Adding d2min doc
This commit is contained in:
jtclemm
@ -8,129 +8,114 @@ Syntax
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.. parsed-literal::
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fix ID group nonaffine/displacement style args reference/style args
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fix ID group nonaffine/displacement style args reference/style nstep
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* ID, group are documented in :doc:`fix <fix>` command
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* gravity = style name of this fix command
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* magnitude = size of acceleration (force/mass units)
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* magnitude can be a variable (see below)
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* style = *chute* or *spherical* or *gradient* or *vector*
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* nonaffine/displacement = style name of this fix command
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* nevery = calculate nonaffine displacement every this many timesteps
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* style = *d2min* or *integrated*
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.. parsed-literal::
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*chute* args = angle
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angle = angle in +x away from -z or -y axis in 3d/2d (in degrees)
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angle can be a variable (see below)
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*spherical* args = phi theta
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phi = azimuthal angle from +x axis (in degrees)
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theta = angle from +z or +y axis in 3d/2d (in degrees)
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phi or theta can be a variable (see below)
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*vector* args = x y z
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x y z = vector direction to apply the acceleration
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x or y or z can be a variable (see below)
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*d2min* args = cutoff args
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cutoff = *type* or *radius* or *custom*
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*type* args = none, cutoffs determined by atom types
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*radius* args = none, cutoffs determined based on atom diameters (atom style sphere)
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*custom* args = *rmax*, cutoff set by a constant numeric value *rmax*
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*integrated* args = none
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* reference/style = *fixed* or *update* or *offset*
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.. parsed-literal::
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*fixed* = use a fixed reference frame at *nstep*
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*update* = update the reference frame every *nstep* timesteps
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*offset* = update the reference frame *nstep* timesteps before calculating the non/affine displacement
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Examples
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""""""""
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.. code-block:: LAMMPS
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fix 1 all gravity 1.0 chute 24.0
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fix 1 all gravity v_increase chute 24.0
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fix 1 all gravity 1.0 spherical 0.0 -180.0
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fix 1 all gravity 10.0 spherical v_phi v_theta
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fix 1 all gravity 100.0 vector 1 1 0
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fix 1 all nonaffine/displacement 100 integrated update 100
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fix 1 all nonaffine/displacement 1000 d2min type fixed 0
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fix 1 all nonaffine/displacement 1000 d2min custom 2.0 offset 100
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Description
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"""""""""""
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Impose an additional acceleration on each particle in the group. This
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fix is typically used with granular systems to include a "gravity"
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term acting on the macroscopic particles. More generally, it can
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represent any kind of driving field, e.g. a pressure gradient inducing
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a Poiseuille flow in a fluid. Note that this fix operates differently
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than the :doc:`fix addforce <fix_addforce>` command. The addforce fix
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adds the same force to each atom, independent of its mass. This
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command imparts the same acceleration to each atom (force/mass).
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This fix computes different metrics of the nonaffine displacement of
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particles. The first metric, *d2min* calculates the :math:`D^2_\mathrm{min}`
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nonaffine displacement by Falk and Langer in :ref:`(Falk) <d2min-Falk>`.
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For each atom, the fix computes the two tensors
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The *magnitude* of the acceleration is specified in force/mass units.
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For granular systems (LJ units) this is typically 1.0. See the
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:doc:`units <units>` command for details.
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.. math::
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Style *chute* is typically used for simulations of chute flow where
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the specified *angle* is the chute angle, with flow occurring in the +x
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direction. For 3d systems, the tilt is away from the z axis; for 2d
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systems, the tilt is away from the y axis.
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X = \sum_{\mathrm{neighbors}} \vec{r} \left(\vec{r}_{0} \right)^T
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Style *spherical* allows an arbitrary 3d direction to be specified for
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the acceleration vector. *Phi* and *theta* are defined in the usual
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spherical coordinates. Thus for acceleration acting in the -z
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direction, *theta* would be 180.0 (or -180.0). *Theta* = 90.0 and
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*phi* = -90.0 would mean acceleration acts in the -y direction. For
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2d systems, *phi* is ignored and *theta* is an angle in the xy plane
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where *theta* = 0.0 is the y-axis.
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and
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Style *vector* imposes an acceleration in the vector direction given
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by (x,y,z). Only the direction of the vector is important; it's
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length is ignored. For 2d systems, the *z* component is ignored.
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.. math::
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Any of the quantities *magnitude*, *angle*, *phi*, *theta*, *x*, *y*,
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*z* which define the gravitational magnitude and direction, can be
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specified as an equal-style :doc:`variable <variable>`. If the value is
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a variable, it should be specified as v_name, where name is the
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variable name. In this case, the variable will be evaluated each
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timestep, and its value used to determine the quantity. You should
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insure that the variable calculates a result in the appropriate units,
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e.g. force/mass or degrees.
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Y = \sum_{\mathrm{neighbors}} \vec{r}_0 \left(\vec{r}_{0} \right)^T
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Equal-style variables can specify formulas with various mathematical
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functions, and include :doc:`thermo_style <thermo_style>` command
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keywords for the simulation box parameters and timestep and elapsed
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time. Thus it is easy to specify a time-dependent gravitational
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field.
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where the neighbors include all other atoms within the distance criterion
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set by the cutoff option, discussed below, :math:`\vec{r}` is the current
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displacement between particles, and :math:`\vec{r}_0` is the reference
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displacement. A deformation gradient tensor is then calculated as
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:math:`F = X Y^{-1}` from which
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----------
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.. math::
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.. include:: accel_styles.rst
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D^2_\mathrm{min} = \sum_{\mathrm{neighbors}} \left| \vec{r} - F \vec{r}_0 \right|^2
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and a strain tensor is calculated :math:`E = F F^{T} - I` where :math:`I`
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is the identity tensor.
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The *integrated* style simply integrates the velocity of particles
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every timestep to calculate a displacement. This style only works if
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used in conjunction with another fix that deforms the box and displaces
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atom positions such as :doc:`the remap x option of fix deform <fix_deform>`,
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:doc:`fix press/berendsen <fix_press_berendsen>`, or :doc:`fix nh <fix_nh>`.
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----------
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Restart, fix_modify, output, run start/stop, minimize info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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No information about this fix is written to :doc:`binary restart files <restart>`.
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The reference state is saved to :doc:`binary restart files <restart>`.
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The :doc:`fix_modify <fix_modify>` *energy* option is supported by
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this fix to add the gravitational potential energy of the system to
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the global potential energy of the system as part of
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:doc:`thermodynamic output <thermo_style>`. The default setting for
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this fix is :doc:`fix_modify energy no <fix_modify>`.
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None of the :doc:`fix_modify <fix_modify>` options are relevant to this
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fix.
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The :doc:`fix_modify <fix_modify>` *respa* option is supported by this
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fix. This allows to set at which level of the :doc:`r-RESPA
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<run_style>` integrator the fix is adding its forces. Default is the
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outermost level.
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This fix computes a peratom array with 3 columns, which can be accessed
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by indices 1-3 using any command that uses per-atom values from a fix
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as input.
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This fix computes a global scalar which can be accessed by various
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:doc:`output commands <Howto_output>`. This scalar is the
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gravitational potential energy of the particles in the defined field,
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namely mass \* (g dot x) for each particles, where x and mass are the
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particles position and mass, and g is the gravitational field. The
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scalar value calculated by this fix is "extensive".
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No parameter of this fix can be used with the *start/stop* keywords of
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the :doc:`run <run>` command. This fix is not invoked during
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:doc:`energy minimization <minimize>`.
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For the *integrated* style, the three columns are the nonaffine
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displacements in the x, y, and z directions. For the *d2min* style,
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the three columns are the calculated :math:`D^2_\mathrm{min}`, the
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volumetric strain, and the deviatoric strain.
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Restrictions
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""""""""""""
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none
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This compute is part of the EXTRA-FIX package. It is only enabled if
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LAMMPS was built with that package. See the
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:doc:`Build package <Build_package>` page for more info.
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Related commands
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""""""""""""""""
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:doc:`atom_style sphere <atom_style>`, :doc:`fix addforce <fix_addforce>`
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none
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Default
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"""""""
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none
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----------
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.. _nh-Martyna:
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**(Martyna)** Martyna, Tobias and Klein, J Chem Phys, 101, 4177 (1994).
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