From 86ebc8260e64a4a8d7f723ae84a5cdc29a296ded Mon Sep 17 00:00:00 2001 From: Richard Berger Date: Sat, 8 Feb 2020 19:24:27 +0100 Subject: [PATCH] Update pair_atm docs --- doc/src/Eqs/pair_atm.jpg | Bin 5474 -> 0 bytes doc/src/Eqs/pair_atm.tex | 9 ---- doc/src/pair_atm.rst | 114 ++++++++++++++++++++------------------- 3 files changed, 59 insertions(+), 64 deletions(-) delete mode 100644 doc/src/Eqs/pair_atm.jpg delete mode 100644 doc/src/Eqs/pair_atm.tex diff --git a/doc/src/Eqs/pair_atm.jpg b/doc/src/Eqs/pair_atm.jpg deleted file mode 100644 index d2e6d704e930c2def4801301c928998f7542f54b..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 5474 zcmd^?XHeA3n#TXb3=BCVISvAnB!hr3ATR{Uh-4*$#32ikkAQ^1L4gBEazHYQB zX9oy4;1)niLINcrCWS(wWMrh|l#EoA6cm)K^b9nNoNU}&oNOE%JpAHG~dw`A!pC=}#re_uwmzGyn*VZ>S4-UT`eLFrm zJv;xC3j~1w6YK9}zi`q0Nmmpv6tp{~kC#O;n3w=USe zUI_MIjvQKV&m;eM`1_gvWIOVF`8+SBB1BhAadF`r`_^aF#R%3%NJmq_|&P>$P0F>;hhPbMaww8F=Ww* zYEdN^!NVQaJjBnX#t2%!{lTo37GUK+E|<%m$bEEBRo{oaE~zp>c0CfE(78``rc)iZ zm}aN5KWSyn%Nu#^c8qG9{d|WT_deB^#~yPt8_aLq@BW_BMg7+OQ!-BeEt3gR{_kFb z6jiA&!bCB##y{N4&5<7a^<%ymonGxyH6xLM z$kWqcexvVFQJcSsK23@)dpM`@5+SvBGN?1;Xmb)*_rrXzGmkd$ri-m$*VBz!Wq}Y4 ztXLUZ1);^WM#QB>+6{yTW?lle`+1-BKLykf@2^^Lse$6uHnNMu7IUEnpYfwU zvSA9cWc#qjG$YR1G1T-F84YI>Fr!aMN|h+P-@F{1oIh^5l{vEV zu6h6K7N40Ow$QdpS+l2a92K3pCwDv;DzTL~y5CW#QnkRzY|uEHuR(NHo_i7=qGpa=Et$yr)<6Q&=r*nLPR^ldYFjfQD;l zcqKa~qY7V86+)G+xEve>o$$T!zW;fX> zI8aX?(YdPE>>ZGz&LQ=E*Ht6SK+8G;3{D<~mM9e=>(Zpkg|23y0C2Nx7A7R;)&boM zxAUs1gQ#es7&y*{!{ z23%B-nuweg$%zQ_^kXnw;p%TI9Dh99f^$Orim)B>)XgxSWhV~qpT$X?*bCH$!Y8ha z#Z2Se_Q6hRj{{ooq!_U0zR&2Vj#p4#ZK-h2TkL1ehEb+zRXawMY7f$kMhSncc7HRg zM=>Y9uFb$?@{tUt5CkUcRh48Cn<#d76}~0&t^=*duU$O%JdoFnAsRg>Ie=89*{%wt zdHlL$%TcN>(|EK0kTFtzz+d1PLhGwG80t_Ja#v)D05Dd5c-|(b@5Di?Uz!|U$K}f% z5k4dXnh-B>I3_vsUXa677RC+xCx`p@D6S=Xvel<|?@f(5G}>8aV$VFr z(sqHO#&er?GAQfm$~tU)7~|WPc$UN?(h~`23?xP(TwC^Ck$ge`0k|@=amka>Y5LW3 z&BIoGhJiAX2{ZpzKo`G43Ts(v2Lcp_5@b@TXNm`FN^#Q~JN0a?6iw%#`6|tDkDEpE zzO&s|+ZJw{U}CD-ckw5Knus5nZZpp|={2r4yLIUv0*~r0H_wS4srEiUiV!s)pSeAvCC13pkTf`S+HJSaZC zWAT_goQ-tGZPNI7rUvqAFGa(Hj9X80RMP{G?KqPR50pbwvYPdRYtyd149g7o(jip@ zlLYVzebqi6F2N&T7Uq+$9b#%=%B~PGuQ>JWOMMwyyTQ+&U~t z-_!uL2t}<9u1fTErlVOR3Sw=p$RXB^KCKD+?U_JHDIN z#;GipSiaVnxHnbTd3a^5BysMdi3RGngF&TG)7=0Z`}7sP9Bmgg$SfFc zskRn79>951MDU*&;u`83Ym@pL;uIXQN{&Vt!Lp@xM5%25Mx(w{^lq29y$PK1R7uOQ zLxeuuv|Db3)mtW&rke#{mpxmqD(zvYw|Av4apR?%Xr&a3hsjgKCDAbP$=kfKPHf2( zzX_J9DH<}$XhV!kQ?L0UOhfK|GJ|+rH*np^8hJCl(i~T{;(B)~I@qsV3pvJ}qINvQ z5;;t9ivWE1^yPaJ0;gc_;>W+D^^f>*8x`NL-Y?zu*jiFR`u_O1GuQ znNnn4^&n$Jtd)q3C)UHY8u93)67spt@M`D#?7Q*VPAeE&Ka-E&xLx|nI({js`Iz3= zHov==Xca!lwiuIqO=QX`=(w~ez8E?ygEI>DQF!vub4?Is@NlTgHN3Wm`-o_m0POqA z69B$(|INH>4GABSMIjMFy~ITmE5>IzR=|dc;_ggXimSdaX1ih0GOKndtB#K{tO9#R zKJ<_KHTvVPro+UX5xw1aTl#gJoeO8(k1y=zl|EvP&M>*V6?Bl;6RnV~N%qi+z;v;f zma{rSaL)HVtG$9>D^>q`#(q7z2Kq4l?Cm+Mz2_uV%INQLtG&1LPIvOsug>Q>M;Oh` z+`5sfM47-+9g065aQcOFJ2( zo=@KR(ex)E_l$pu|1}fZ6n2xggP_dH*|Q+5y}JxG?3uq!T}~(-R1>ruj9phc`aJZ@ z{!XgFi5ZRmwK5s63%_oW;`mtxr?fu2V!lcI{Q9tjY)~T56G?jdK>K^+{%+dH(Tpbs zc8IeIYRH(7tC^Xx?)LGa#c>!FXsE3Nc=GH-Kj_SHXfuAh*GT55i1%OEl$+tHcPx= zH%KO)tgguegP7G0q*-SToifr-9CuZHPXpTj5@p2ICzTir)XK;xJ z-9`sj!-!*&L5syg8kO8c*hBR*3Xvjv9kHg=7DMRn`B!t^>`CFuP6EQ2Qf?7u+F#_ryR#Sj*xyCZqT;DlOK^UiJIyp zb+M`B2HNxMFW;Pasxs^xO%%lPFVDK4WY!?c}Q9M_bj#a7c+r zex;2vqb-5BHr^g4S!j;7(v;R><86W4Jc=DZH+Md(Yi_S;YRsPZ(p6Ya>t}A2tSpC9 zPuc8(VYwx&oYFRP)j7m_-IkLi76G}+GC3_WC-hk=_QQA{9(7n1q(!xlzvapv!npXDc;VMOO;CmEOg!vADe#3CM z)SxtJX>%tv;i#Q?;rsbSPLVCUh(D75K%@-Gr$ok@m9zGd3kEYHimPQpymeiUv)Fp&+fKVJ>M4Famsvv@J(LcHcbZf z<-6^8Jwg`VG}cYP+mZq@gF>CgWF+$>B;x70d}-!35%AC%A#nbik)w9QKdvbHZ}?el zl=Hb&7SARpvBxDV;A0QVcrIeIam`s?RnEDi2<_okQDmkAFh~@oqtf}zWCYG3{T8^FP;xyv_t!q(-cdaW3VpP{`C4v3ci!X> z;o)s`7V8f%H9|fZ$%iHG2^EkBW!vVaeEYW2X6=2w$Wol6=4yX|=GHKPiM}Hn_BPYV z(#C4wM?R7<&ZFs7fTV;-eS{jiRcsJ3*L$NXR0#aZ+hIKZ!;ZiHGs6}!zBz06r` potential for the energy E of a system of atoms as -.. image:: Eqs/pair_atm.jpg - :align: center +.. math:: -where nu is the three-body interaction strength. The distances -between pairs of atoms r12, r23, r31 and the angles gamma1, gamma2, -gamma3 are as shown in this diagram: + E & = \nu\frac{1+3\cos\gamma_1\cos\gamma_2\cos\gamma_3}{r_{12}^3r_{23}^3r_{31}^3} \\ + + +where :math:`\nu` is the three-body interaction strength. The distances +between pairs of atoms :math:`r_{12}`, :math:`r_{23}`, :math:`r_{31}` and the angles :math:`\gamma_1`, :math:`\gamma_2`, +:math:`\gamma_3` are as shown in this diagram: .. image:: JPG/pair_atm_dia.jpg :align: center -Note that for the interaction between a triplet of atoms I,J,K, there +Note that for the interaction between a triplet of atoms :math:`I,J,K`, there is no "central" atom. The interaction is symmetric with respect to -permutation of the three atoms. Thus the nu value is -the same for all those permutations of the atom types of I,J,K +permutation of the three atoms. Thus the :math:`\nu` value is +the same for all those permutations of the atom types of :math:`I,J,K` and needs to be specified only once, as discussed below. The *atm* potential is typically used in combination with a two-body potential using the :doc:`pair_style hybrid/overlay ` command as in the example above. -The potential for a triplet of atom is calculated only if all 3 -distances r12, r23, r31 between the 3 atoms satisfy rIJ < cutoff. -In addition, the product of the 3 distances r12\*r23\*r31 < -cutoff\_triple\^3 is required, which excludes from calculation the -triplets with small contribution to the interaction. +The potential for a triplet of atom is calculated only if all 3 distances +:math:`r_{12}`, :math:`r_{23}`, :math:`r_{31}` between the 3 atoms satisfy +:math:`r_{IJ} < \text{cutoff}`. In addition, the product of the 3 distances +:math:`r_{12} r_{23} r_{31} < \text{cutoff_triple}^3` is required, which +excludes from calculation the triplets with small contribution to the +interaction. The following coefficients must be defined for each pair of atoms types via the :doc:`pair_coeff ` command as in the examples above, or in the restart files read by the :doc:`read_restart ` commands: -* K = atom type of the third atom (1 to Ntypes) -* nu = prefactor (energy/distance\^9 units) +* :math:`K` = atom type of the third atom (1 to :math:`N_{\text{types}}`) +* :math:`\nu` = prefactor (energy/distance\^9 units) -K can be specified in one of two ways. An explicit numeric value can -be used, as in the 2nd example above. J <= K is required. LAMMPS -sets the coefficients for the other 5 symmetric interactions to the -same values. E.g. if I = 1, J = 2, K = 3, then these 6 values are set -to the specified nu: nu123, nu132, nu213, nu231, nu312, nu321. This -enforces the symmetry discussed above. +:math:`K` can be specified in one of two ways. An explicit numeric value can +be used, as in the 2nd example above. :math:`J \leq K` is required. LAMMPS +sets the coefficients for the other 5 symmetric interactions to the same +values. E.g. if :math:`I = 1`, :math:`J = 2`, :math:`K = 3`, then these 6 +values are set to the specified :math:`\nu`: :math:`\nu_{123}`, +:math:`\nu_{132}`, :math:`\nu_{213}`, :math:`\nu_{231}`, :math:`\nu_{312}`, +:math:`\nu_{321}`. This enforces the symmetry discussed above. A wildcard asterisk can be used for K to set the coefficients for multiple triplets of atom types. This takes the form "\*" or "\*n" or -"n\*" or "m\*n". If N = the number of atom types, then an asterisk with -no numeric values means all types from 1 to N. A leading asterisk -means all types from 1 to n (inclusive). A trailing asterisk means -all types from n to N (inclusive). A middle asterisk means all types -from m to n (inclusive). Note that only type triplets with J <= K are -considered; if asterisks imply type triplets where K < J, they are +"n\*" or "m\*n". If :math:`N` equals the number of atom types, then an asterisk with +no numeric values means all types from 1 to :math:`N`. A leading asterisk +means all types from 1 to :math:`n` (inclusive). A trailing asterisk means +all types from :math:`n` to :math:`N` (inclusive). A middle asterisk means all types +from :math:`m` to :math:`n` (inclusive). Note that only type triplets with :math:`J \leq K` are +considered; if asterisks imply type triplets where :math:`K < J`, they are ignored. -Note that a pair\_coeff command can override a previous setting for the -same I,J,K triplet. For example, these commands set nu for all I,J.K -triplets, then overwrite nu for just the I,J,K = 2,3,4 triplet: +Note that a pair_coeff command can override a previous setting for the +same :math:`I,J,K` triplet. For example, these commands set :math:`\nu` for all :math:`I,J.K` +triplets, then overwrite nu for just the :math:`I,J,K = 2,3,4` triplet: -.. parsed-literal:: +.. code-block:: LAMMPS - pair_coeff \* \* \* 0.25 + pair_coeff * * * 0.25 pair_coeff 2 3 4 0.1 Note that for a simulation with a single atom type, only a single entry is required, e.g. -.. parsed-literal:: +.. code-block:: LAMMPS pair_coeff 1 1 1 0.25 -For a simulation with two atom types, four pair\_coeff commands will +For a simulation with two atom types, four pair_coeff commands will specify all possible nu values: -.. parsed-literal:: +.. code-block:: LAMMPS pair_coeff 1 1 1 nu1 pair_coeff 1 1 2 nu2 pair_coeff 1 2 2 nu3 pair_coeff 2 2 2 nu4 -For a simulation with three atom types, ten pair\_coeff commands will +For a simulation with three atom types, ten pair_coeff commands will specify all possible nu values: -.. parsed-literal:: +.. code-block:: LAMMPS pair_coeff 1 1 1 nu1 pair_coeff 1 1 2 nu2 @@ -133,12 +137,12 @@ specify all possible nu values: pair_coeff 2 3 3 nu9 pair_coeff 3 3 3 nu10 -By default the nu value for all triplets is set to 0.0. Thus it is -not required to provide pair\_coeff commands that enumerate triplet -interactions for all K types. If some I,J,K combination is not +By default the :math:`\nu` value for all triplets is set to 0.0. Thus it is +not required to provide pair_coeff commands that enumerate triplet +interactions for all :math:`K` types. If some :math:`I,J,K` combination is not specified, then there will be no 3-body ATM interactions for that combination and all its permutations. However, as with all pair -styles, it is required to specify a pair\_coeff command for all I,J +styles, it is required to specify a pair_coeff command for all :math:`I,J` combinations, else an error will result. @@ -150,16 +154,16 @@ combinations, else an error will result. This pair styles do not support the :doc:`pair_modify ` mix, shift, table, and tail options. -This pair style writes its information to :doc:`binary restart files `, so pair\_style and pair\_coeff commands do not need -to be specified in an input script that reads a restart file. -However, if the *atm* potential is used in combination with other -potentials using the :doc:`pair_style hybrid/overlay ` -command then pair\_coeff commands need to be re-specified -in the restart input script. +This pair style writes its information to :doc:`binary restart files +`, so pair_style and pair_coeff commands do not need to be specified +in an input script that reads a restart file. However, if the *atm* potential +is used in combination with other potentials using the :doc:`pair_style +hybrid/overlay ` command then pair_coeff commands need to be +re-specified in the restart input script. This pair style can only be used via the *pair* keyword of the :doc:`run_style respa ` command. It does not support the -*inner*\ , *middle*\ , *outer* keywords. +*inner* , *middle* , *outer* keywords. ----------