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a couple more doc tweaks

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This commit is contained in:
Axel Kohlmeyer
2024-08-14 06:44:44 -04:00
parent a7df221b14
commit e0dad96e53
2 changed files with 28 additions and 24 deletions
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37
doc/src/fix_hyper_global.rst
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@ -111,15 +111,17 @@ The time boost factor for the system is given each timestep I by
B_i = e^{\beta V^{max}_{ij}}
where :math:`\beta = \frac{1}{kT_{equil}}`, and :math:`T_{equil}` is the temperature of the system
and an argument to this fix. Note that :math:`B_i >= 1` at every step.
where :math:`\beta = \frac{1}{kT_{equil}}`, and :math:`T_{equil}` is the
temperature of the system and an argument to this fix. Note that
:math:`B_i >= 1` at every step.
.. note::
To run a GHD simulation, the input script must also use the :doc:`fix langevin <fix_langevin>` 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.
To run a GHD simulation, the input script must also use the :doc:`fix
langevin <fix_langevin>` command to thermostat the atoms at the same
:math:`T_{equil}` 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 time :math:`t_{hyper}` for a GHD simulation running for *N*
timesteps is simply
@ -142,19 +144,19 @@ factor is an input parameter; see the :doc:`fix hyper/local <fix_hyper_local>` p
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 *ij* atoms in their
equilibrium, minimum-energy configuration, which are separated by a
distance :math:`R_{ij} < cutbond`, are flagged as a bonded pair. Setting
The *cutbond* argument is the cutoff distance for defining bonds between
pairs of nearby atoms. A pair of *ij* atoms in their equilibrium,
minimum-energy configuration, which are separated by a distance
:math:`R_{ij} < 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.
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.
equilibrium (quenched) :math:`R^0_{ij}` 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 potential is non-zero at the
@ -187,9 +189,10 @@ correctly. There will just be fewer events because the hyper time
rate does not change (as a function of hyper time).
The *Tequil* argument is the temperature at which the system is
simulated; see the comment above about the :doc:`fix langevin <fix_langevin>` 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.
simulated; see the comment above about the :doc:`fix langevin
<fix_langevin>` 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 time boost will be achievable by the GHD

15
doc/src/fix_hyper_local.rst
View File

@ -135,9 +135,9 @@ to this fix.
To run an LHD simulation, the input script must also use the
:doc:`fix langevin <fix_langevin>` 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 same :math:`T_{equil}` as specified by this fix, so that the
system is running constant-temperature (NVT) dynamics. LAMMPS does
not check that this is done.
Note that if *ij*\ == *kl*, then bond *ij* is a biased bond on that
timestep, otherwise it is not. But regardless, the boost factor
@ -219,10 +219,11 @@ guarantee an accelerated time-accurate trajectory of the system.
as for GHD), so that the :math:`C_{ij}` remain near unity.
The *Tequil* argument is the temperature at which the system is
simulated; see the comment above about the :doc:`fix langevin <fix_langevin>` 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. See the discussion of
the *Btarget* argument below.
simulated; see the comment above about the :doc:`fix langevin
<fix_langevin>` 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. See the discussion of the *Btarget*
argument below.
As discussed above, the *Dcut* argument is the distance required
between two locally maxstrain bonds for them to both be selected as