From af168d5f8042e3a4cdcff89c577101bd0ff584ba Mon Sep 17 00:00:00 2001 From: Karl Hammond Date: Thu, 1 Sep 2022 16:15:18 -0500 Subject: [PATCH] Math and other minor edits to some fix style doc pages --- doc/src/fix_atc.rst | 20 ++--- doc/src/fix_atom_swap.rst | 19 +++-- doc/src/fix_ave_atom.rst | 99 ++++++++++++++----------- doc/src/fix_ave_chunk.rst | 152 +++++++++++++++++++------------------- 4 files changed, 151 insertions(+), 139 deletions(-) diff --git a/doc/src/fix_atc.rst b/doc/src/fix_atc.rst index 6095f4fa87..0aa91dbc6f 100644 --- a/doc/src/fix_atc.rst +++ b/doc/src/fix_atc.rst @@ -6,7 +6,7 @@ fix atc command Syntax """""" -.. parsed-literal:: +.. code-block:: LAMMPS fix atc @@ -40,8 +40,8 @@ This fix is the beginning to creating a coupled FE/MD simulation and/or an on-the-fly estimation of continuum fields. The coupled versions of this fix do Verlet integration and the post-processing does not. After instantiating this fix, several other fix_modify commands will be -needed to set up the problem, e.g. define the finite element mesh and -prescribe initial and boundary conditions. +needed to set up the problem (i.e., define the finite element mesh and +prescribe initial and boundary conditions). .. image:: JPG/atc_nanotube.jpg :align: center @@ -135,7 +135,7 @@ fix are listed below. This fix computes a global scalar which can be accessed by various :doc:`output commands `. The scalar is the energy -discussed in the previous paragraph. The scalar value is "extensive". +discussed in the previous paragraph. The scalar value is "extensive." No parameter of this fix can be used with the *start/stop* keywords of the :doc:`run ` command. This fix is not @@ -147,7 +147,7 @@ Restrictions Thermal and two_temperature (coupling) types use a Verlet time-integration algorithm. The hardy type does not contain its own time-integrator and must be used with a separate fix that does contain -one, e.g. nve, nvt, etc. In addition, currently: +one (e.g., nve, nvt). In addition, currently: * the coupling is restricted to thermal physics * the FE computations are done in serial on each processor. @@ -159,8 +159,8 @@ Related commands After specifying this fix in your input script, several :doc:`fix_modify AtC ` commands are used to setup the -problem, e.g. define the finite element mesh and prescribe initial and -boundary conditions. Each of these options has its own doc page. +problem (e.g., define the finite element mesh and prescribe initial and +boundary conditions). Each of these options has its own doc page. *fix_modify* commands for setup: @@ -311,6 +311,6 @@ and Computation (2011), 7:1736. as a field variable from molecular dynamics simulations." Journal of Chemical Physics (2013), 139:054115. -Please refer to the standard finite element (FE) texts, e.g. T.J.R -Hughes " The finite element method ", Dover 2003, for the basics of FE -simulation. +Please refer to the standard finite element (FE) texts (e.g., T.J.R. +Hughes, *The Finite Element Method,* Dover 2003) for the basics of FE +simulations. diff --git a/doc/src/fix_atom_swap.rst b/doc/src/fix_atom_swap.rst index 8a81e32818..5948f675c2 100644 --- a/doc/src/fix_atom_swap.rst +++ b/doc/src/fix_atom_swap.rst @@ -6,7 +6,7 @@ fix atom/swap command Syntax """""" -.. parsed-literal:: +.. code-block:: LAMMPS fix ID group-ID atom/swap N X seed T keyword values ... @@ -48,7 +48,7 @@ This fix performs Monte Carlo swaps of atoms of one given atom type with atoms of the other given atom types. The specified T is used in the Metropolis criterion dictating swap probabilities. -Perform X swaps of atoms of one type with atoms of another type +Perform :math:`X` swaps of atoms of one type with atoms of another type according to a Monte Carlo probability. Swap candidates must be in the fix group, must be in the region (if specified), and must be of one of the listed types. Swaps are attempted between candidates that are @@ -57,7 +57,7 @@ atoms. Swaps are not attempted between atoms of the same type since nothing would happen. All atoms in the simulation domain can be moved using regular time -integration displacements, e.g. via :doc:`fix nvt `, resulting +integration displacements (e.g., via :doc:`fix nvt `), resulting in a hybrid MC+MD simulation. A smaller-than-usual timestep size may be needed when running such a hybrid simulation, especially if the swapped atoms are not well equilibrated. @@ -83,9 +83,8 @@ canonical ensemble, the composition of the system can change. Note that when using *semi-grand*, atoms in the fix group whose type is not listed in the *types* keyword are ineligible for attempted conversion. An attempt is made to switch the selected atom (if -eligible) to one of the other listed types with equal -probability. Acceptance of each attempt depends upon the Metropolis -criterion. +eligible) to one of the other listed types with equal probability. +Acceptance of each attempt depends upon the Metropolis criterion. The *mu* keyword allows users to specify chemical potentials. This is required and allowed only when using *semi-grand*\ . All chemical @@ -97,8 +96,8 @@ amount will have no effect on the simulation. This command may optionally use the *region* keyword to define swap volume. The specified region must have been previously defined with a -:doc:`region ` command. It must be defined with side = *in*\ -. Swap attempts occur only between atoms that are both within the +:doc:`region ` command. It must be defined with side = *in*\ . +Swap attempts occur only between atoms that are both within the specified region. Swaps are not otherwise attempted. You should ensure you do not swap atoms belonging to a molecule, or @@ -147,7 +146,7 @@ Restart, fix_modify, output, run start/stop, minimize info This fix writes the state of the fix to :doc:`binary restart files `. This includes information about the random number generator seed, the next timestep for MC exchanges, the number of -exchange attempts and successes etc. See the :doc:`read_restart +exchange attempts and successes, etc. See the :doc:`read_restart ` command for info on how to re-specify a fix in an input script that reads a restart file, so that the operation of the fix continues in an uninterrupted fashion. @@ -168,7 +167,7 @@ the following global cumulative quantities: * 1 = swap attempts * 2 = swap accepts -The vector values calculated by this fix are "extensive". +The vector values calculated by this fix are "extensive." No parameter of this fix can be used with the *start/stop* keywords of the :doc:`run ` command. This fix is not invoked during diff --git a/doc/src/fix_ave_atom.rst b/doc/src/fix_ave_atom.rst index 63952a291f..1c483e75e1 100644 --- a/doc/src/fix_ave_atom.rst +++ b/doc/src/fix_ave_atom.rst @@ -6,7 +6,7 @@ fix ave/atom command Syntax """""" -.. parsed-literal:: +.. code-block:: LAMMPS fix ID group-ID ave/atom Nevery Nrepeat Nfreq value1 value2 ... @@ -41,7 +41,9 @@ Description Use one or more per-atom vectors as inputs every few timesteps, and average them atom by atom over longer timescales. The resulting -per-atom averages can be used by other :doc:`output commands ` such as the :doc:`fix ave/chunk ` or :doc:`dump custom ` commands. +per-atom averages can be used by other :doc:`output commands ` +such as the :doc:`fix ave/chunk ` or :doc:`dump custom ` +commands. The group specified with the command means only atoms within the group have their averages computed. Results are set to 0.0 for atoms not in @@ -53,7 +55,8 @@ component) or can be the result of a :doc:`compute ` or :doc:`variable `. In the latter cases, the compute, fix, or variable must produce a per-atom vector, not a global quantity or local quantity. If you wish to time-average global quantities from a -compute, fix, or variable, then see the :doc:`fix ave/time ` command. +compute, fix, or variable, then see the :doc:`fix ave/time ` +command. Each per-atom value of each input vector is averaged independently. @@ -66,18 +69,18 @@ per-atom vectors. Note that for values from a compute or fix, the bracketed index I can be specified using a wildcard asterisk with the index to effectively -specify multiple values. This takes the form "\*" or "\*n" or "n\*" or -"m\*n". If N = the size of the vector (for *mode* = scalar) or the +specify multiple values. This takes the form "\*" or "\*n" or "m\*" or +"m\*n." If :math:`N` is the size of the vector (for *mode* = scalar) or the number of columns in the array (for *mode* = vector), then an asterisk -with no numeric values means all indices from 1 to N. A leading +with no numeric values means all indices from 1 to :math:`N`. A leading asterisk means all indices from 1 to n (inclusive). A trailing -asterisk means all indices from n to N (inclusive). A middle asterisk +asterisk means all indices from m to :math:`N` (inclusive). A middle asterisk means all indices from m to n (inclusive). Using a wildcard is the same as if the individual columns of the array -had been listed one by one. E.g. these 2 fix ave/atom commands are +had been listed one by one. For example, these two fix ave/atom commands are equivalent, since the :doc:`compute stress/atom ` -command creates a per-atom array with 6 columns: +command creates a per-atom array with six columns: .. code-block:: LAMMPS @@ -96,54 +99,58 @@ that are a multiple of *Nfreq*\ . The average is over *Nrepeat* quantities, computed in the preceding portion of the simulation every *Nevery* timesteps. *Nfreq* must be a multiple of *Nevery* and *Nevery* must be non-zero even if *Nrepeat* is 1. Also, the timesteps -contributing to the average value cannot overlap, -i.e. Nrepeat\*Nevery can not exceed Nfreq. +contributing to the average value cannot overlap; +that is, :math:`N_\text{repeat} N_\text{every}` cannot exceed +:math:`N_\text{freq}`. -For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on -timesteps 90,92,94,96,98,100 will be used to compute the final average -on timestep 100. Similarly for timesteps 190,192,194,196,198,200 on -timestep 200, etc. +For example, if :math:`N_\text{every}=2`, :math:`N_\text{repeat}=6`, and +:math:`N_\text{freq}=100`, then values on timesteps 90, 92, 94, 96, 98, and 100 +will be used to compute the final average on time step 100. Similarly for +timesteps 190, 192, 194, 196, 198, and 200 on time step 200, etc. ---------- -The atom attribute values (x,y,z,vx,vy,vz,fx,fy,fz) are -self-explanatory. Note that other atom attributes can be used as -inputs to this fix by using the :doc:`compute property/atom ` command and then specifying -an input value from that compute. +The atom attribute values (*x*, *y*, *z*, *vx*, *vy*, *vz*, *fx*, *fy*, and +*fz*) are self-explanatory. Note that other atom attributes can be used as +inputs to this fix by using the +:doc:`compute property/atom ` command and then +specifying an input value from that compute. .. note:: - The x,y,z attributes are values that are re-wrapped inside the - periodic box whenever an atom crosses a periodic boundary. Thus if - you time average an atom that spends half its time on either side of + The *x*,*y*,*z* attributes are values that are re-wrapped inside the + periodic box whenever an atom crosses a periodic boundary. Thus, if + you time-average an atom that spends half of its time on either side of the periodic box, you will get a value in the middle of the box. If this is not what you want, consider averaging unwrapped coordinates, - which can be provided by the :doc:`compute property/atom ` command via its xu,yu,zu - attributes. + which can be provided by the + :doc:`compute property/atom ` + command via its *xu*, *yu*, and *zu* attributes. If a value begins with "c\_", a compute ID must follow which has been previously defined in the input script. If no bracketed term is appended, the per-atom vector calculated by the compute is used. If a -bracketed term containing an index I is appended, the Ith column of -the per-atom array calculated by the compute is used. Users can also -write code for their own compute styles and :doc:`add them to LAMMPS `. See the discussion above for how I can +bracketed term containing an index :math:`I` is appended, the +:math:`I^\text{th}` column of the per-atom array calculated by the compute is +used. Users can also write code for their own compute styles and +:doc:`add them to LAMMPS `. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values. -If a value begins with "f\_", a fix ID must follow which has been -previously defined in the input script. If no bracketed term is -appended, the per-atom vector calculated by the fix is used. If a -bracketed term containing an index I is appended, the Ith column of -the per-atom array calculated by the fix is used. Note that some -fixes only produce their values on certain timesteps, which must be -compatible with *Nevery*, else an error will result. Users can also -write code for their own fix styles and :doc:`add them to LAMMPS `. See the discussion above for how I can be -specified with a wildcard asterisk to effectively specify multiple -values. +If a value begins with "f\_," a fix ID must follow which has been previously +defined in the input script. If no bracketed term is appended, the per-atom +vector calculated by the fix is used. If a bracketed term containing an index +:math:`I` is appended, the :math:`I^\text{th}` column of the per-atom array +calculated by the fix is used. Note that some fixes only produce their values +on certain timesteps, which must be compatible with *Nevery*, else an error +will result. Users can also write code for their own fix styles and +:doc:`add them to LAMMPS `. See the discussion above for how I can be +specified with a wildcard asterisk to effectively specify multiple values. If a value begins with "v\_", a variable name must follow which has -been previously defined in the input script as an :doc:`atom-style variable ` Variables of style *atom* can reference -thermodynamic keywords, or invoke other computes, fixes, or variables +been previously defined in the input script as an +:doc:`atom-style variable `. Variables of style *atom* can reference +thermodynamic keywords or invoke other computes, fixes, or variables when they are evaluated, so this is a very general means of generating per-atom quantities to time average. @@ -152,9 +159,11 @@ per-atom quantities to time average. Restart, fix_modify, output, run start/stop, minimize info """"""""""""""""""""""""""""""""""""""""""""""""""""""""""" -No information about this fix is written to :doc:`binary restart files `. None of the :doc:`fix_modify ` options -are relevant to this fix. No global scalar or vector quantities are -stored by this fix for access by various :doc:`output commands `. +No information about this fix is written to +:doc:`binary restart files `. None of the +:doc:`fix_modify ` options are relevant to this fix. +No global scalar or vector quantities are stored by this fix for access by +various :doc:`output commands `. This fix produces a per-atom vector or array which can be accessed by various :doc:`output commands `. A vector is produced if @@ -164,7 +173,8 @@ per-atom values can only be accessed on timesteps that are multiples of *Nfreq* since that is when averaging is performed. No parameter of this fix can be used with the *start/stop* keywords of -the :doc:`run ` command. This fix is not invoked during :doc:`energy minimization `. +the :doc:`run ` command. This fix is not invoked during +:doc:`energy minimization `. Restrictions """""""""""" @@ -173,7 +183,8 @@ Restrictions Related commands """""""""""""""" -:doc:`compute `, :doc:`fix ave/histo `, :doc:`fix ave/chunk `, :doc:`fix ave/time `, +:doc:`compute `, :doc:`fix ave/histo `, +:doc:`fix ave/chunk `, :doc:`fix ave/time `, :doc:`variable `, Default diff --git a/doc/src/fix_ave_chunk.rst b/doc/src/fix_ave_chunk.rst index bd25ea6649..2ea3bce905 100644 --- a/doc/src/fix_ave_chunk.rst +++ b/doc/src/fix_ave_chunk.rst @@ -143,19 +143,19 @@ produce global quantities. Note that for values from a compute or fix, the bracketed index I can be specified using a wildcard asterisk with the index to effectively -specify multiple values. This takes the form "\*" or "\*n" or "n\*" or -"m\*n". If N = the size of the vector (for *mode* = scalar) or the +specify multiple values. This takes the form "\*" or "\*n" or "m\*" or +"m\*n". If :math:`N` is the size of the vector (for *mode* = scalar) or the number of columns in the array (for *mode* = vector), then an asterisk -with no numeric values means all indices from 1 to N. A leading +with no numeric values means all indices from 1 to :math:`N`. A leading asterisk means all indices from 1 to n (inclusive). A trailing -asterisk means all indices from n to N (inclusive). A middle asterisk +asterisk means all indices from m to :math:`N` (inclusive). A middle asterisk means all indices from m to n (inclusive). Using a wildcard is the same as if the individual columns of the array -had been listed one by one. E.g. these 2 fix ave/chunk commands are +had been listed one by one. For example, these two fix ave/chunk commands are equivalent, since the :doc:`compute property/atom ` command creates, in this case, a per-atom -array with 3 columns: +array with three columns: .. code-block:: LAMMPS @@ -178,25 +178,26 @@ array with 3 columns: ---------- The *Nevery*, *Nrepeat*, and *Nfreq* arguments specify on what -timesteps the input values will be accessed and contribute to the -average. The final averaged quantities are generated on timesteps +time steps the input values will be accessed and contribute to the +average. The final averaged quantities are generated on time steps that are a multiples of *Nfreq*\ . The average is over *Nrepeat* quantities, computed in the preceding portion of the simulation every -*Nevery* timesteps. *Nfreq* must be a multiple of *Nevery* and -*Nevery* must be non-zero even if *Nrepeat* is 1. Also, the timesteps -contributing to the average value cannot overlap, i.e. Nrepeat\*Nevery -can not exceed Nfreq. +*Nevery* time steps. *Nfreq* must be a multiple of *Nevery* and +*Nevery* must be non-zero even if *Nrepeat* is 1. Also, the time steps +contributing to the average value cannot overlap (i.e., +:math:`N_\text{repeat}N_\text{every}` cannot exceed :math:`N_\text{freq}`). -For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on -timesteps 90,92,94,96,98,100 will be used to compute the final average -on timestep 100. Similarly for timesteps 190,192,194,196,198,200 on -timestep 200, etc. If Nrepeat=1 and Nfreq = 100, then no time -averaging is done; values are simply generated on timesteps -100,200,etc. +For example, if :math:`N_\text{every}=2`, :math:`N_\text{repeat}=6`, and +:math:`N_\text{freq}=100`, then values on +time steps 90, 92, 94, 96, 98, 100 will be used to compute the final average +on time step 100. Similarly for time steps 190, 192, 194, 196, 198, 200 on +time step 200, etc. If :math:`N_\text{repeat}=1` and +:math:`N_\text{freq} = 100`, then no time averaging is done; values are simply +generated on time steps 100, 200, etc. Each input value can also be averaged over the atoms in each chunk. -The way the averaging is done across the *Nrepeat* timesteps to -produce output on the *Nfreq* timesteps, and across multiple *Nfreq* +The way the averaging is done across the *Nrepeat* time steps to +produce output on the *Nfreq* time steps, and across multiple *Nfreq* outputs, is determined by the *norm* and *ave* keyword settings, as discussed below. @@ -218,52 +219,53 @@ discussed below. window, which can affect which atoms are discarded if the simulation box size changes. If its *units* keyword is set to *reduced*, then the number of bins *Nchunk* will still be fixed, - but the size of each bin can vary at each timestep if the - simulation box size changes, e.g. for an NPT simulation. + but the size of each bin can vary at each time step if the + simulation box size changes (e.g., for an NPT simulation). ---------- -The atom attribute values (vx,vy,vz,fx,fy,fz,mass) are +The atom attribute values (*vx*, *vy*, *vz*, *fx*, *fy*, *fz*, *mass*) are self-explanatory. As noted above, any other atom attributes can be used as input values to this fix by using the :doc:`compute property/atom ` command and then specifying an input value from that compute. The *density/number* value means the number density is computed for -each chunk, i.e. number/volume. The *density/mass* value means the -mass density is computed for each chunk, i.e. total-mass/volume. The -output values are in units of 1/volume or density (mass/volume). See +each chunk (i.e., number/volume). The *density/mass* value means the +mass density is computed for each chunk (i.e., total-mass/volume). The +output values are in units of 1/volume or mass density (mass/volume). See the :doc:`units ` command page for the definition of density -for each choice of units, e.g. gram/cm\^3. If the chunks defined by +for each choice of units (e.g., g/cm\ :math:`^3`). If the chunks defined by the :doc:`compute chunk/atom ` command are spatial -bins, the volume is the bin volume. Otherwise it is the volume of the +bins, the volume is the bin volume. Otherwise, it is the volume of the entire simulation box. -The *temp* value means the temperature is computed for each chunk, by -the formula +The *temp* value means the temperature is computed for each chunk, +by the formula .. math:: \text{KE} = \frac{\text{DOF}}{2} k_B T, -where KE = total kinetic energy of the chunk of atoms (sum of -:math:`\frac{1}{2} m v^2`), DOF = the total number of degrees of freedom -for all atoms in the chunk, :math:`k_B` = Boltzmann constant, and -:math:`T` = temperature. +where KE is the total kinetic energy of the chunk of atoms (sum of +:math:`\frac{1}{2} m v^2`), DOF is the the total number of degrees of freedom +for all atoms in the chunk, :math:`k_B` is the Boltzmann constant, and +:math:`T` is the absolute temperature. -The DOF is calculated as N\*adof + cdof, where N = number of atoms in -the chunk, adof = degrees of freedom per atom, and cdof = degrees of -freedom per chunk. By default adof = 2 or 3 = dimensionality of -system, as set via the :doc:`dimension ` command, and cdof = -0.0. This gives the usual formula for temperature. +The DOF is calculated as :math:`N`\ \*adof + cdof, where :math:`N` is the +number of atoms in the chunk, adof is the number of degrees of freedom per +atom, and cdof is the number of degrees of freedom per chunk. By default, +adof = 2 or 3 = dimensionality of system, +as set via the :doc:`dimension ` command, and cdof = 0.0. +This gives the usual formula for temperature. Note that currently this temperature only includes translational degrees of freedom for each atom. No rotational degrees of freedom -are included for finite-size particles. Also no degrees of freedom +are included for finite-size particles. Also, no degrees of freedom are subtracted for any velocity bias or constraints that are applied, -such as :doc:`compute temp/partial `, or -:doc:`fix shake ` or :doc:`fix rigid `. This is -because those degrees of freedom (e.g. a constrained bond) could apply +such as :doc:`compute temp/partial `, +:doc:`fix shake `, or :doc:`fix rigid `. This is +because those degrees of freedom (e.g., a constrained bond) could apply to sets of atoms that are both included and excluded from a specific chunk, and hence the concept is somewhat ill-defined. In some cases, you can use the *adof* and *cdof* keywords to adjust the calculated @@ -279,7 +281,7 @@ Note that the per-chunk temperature calculated by this fix and the different. The compute calculates the temperature for each chunk for a single snapshot. This fix can do that but can also time average those values over many snapshots, or it can compute a temperature as -if the atoms in the chunk on different timesteps were collected +if the atoms in the chunk on different time steps were collected together as one set of atoms to calculate their temperature. The compute allows the center-of-mass velocity of each chunk to be subtracted before calculating the temperature; this fix does not. @@ -289,8 +291,8 @@ previously defined in the input script. If no bracketed integer is appended, the per-atom vector calculated by the compute is used. If a bracketed integer is appended, the Ith column of the per-atom array calculated by the compute is used. Users can also write code for -their own compute styles and :doc:`add them to LAMMPS `. See -the discussion above for how I can be specified with a wildcard +their own compute styles and :doc:`add them to LAMMPS `. +See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values. If a value begins with "f\_", a fix ID must follow which has been @@ -298,7 +300,7 @@ previously defined in the input script. If no bracketed integer is appended, the per-atom vector calculated by the fix is used. If a bracketed integer is appended, the Ith column of the per-atom array calculated by the fix is used. Note that some fixes only produce -their values on certain timesteps, which must be compatible with +their values on certain time steps, which must be compatible with *Nevery*, else an error results. Users can also write code for their own fix styles and :doc:`add them to LAMMPS `. See the discussion above for how I can be specified with a wildcard asterisk @@ -317,16 +319,16 @@ Additional optional keywords also affect the operation of this fix and its outputs. The *norm* keyword affects how averaging is done for the per-chunk -values that are output every *Nfreq* timesteps. +values that are output every *Nfreq* time steps. It the *norm* setting is *all*, which is the default, a chunk value is summed over all atoms in all *Nrepeat* samples, as is the count of atoms in the chunk. The averaged output value for the chunk on the -*Nfreq* timesteps is Total-sum / Total-count. In other words it is an +*Nfreq* time steps is Total-sum / Total-count. In other words it is an average over atoms across the entire *Nfreq* timescale. For the *density/number* and *density/mass* values, the volume (bin volume or system volume) used in the final normalization will be the volume at -the final *Nfreq* timestep. For the *temp* values, degrees of freedom +the final *Nfreq* time step. For the *temp* values, degrees of freedom and kinetic energy are summed separately across the entire *Nfreq* timescale, and the output value is calculated by dividing those two sums. @@ -334,9 +336,9 @@ sums. If the *norm* setting is *sample*, the chunk value is summed over atoms for each sample, as is the count, and an "average sample value" is computed for each sample, i.e. Sample-sum / Sample-count. The -output value for the chunk on the *Nfreq* timesteps is the average of -the *Nrepeat* "average sample values", i.e. the sum of *Nrepeat* -"average sample values" divided by *Nrepeat*\ . In other words it is an +output value for the chunk on the *Nfreq* time steps is the average of +the *Nrepeat* "average sample values" (i.e., the sum of *Nrepeat* +"average sample values" divided by *Nrepeat*\ ). In other words, it is an average of an average. For the *density/number* and *density/mass* values, the volume (bin volume or system volume) used in the per-sample normalization will be the current volume at each sampling @@ -348,8 +350,8 @@ values" are "summed sample values". A summed sample value is simply the chunk value summed over atoms in the sample, without dividing by the number of atoms in the sample. The output value for the chunk on the *Nfreq* timesteps is the average of the *Nrepeat* "summed sample -values", i.e. the sum of *Nrepeat* "summed sample values" divided by -*Nrepeat*\ . For the *density/number* and *density/mass* values, the +values" (i.e., the sum of *Nrepeat* "summed sample values" divided by +*Nrepeat*\ ). For the *density/number* and *density/mass* values, the volume (bin volume or system volume) used in the per-sample sum normalization will be the current volume at each sampling step. @@ -360,8 +362,7 @@ command or written to a file. If the *ave* setting is *one*, which is the default, then the chunk values produced on timesteps that are multiples of *Nfreq* are -independent of each other; they are output as-is without further -averaging. +independent of each other; they are output as-is without further averaging. If the *ave* setting is *running*, then the chunk values produced on timesteps that are multiples of *Nfreq* are summed and averaged in a @@ -369,48 +370,49 @@ cumulative sense before being output. Each output chunk value is thus the average of the chunk value produced on that timestep with all preceding values for the same chunk. This running average begins when the fix is defined; it can only be restarted by deleting the fix via -the :doc:`unfix ` command, or re-defining the fix by -re-specifying it. +the :doc:`unfix ` command, or re-defining the fix by re-specifying it. If the *ave* setting is *window*, then the chunk values produced on timesteps that are multiples of *Nfreq* are summed and averaged within -a moving "window" of time, so that the last M values for the same -chunk are used to produce the output. E.g. if M = 3 and Nfreq = 1000, -then the output on step 10000 will be the average of the individual -chunk values on steps 8000,9000,10000. Outputs on early steps will -average over less than M values if they are not available. +a moving "window" of time, so that the last :math:`M` values for the same +chunk are used to produce the output. For example, if :math:`M = 3` and +:math:`N_\text{freq} = 1000`, then the output on step 10000 will be the average +of the individual chunk values on steps 8000,9000,10000. Outputs on early +steps will average over less than :math:`M` values if they are not available. The *bias* keyword specifies the ID of a temperature compute that -removes a "bias" velocity from each atom, specified as *bias-ID*\ . It -is only used when the *temp* value is calculated, to compute the +removes a "bias" velocity from each atom, specified as *bias-ID*\ . +It is only used when the *temp* value is calculated, to compute the thermal temperature of each chunk after the translational kinetic -energy components have been altered in a prescribed way, e.g. to -remove a flow velocity profile. See the doc pages for individual -computes that calculate a temperature to see which ones implement a -bias. +energy components have been altered in a prescribed way, (e.g., to +remove a flow velocity profile). See the doc pages for individual +computes that calculate a temperature to see which ones implement a bias. The *adof* and *cdof* keywords define the values used in the degree of freedom (DOF) formula described above for temperature calculation for each chunk. They are only used when the *temp* value is calculated. They can be used to calculate a more appropriate -temperature for some kinds of chunks. Here are 3 examples: +temperature for some kinds of chunks. Here are three examples: If spatially binned chunks contain some number of water molecules and :doc:`fix shake ` is used to make each molecule rigid, then -you could calculate a temperature with 6 degrees of freedom (DOF) (3 -translational, 3 rotational) per molecule by setting *adof* to 2.0. +you could calculate a temperature with 6 degrees of freedom (DOF) (three +translational, three rotational) per molecule by setting *adof* to 2.0. If :doc:`compute temp/partial ` is used with the -*bias* keyword to only allow the x component of velocity to contribute +*bias* keyword to only allow the :math:`x` component of velocity to contribute to the temperature, then *adof* = 1.0 would be appropriate. If each chunk consists of a large molecule, with some number of its bonds constrained by :doc:`fix shake ` or the entire molecule by :doc:`fix rigid/small `, *adof* = 0.0 and *cdof* could be set to the remaining degrees of freedom for the entire molecule -(entire chunk in this case), e.g. 6 for 3d, or 3 for 2d, for a rigid +(entire chunk in this case), that is, 6 for 3d or 3 for 2d for a rigid molecule. +.. + FIXME need to make *Nfreq* vs. :math:`N_\text{freq}` consistent. + The *file* keyword allows a filename to be specified. Every *Nfreq* timesteps, a section of chunk info will be written to a text file in the following format. A line with the timestep and number of chunks