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use k_B consistently, fix some more math. convert some transcriptions to math

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This commit is contained in:
Axel Kohlmeyer
2020-02-29 11:37:31 -05:00
parent 07fc624509
commit 6f47f110f1
11 changed files with 274 additions and 258 deletions
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17
doc/src/compute_ke.rst
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@ -28,8 +28,8 @@ Description
Define a computation that calculates the translational kinetic energy
of a group of particles.
The kinetic energy of each particle is computed as 1/2 m v\^2, where m
and v are the mass and velocity of the particle.
The kinetic energy of each particle is computed as :math:`\frac{1}{2} m
v^2`, where *m* and *v* are the mass and velocity of the particle.
There is a subtle difference between the quantity calculated by this
compute and the kinetic energy calculated by the *ke* or *etotal*
@ -37,12 +37,13 @@ keyword used in thermodynamic output, as specified by the
:doc:`thermo_style <thermo_style>` command. For this compute, kinetic
energy is "translational" kinetic energy, calculated by the simple
formula above. For thermodynamic output, the *ke* keyword infers
kinetic energy from the temperature of the system with 1/2 Kb T of
energy for each degree of freedom. For the default temperature
computation via the :doc:`compute temp <compute_temp>` command, these
are the same. But different computes that calculate temperature can
subtract out different non-thermal components of velocity and/or
include different degrees of freedom (translational, rotational, etc).
kinetic energy from the temperature of the system with
:math:`\frac{1}{2} k_B T` of energy for each degree of freedom. For the
default temperature computation via the :doc:`compute temp
<compute_temp>` command, these are the same. But different computes
that calculate temperature can subtract out different non-thermal
components of velocity and/or include different degrees of freedom
(translational, rotational, etc).
**Output info:**

19
doc/src/compute_ke_atom_eff.rst
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@ -18,7 +18,7 @@ Examples
""""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute 1 all ke/atom/eff
@ -30,11 +30,12 @@ Define a computation that calculates the per-atom translational
group. The particles are assumed to be nuclei and electrons modeled
with the :doc:`electronic force field <pair_eff>`.
The kinetic energy for each nucleus is computed as 1/2 m v\^2, where m
corresponds to the corresponding nuclear mass, and the kinetic energy
for each electron is computed as 1/2 (me v\^2 + 3/4 me s\^2), where me
and v correspond to the mass and translational velocity of each
electron, and s to its radial velocity, respectively.
The kinetic energy for each nucleus is computed as :math:`\frac{1}{2} m
v^2`, where *m* corresponds to the corresponding nuclear mass, and the
kinetic energy for each electron is computed as :math:`\frac{1}{2} (m_e
v^2 + \frac{3}{4} m_e s^2)`, where :math:`m_e` and *v* correspond to the mass
and translational velocity of each electron, and *s* to its radial
velocity, respectively.
There is a subtle difference between the quantity calculated by this
compute and the kinetic energy calculated by the *ke* or *etotal*
@ -43,8 +44,8 @@ keyword used in thermodynamic output, as specified by the
energy is "translational" plus electronic "radial" kinetic energy,
calculated by the simple formula above. For thermodynamic output, the
*ke* keyword infers kinetic energy from the temperature of the system
with 1/2 Kb T of energy for each (nuclear-only) degree of freedom in
eFF.
with :math:`\frac{1}{2} k_B T` of energy for each (nuclear-only) degree
of freedom in eFF.
.. note::
@ -53,7 +54,7 @@ eFF.
command, as shown in the following example:
.. parsed-literal::
.. code-block:: LAMMPS
compute effTemp all temp/eff
thermo_style custom step etotal pe ke temp press

27
doc/src/compute_ke_eff.rst
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@ -29,11 +29,12 @@ Define a computation that calculates the kinetic energy of motion of a
group of eFF particles (nuclei and electrons), as modeled with the
:doc:`electronic force field <pair_eff>`.
The kinetic energy for each nucleus is computed as 1/2 m v\^2 and the
kinetic energy for each electron is computed as 1/2(me v\^2 + 3/4 me
s\^2), where m corresponds to the nuclear mass, me to the electron
mass, v to the translational velocity of each particle, and s to the
radial velocity of the electron, respectively.
The kinetic energy for each nucleus is computed as :math:`\frac{1}{2} m
v^2` and the kinetic energy for each electron is computed as
:math:`\frac{1}{2}(m_e v^2 + \frac{3}{4} m_e s^2)`, where *m*
corresponds to the nuclear mass, :math:`m_e` to the electron mass, *v*
to the translational velocity of each particle, and *s* to the radial
velocity of the electron, respectively.
There is a subtle difference between the quantity calculated by this
compute and the kinetic energy calculated by the *ke* or *etotal*
@ -42,19 +43,21 @@ keyword used in thermodynamic output, as specified by the
energy is "translational" and "radial" (only for electrons) kinetic
energy, calculated by the simple formula above. For thermodynamic
output, the *ke* keyword infers kinetic energy from the temperature of
the system with 1/2 Kb T of energy for each degree of freedom. For
the eFF temperature computation via the :doc:`compute temp\_eff <compute_temp_eff>` command, these are the same. But
different computes that calculate temperature can subtract out
different non-thermal components of velocity and/or include other
degrees of freedom.
the system with :math:`\frac{1}{2} k_B T` of energy for each degree of
freedom. For the eFF temperature computation via the :doc:`compute
temp\_eff <compute_temp_eff>` command, these are the same. But
different computes that calculate temperature can subtract out different
non-thermal components of velocity and/or include other degrees of
freedom.
IMPRORTANT NOTE: The temperature in eFF models should be monitored via
.. warning::
The temperature in eFF models should be monitored via
the :doc:`compute temp/eff <compute_temp_eff>` command, which can be
printed with thermodynamic output by using the
:doc:`thermo_modify <thermo_modify>` command, as shown in the following
example:
.. parsed-literal::
compute effTemp all temp/eff

30
doc/src/compute_pressure.rst
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@ -21,7 +21,7 @@ Examples
""""""""
.. parsed-literal::
.. code-block:: LAMMPS
compute 1 all pressure thermo_temp
compute 1 all pressure NULL pair bond
@ -42,20 +42,20 @@ The pressure is computed by the formula
P = \frac{N k_B T}{V} + \frac{\sum_{i}^{N'} r_i \bullet f_i}{dV}
where N is the number of atoms in the system (see discussion of DOF
below), Kb is the Boltzmann constant, T is the temperature, d is the
dimensionality of the system (2 or 3 for 2d/3d), and V is the system
volume (or area in 2d). The second term is the virial, equal to
where *N* is the number of atoms in the system (see discussion of DOF
below), :math:`k_B` is the Boltzmann constant, *T* is the temperature, d
is the dimensionality of the system (2 or 3 for 2d/3d), and *V* is the
system volume (or area in 2d). The second term is the virial, equal to
-dU/dV, computed for all pairwise as well as 2-body, 3-body, 4-body,
many-body, and long-range interactions, where r\_i and f\_i are the
position and force vector of atom i, and the black dot indicates a dot
product. When periodic boundary conditions are used, N' necessarily
includes periodic image (ghost) atoms outside the central box, and the
position and force vectors of ghost atoms are thus included in the
summation. When periodic boundary conditions are not used, N' = N =
the number of atoms in the system. :doc:`Fixes <fix>` that impose
constraints (e.g. the :doc:`fix shake <fix_shake>` command) also
contribute to the virial term.
many-body, and long-range interactions, where :math:`r_i` and
:math:`f_i` are the position and force vector of atom *i*, and the black
dot indicates a dot product. When periodic boundary conditions are
used, N' necessarily includes periodic image (ghost) atoms outside the
central box, and the position and force vectors of ghost atoms are thus
included in the summation. When periodic boundary conditions are not
used, N' = N = the number of atoms in the system. :doc:`Fixes <fix>`
that impose constraints (e.g. the :doc:`fix shake <fix_shake>` command)
also contribute to the virial term.
A symmetric pressure tensor, stored as a 6-element vector, is also
calculated by this compute. The 6 components of the vector are
@ -108,7 +108,7 @@ A compute of this style with the ID of "thermo\_press" is created when
LAMMPS starts up, as if this command were in the input script:
.. parsed-literal::
.. code-block:: LAMMPS
compute thermo_press all pressure thermo_temp

133
doc/src/fix_langevin.rst
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@ -51,7 +51,7 @@ Examples
""""""""
.. parsed-literal::
.. code-block:: LAMMPS
fix 3 boundary langevin 1.0 1.0 1000.0 699483
fix 1 all langevin 1.0 1.1 100.0 48279 scale 3 1.5
@ -67,35 +67,35 @@ performs Brownian dynamics (BD), since the total force on each atom
will have the form:
.. parsed-literal::
.. math::
F = Fc + Ff + Fr
Ff = - (m / damp) v
Fr is proportional to sqrt(Kb T m / (dt damp))
F = & F_c + F_f + F_r \\
F_f = & - \frac{m}{\mathrm{damp}} v \\
F_r \propto & \sqrt{\frac{k_B T m}{dt~\mathrm{damp}}}
Fc is the conservative force computed via the usual inter-particle
interactions (:doc:`pair_style <pair_style>`,
:doc:`bond_style <bond_style>`, etc).
:math:`F_c` is the conservative force computed via the usual
inter-particle interactions (:doc:`pair_style <pair_style>`,
:doc:`bond_style <bond_style>`, etc). The :math:`F_f` and :math:`F_r`
terms are added by this fix on a per-particle basis. See the
:doc:`pair_style dpd/tstat <pair_dpd>` command for a thermostatting
option that adds similar terms on a pairwise basis to pairs of
interacting particles.
The Ff and Fr terms are added by this fix on a per-particle basis.
See the :doc:`pair_style dpd/tstat <pair_dpd>` command for a
thermostatting option that adds similar terms on a pairwise basis to
pairs of interacting particles.
:math:`F_f` is a frictional drag or viscous damping term proportional to
the particle's velocity. The proportionality constant for each atom is
computed as :math:`\frac{m}{\mathrm{damp}}`, where *m* is the mass of the
particle and damp is the damping factor specified by the user.
Ff is a frictional drag or viscous damping term proportional to the
particle's velocity. The proportionality constant for each atom is
computed as m/damp, where m is the mass of the particle and damp is
the damping factor specified by the user.
Fr is a force due to solvent atoms at a temperature T randomly bumping
into the particle. As derived from the fluctuation/dissipation
theorem, its magnitude as shown above is proportional to sqrt(Kb T m /
dt damp), where Kb is the Boltzmann constant, T is the desired
temperature, m is the mass of the particle, dt is the timestep size,
and damp is the damping factor. Random numbers are used to randomize
the direction and magnitude of this force as described in
:ref:`(Dunweg) <Dunweg1>`, where a uniform random number is used (instead of
a Gaussian random number) for speed.
:math:`F_r` is a force due to solvent atoms at a temperature *T*
randomly bumping into the particle. As derived from the
fluctuation/dissipation theorem, its magnitude as shown above is
proportional to :math:`\sqrt{\frac{k_B T m}{dt~\mathrm{damp}}}`, where
:math:`k_B` is the Boltzmann constant, *T* is the desired temperature,
*m* is the mass of the particle, *dt* is the timestep size, and damp is
the damping factor. Random numbers are used to randomize the direction
and magnitude of this force as described in :ref:`(Dunweg) <Dunweg1>`,
where a uniform random number is used (instead of a Gaussian random
number) for speed.
Note that unless you use the *omega* or *angmom* keywords, the
thermostat effect of this fix is applied to only the translational
@ -107,14 +107,15 @@ thermostatting takes place; see the description below.
.. note::
Unlike the :doc:`fix nvt <fix_nh>` command which performs
Nose/Hoover thermostatting AND time integration, this fix does NOT
perform time integration. It only modifies forces to effect
thermostatting. Thus you must use a separate time integration fix,
like :doc:`fix nve <fix_nve>` to actually update the velocities and
positions of atoms using the modified forces. Likewise, this fix
should not normally be used on atoms that also have their temperature
controlled by another fix - e.g. by :doc:`fix nvt <fix_nh>` or :doc:`fix temp/rescale <fix_temp_rescale>` commands.
Unlike the :doc:`fix nvt <fix_nh>` command which performs Nose/Hoover
thermostatting AND time integration, this fix does NOT perform time
integration. It only modifies forces to effect thermostatting. Thus
you must use a separate time integration fix, like :doc:`fix nve
<fix_nve>` to actually update the velocities and positions of atoms
using the modified forces. Likewise, this fix should not normally be
used on atoms that also have their temperature controlled by another
fix - e.g. by :doc:`fix nvt <fix_nh>` or :doc:`fix temp/rescale
<fix_temp_rescale>` commands.
See the :doc:`Howto thermostat <Howto_thermostat>` doc page for
a discussion of different ways to compute temperature and perform
@ -154,13 +155,14 @@ the remaining thermal degrees of freedom, and the bias is added back
in.
The *damp* parameter is specified in time units and determines how
rapidly the temperature is relaxed. For example, a value of 100.0
means to relax the temperature in a timespan of (roughly) 100 time
units (tau or fmsec or psec - see the :doc:`units <units>` command).
The damp factor can be thought of as inversely related to the
viscosity of the solvent. I.e. a small relaxation time implies a
hi-viscosity solvent and vice versa. See the discussion about gamma
and viscosity in the documentation for the :doc:`fix viscous <fix_viscous>` command for more details.
rapidly the temperature is relaxed. For example, a value of 100.0 means
to relax the temperature in a timespan of (roughly) 100 time units
(:math:`\tau` or fs or ps - see the :doc:`units <units>` command). The
damp factor can be thought of as inversely related to the viscosity of
the solvent. I.e. a small relaxation time implies a high-viscosity
solvent and vice versa. See the discussion about :math:`\gamma` and
viscosity in the documentation for the :doc:`fix viscous <fix_viscous>`
command for more details.
The random # *seed* must be a positive integer. A Marsaglia random
number generator is used. Each processor uses the input seed to
@ -191,39 +193,40 @@ The rotational temperature of the particles can be monitored by the
:doc:`compute temp/sphere <compute_temp_sphere>` and :doc:`compute temp/asphere <compute_temp_asphere>` commands with their rotate
options.
For the *omega* keyword there is also a scale factor of 10.0/3.0 that
is applied as a multiplier on the Ff (damping) term in the equation
above and of sqrt(10.0/3.0) as a multiplier on the Fr term. This does
not affect the thermostatting behavior of the Langevin formalism but
insures that the randomized rotational diffusivity of spherical
particles is correct.
For the *omega* keyword there is also a scale factor of
:math:`\frac{10.0}{3.0}` that is applied as a multiplier on the
:math:`F_f` (damping) term in the equation above and of
:math:`\sqrt{\frac{10.0}{3.0}}` as a multiplier on the :math:`F_r` term.
This does not affect the thermostatting behavior of the Langevin
formalism but insures that the randomized rotational diffusivity of
spherical particles is correct.
For the *angmom* keyword a similar scale factor is needed which is
10.0/3.0 for spherical particles, but is anisotropic for aspherical
particles (e.g. ellipsoids). Currently LAMMPS only applies an
isotropic scale factor, and you can choose its magnitude as the
:math:`\frac{10.0}{3.0}` for spherical particles, but is anisotropic for
aspherical particles (e.g. ellipsoids). Currently LAMMPS only applies
an isotropic scale factor, and you can choose its magnitude as the
specified value of the *angmom* keyword. If your aspherical particles
are (nearly) spherical than a value of 10.0/3.0 = 3.333 is a good
choice. If they are highly aspherical, a value of 1.0 is as good a
choice as any, since the effects on rotational diffusivity of the
particles will be incorrect regardless. Note that for any reasonable
scale factor, the thermostatting effect of the *angmom* keyword on the
rotational temperature of the aspherical particles should still be
valid.
are (nearly) spherical than a value of :math:`\frac{10.0}{3.0} =
3.\overline{3}` is a good choice. If they are highly aspherical, a
value of 1.0 is as good a choice as any, since the effects on rotational
diffusivity of the particles will be incorrect regardless. Note that
for any reasonable scale factor, the thermostatting effect of the
*angmom* keyword on the rotational temperature of the aspherical
particles should still be valid.
The keyword *scale* allows the damp factor to be scaled up or down by
the specified factor for atoms of that type. This can be useful when
different atom types have different sizes or masses. It can be used
multiple times to adjust damp for several atom types. Note that
specifying a ratio of 2 increases the relaxation time which is
equivalent to the solvent's viscosity acting on particles with 1/2 the
diameter. This is the opposite effect of scale factors used by the
:doc:`fix viscous <fix_viscous>` command, since the damp factor in fix
*langevin* is inversely related to the gamma factor in fix *viscous*\ .
Also note that the damping factor in fix *langevin* includes the
particle mass in Ff, unlike fix *viscous*\ . Thus the mass and size of
different atom types should be accounted for in the choice of ratio
values.
equivalent to the solvent's viscosity acting on particles with
:math:`\frac{1}{2}` the diameter. This is the opposite effect of scale
factors used by the :doc:`fix viscous <fix_viscous>` command, since the
damp factor in fix *langevin* is inversely related to the :math:`\gamma`
factor in fix *viscous*\ . Also note that the damping factor in fix
*langevin* includes the particle mass in Ff, unlike fix *viscous*\ .
Thus the mass and size of different atom types should be accounted for
in the choice of ratio values.
The keyword *tally* enables the calculation of the cumulative energy
added/subtracted to the atoms as they are thermostatted. Effectively

35
doc/src/fix_langevin_eff.rst
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@ -41,7 +41,7 @@ Examples
""""""""
.. parsed-literal::
.. code-block:: LAMMPS
fix 3 boundary langevin/eff 1.0 1.0 10.0 699483
fix 1 all langevin/eff 1.0 1.1 10.0 48279 scale 3 1.5
@ -55,28 +55,31 @@ this command performs Brownian dynamics (BD), since the total force on
each atom will have the form:
.. parsed-literal::
.. math::
F = Fc + Ff + Fr
Ff = - (m / damp) v
Fr is proportional to sqrt(Kb T m / (dt damp))
F = & F_c + F_f + F_r \\
F_f = & - \frac{m}{\mathrm{damp}} v \\
F_r \propto & \sqrt{\frac{k_B T m}{dt~\mathrm{damp}}}
Fc is the conservative force computed via the usual inter-particle
interactions (:doc:`pair_style <pair_style>`).
The Ff and Fr terms are added by this fix on a per-particle basis.
:math:`F_c` is the conservative force computed via the usual
inter-particle interactions (:doc:`pair_style <pair_style>`).
The :math:`F_f` and :math:`F_r` terms are added by this fix on a
per-particle basis.
The operation of this fix is exactly like that described by the :doc:`fix langevin <fix_langevin>` command, except that the thermostatting
is also applied to the radial electron velocity for electron
particles.
The operation of this fix is exactly like that described by the
:doc:`fix langevin <fix_langevin>` command, except that the
thermostatting is also applied to the radial electron velocity for
electron particles.
**Restart, fix\_modify, output, run start/stop, minimize info:**
No information about this fix is written to :doc:`binary restart files <restart>`. Because the state of the random number generator
is not saved in restart files, this means you cannot do "exact"
restarts with this fix, where the simulation continues on the same as
if no restart had taken place. However, in a statistical sense, a
restarted simulation should produce the same behavior.
No information about this fix is written to :doc:`binary restart files
<restart>`. Because the state of the random number generator is not
saved in restart files, this means you cannot do "exact" restarts with
this fix, where the simulation continues on the same as if no restart
had taken place. However, in a statistical sense, a restarted
simulation should produce the same behavior.
The :doc:`fix_modify <fix_modify>` *temp* option is supported by this
fix. You can use it to assign a temperature :doc:`compute <compute>`

56
doc/src/fix_nve_dotc_langevin.rst
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@ -29,7 +29,7 @@ Examples
""""""""
.. parsed-literal::
.. code-block:: LAMMPS
fix 1 all nve/dotc/langevin 1.0 1.0 0.03 457145 angmom 10
fix 1 all nve/dotc/langevin 0.1 0.1 78.9375 457145 angmom 10
@ -61,33 +61,33 @@ over the standard integrator, permitting slightly larger timestep sizes.
The total force on each atom will have the form:
.. parsed-literal::
.. math::
F = Fc + Ff + Fr
Ff = - (m / damp) v
Fr is proportional to sqrt(Kb T m / (dt damp))
F = & F_c + F_f + F_r \\
F_f = & - \frac{m}{\mathrm{damp}} v \\
F_r \propto & \sqrt{\frac{k_B T m}{dt~\mathrm{damp}}}
Fc is the conservative force computed via the usual inter-particle
interactions (:doc:`pair_style <pair_style>`,
:doc:`bond_style <bond_style>`, etc).
:math:`F_c` is the conservative force computed via the usual
inter-particle interactions (:doc:`pair_style <pair_style>`,
:doc:`bond_style <bond_style>`, etc). The :math:`F_f` and :math:`F_r`
terms are implicitly taken into account by this fix on a per-particle
basis.
The Ff and Fr terms are implicitly taken into account by this fix
on a per-particle basis.
:math:`F_f` is a frictional drag or viscous damping term proportional to
the particle's velocity. The proportionality constant for each atom is
computed as :math:`\frac{m}{\mathrm{damp}}`, where *m* is the mass of
the particle and damp is the damping factor specified by the user.
Ff is a frictional drag or viscous damping term proportional to the
particle's velocity. The proportionality constant for each atom is
computed as m/damp, where m is the mass of the particle and damp is
the damping factor specified by the user.
Fr is a force due to solvent atoms at a temperature T randomly bumping
into the particle. As derived from the fluctuation/dissipation
theorem, its magnitude as shown above is proportional to sqrt(Kb T m /
dt damp), where Kb is the Boltzmann constant, T is the desired
temperature, m is the mass of the particle, dt is the timestep size,
and damp is the damping factor. Random numbers are used to randomize
the direction and magnitude of this force as described in
:ref:`(Dunweg) <Dunweg5>`, where a uniform random number is used (instead of
a Gaussian random number) for speed.
:math:`F_r` is a force due to solvent atoms at a temperature *T*
randomly bumping into the particle. As derived from the
fluctuation/dissipation theorem, its magnitude as shown above is
proportional to :math:`\sqrt{\frac{k_B T m}{dt~\mathrm{damp}}}`, where
:math:`k_B` is the Boltzmann constant, *T* is the desired temperature,
*m* is the mass of the particle, *dt* is the timestep size, and damp is
the damping factor. Random numbers are used to randomize the direction
and magnitude of this force as described in :ref:`(Dunweg) <Dunweg5>`,
where a uniform random number is used (instead of a Gaussian random
number) for speed.
----------
@ -104,7 +104,7 @@ means to relax the temperature in a timespan of (roughly) 0.03 time
units tau (see the :doc:`units <units>` command).
The damp factor can be thought of as inversely related to the
viscosity of the solvent, i.e. a small relaxation time implies a
hi-viscosity solvent and vice versa. See the discussion about gamma
high-viscosity solvent and vice versa. See the discussion about gamma
and viscosity in the documentation for the :doc:`fix viscous <fix_viscous>` command for more details.
Note that the value 78.9375 in the second example above corresponds
to a diffusion constant, which is about an order of magnitude larger
@ -124,10 +124,10 @@ particles are always considered to have a finite size.
The keyword *angmom* enables thermostatting of the rotational degrees of
freedom in addition to the usual translational degrees of freedom.
The scale factor after the *angmom* keyword gives the ratio of the rotational to
the translational friction coefficient.
The scale factor after the *angmom* keyword gives the ratio of the
rotational to the translational friction coefficient.
An example input file can be found in /examples/USER/cgdna/examples/duplex2/.
An example input file can be found in examples/USER/cgdna/examples/duplex2/.
Further details of the implementation and stability of the integrators are contained in :ref:`(Henrich) <Henrich5>`.
The preprint version of the article can be found `here <PDF/USER-CGDNA.pdf>`_.

111
doc/src/fix_srd.rst
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@ -84,36 +84,37 @@ the implementation and usage of mixture systems (solute particles in
an SRD fluid). See the examples/srd directory for sample input
scripts using SRD particles in both settings.
This fix does 2 things:
This fix does two things:
(1) It advects the SRD particles, performing collisions between SRD
1. It advects the SRD particles, performing collisions between SRD
and big particles or walls every timestep, imparting force and torque
to the big particles. Collisions also change the position and
velocity of SRD particles.
(2) It resets the velocity distribution of SRD particles via random
2. It resets the velocity distribution of SRD particles via random
rotations every N timesteps.
SRD particles have a mass, temperature, characteristic timestep
dt\_SRD, and mean free path between collisions (lamda). The
fundamental equation relating these 4 quantities is
:math:`dt_{SRD}`, and mean free path between collisions
(:math:`\lambda`). The fundamental equation relating these 4 quantities
is
.. parsed-literal::
.. math::
lamda = dt_SRD \* sqrt(Kboltz \* Tsrd / mass)
\lambda = dt_{SRD} \sqrt{\frac{k_B T_{SRD}}{m}}
The mass of SRD particles is set by the :doc:`mass <mass>` command
elsewhere in the input script. The SRD timestep dt\_SRD is N times the
step dt defined by the :doc:`timestep <timestep>` command. Big
particles move in the normal way via a time integration :doc:`fix <fix>`
with a short timestep dt. SRD particles advect with a large timestep
dt\_SRD >= dt.
The mass *m* of SRD particles is set by the :doc:`mass <mass>` command
elsewhere in the input script. The SRD timestep :math:`dt_{SRD}` is N
times the step *dt* defined by the :doc:`timestep <timestep>` command.
Big particles move in the normal way via a time integration :doc:`fix
<fix>` with a short timestep dt. SRD particles advect with a large
timestep :math:`dt_{SRD} \ge dt`.
If the *lamda* keyword is not specified, the SRD temperature
*Tsrd* is used in the above formula to compute lamda. If the *lamda*
keyword is specified, then the *Tsrd* setting is ignored and the above
equation is used to compute the SRD temperature.
:math:`T_{SRD}` is used in the above formula to compute :math:`\lambda`.
If the *lamda* keyword is specified, then the *Tsrd* setting is ignored
and the above equation is used to compute the SRD temperature.
The characteristic length scale for the SRD fluid is set by *hgrid*
which is used to bin SRD particles for purposes of resetting their
@ -121,13 +122,14 @@ velocities. Normally hgrid is set to be 1/4 of the big particle
diameter or smaller, to adequately resolve fluid properties around the
big particles.
Lamda cannot be smaller than 0.6 \* hgrid, else an error is generated
(unless the *shift* keyword is used, see below). The velocities of
SRD particles are bounded by Vmax, which is set so that an SRD
particle will not advect further than Dmax = 4\*lamda in dt\_SRD. This
means that roughly speaking, Dmax should not be larger than a big
particle diameter, else SRDs may pass through big particles without
colliding. A warning is generated if this is the case.
:math:`\lambda` cannot be smaller than 0.6 \* hgrid, else an error is
generated (unless the *shift* keyword is used, see below). The
velocities of SRD particles are bounded by Vmax, which is set so that an
SRD particle will not advect further than :math:`D_{max} = 4 \lambda` in
:math:`dt_{SRD}`. This means that roughly speaking, :math:`D_{max}`
should not be larger than a big particle diameter, else SRDs may pass
through big particles without colliding. A warning is generated if this
is the case.
Collisions between SRD particles and big particles or walls are
modeled as a lightweight SRD point particle hitting a heavy big
@ -160,11 +162,12 @@ the big particles appropriately should be used.
The *overlap* keyword should be set to *yes* if two (or more) big
particles can ever overlap. This depends on the pair potential
interaction used for big-big interactions, or could be the case if
multiple big particles are held together as rigid bodies via the :doc:`fix rigid <fix_rigid>` command. If the *overlap* keyword is *no* and
big particles do in fact overlap, then SRD/big collisions can generate
an error if an SRD ends up inside two (or more) big particles at once.
How this error is treated is determined by the *inside* keyword.
Running with *overlap* set to *no* allows for faster collision
multiple big particles are held together as rigid bodies via the
:doc:`fix rigid <fix_rigid>` command. If the *overlap* keyword is *no*
and big particles do in fact overlap, then SRD/big collisions can
generate an error if an SRD ends up inside two (or more) big particles
at once. How this error is treated is determined by the *inside*
keyword. Running with *overlap* set to *no* allows for faster collision
checking, so it should only be set to *yes* if needed.
The *inside* keyword determines how a collision is treated if the
@ -258,30 +261,30 @@ warning is generated.
reneighboring. Note that changing the SRD bin size may alter the
properties of the SRD fluid, such as its viscosity.
The *shift* keyword determines whether the coordinates of SRD
particles are randomly shifted when binned for purposes of rotating
their velocities. When no shifting is performed, SRD particles are
binned and the velocity distribution of the set of SRD particles in
each bin is adjusted via a rotation operator. This is a statistically
valid operation if SRD particles move sufficiently far between
successive rotations. This is determined by their mean-free path
lamda. If lamda is less than 0.6 of the SRD bin size, then shifting
is required. A shift means that all of the SRD particles are shifted
by a vector whose coordinates are chosen randomly in the range [-1/2
bin size, 1/2 bin size]. Note that all particles are shifted by the
same vector. The specified random number *shiftseed* is used to
generate these vectors. This operation sufficiently randomizes which
SRD particles are in the same bin, even if lamda is small.
The *shift* keyword determines whether the coordinates of SRD particles
are randomly shifted when binned for purposes of rotating their
velocities. When no shifting is performed, SRD particles are binned and
the velocity distribution of the set of SRD particles in each bin is
adjusted via a rotation operator. This is a statistically valid
operation if SRD particles move sufficiently far between successive
rotations. This is determined by their mean-free path :math:`\lambda`.
If :math:`\lambda` is less than 0.6 of the SRD bin size, then shifting
is required. A shift means that all of the SRD particles are shifted by
a vector whose coordinates are chosen randomly in the range [-1/2 bin
size, 1/2 bin size]. Note that all particles are shifted by the same
vector. The specified random number *shiftseed* is used to generate
these vectors. This operation sufficiently randomizes which SRD
particles are in the same bin, even if :math:`lambda` is small.
If the *shift* flag is set to *no*\ , then no shifting is performed, but
bin data will be communicated if bins overlap processor boundaries.
An error will be generated if lamda < 0.6 of the SRD bin size. If the
*shift* flag is set to *possible*\ , then shifting is performed only if
lamda < 0.6 of the SRD bin size. A warning is generated to let you
know this is occurring. If the *shift* flag is set to *yes* then
shifting is performed regardless of the magnitude of lamda. Note that
the *shiftseed* is not used if the *shift* flag is set to *no*\ , but
must still be specified.
bin data will be communicated if bins overlap processor boundaries. An
error will be generated if :math:`\lambda < 0.6` of the SRD bin size.
If the *shift* flag is set to *possible*\ , then shifting is performed
only if :math:`\lambda < 0.6` of the SRD bin size. A warning is
generated to let you know this is occurring. If the *shift* flag is set
to *yes* then shifting is performed regardless of the magnitude of
:math:`\lambda`. Note that the *shiftseed* is not used if the *shift*
flag is set to *no*\ , but must still be specified.
Note that shifting of SRD coordinates requires extra communication,
hence it should not normally be enabled unless required.
@ -398,10 +401,10 @@ Related commands
Default
"""""""
The option defaults are lamda inferred from Tsrd, collision = noslip,
overlap = no, inside = error, exact = yes, radius = 1.0, bounce = 0,
search = hgrid, cubic = error 0.01, shift = no, tstat = no, and
rescale = yes.
The option defaults are: *lamda* (:math:`\lambda`) is inferred from *Tsrd*,
collision = noslip, overlap = no, inside = error, exact = yes, radius =
1.0, bounce = 0, search = hgrid, cubic = error 0.01, shift = no, tstat =
no, and rescale = yes.
----------

56
doc/src/fix_viscous.rst
View File

@ -47,11 +47,11 @@ energy to the system), it has the effect of slowly (or rapidly)
freezing the system; hence it can also be used as a simple energy
minimization technique.
The damping force F is given by F = - gamma \* velocity. The larger
the coefficient, the faster the kinetic energy is reduced. If the
optional keyword *scale* is used, gamma can scaled up or down by the
specified factor for atoms of that type. It can be used multiple
times to adjust gamma for several atom types.
The damping force :math:`F_i` is given by :math:`F_i = - \gamma v_i`.
The larger the coefficient, the faster the kinetic energy is reduced.
If the optional keyword *scale* is used, :math:`\gamma` can scaled up or
down by the specified factor for atoms of that type. It can be used
multiple times to adjust :math:`\gamma` for several atom types.
.. note::
@ -60,38 +60,40 @@ times to adjust gamma for several atom types.
:doc:`units <units>` options like "real" or "metal" that are not
self-consistent.
In a Brownian dynamics context, gamma = Kb T / D, where Kb =
Boltzmann's constant, T = temperature, and D = particle diffusion
coefficient. D can be written as Kb T / (3 pi eta d), where eta =
dynamic viscosity of the frictional fluid and d = diameter of
particle. This means gamma = 3 pi eta d, and thus is proportional to
the viscosity of the fluid and the particle diameter.
In a Brownian dynamics context, :math:`\gamma = \frac{k_B T}{D}`, where
:math:`k_B =` Boltzmann's constant, *T* = temperature, and *D* = particle
diffusion coefficient. *D* can be written as :math:`\frac{k_B T}{3 \pi
\eta d}`, where :math:`\eta =` dynamic viscosity of the frictional fluid
and d = diameter of particle. This means :math:`\gamma = 3 \pi \eta d`,
and thus is proportional to the viscosity of the fluid and the particle
diameter.
In the current implementation, rather than have the user specify a
viscosity, gamma is specified directly in force/velocity units. If
needed, gamma can be adjusted for atoms of different sizes
(i.e. sigma) by using the *scale* keyword.
viscosity, :math:`\gamma` is specified directly in force/velocity units.
If needed, :math:`\gamma` can be adjusted for atoms of different sizes
(i.e. :math:`\sigma`) by using the *scale* keyword.
Note that Brownian dynamics models also typically include a randomized
force term to thermostat the system at a chosen temperature. The :doc:`fix langevin <fix_langevin>` command does this. It has the same
force term to thermostat the system at a chosen temperature. The
:doc:`fix langevin <fix_langevin>` command does this. It has the same
viscous damping term as fix viscous and adds a random force to each
atom. The random force term is proportional to the sqrt of the chosen
thermostatting temperature. Thus if you use fix langevin with a
target T = 0, its random force term is zero, and you are essentially
performing the same operation as fix viscous. Also note that the
gamma of fix viscous is related to the damping parameter of :doc:`fix langevin <fix_langevin>`, however the former is specified in units
of force/velocity and the latter in units of time, so that it can more
easily be used as a thermostat.
atom. The random force term is proportional to the square root of the
chosen thermostatting temperature. Thus if you use fix langevin with a
target :math:`T = 0`, its random force term is zero, and you are
essentially performing the same operation as fix viscous. Also note
that the gamma of fix viscous is related to the damping parameter of
:doc:`fix langevin <fix_langevin>`, however the former is specified in
units of force/velocity and the latter in units of time, so that it can
more easily be used as a thermostat.
----------
**Restart, fix\_modify, output, run start/stop, minimize info:**
No information about this fix is written to :doc:`binary restart files <restart>`. None of the :doc:`fix_modify <fix_modify>` options
are relevant to this fix. No global or per-atom quantities are stored
by this fix for access by various :doc:`output commands <Howto_output>`.
No information about this fix is written to :doc:`binary restart files
<restart>`. None of the :doc:`fix_modify <fix_modify>` options are
relevant to this fix. No global or per-atom quantities are stored by
this fix for access by various :doc:`output commands <Howto_output>`.
No parameter of this fix can be used with the *start/stop* keywords of
the :doc:`run <run>` command.

20
doc/src/thermo_style.rst
View File

@ -50,7 +50,7 @@ Syntax
ke = kinetic energy
etotal = total energy (pe + ke)
enthalpy = enthalpy (etotal + press\*vol)
evdwl = VanderWaal pairwise energy (includes etail)
evdwl = van der Waals pairwise energy (includes etail)
ecoul = Coulombic pairwise energy
epair = pairwise energy (evdwl + ecoul + elong)
ebond = bond energy
@ -59,7 +59,7 @@ Syntax
eimp = improper energy
emol = molecular energy (ebond + eangle + edihed + eimp)
elong = long-range kspace energy
etail = VanderWaal energy long-range tail correction
etail = van der Waals energy long-range tail correction
vol = volume
density = mass density of system
lx,ly,lz = box lengths in x,y,z
@ -205,13 +205,13 @@ change the attributes of this potential energy via the
The kinetic energy of the system *ke* is inferred from the temperature
of the system with 1/2 Kb T of energy for each degree of freedom.
Thus, using different :doc:`compute commands <compute>` for calculating
temperature, via the :doc:`thermo_modify temp <thermo_modify>` command,
may yield different kinetic energies, since different computes that
calculate temperature can subtract out different non-thermal
components of velocity and/or include different degrees of freedom
(translational, rotational, etc).
of the system with :math:`\frac{1}{2} k_B T` of energy for each degree
of freedom. Thus, using different :doc:`compute commands <compute>` for
calculating temperature, via the :doc:`thermo_modify temp
<thermo_modify>` command, may yield different kinetic energies, since
different computes that calculate temperature can subtract out different
non-thermal components of velocity and/or include different degrees of
freedom (translational, rotational, etc).
The potential energy of the system *pe* will include contributions
from fixes if the :doc:`fix_modify thermo <fix_modify>` option is set
@ -219,7 +219,7 @@ for a fix that calculates such a contribution. For example, the :doc:`fix wall/
interacting with the wall. See the doc pages for "individual fixes"
to see which ones contribute.
A long-range tail correction *etail* for the VanderWaal pairwise
A long-range tail correction *etail* for the van der Waals pairwise
energy will be non-zero only if the :doc:`pair_modify tail <pair_modify>` option is turned on. The *etail* contribution
is included in *evdwl*\ , *epair*\ , *pe*\ , and *etotal*\ , and the
corresponding tail correction to the pressure is included in *press*

14
doc/src/units.rst
View File

@ -57,13 +57,13 @@ is often not simple to do.
For style *lj*\ , all quantities are unitless. Without loss of
generality, LAMMPS sets the fundamental quantities mass, :math:`\sigma`,
:math:`\epsilon`, and the Boltzmann constant :math:`k_B = 1`.
The masses, distances,
energies you specify are multiples of these fundamental values. The
formulas relating the reduced or unitless quantity (with an asterisk)
to the same quantity with units is also given. Thus you can use the
mass & sigma & epsilon values for a specific material and convert the
results from a unitless LJ simulation into physical quantities.
:math:`\epsilon`, and the Boltzmann constant :math:`k_B = 1`. The
masses, distances, energies you specify are multiples of these
fundamental values. The formulas relating the reduced or unitless
quantity (with an asterisk) to the same quantity with units is also
given. Thus you can use the mass & :math:`\sigma` & :math:`\epsilon`
values for a specific material and convert the results from a unitless
LJ simulation into physical quantities.
* mass = mass or *m*
* distance = :math:`\sigma`, where :math:`x^* = \frac{x}{\sigma}`