🧕🏾 🙆🏻 👫 Cómo impulsamos el logotipo de la conferencia con SciArt 💳 🤱 ☝️

El año pasado (2020), en relación con la pandemia, celebramos una conferencia científica en línea sobre química computacional e hicimos un logotipo para ella, que era, por decirlo suavemente, regular. Debajo del corte hay una historia sobre cómo lo bombeamos para la conferencia de este año (2021) utilizando una pequeña cantidad de mecánica cuántica, el método de Monte Carlo, Python y Gnuplot.

Un poco de historia

2020, el coronavirus está ganando impulso, se imponen restricciones y, para mantener el nivel de discusión científica, mejorar la cooperación científica entre los científicos de habla rusa repartidos por todo el mundo, y para todos los demás, organizamos un mini-simposio sobre química computacional en línea .

Pero, ¿qué es una conferencia sin logo? Y habiendo reunido en un puño todas las posibilidades artísticas (de la palabra "mala") del comité organizador de la conferencia, se creó un logo en Inkscape :

El logo original que hicimos con Inkscape y Jmol + Gimp (para dibujar fullerenos).

. , d- . - Firefly, , , , . , . : ψ, , . , . to Pimp My ~~Ride~~ Logo.

, 2020 , -. . , - ?

. :

- ψ ( ), (x,y,z)=r. . r₀, r₁, r₂, ..., r_N, N - . ψ_n=ψ(r_n). , Python :

r_n r_trial, (x_n,y_n,z_n) r_n -δ +δ, δ — , ,
p_acc = |ψ_trial|²/|ψ_n|², q 0 1, p_acc q: p_acc<q, (r_n₊₁=r_n), , (r_n₊₁=r_trial),
, , -0.1⋅δ +0.1⋅δ.

, , . 10% , , , . .

. d- :

$\ psi (x, y, z) = x \ cdot y \ cdot \ exp (-r)$

r — r, , . , . , , :

$\ psi (x, y, z) = (0.05 \ cdot y ^ 3 + 0.9 \ cdot x \ cdot y) \ cdot \ exp (-r)$

, , .

Python

import numpy as np
import random as rnd

DXYZ = 4.0
dxyz = 0.1*DXYZ

def getWFN(R, a=0.05, b=0.9, R0=1.0):
    return (a*(R[1])**3 + b*R[0]*R[1])*np.exp(-np.sqrt(np.dot(R,R))/R0)

Npts = 40000
N2ignore = Npts/10

outf = open("wfn.dat", "w")
outfp = open("wfn_pos.dat", "w")
outfn = open("wfn_neg.dat", "w")

genNewXYZ = lambda xyz, shift: xyz + np.array([rnd.uniform(-shift,shift) for q in range(0,3)])

XYZ = np.array([1.0,1.0,0.0])
Psi = getWFN(XYZ, DXYZ)

for i in range(0,Npts):
    trialXYZ = genNewXYZ(XYZ, DXYZ)
    trialPsi = getWFN(trialXYZ)
    if i % N2ignore == 0:
        print("step #%i" % (i))

    Ptrial = rnd.random()
    Ptest = trialPsi**2/Psi**2

    Accepted = False
    if Ptrial < Ptest:
        Psi = trialPsi
        XYZ = trialXYZ
        Accepted = True

    if i>N2ignore:
        r2save = XYZ
        if not Accepted:
            r2save = genNewXYZ(XYZ, dxyz)
        outf.write(" %15.10f %15.10f %15.10f %15.5e\n" % tuple(list(r2save)+[Psi]))
        if Psi > 0.0:
            outfp.write(" %15.10f %15.10f %15.10f %15.5e\n" % tuple(list(r2save)+[Psi]))
        else:
            outfn.write(" %15.10f %15.10f %15.10f %15.5e\n" % tuple(list(r2save)+[Psi]))

$\ psi (x, y, z) = \ begin {cases} (y ^ 3 + 0.5 \ cdot y) \ cdot \ exp \ left (- \ frac {| x |} {0.2} - \ frac {| y | } {0.5} - \ frac {| z |} {0.2} \ right) \, \ y <0 \\ 0, \ y \ geq 0 \ end {cases}$

Python

import numpy as np
import random as rnd

DXYZ = 0.5
dxyz = 0.1*DXYZ

def getWFN(R, a=1.0, b=0.5, X0=0.2, Y0=0.5, Z0=0.2):
    if R[1]<0.:
        return (a*(R[1])**3 + b*R[1])*np.exp(-np.abs(R[0])/X0 - np.abs(R[1])/Y0 - np.abs(R[2])/Z0)
    else: 
        return 0.0

Npts = 20000
N2ignore = Npts/10

outf = open("body.dat", "w")

genNewXYZ = lambda xyz, shift: xyz + np.array([rnd.uniform(-shift,shift) for q in range(0,3)])

XYZ = np.array([0.0,-0.2,0.0])
Psi = getWFN(XYZ, DXYZ)

for i in range(0,Npts):
    trialXYZ = genNewXYZ(XYZ, DXYZ)
    trialPsi = getWFN(trialXYZ)
    if i % N2ignore == 0:
        print("step #%i" % (i))

    Ptrial = rnd.random()
    Ptest = trialPsi**2/Psi**2

    Accepted = False
    if Ptrial < Ptest:
        Psi = trialPsi
        XYZ = trialXYZ
        Accepted = True

    if i>N2ignore:
        r2save = XYZ
        if not Accepted:
            r2save = genNewXYZ(XYZ, dxyz)

        outf.write(" %15.10f %15.10f %15.10f %15.5e\n" % tuple(list(r2save)+[Psi]))

, s-:

$\ psi (x, y, z) = \ exp \ left (- \ frac {| x |} {0.3} - \ frac {| y |} {0.5} - \ frac {| z |} {0.3} \ right )$

Python

import numpy as np
import random as rnd

DXYZ = 0.9
dxyz = 0.1*DXYZ

def getWFN(R, a=1.0, b=0.5, X0=0.3, Y0=0.5, Z0=0.3):
    return np.exp(-np.abs(R[0])/X0 - np.abs(R[1])/Y0 - np.abs(R[2])/Z0)

Npts = 10000
N2ignore = Npts/10

outf = open("head.dat", "w")

genNewXYZ = lambda xyz, shift: xyz + np.array([rnd.uniform(-shift,shift) for q in range(0,3)])

XYZ = np.array([0.0,-0.2,0.0])
Psi = getWFN(XYZ, DXYZ)

for i in range(0,Npts):
    trialXYZ = genNewXYZ(XYZ, DXYZ)
    trialPsi = getWFN(trialXYZ)
    if i % N2ignore == 0:
        print("step #%i" % (i))

    Ptrial = rnd.random()
    Ptest = trialPsi**2/Psi**2

    Accepted = False
    if Ptrial < Ptest:
        Psi = trialPsi
        XYZ = trialXYZ
        Accepted = True

    if i>N2ignore:
        r2save = XYZ
        if not Accepted:
            r2save = genNewXYZ(XYZ, dxyz)

        outf.write(" %15.10f %15.10f %15.10f %15.5e\n" % tuple(list(r2save)+[Psi]))

, , :

$\ psi (x, y, z) = \ begin {cases} (y ^ 3 + 0.5 \ cdot y) \ cdot \ exp \ left (- \ frac {| x |} {0.4} - \ frac {| y | } {0.68} - \ frac {| z |} {0.3} \ right) \, \ y <0 \\ 0, \ y \ geq 0 \ end {cases}$

Python

import numpy as np
import random as rnd

DXYZ = 0.9
dxyz = 0.1*DXYZ

def getWFN(R, a=1.0, b=0.5, X0=0.4, Y0=0.68, Z0=0.3):
    if R[1]<0.:
        return (a*(R[1])**3 + b*R[1])*np.exp(-np.abs(R[0])/X0 - np.abs(R[1])/Y0 - np.abs(R[2])/Z0)
    else: 
        return 0.0

Npts = 1000
N2ignore = Npts/10

outf = open("body_fire.dat", "w")

genNewXYZ = lambda xyz, shift: xyz + np.array([rnd.uniform(-shift,shift) for q in range(0,3)])

XYZ = np.array([0.0,-0.2,0.0])
Psi = getWFN(XYZ, DXYZ)

for i in range(0,Npts):
    trialXYZ = genNewXYZ(XYZ, DXYZ)
    trialPsi = getWFN(trialXYZ)
    if i % N2ignore == 0:
        print("step #%i" % (i))

    Ptrial = rnd.random()
    Ptest = trialPsi**2/Psi**2

    Accepted = False
    if Ptrial < Ptest:
        Psi = trialPsi
        XYZ = trialXYZ
        Accepted = True

    if i>N2ignore:
        r2save = XYZ
        if not Accepted:
            r2save = genNewXYZ(XYZ, dxyz)

        outf.write(" %15.10f %15.10f %15.10f %15.5e\n" % tuple(list(r2save)+[Psi]))

(x_n, y_n, z_n, ψ_n) n=0,1,2,..., . Gnuplot multiplot. (set view map). , : https://github.com/Gnuplotting/gnuplot-palettes.

inferno, — ylrd, . - : plasma, parula, — prgn.

Plasma — , - , . Parula , , ... , , , . prgn, : , , . Inkscape .

Gnuplot

#set terminal pngcairo size 1500,1500   transparent 
set terminal pngcairo size 1500,1500  background rgb '#080045' 
set output "ff_v2.png" 

set multiplot

set view map 
set size ratio 1

unset colorbox
unset border
unset key
unset xtics
unset ytics

XMax = 7.

set xrange [-XMax:XMax]
set yrange [-XMax:XMax]

set pm3d depthorder hidden3d 1
set hidden3d

set style fill  transparent solid 0.35 noborder
set style circle radius 0.02

load 'prgn.pal'

#load 'plasma.pal'
#load 'parula.pal'
splot 'wfn_pos.dat' u 2:1:3:4 w p pt 7 ps 2 lc palette


splot 'wfn_neg.dat' u 2:1:3:4 w p pt 7 ps 2 lc palette
      
load 'inferno.pal'
splot 'body.dat' u 1:2:3:4 w l lc palette
      
splot 'head.dat' u 1:2:3:4 w l lc palette

load 'ylrd.pal'
splot 'body_fire.dat' u 1:2:3:(-$4)  w l lw 3 lc palette

— (. ): , , . :)

P.S.

, - , . , , YouTube .

Cómo impulsamos el logotipo de la conferencia con SciArt

Un poco de historia

P.S.

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