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lammps/doc/html/fix_hyper_global.html
2025-01-13 14:55:48 +00:00

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<title>fix hyper/global command &mdash; LAMMPS documentation</title>
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<div class="lammps_version">Version: <b>19 Nov 2024</b></div>
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<li class="toctree-l1"><a class="reference internal" href="Intro.html">1. Introduction</a></li>
<li class="toctree-l1"><a class="reference internal" href="Install.html">2. Install LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Build.html">3. Build LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Run_head.html">4. Run LAMMPS</a></li>
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<p class="caption" role="heading"><span class="caption-text">Programmer Guide</span></p>
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<li class="toctree-l1"><a class="reference internal" href="Library.html">1. LAMMPS Library Interfaces</a></li>
<li class="toctree-l1"><a class="reference internal" href="Python_head.html">2. Use Python with LAMMPS</a></li>
<li class="toctree-l1"><a class="reference internal" href="Modify.html">3. Modifying &amp; extending LAMMPS</a></li>
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<p class="caption" role="heading"><span class="caption-text">Command Reference</span></p>
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<li class="toctree-l1"><a class="reference internal" href="commands_list.html">Commands</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="fixes.html">Fix Styles</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="fix_accelerate_cos.html">fix accelerate/cos command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_acks2_reaxff.html">fix acks2/reaxff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_adapt.html">fix adapt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_adapt_fep.html">fix adapt/fep command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_add_heat.html">fix add/heat command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_addforce.html">fix addforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_addtorque.html">fix addtorque command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_alchemy.html">fix alchemy command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_amoeba_bitorsion.html">fix amoeba/bitorsion command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_amoeba_pitorsion.html">fix amoeba/pitorsion command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_append_atoms.html">fix append/atoms command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_atc.html">fix atc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_atom_swap.html">fix atom/swap command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_atom.html">fix ave/atom command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_chunk.html">fix ave/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_correlate.html">fix ave/correlate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_correlate_long.html">fix ave/correlate/long command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_grid.html">fix ave/grid command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_histo.html">fix ave/histo command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_histo.html#fix-ave-histo-weight-command">fix ave/histo/weight command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_spatial.html">fix ave/spatial command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_spatial_sphere.html">fix ave/spatial/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ave_time.html">fix ave/time command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_aveforce.html">fix aveforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_balance.html">fix balance command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bocs.html">fix bocs command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bond_break.html">fix bond/break command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bond_create.html">fix bond/create command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bond_create.html#fix-bond-create-angle-command">fix bond/create/angle command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bond_react.html">fix bond/react command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_bond_swap.html">fix bond/swap command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_box_relax.html">fix box/relax command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_brownian.html">fix brownian command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_brownian.html#fix-brownian-sphere-command">fix brownian/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_brownian.html#fix-brownian-asphere-command">fix brownian/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_charge_regulation.html">fix charge/regulation command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_cmap.html">fix cmap command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_colvars.html">fix colvars command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_controller.html">fix controller command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_damping_cundall.html">fix damping/cundall command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_deform.html">fix deform command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_deform_pressure.html">fix deform/pressure command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_deposit.html">fix deposit command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_dpd_energy.html">fix dpd/energy command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_dpd_source.html">fix edpd/source command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_dpd_source.html#fix-tdpd-source-command">fix tdpd/source command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_drag.html">fix drag command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_drude.html">fix drude command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_drude_transform.html">fix drude/transform/direct command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_drude_transform.html#fix-drude-transform-inverse-command">fix drude/transform/inverse command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_dt_reset.html">fix dt/reset command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_efield.html">fix efield command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_efield.html#fix-efield-tip4p-command">fix efield/tip4p command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ehex.html">fix ehex command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_electrode.html">fix electrode/conp command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_electrode.html#fix-electrode-conq-command">fix electrode/conq command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_electrode.html#fix-electrode-thermo-command">fix electrode/thermo command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_electron_stopping.html">fix electron/stopping command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_electron_stopping.html#fix-electron-stopping-fit-command">fix electron/stopping/fit command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_enforce2d.html">fix enforce2d command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_eos_cv.html">fix eos/cv command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_eos_table.html">fix eos/table command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_eos_table_rx.html">fix eos/table/rx command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_evaporate.html">fix evaporate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_external.html">fix external command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ffl.html">fix ffl command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_filter_corotate.html">fix filter/corotate command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_flow_gauss.html">fix flow/gauss command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_freeze.html">fix freeze command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gcmc.html">fix gcmc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gld.html">fix gld command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gle.html">fix gle command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_gravity.html">fix gravity command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_grem.html">fix grem command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_halt.html">fix halt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_heat.html">fix heat command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_heat_flow.html">fix heat/flow command</a></li>
<li class="toctree-l2 current"><a class="current reference internal" href="#">fix hyper/global command</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#syntax">Syntax</a></li>
<li class="toctree-l3"><a class="reference internal" href="#examples">Examples</a></li>
<li class="toctree-l3"><a class="reference internal" href="#description">Description</a></li>
<li class="toctree-l3"><a class="reference internal" href="#restart-fix-modify-output-run-start-stop-minimize-info">Restart, fix_modify, output, run start/stop, minimize info</a></li>
<li class="toctree-l3"><a class="reference internal" href="#restrictions">Restrictions</a></li>
<li class="toctree-l3"><a class="reference internal" href="#related-commands">Related commands</a></li>
<li class="toctree-l3"><a class="reference internal" href="#default">Default</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="fix_hyper_local.html">fix hyper/local command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_imd.html">fix imd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_indent.html">fix indent command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_ipi.html">fix ipi command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_langevin.html">fix langevin command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_langevin_drude.html">fix langevin/drude command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_langevin_eff.html">fix langevin/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_langevin_spin.html">fix langevin/spin command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lb_fluid.html">fix lb/fluid command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lb_momentum.html">fix lb/momentum command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lb_viscous.html">fix lb/viscous command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_lineforce.html">fix lineforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_manifoldforce.html">fix manifoldforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_mdi_qm.html">fix mdi/qm command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_mdi_qmmm.html">fix mdi/qmmm command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_meso_move.html">fix meso/move command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_mol_swap.html">fix mol/swap command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_momentum.html">fix momentum command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_momentum.html#fix-momentum-chunk-command">fix momentum/chunk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_move.html">fix move command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_msst.html">fix msst command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_mvv_dpd.html">fix mvv/dpd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_mvv_dpd.html#fix-mvv-edpd-command">fix mvv/edpd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_mvv_dpd.html#fix-mvv-tdpd-command">fix mvv/tdpd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_neb.html">fix neb command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_neb_spin.html">fix neb/spin command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html">fix nvt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-npt-command">fix npt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh.html#fix-nph-command">fix nph command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh_eff.html">fix nvt/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh_eff.html#fix-npt-eff-command">fix npt/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh_eff.html#fix-nph-eff-command">fix nph/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh_uef.html">fix nvt/uef command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nh_uef.html#fix-npt-uef-command">fix npt/uef command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nonaffine_displacement.html">fix nonaffine/displacement command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nph_asphere.html">fix nph/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nph_body.html">fix nph/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nph_sphere.html">fix nph/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nphug.html">fix nphug command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_asphere.html">fix npt/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_body.html">fix npt/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_cauchy.html">fix npt/cauchy command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_npt_sphere.html">fix npt/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_numdiff.html">fix numdiff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_numdiff_virial.html">fix numdiff/virial command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve.html">fix nve command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_asphere.html">fix nve/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_asphere_noforce.html">fix nve/asphere/noforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_awpmd.html">fix nve/awpmd command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_body.html">fix nve/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_bpm_sphere.html">fix nve/bpm/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_dot.html">fix nve/dot command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_dotc_langevin.html">fix nve/dotc/langevin command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_eff.html">fix nve/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_limit.html">fix nve/limit command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_line.html">fix nve/line command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_manifold_rattle.html">fix nve/manifold/rattle command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_noforce.html">fix nve/noforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_sphere.html">fix nve/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_spin.html">fix nve/spin command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nve_tri.html">fix nve/tri command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvk.html">fix nvk command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_asphere.html">fix nvt/asphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_body.html">fix nvt/body command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_manifold_rattle.html">fix nvt/manifold/rattle command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sllod.html">fix nvt/sllod command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sllod_eff.html">fix nvt/sllod/eff command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_nvt_sphere.html">fix nvt/sphere command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_oneway.html">fix oneway command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_orient.html">fix orient/fcc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_orient.html#fix-orient-bcc-command">fix orient/bcc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_orient_eco.html">fix orient/eco command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pafi.html">fix pafi command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pair.html">fix pair command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_phonon.html">fix phonon command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pimd.html">fix pimd/langevin command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pimd.html#fix-pimd-nvt-command">fix pimd/nvt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pimdb.html">fix pimdb/langevin command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pimdb.html#fix-pimdb-nvt-command">fix pimdb/nvt command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_planeforce.html">fix planeforce command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_plumed.html">fix plumed command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_poems.html">fix poems command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_polarize.html">fix polarize/bem/gmres command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_polarize.html#fix-polarize-bem-icc-command">fix polarize/bem/icc command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_polarize.html#fix-polarize-functional-command">fix polarize/functional command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_pour.html">fix pour command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="fix_qbmsst.html">fix qbmsst command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="fix_reaxff_species.html">fix reaxff/species command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="fix_viscous_sphere.html">fix viscous/sphere command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="fix_wall_ees.html">fix wall/ees command</a></li>
<li class="toctree-l2"><a class="reference internal" href="fix_wall_ees.html#fix-wall-region-ees-command">fix wall/region/ees command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="fix_wall_gran.html">fix wall/gran command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="fix_wall_piston.html">fix wall/piston command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="fix_wall_srd.html">fix wall/srd command</a></li>
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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
<section id="fix-hyper-global-command">
<span id="index-0"></span><h1>fix hyper/global command<a class="headerlink" href="#fix-hyper-global-command" title="Link to this heading"></a></h1>
<section id="syntax">
<h2>Syntax<a class="headerlink" href="#syntax" title="Link to this heading"></a></h2>
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">fix </span><span class="nv nv-Identifier">ID</span><span class="w"> </span><span class="nv nv-Identifier">group-ID</span><span class="w"> </span><span class="n">hyper</span><span class="o">/</span><span class="n">global</span><span class="w"> </span><span class="n">cutbond</span><span class="w"> </span><span class="n">qfactor</span><span class="w"> </span><span class="n">Vmax</span><span class="w"> </span><span class="n">Tequil</span>
</pre></div>
</div>
<ul class="simple">
<li><p>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</p></li>
<li><p>hyper/global = style name of this fix command</p></li>
<li><p>cutbond = max distance at which a pair of atoms is considered bonded (distance units)</p></li>
<li><p>qfactor = max strain at which bias potential goes to 0.0 (unitless)</p></li>
<li><p>Vmax = height of bias potential (energy units)</p></li>
<li><p>Tequil = equilibration temperature (temperature units)</p></li>
</ul>
</section>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading"></a></h2>
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">fix </span><span class="nv nv-Identifier">1</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">hyper</span><span class="o">/</span><span class="n">global</span><span class="w"> </span><span class="m">1.0</span><span class="w"> </span><span class="m">0.3</span><span class="w"> </span><span class="m">0.8</span><span class="w"> </span><span class="m">300.0</span>
</pre></div>
</div>
</section>
<section id="description">
<h2>Description<a class="headerlink" href="#description" title="Link to this heading"></a></h2>
<p>This fix is meant to be used with the <a class="reference internal" href="hyper.html"><span class="doc">hyper</span></a> command to
perform a bond-boost global hyperdynamics (GHD) simulation. The role
of this fix is to a select a single pair of atoms in the system at
each timestep to add a global bias potential to, which will alter the
dynamics of the system in a manner that effectively accelerates time.
This is in contrast to the <a class="reference internal" href="fix_hyper_local.html"><span class="doc">fix hyper/local</span></a>
command, which can be user to perform a local hyperdynamics (LHD)
simulation, by adding a local bias potential to multiple pairs of
atoms at each timestep. GHD can time accelerate a small simulation
with up to a few 100 atoms. For larger systems, LHD is needed to
achieve good time acceleration.</p>
<p>For a system that undergoes rare transition events, where one or more
atoms move over an energy barrier to a new potential energy basin, the
effect of the bias potential is to induce more rapid transitions.
This can lead to a dramatic speed-up in the rate at which events
occurs, without altering their relative frequencies, thus leading to
an overall increase in the elapsed real time of the simulation as
compared to running for the same number of timesteps with normal MD.
See the <a class="reference internal" href="hyper.html"><span class="doc">hyper</span></a> page for a more general discussion of
hyperdynamics and citations that explain both GHD and LHD.</p>
<p>The equations and logic used by this fix and described here to perform
GHD follow the description given in <a class="reference internal" href="#voter2013ghd"><span class="std std-ref">(Voter2013)</span></a>. The
bond-boost form of a bias potential for HD is due to Miron and
Fichthorn as described in <a class="reference internal" href="#mironghd"><span class="std std-ref">(Miron)</span></a>. In LAMMPS we use a
simplified version of bond-boost GHD where a single bond in the system
is biased at any one timestep.</p>
<p>Bonds are defined between each pair of atoms <em>ij</em>, whose <span class="math notranslate nohighlight">\(R^0_{ij}\)</span>
distance is less than <em>cutbond</em>, when the system is in a quenched state
(minimum) energy. Note that these are not “bonds” in a covalent
sense. A bond is simply any pair of atoms that meet the distance
criterion. <em>Cutbond</em> is an argument to this fix; it is discussed
below. A bond is only formed if one or both of the <em>ij</em> atoms are in
the specified group.</p>
<p>The current strain of bond <em>ij</em> (when running dynamics) is defined as</p>
<div class="math notranslate nohighlight">
\[E_{ij} = \frac{R_{ij} - R^0_{ij}}{R^0_{ij}}\]</div>
<p>where <span class="math notranslate nohighlight">\(R_{ij}\)</span> is the current distance between atoms <em>i</em> and <em>j</em>,
and <span class="math notranslate nohighlight">\(R^0_{ij}\)</span> is the equilibrium distance in the quenched state.</p>
<p>The bias energy <span class="math notranslate nohighlight">\(V_{ij}\)</span> of any bond between atoms <em>i</em> and <em>j</em>
is defined as</p>
<div class="math notranslate nohighlight">
\[V_{ij} = V^{max} \cdot \left( 1 - \left(\frac{E_{ij}}{q}\right)^2 \right) \textrm{ for } \left|E_{ij}\right| &lt; qfactor \textrm{ or } 0 \textrm{ otherwise}\]</div>
<p>where the prefactor <span class="math notranslate nohighlight">\(V^{max}\)</span> and the cutoff <em>qfactor</em> are arguments to
this fix; they are discussed below. This functional form is an
inverse parabola centered at 0.0 with height <span class="math notranslate nohighlight">\(V^{max}\)</span> and
which goes to 0.0 at +/- qfactor.</p>
<p>Let <span class="math notranslate nohighlight">\(E^{max}\)</span> be the maximum of <span class="math notranslate nohighlight">\(\left| E_{ij} \right|\)</span>
for all <em>ij</em> bonds in the system on a
given timestep. On that step, <span class="math notranslate nohighlight">\(V_{ij}\)</span> is added as a bias potential
to only the single bond with strain <span class="math notranslate nohighlight">\(E^{max}\)</span>, call it
<span class="math notranslate nohighlight">\(V^{max}_{ij}\)</span>. Note that <span class="math notranslate nohighlight">\(V^{max}_{ij}\)</span> will be 0.0
if <span class="math notranslate nohighlight">\(E^{max} &gt;= \textrm{qfactor}\)</span> on that timestep. Also note
that <span class="math notranslate nohighlight">\(V^{max}_{ij}\)</span> is added to the normal interatomic potential
that is computed between all atoms in the system at every step.</p>
<p>The derivative of <span class="math notranslate nohighlight">\(V^{max}_{ij}\)</span> with respect to the position of
each atom in the <span class="math notranslate nohighlight">\(E^{max}\)</span> bond gives a bias force
<span class="math notranslate nohighlight">\(F^{max}_{ij}\)</span> acting on the bond as</p>
<div class="math notranslate nohighlight">
\[F^{max}_{ij} = - \frac{dV^{max}_{ij}}{dE_{ij}} = \frac{2 V^{max} E-{ij}}{\textrm{qfactor}^2} \textrm{ for } \left|E_{ij}\right| &lt; \textrm{qfactor} \textrm{ or } 0 \textrm{ otherwise}\]</div>
<p>which can be decomposed into an equal and opposite force acting on
only the two <em>ij</em> atoms in the <span class="math notranslate nohighlight">\(E^{max}\)</span> bond.</p>
<p>The time boost factor for the system is given each timestep I by</p>
<div class="math notranslate nohighlight">
\[B_i = e^{\beta V^{max}_{ij}}\]</div>
<p>where <span class="math notranslate nohighlight">\(\beta = \frac{1}{kT_{equil}}\)</span>, and <span class="math notranslate nohighlight">\(T_{equil}\)</span> is the
temperature of the system and an argument to this fix. Note that
<span class="math notranslate nohighlight">\(B_i &gt;= 1\)</span> at every step.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>To run a GHD simulation, the input script must also use the <a class="reference internal" href="fix_langevin.html"><span class="doc">fix
langevin</span></a> command to thermostat the atoms at the same
<span class="math notranslate nohighlight">\(T_{equil}\)</span> as specified by this fix, so that the system is
running constant-temperature (NVT) dynamics. LAMMPS does not check
that this is done.</p>
</div>
<p>The elapsed time <span class="math notranslate nohighlight">\(t_{hyper}\)</span> for a GHD simulation running for <em>N</em>
timesteps is simply</p>
<div class="math notranslate nohighlight">
\[t_{hyper} = \sum_{i=1,N} B-i \cdot dt\]</div>
<p>where <em>dt</em> is the timestep size defined by the <a class="reference internal" href="timestep.html"><span class="doc">timestep</span></a>
command. The effective time acceleration due to GHD is thus t_hyper /
N*dt, where N*dt is elapsed time for a normal MD run of N timesteps.</p>
<p>Note that in GHD, the boost factor varies from timestep to timestep.
Likewise, which bond has <span class="math notranslate nohighlight">\(E^{max}\)</span> strain and thus which pair of
atoms the bias potential is added to, will also vary from timestep to timestep.
This is in contrast to local hyperdynamics (LHD) where the boost
factor is an input parameter; see the <a class="reference internal" href="fix_hyper_local.html"><span class="doc">fix hyper/local</span></a> page for details.</p>
<hr class="docutils" />
<p>Here is additional information on the input parameters for GHD.</p>
<p>The <em>cutbond</em> argument is the cutoff distance for defining bonds between
pairs of nearby atoms. A pair of <em>ij</em> atoms in their equilibrium,
minimum-energy configuration, which are separated by a distance
<span class="math notranslate nohighlight">\(R_{ij} &lt; cutbond\)</span>, are flagged as a bonded pair. Setting
<em>cubond</em> to be ~25% larger than the nearest-neighbor distance in a
crystalline lattice is a typical choice for solids, so that bonds exist
only between nearest neighbor pairs.</p>
<p>The <em>qfactor</em> argument is the limiting strain at which the bias
potential goes to 0.0. It is dimensionless, so a value of 0.3 means a
bond distance can be up to 30% larger or 30% smaller than the
equilibrium (quenched) <span class="math notranslate nohighlight">\(R^0_{ij}\)</span> distance and the two atoms in
the bond could still experience a non-zero bias force.</p>
<p>If <em>qfactor</em> is set too large, then transitions from one energy basin
to another are affected because the bias potential is non-zero at the
transition state (e.g. saddle point). If <em>qfactor</em> is set too small
than little boost is achieved because the <span class="math notranslate nohighlight">\(E_{ij}\)</span> strain of some bond in
the system will (nearly) always exceed <em>qfactor</em>. A value of 0.3 for
<em>qfactor</em> is typically reasonable.</p>
<p>The <em>Vmax</em> argument is the prefactor on the bias potential. Ideally,
tt should be set to a value slightly less than the smallest barrier
height for an event to occur. Otherwise the applied bias potential
may be large enough (when added to the interatomic potential) to
produce a local energy basin with a maxima in the center. This can
produce artificial energy minima in the same basin that trap an atom.
Or if <em>Vmax</em> is even larger, it may induce an atom(s) to rapidly
transition to another energy basin. Both cases are “bad dynamics”
which violate the assumptions of GHD that guarantee an accelerated
time-accurate trajectory of the system.</p>
<p>Note that if <em>Vmax</em> is set too small, the GHD simulation will run
correctly. There will just be fewer events because the hyper time
(t_hyper equation above) will be shorter.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>If you have no physical intuition as to the smallest barrier
height in your system, a reasonable strategy to determine the largest
<em>Vmax</em> you can use for a GHD model, is to run a sequence of
simulations with smaller and smaller <em>Vmax</em> values, until the event
rate does not change (as a function of hyper time).</p>
</div>
<p>The <em>Tequil</em> argument is the temperature at which the system is
simulated; see the comment above about the <a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a> thermostatting. It is also part of the beta term in the
exponential factor that determines how much boost is achieved as a
function of the bias potential.</p>
<p>In general, the lower the value of <em>Tequil</em> and the higher the value
of <em>Vmax</em>, the more time boost will be achievable by the GHD
algorithm.</p>
</section>
<hr class="docutils" />
<section id="restart-fix-modify-output-run-start-stop-minimize-info">
<h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Link to this heading"></a></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>.</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 of the bias potential to the global
potential energy of the system as part of <a class="reference internal" href="thermo_style.html"><span class="doc">thermodynamic output</span></a>. The default setting for this fix is <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify
energy no</span></a>.</p>
<p>This fix computes a global scalar and global vector of length 12,
which can be accessed by various <a class="reference internal" href="Howto_output.html"><span class="doc">output commands</span></a>. The scalar is the magnitude of the bias potential
(energy units) applied on the current timestep. The vector stores the
following quantities:</p>
<blockquote>
<div><ol class="arabic simple">
<li><p>boost factor on this step (unitless)</p></li>
<li><p>max strain <span class="math notranslate nohighlight">\(E_{ij}\)</span> of any bond on this step (absolute value, unitless)</p></li>
<li><p>ID of first atom in the max-strain bond</p></li>
<li><p>ID of second atom in the max-strain bond</p></li>
<li><p>average # of bonds/atom on this step</p></li>
<li><p>fraction of timesteps where the biased bond has bias = 0.0 during this run</p></li>
<li><p>fraction of timesteps where the biased bond has negative strain during this run</p></li>
<li><p>max drift distance of any atom during this run (distance units)</p></li>
<li><p>max bond length during this run (distance units)</p></li>
<li><p>cumulative hyper time since fix was defined (time units)</p></li>
<li><p>cumulative count of event timesteps since fix was defined</p></li>
<li><p>cumulative count of atoms in events since fix was defined</p></li>
</ol>
</div></blockquote>
<p>The first 5 quantities are for the current timestep. Quantities 6-9
are for the current hyper run. They are reset each time a new hyper
run is performed. Quantities 19-12 are cumulative across multiple
runs (since the point in the input script the fix was defined).</p>
<p>For value 8, drift is the distance an atom moves between two quenched
states when the second quench determines an event has occurred. Atoms
involved in an event will typically move the greatest distance since
others typically remain near their original quenched position.</p>
<p>For value 11, events are checked for by the <a class="reference internal" href="hyper.html"><span class="doc">hyper</span></a> command
once every <em>Nevent</em> timesteps. This value is the count of those
timesteps on which one (or more) events was detected. It is NOT the
number of distinct events, since more than one event may occur in the
same <em>Nevent</em> time window.</p>
<p>For value 12, each time the <a class="reference internal" href="hyper.html"><span class="doc">hyper</span></a> command checks for an
event, it invokes a compute to flag zero or more atoms as
participating in one or more events. E.g. atoms that have displaced
more than some distance from the previous quench state. Value 11 is
the cumulative count of the number of atoms participating in any of
the events that were found.</p>
<p>The scalar and vector values calculated by this fix are all
“intensive”.</p>
<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command. This fix is not invoked during
<a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>.</p>
</section>
<section id="restrictions">
<h2>Restrictions<a class="headerlink" href="#restrictions" title="Link to this heading"></a></h2>
<p>This command can only be used if LAMMPS was built with the REPLICA
package. See the <a class="reference internal" href="Build_package.html"><span class="doc">Build package</span></a> page for more
info.</p>
</section>
<section id="related-commands">
<h2>Related commands<a class="headerlink" href="#related-commands" title="Link to this heading"></a></h2>
<p><a class="reference internal" href="hyper.html"><span class="doc">hyper</span></a>, <a class="reference internal" href="fix_hyper_local.html"><span class="doc">fix hyper/local</span></a></p>
</section>
<section id="default">
<h2>Default<a class="headerlink" href="#default" title="Link to this heading"></a></h2>
<p>none</p>
<hr class="docutils" />
<p id="voter2013ghd"><strong>(Voter2013)</strong> S. Y. Kim, D. Perez, A. F. Voter, J Chem Phys, 139,
144110 (2013).</p>
<p id="mironghd"><strong>(Miron)</strong> R. A. Miron and K. A. Fichthorn, J Chem Phys, 119, 6210 (2003).</p>
</section>
</section>
</div>
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