one or both of the I.J atoms are in
+the specified group.
 
 The current strain of bond IJ (when running dynamics) is defined as
 
@@ -74,16 +75,16 @@ Vij = Vmax * (1 - (Eij/q)^2) for abs(Eij) < qfactor
     = 0 otherwise :pre
 
 where the prefactor {Vmax} and the cutoff {qfactor} are arguments to
-this fix; they are discussed more below.  This functional form is an
+this fix; they are discussed below.  This functional form is an
 inverse parabola centered at 0.0 with height Vmax and which goes to
 0.0 at +/- qfactor.
 
 Let Emax = the maximum of abs(Eij) for all IJ bonds in the system on a
 given timestep.  On that step, Vij is added as a bias potential to
-only the two atoms IJ in the bond with strain Emax, call it Vij(max).
-Note that Vij(max) will be 0.0 if Emax >= qfactor on that timestep.
-Also note that Vij(max) is added to the normal interatomic potential
-that is computed between all atoms in the system.
+only the single bond with strain Emax, call it Vij(max).  Note that
+Vij(max) will be 0.0 if Emax >= qfactor on that timestep.  Also note
+that Vij(max) is added to the normal interatomic potential that is
+computed between all atoms in the system at every step.
 
 The derivative of Vij(max) with respect to the position of each atom
 in the Emax bond gives a force Fij(max) acting on the bond as
@@ -91,19 +92,21 @@ in the Emax bond gives a force Fij(max) acting on the bond as
 Fij(max) = - dVij(max)/dEij = 2 Vmax Eij / qfactor^2   for abs(Eij) < qfactor
          = 0 otherwise :pre
 
-which can be decomposed into an equal and opposite force acting (only)
-on the two I,J atoms in the Emax bond.
+which can be decomposed into an equal and opposite force acting on
+only the two I,J atoms in the Emax bond.
 
-The boost factor in time for the system is given each timestep I by
+The time boost factor for the system is given each timestep I by
 
 Bi = exp(beta * Vij(max)) :pre
 
 where beta = 1/kTequil, and {Tequil} is the temperature of the system
 and an arguement to this fix.  Note that Bi >= 1 at every step.
 
-NOTE: Must use langevin set to Tequil also.  LAMMPS does not
-check that you do this.
-as maintained by a thermostat for constant NVT dynamics. 
+NOTE: To run GHD, the input script must also use the "fix
+langevin"_fix_langevin.html command to thermostat the atoms at the
+same {Tequil} as specified by this fix, so that the system is running
+constant-temperature (NVT) dynamics.  LAMMPS does not check that this
+is done.
 
 The elapsed system time t_hyper for a GHD simulation running for {N}
 timesteps is simply
@@ -114,34 +117,59 @@ where dt is the timestep size defined by the "timestep"_timestep.html
 command.  The effective time acceleration due to GHD is thus t_hyper /
 N*dt, where the denominator is elapsed time for a normal MD run.
 
-Note that in global hyperdynamics, the boost factor varies from
-timestep to timestep.  Likewise, which bond has Emax strain and thus
-which pair of atoms the bias potential is added to, will also vary
-from timestep to timestep.
+Note that in GHD, the boost factor varies from timestep to timestep.
+Likewise, which bond has Emax strain and thus which pair of atoms the
+bias potential is added to, will also vary from timestep to timestep.
+This in contrast to local hyperdynamics (LHD) where the boost factor
+is an input parameter; see the "fix hyper/local"_fix_hyper_local.html
+doc page for details.
 
 :line
 
+Here is additional information on the input parameters for GHD.
+
 The {cutbond} argument is the cutoff distance for defining bonds
-between pairs of nearby atoms.  A pair of atoms in their equilibrium,
-minimum-energy config, which are a distance Rij < cutbond, are defined
-as a bonded pair.  This should normally be roughly ~25% larger than
-the nearest-neighbor distance in a crystalline lattice.
+between pairs of nearby atoms.  A pair of I,J atoms in their
+equilibrium, minimum-energy configuration, which are separated by a
+distance Rij < {cutbond}, are flagged as a bonded pair.  Setting
+{cubond} to be ~25% larger than the nearest-neighbor distance in a
+crystalline lattice is a typical choice for solids, so that bonds
+exist only between nearest neighbor pairs.
 
 The {qfactor} argument is the limiting strain at which the bias
-potential goes to 0.0.
+potential goes to 0.0.  It is dimensionless, so a value of 0.3 means a
+bond distance can be up to 30% larger or 30% smaller than the
+equilibrium (quenched) R0ij distance and the two atoms in the bond
+could still experience a non-zero bias force.
 
 If {qfactor} is set too large, then transitions from one energy basin
 to another are affected because the bias potneial is non-zero at the
-transitions.  If {qfactor} is set too small than little boost is
-achieved because some the Eij strain of some bond is (nearly) always
-exceeding {qfactor).  Note
-
-The {Vmax} argument is the prefactor on the bias potential.
-It should be set to a value smaller than 
+transition state (e.g. saddle point).  If {qfactor} is set too small
+than little boost is achieved because the Eij strain of some bond in
+the system will (nearly) always exceed {qfactor).  A value of 0.3 for
+{qfactor} is typically a reasonable value.
+
+The {Vmax} argument is the prefactor on the bias potential.  It should
+be set to a value less than the smallest barrier height for an event
+to occur.  Otherwise the applied bias potential may be large enough
+(when added to the interatomic potential) to produce a local energy
+basin with a maxima in the center.  This can produce artificial energy
+minima in the same basin that trap an atom.  Or if {Vmax} is even
+larger, it may induce an atom(s) to rapidly transition to another
+energy basin.  Both cases are "bad dynamics" which violate the
+assumptions of GHD that guarantee an accelerated time-accurate
+trajectory of the system.
+
+The {Tequil} argument is the temperature at which the system is
+simulated; see the comment above about the "fix
+langevin"_fix_langevin.html thermostatting.  It is also part of the
+beta term in the exponential factor that determines how much boost is
+achieved as a function of the bias potential.
+
+In general, the lower the value of {Tequil} and the higher the value
+of {Vmax}, the more boost will be achieved by the GHD algorithm.
 
-The {Tequil} argument is part of the beta term in the exponential
-factor that determines how much boost is achieved as a function of the
-bias potential.
+:line
 
 [Restart, fix_modify, output, run start/stop, minimize info:]
 
@@ -152,7 +180,7 @@ The "fix_modify"_fix_modify.html {energy} option is supported by this
 fix to add the energy of the bias potential to the the system's
 potential energy as part of "thermodynamic output"_thermo_style.html.
 
-This fix computes a global scalar and global vector of length 10,
+This fix computes a global scalar and global vector of length 11,
 which can be accessed by various "output
 commands"_Section_howto.html#howto_15.  The scalar is the magnitude of
 the bias potential (energy units) applied on the current timestep.
@@ -164,30 +192,30 @@ The vector stores the following quantities:
 4 = ID of second atom in the max-strain bond
 5 = average # of bonds/atom on this step :ul
 
-6 = fraction of steps with bias = 0.0 during this run
+6 = fraction of timesteps with bias = 0.0 during this run
 7 = max drift distance of any atom during this run (distance units)
 8 = max bond length during this run (distance units) :ul
 
-9 = cummulative hyper time since fix created (time units)
-10 = cummulative count of event timesteps since fix created
-11 = cummulative count of atoms in events since fix created :ul
+9 = cummulative hyper time since fix was defined (time units)
+10 = cummulative count of event timesteps since fix was defined
+11 = cummulative count of atoms in events since fix was defined :ul
 
-The first 5 quantities are for the current timestep.  The quantities
-6-8 are for the current run.  The quantities 9-11 are cummulative
-across multiple runs (since the fix was defined in the input script).
+The first 5 quantities are for the current timestep.  Quantities 6-8
+are for the current hyper run.  Quantities 9-11 are cummulative across
+multiple runs (since the fix was defined in the input script).
 
 For value 10, events are checked for by the "hyper"_hyper.html command
-once every {Nevent} timesteps.  This value is the count of the number
-of timesteps on which one (or more) events was detected.  It is NOT
-the number of distinct events, since more than one physical event may
+once every {Nevent} timesteps.  This value is the count of those
+timesteps on which one (or more) events was detected.  It is NOT the
+number of distinct events, since more than one physical event may
 occur in the same {Nevent} time window.
 
 For value 11, each time the "hyper"_hyper.html command checks for an
-event, the event compute it uses will flag zero or more atoms as
+event, it invokes a compute to flag zero or more atoms as
 participating in an event.  E.g. atoms that have displaced more than
-some distance from the previous quench state.  This value is the count
-of the number of atoms participating in any of the events that were
-found.
+some distance from the previous quench state.  Value 11 is the
+cummulative count of the number of atoms participating in any of the
+events that were found.
 
 The scalar and vector values calculated by this fix are all
 "intensive".
@@ -199,8 +227,8 @@ minimization"_minimize.html.
 [Restrictions:]
 
 This command can only be used if LAMMPS was built with the REPLICA
-package.  See the "Build package"_Build_package.html doc
-page for more info.
+package.  See the "Build package"_Build_package.html doc page for more
+info.
 
 [Related commands:]
 
@@ -208,9 +236,11 @@ page for more info.
 
 [Default:] None
 
-:link(Voter2013)
+:line
+
+:link(Voter2013ghd)
 [(Voter2013)] S. Y. Kim, D. Perez, A. F. Voter, J Chem Phys, 139,
 144110 (2013).
 
-:link(Miron)
+:link(Mironghd)
 [(Miron)] R. A. Miron and K. A. Fichthorn, J Chem Phys, 119, 6210 (2003).

doc/src/fix_hyper_local.txt

@@ -18,7 +18,7 @@ cutbond = max distance at which a pair of atoms is considered bonded (distance u
 qfactor = max strain at which bias potential goes to 0.0 (unitless) :l
 Vmax = estimated height of bias potential (energy units) :l
 Tequil = equilibration temperature (temperature units) :l
-Dcut = min distance between boosted bonds (distance units) :l
+Dcut = minimum distance between boosted bonds (distance units) :l
 alpha = boostostat relaxation time (time units) :l
 boost = desired time boost factor (unitless) :l
 zero or more keyword/value pairs may be appended :l
@@ -40,66 +40,115 @@ fix 1 all hyper/local 1.0 0.3 0.8 300.0 :pre
 [Description:]
 
 This fix is meant to be used with the "hyper"_hyper.html command to
-perform a bond-boost hyperdynamics simulation.  The role of this fix
-is a select a multiple pairs of atoms within the system at each
-timestep to add a local bias potential to, which will alter their
-dynamics.  This is in contrast to the "fix
-hyper/global"_fix_hyper_global.html command, which adds a global bias
-potential to a single pair of atoms at each timestep.
+perform a bond-boost local hyperdynamics (LHD) simulation.  The role
+of this fix is to a select multiple pairs of atoms in the system at
+each timestep to add a local bias potential to, which will alter the
+dynamics of the system in a manner that effectively accelerates time.
+This is in contrast to the "fix hyper/global"_fix_hyper_global.html
+command, which can be user to perform a global hyperdynamics (GHD)
+simulation, by adding a global bias potential to a single pair of
+atoms at each timestep.  GHD can time accelerate a small simulation
+with up to a few 100 atoms.  For larger systems, LHD is needed to
+achieve good time acceleration.
 
 For a system that undergoes rare transition events, where one or more
-atoms move across an energy barrier to a new potential energy basin,
-the effect of the bias potential is to induce more rapid transitions.
+atoms move over an energy barrier to a new potential energy basin, the
+effect of the bias potential is to induce more rapid transitions.
 This can lead to a dramatic speed-up in the rate at which events
 occurs, without altering their relative frequencies, thus leading to
-an overall dramatic speed-up in the effective wall-clock time of the
-simulation.
+an overall increase in the elapsed real time of the simulation as
+compared to running for the same number of timesteps with normal MD.
+See the "hyper"_hyper.html doc page for a more general discussion of
+hyperdynamics and citations that explain both GHD and LHD.
 
-Cite various papers.
+The equations and logic used by this fix to perform LHD follow the
+description given in "(Voter2013)"_#Voter2013lhd.  The bond-boost form
+of a bias potential for HD is due to Miron and Fichthorn as described
+in "(Miron)"_#Mironlhd.  
 
-The current strain of a bond IJ is defined as
+To understand this description, you should first read the description
+of the GHD algorithm on the "fix hyper/global"_fix_hyper/global.html
+doc page.  This description of LHD builds on the GHD description.
 
-Eij = (Rij - R0ij) / R0ij
+The definition of bonds, Eij, and Emax are the same for GHD and LHD.
+The formula for Vij(max) and Fij(max) are also the same except for a
+pre-factor Cij, explained below.
 
-Emax = is the max of the absolute value of Eij for all IJ bonds.
+The bias energy Vij applied to a bond IJ with maximum strain is
 
-dVij = Vmax * (1 - (Eij/q)^2) for abs(Eij) < q
-     = 0  otherwise
+Vij(max) = Cij * Vmax * (1 - (Eij/q)^2) for abs(Eij) < qfactor
+    = 0 otherwise :pre
 
-Delta Vbias = minimum of dVij for all IJ bonds
+The derivative of Vij(max) with respect to the position of each atom
+in the IJ bond gives a force Fij(max) acting on the bond as
 
-The boost factor B = exp(beta * Delta Vbias)
-for a single timestep.
+Fij(max) = - dVij(max)/dEij = 2 Cij Vmax Eij / qfactor^2   for abs(Eij) < qfactor
+         = 0 otherwise :pre
 
-Thus the accumulated hypertime is simply
+which can be decomposed into an equal and opposite force acting on
+only the two I,J atoms in the IJ bond.
+
+The key difference is that in GHD this bias energy and force is added
+(on a particular timestep) to only one bond (pair of atoms) in the
+system, the bond which has maximum strain Emax.
+
+In LHD, the bias energy and force 
 
-t_hyper = Sum (i = 1 to Nsteps) Bi * dt
 
 NOTE: Add eqs for boostostat and boost coeff.
 Explain how many bonds are boosted simultaneously
 and how to choose boost factor and initial Vmax.
 
-The {cutbond} argument is the cutoff distance for defining bonds
-between pairs of nearby atoms.  A pair of atoms in their equilibrium,
-minimum-energy config, which are a distance Rij < cutbond, are
-defined as a bonded pair.
 
-The {qfactor} argument is the limiting strain at which
-the Vbias (the bias potential) goes to 0.0.
 
-If qfactor is too big, then transitions are affected b/c
-the bias energy is non-zero at the transitions.  If it is
-too small than not must boost is achieved for a large system
-with many bonds (some bonds Eij always exceeds qfactor).
+:line
 
-The {Vmax} argument is the initial prefactor on the bias potential.
-Should be chosen as estimate of final.  Will be adjusted by
-boost cooeficient
+Here is additional information on the input parameters for GHD.
 
-The {Tequil} argument is part of the beta term in the
-exponential factor that determines how much boost is
+The {cutbond} argument is the cutoff distance for defining bonds
+between pairs of nearby atoms.  A pair of I,J atoms in their
+equilibrium, minimum-energy configuration, which are separated by a
+distance Rij < {cutbond}, are flagged as a bonded pair.  Setting
+{cubond} to be ~25% larger than the nearest-neighbor distance in a
+crystalline lattice is a typical choice for solids, so that bonds
+exist only between nearest neighbor pairs.
+
+The {qfactor} argument is the limiting strain at which the bias
+potential goes to 0.0.  It is dimensionless, so a value of 0.3 means a
+bond distance can be up to 30% larger or 30% smaller than the
+equilibrium (quenched) R0ij distance and the two atoms in the bond
+could still experience a non-zero bias force.
+
+If {qfactor} is set too large, then transitions from one energy basin
+to another are affected because the bias potneial is non-zero at the
+transition state (e.g. saddle point).  If {qfactor} is set too small
+than little boost can be achieved because the Eij strain of some bond in
+the system will (nearly) always exceed {qfactor).  A value of 0.3 for
+{qfactor} is typically a reasonable value.
+
+What about requested boost
+
+
+The {Vmax} argument is the prefactor on the bias potential.  It should
+be set to a value less than the smallest barrier height for an event
+to occur.  Otherwise the applied bias potential may be large enough
+(when added to the interatomic potential) to produce a local energy
+basin with a maxima in the center.  This can produce artificial energy
+minima in the same basin that trap an atom.  Or if {Vmax} is even
+larger, it may induce an atom(s) to rapidly transition to another
+energy basin.  Both cases are "bad dynamics" which violate the
+assumptions of GHD that guarantee an accelerated time-accurate
+trajectory of the system.
+
+The {Tequil} argument is the temperature at which the system is
+simulated; see the comment above about the "fix
+langevin"_fix_langevin.html thermostatting.  It is also part of the
+beta term in the exponential factor that determines how much boost is
 achieved as a function of the bias potential.
 
+In general, the lower the value of {Tequil} and the higher the value
+of {Vmax}, the more boost will be achieved by the GHD algorithm.
+
 The {Dcut} argument is the distance required between two bonds for
 them to be selected as both being boosted.  The distance is between
 the center points of each bond.  Actually between any pair of atoms in
@@ -122,6 +171,8 @@ bonded atoms may become unphysically large, leading to bad dynamics.
 If chosen too small, the hyperdynamics run may be inefficient in the
 sense that events take a long time to occur.
 
+:line
+
 [Restart, fix_modify, output, run start/stop, minimize info:]
 
 No information about this fix is written to "binary restart
@@ -165,11 +216,10 @@ is run (distance units)
 22 = cummulative count of atoms in events since fix created
 23 = cummulative # of new bonds since fix created :ul
 
-The first quantities (1-5) are for the current timestep.  The
-quantities 6-19 are for the current hyper run.  They are reset each
-time a new hyper run is performed.  The quantities 20-23 are
-cummulative across multiple hyper runs,  They are only set to initial
-values once, when this fix is defined in the input script.
+The first quantities (1-5) are for the current timestep.  Quantities
+6-19 are for the current hyper run.  They are reset each time a new
+hyper run is performed.  Quantities 20-23 are cummulative across
+multiple runs (since the fix was defined in the input script).
 
 For value 6, the numerator is a count of all biased bonds on every
 timestep whose bias value = 0.0.  The denominator is the count of all
@@ -198,3 +248,12 @@ LAMMPS"_Section_start.html#start_3 section for more info.
 
 [Default:] None
 
+:line
+
+:link(Voter2013lhd)
+[(Voter2013)] S. Y. Kim, D. Perez, A. F. Voter, J Chem Phys, 139,
+144110 (2013).
+
+:link(Mironlhd)
+[(Miron)] R. A. Miron and K. A. Fichthorn, J Chem Phys, 119, 6210 (2003).
+