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<li>fix langevin command</li>
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<div class="section" id="fix-langevin-command">
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<span id="index-0"></span><h1>fix langevin command</h1>
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</div>
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<div class="section" id="fix-langevin-kk-command">
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<h1>fix langevin/kk command</h1>
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<div class="section" id="syntax">
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<h2>Syntax</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">langevin</span> <span class="n">Tstart</span> <span class="n">Tstop</span> <span class="n">damp</span> <span class="n">seed</span> <span class="n">keyword</span> <span class="n">values</span> <span class="o">...</span>
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</li>
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<li>langevin = style name of this fix command</li>
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<li>Tstart,Tstop = desired temperature at start/end of run (temperature units)</li>
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<li>Tstart can be a variable (see below)</li>
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<li>damp = damping parameter (time units)</li>
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<li>seed = random number seed to use for white noise (positive integer)</li>
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<li>zero or more keyword/value pairs may be appended</li>
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<li>keyword = <em>angmom</em> or <em>omega</em> or <em>scale</em> or <em>tally</em> or <em>zero</em></li>
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</ul>
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<pre class="literal-block">
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<em>angmom</em> value = <em>no</em> or factor
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<em>no</em> = do not thermostat rotational degrees of freedom via the angular momentum
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factor = do thermostat rotational degrees of freedom via the angular momentum and apply numeric scale factor as discussed below
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<em>gjf</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = use standard formulation
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<em>yes</em> = use Gronbech-Jensen/Farago formulation
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<em>omega</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = do not thermostat rotational degrees of freedom via the angular velocity
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<em>yes</em> = do thermostat rotational degrees of freedom via the angular velocity
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<em>scale</em> values = type ratio
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type = atom type (1-N)
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ratio = factor by which to scale the damping coefficient
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<em>tally</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = do not tally the energy added/subtracted to atoms
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<em>yes</em> = do tally the energy added/subtracted to atoms
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<em>zero</em> value = <em>no</em> or <em>yes</em>
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<em>no</em> = do not set total random force to zero
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<em>yes</em> = set total random force to zero
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</pre>
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</div>
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<div class="section" id="examples">
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<h2>Examples</h2>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="mi">3</span> <span class="n">boundary</span> <span class="n">langevin</span> <span class="mf">1.0</span> <span class="mf">1.0</span> <span class="mf">1000.0</span> <span class="mi">699483</span>
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<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">langevin</span> <span class="mf">1.0</span> <span class="mf">1.1</span> <span class="mf">100.0</span> <span class="mi">48279</span> <span class="n">scale</span> <span class="mi">3</span> <span class="mf">1.5</span>
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<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">langevin</span> <span class="mf">1.0</span> <span class="mf">1.1</span> <span class="mf">100.0</span> <span class="mi">48279</span> <span class="n">angmom</span> <span class="mf">3.333</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description</h2>
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<p>Apply a Langevin thermostat as described in <a class="reference internal" href="fix_langevin_eff.html#schneider"><span class="std std-ref">(Schneider)</span></a>
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to a group of atoms which models an interaction with a background
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implicit solvent. Used with <a class="reference internal" href="fix_nve.html"><span class="doc">fix nve</span></a>, this command
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performs Brownian dynamics (BD), since the total force on each atom
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will have the form:</p>
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<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">Fc</span> <span class="o">+</span> <span class="n">Ff</span> <span class="o">+</span> <span class="n">Fr</span>
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<span class="n">Ff</span> <span class="o">=</span> <span class="o">-</span> <span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="n">damp</span><span class="p">)</span> <span class="n">v</span>
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<span class="n">Fr</span> <span class="ow">is</span> <span class="n">proportional</span> <span class="n">to</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">Kb</span> <span class="n">T</span> <span class="n">m</span> <span class="o">/</span> <span class="p">(</span><span class="n">dt</span> <span class="n">damp</span><span class="p">))</span>
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</pre></div>
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</div>
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<p>Fc is the conservative force computed via the usual inter-particle
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interactions (<a class="reference internal" href="pair_style.html"><span class="doc">pair_style</span></a>,
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<a class="reference internal" href="bond_style.html"><span class="doc">bond_style</span></a>, etc).</p>
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<p>The Ff and Fr terms are added by this fix on a per-particle basis.
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See the <a class="reference internal" href="pair_dpd.html"><span class="doc">pair_style dpd/tstat</span></a> command for a
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thermostatting option that adds similar terms on a pairwise basis to
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pairs of interacting particles.</p>
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<p>Ff is a frictional drag or viscous damping term proportional to the
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particle’s velocity. The proportionality constant for each atom is
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computed as m/damp, where m is the mass of the particle and damp is
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the damping factor specified by the user.</p>
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<p>Fr is a force due to solvent atoms at a temperature T randomly bumping
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into the particle. As derived from the fluctuation/dissipation
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theorem, its magnitude as shown above is proportional to sqrt(Kb T m /
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dt damp), where Kb is the Boltzmann constant, T is the desired
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temperature, m is the mass of the particle, dt is the timestep size,
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and damp is the damping factor. Random numbers are used to randomize
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the direction and magnitude of this force as described in
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<a class="reference internal" href="fix_langevin_eff.html#dunweg"><span class="std std-ref">(Dunweg)</span></a>, where a uniform random number is used (instead of
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a Gaussian random number) for speed.</p>
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<p>Note that unless you use the <em>omega</em> or <em>angmom</em> keywords, the
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thermostat effect of this fix is applied to only the translational
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degrees of freedom for the particles, which is an important
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consideration for finite-size particles, which have rotational degrees
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of freedom, are being thermostatted. The translational degrees of
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freedom can also have a bias velocity removed from them before
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thermostatting takes place; see the description below.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">Unlike the <a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a> command which performs
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Nose/Hoover thermostatting AND time integration, this fix does NOT
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perform time integration. It only modifies forces to effect
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thermostatting. Thus you must use a separate time integration fix,
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like <a class="reference internal" href="fix_nve.html"><span class="doc">fix nve</span></a> to actually update the velocities and
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positions of atoms using the modified forces. Likewise, this fix
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should not normally be used on atoms that also have their temperature
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controlled by another fix - e.g. by <a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a> or <a class="reference internal" href="fix_temp_rescale.html"><span class="doc">fix temp/rescale</span></a> commands.</p>
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</div>
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<p>See <a class="reference internal" href="Section_howto.html#howto-16"><span class="std std-ref">this howto section</span></a> of the manual for
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a discussion of different ways to compute temperature and perform
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thermostatting.</p>
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<p>The desired temperature at each timestep is a ramped value during the
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run from <em>Tstart</em> to <em>Tstop</em>.</p>
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<p><em>Tstart</em> can be specified as an equal-style or atom-style
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<a class="reference internal" href="variable.html"><span class="doc">variable</span></a>. In this case, the <em>Tstop</em> setting is
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ignored. If the value is a variable, it should be specified as
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v_name, where name is the variable name. In this case, the variable
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will be evaluated each timestep, and its value used to determine the
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target temperature.</p>
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<p>Equal-style variables can specify formulas with various mathematical
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functions, and include <a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style</span></a> 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 temperature.</p>
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<p>Atom-style variables can specify the same formulas as equal-style
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variables but can also include per-atom values, such as atom
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coordinates. Thus it is easy to specify a spatially-dependent
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temperature with optional time-dependence as well.</p>
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<p>Like other fixes that perform thermostatting, this fix can be used
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with <a class="reference internal" href="compute.html"><span class="doc">compute commands</span></a> that remove a “bias” from the
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atom velocities. E.g. removing the center-of-mass velocity from a
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group of atoms or removing the x-component of velocity from the
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calculation. This is not done by default, but only if the
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<a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> command is used to assign a temperature
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compute to this fix that includes such a bias term. See the doc pages
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for individual <a class="reference internal" href="compute.html"><span class="doc">compute commands</span></a> to determine which ones
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include a bias. In this case, the thermostat works in the following
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manner: bias is removed from each atom, thermostatting is performed on
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the remaining thermal degrees of freedom, and the bias is added back
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in.</p>
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<p>The <em>damp</em> parameter is specified in time units and determines how
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rapidly the temperature is relaxed. For example, a value of 100.0
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means to relax the temperature in a timespan of (roughly) 100 time
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units (tau or fmsec or psec - see the <a class="reference internal" href="units.html"><span class="doc">units</span></a> command).
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The damp factor can be thought of as inversely related to the
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viscosity of the solvent. I.e. a small relaxation time implies a
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hi-viscosity solvent and vice versa. See the discussion about gamma
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and viscosity in the documentation for the <a class="reference internal" href="fix_viscous.html"><span class="doc">fix viscous</span></a> command for more details.</p>
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<p>The random # <em>seed</em> must be a positive integer. A Marsaglia random
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number generator is used. Each processor uses the input seed to
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generate its own unique seed and its own stream of random numbers.
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Thus the dynamics of the system will not be identical on two runs on
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different numbers of processors.</p>
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<hr class="docutils" />
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<p>The keyword/value option pairs are used in the following ways.</p>
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<p>The keyword <em>angmom</em> and <em>omega</em> keywords enable thermostatting of
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rotational degrees of freedom in addition to the usual translational
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degrees of freedom. This can only be done for finite-size particles.</p>
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<p>A simulation using atom_style sphere defines an omega for finite-size
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spheres. A simulation using atom_style ellipsoid defines a finite
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size and shape for aspherical particles and an angular momentum.
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The Langevin formulas for thermostatting the rotational degrees of
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freedom are the same as those above, where force is replaced by
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torque, m is replaced by the moment of inertia I, and v is replaced by
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omega (which is derived from the angular momentum in the case of
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aspherical particles).</p>
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<p>The rotational temperature of the particles can be monitored by the
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<a class="reference internal" href="compute_temp_sphere.html"><span class="doc">compute temp/sphere</span></a> and <a class="reference internal" href="compute_temp_asphere.html"><span class="doc">compute temp/asphere</span></a> commands with their rotate
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options.</p>
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<p>For the <em>omega</em> keyword there is also a scale factor of 10.0/3.0 that
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is applied as a multiplier on the Ff (damping) term in the equation
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above and of sqrt(10.0/3.0) as a multiplier on the Fr term. This does
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not affect the thermostatting behaviour of the Langevin formalism but
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insures that the randomized rotational diffusivity of spherical
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particles is correct.</p>
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<p>For the <em>angmom</em> keyword a similar scale factor is needed which is
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10.0/3.0 for spherical particles, but is anisotropic for aspherical
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particles (e.g. ellipsoids). Currently LAMMPS only applies an
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isotropic scale factor, and you can choose its magnitude as the
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specified value of the <em>angmom</em> keyword. If your aspherical particles
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are (nearly) spherical than a value of 10.0/3.0 = 3.333 is a good
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choice. If they are highly aspherical, a value of 1.0 is as good a
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choice as any, since the effects on rotational diffusivity of the
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particles will be incorrect regardless. Note that for any reasonable
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scale factor, the thermostatting effect of the <em>angmom</em> keyword on the
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rotational temperature of the aspherical particles should still be
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valid.</p>
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<p>The keyword <em>scale</em> allows the damp factor to be scaled up or down by
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the specified factor for atoms of that type. This can be useful when
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different atom types have different sizes or masses. It can be used
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multiple times to adjust damp for several atom types. Note that
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specifying a ratio of 2 increases the relaxation time which is
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equivalent to the solvent’s viscosity acting on particles with 1/2 the
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diameter. This is the opposite effect of scale factors used by the
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<a class="reference internal" href="fix_viscous.html"><span class="doc">fix viscous</span></a> command, since the damp factor in fix
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<em>langevin</em> is inversely related to the gamma factor in fix <em>viscous</em>.
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Also note that the damping factor in fix <em>langevin</em> includes the
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particle mass in Ff, unlike fix <em>viscous</em>. Thus the mass and size of
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different atom types should be accounted for in the choice of ratio
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values.</p>
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<p>The keyword <em>tally</em> enables the calculation of the cumulative energy
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added/subtracted to the atoms as they are thermostatted. Effectively
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it is the energy exchanged between the infinite thermal reservoir and
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the particles. As described below, this energy can then be printed
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out or added to the potential energy of the system to monitor energy
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conservation.</p>
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<div class="admonition note">
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<p class="first admonition-title">Note</p>
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<p class="last">this accumulated energy does NOT include kinetic energy removed
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by the <em>zero</em> flag. LAMMPS will print a warning when both options are
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active.</p>
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</div>
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<p>The keyword <em>zero</em> can be used to eliminate drift due to the
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thermostat. Because the random forces on different atoms are
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independent, they do not sum exactly to zero. As a result, this fix
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applies a small random force to the entire system, and the
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center-of-mass of the system undergoes a slow random walk. If the
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keyword <em>zero</em> is set to <em>yes</em>, the total random force is set exactly
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to zero by subtracting off an equal part of it from each atom in the
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group. As a result, the center-of-mass of a system with zero initial
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momentum will not drift over time.</p>
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<p>The keyword <em>gjf</em> can be used to run the <a class="reference internal" href="#gronbech-jensen"><span class="std std-ref">Gronbech-Jensen/Farago</span></a> time-discretization of the Langevin model. As
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described in the papers cited below, the purpose of this method is to
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enable longer timesteps to be used (up to the numerical stability
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limit of the integrator), while still producing the correct Boltzmann
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distribution of atom positions. It is implemented within LAMMPS, by
|
|
changing how the the random force is applied so that it is composed of
|
|
the average of two random forces representing half-contributions from
|
|
the previous and current time intervals.</p>
|
|
<p>In common with all methods based on Verlet integration, the
|
|
discretized velocities generated by this method in conjunction with
|
|
velocity-Verlet time integration are not exactly conjugate to the
|
|
positions. As a result the temperature (computed from the discretized
|
|
velocities) will be systematically lower than the target temperature,
|
|
by a small amount which grows with the timestep. Nonetheless, the
|
|
distribution of atom positions will still be consistent with the
|
|
target temperature.</p>
|
|
<p>As an example of using the <em>gjf</em> keyword, for molecules containing C-H
|
|
bonds, configurational properties generated with dt = 2.5 fs and tdamp
|
|
= 100 fs are indistinguishable from dt = 0.5 fs. Because the velocity
|
|
distribution systematically decreases with increasing timestep, the
|
|
method should not be used to generate properties that depend on the
|
|
velocity distribution, such as the velocity autocorrelation function
|
|
(VACF). In this example, the velocity distribution at dt = 2.5fs
|
|
generates an average temperature of 220 K, instead of 300 K.</p>
|
|
<hr class="docutils" />
|
|
<p>Styles with a <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
|
|
functionally the same as the corresponding style without the suffix.
|
|
They have been optimized to run faster, depending on your available
|
|
hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><span class="doc">Section_accelerate</span></a>
|
|
of the manual. The accelerated styles take the same arguments and
|
|
should produce the same results, except for round-off and precision
|
|
issues.</p>
|
|
<p>These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
|
|
USER-OMP and OPT packages, respectively. They are only enabled if
|
|
LAMMPS was built with those packages. See the <a class="reference internal" href="Section_start.html#start-3"><span class="std std-ref">Making LAMMPS</span></a> section for more info.</p>
|
|
<p>You can specify the accelerated styles explicitly in your input script
|
|
by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span class="std std-ref">-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
|
|
use the <a class="reference internal" href="suffix.html"><span class="doc">suffix</span></a> command in your input script.</p>
|
|
<p>See <a class="reference internal" href="Section_accelerate.html"><span class="doc">Section_accelerate</span></a> of the manual for
|
|
more instructions on how to use the accelerated styles effectively.</p>
|
|
</div>
|
|
<hr class="docutils" />
|
|
<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
|
|
<h2>Restart, fix_modify, output, run start/stop, minimize info</h2>
|
|
<p>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. 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.</p>
|
|
<p>The <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> <em>temp</em> option is supported by this
|
|
fix. You can use it to assign a temperature <a class="reference internal" href="compute.html"><span class="doc">compute</span></a>
|
|
you have defined to this fix which will be used in its thermostatting
|
|
procedure, as described above. For consistency, the group used by
|
|
this fix and by the compute should be the same.</p>
|
|
<p>The <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> <em>energy</em> option is supported by this
|
|
fix to add the energy change induced by Langevin thermostatting to the
|
|
system’s potential energy as part of <a class="reference internal" href="thermo_style.html"><span class="doc">thermodynamic output</span></a>. Note that use of this option requires
|
|
setting the <em>tally</em> keyword to <em>yes</em>.</p>
|
|
<p>This fix computes a global scalar which can be accessed by various
|
|
<a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>. The scalar is the
|
|
cummulative energy change due to this fix. The scalar value
|
|
calculated by this fix is “extensive”. Note that calculation of this
|
|
quantity requires setting the <em>tally</em> keyword to <em>yes</em>.</p>
|
|
<p>This fix can ramp its target temperature over multiple runs, using the
|
|
<em>start</em> and <em>stop</em> keywords of the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command. See the
|
|
<a class="reference internal" href="run.html"><span class="doc">run</span></a> command for details of how to do this.</p>
|
|
<p>This fix is not invoked during <a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>.</p>
|
|
</div>
|
|
<div class="section" id="restrictions">
|
|
<h2>Restrictions</h2>
|
|
<blockquote>
|
|
<div>none</div></blockquote>
|
|
</div>
|
|
<div class="section" id="related-commands">
|
|
<h2>Related commands</h2>
|
|
<p><a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a>, <a class="reference internal" href="fix_temp_rescale.html"><span class="doc">fix temp/rescale</span></a>, <a class="reference internal" href="fix_viscous.html"><span class="doc">fix viscous</span></a>, <a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a>, <a class="reference internal" href="pair_dpd.html"><span class="doc">pair_style dpd/tstat</span></a></p>
|
|
</div>
|
|
<div class="section" id="default">
|
|
<h2>Default</h2>
|
|
<p>The option defaults are angmom = no, omega = no, scale = 1.0 for all
|
|
types, tally = no, zero = no, gjf = no.</p>
|
|
<hr class="docutils" />
|
|
<p id="dunweg"><strong>(Dunweg)</strong> Dunweg and Paul, Int J of Modern Physics C, 2, 817-27 (1991).</p>
|
|
<p id="schneider"><strong>(Schneider)</strong> Schneider and Stoll, Phys Rev B, 17, 1302 (1978).</p>
|
|
<p id="gronbech-jensen"><strong>(Gronbech-Jensen)</strong> Gronbech-Jensen and Farago, Mol Phys, 111, 983
|
|
(2013); Gronbech-Jensen, Hayre, and Farago, Comp Phys Comm,
|
|
185, 524 (2014)</p>
|
|
</div>
|
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