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from plplot import *
from Numeric import *
# Pairs of points making the line segments used to plot the user defined arrow
arrow_x = [-0.5, 0.5, 0.3, 0.5, 0.3, 0.5]
arrow_y = [0.0, 0.0, 0.2, 0.0, -0.2, 0.0]
arrow2_x = [-0.5, 0.3, 0.3, 0.5, 0.3, 0.3]
arrow2_y = [0.0, 0.0, 0.2, 0.0, -0.2, 0.0]
def circulation():
nx = 20
ny = 20
dx = 1.0
dy = 1.0
xmin = -nx/2*dx
xmax = nx/2*dx
ymin = -ny/2*dy
ymax = ny/2*dy
# Create data - circulation around the origin.
ix = ones(nx)
iy = ones(ny)
x = arange(nx)+0.5-nx/2.0
y = arange(ny)+0.5-ny/2.0
xg = multiply.outer(x,iy)
yg = multiply.outer(ix,y)
u = yg
v = -xg
# Plot vectors with default arrows
plenv(xmin, xmax, ymin, ymax, 0, 0)
pllab("(x)", "(y)", "#frPLplot Example 22 - circulation")
plcol0(2)
scaling = 0.0
plvect(u,v,scaling,pltr2,xg,yg)
plcol0(1)
# Vector plot of flow through a constricted pipe
def constriction():
nx = 20
ny = 20
dx = 1.0
dy = 1.0
xmin = -nx/2*dx
xmax = nx/2*dx
ymin = -ny/2*dy
ymax = ny/2*dy
Q = 2.0
ix = ones(nx)
iy = ones(ny)
x = (arange(nx)-nx/2+0.5)*dx
y = (arange(ny)-ny/2+0.5)*dy
xg = multiply.outer(x,iy)
yg = multiply.outer(ix,y)
b = ymax/4.0*(3-cos(pi*x/xmax))
b2 = multiply.outer(b,iy)
mask = greater.outer(b,abs(y))
dbdx = ymax/4.0*(sin(pi*xg/xmax)*yg/b2)
u = Q*ymax/b2*mask
v = dbdx*u
plenv(xmin, xmax, ymin, ymax, 0, 0)
pllab("(x)", "(y)", "#frPLplot Example 22 - constriction")
plcol0(2)
scaling=-0.5
plvect(u,v,scaling,pltr2,xg,yg)
plcol0(1)
# Vector plot of the gradient of a shielded potential (see example 9)
def potential():
nper = 100
nlevel = 10
nr = 20
ntheta = 20
# Create data to be contoured
r = 0.5+arange(nr)
r.shape = (-1,1)
theta = (2.*pi/float(ntheta-1))*(0.5+arange(ntheta-1))
xg = r*cos(theta)
yg = r*sin(theta)
rmax = nr
xmin = min(xg.flat)
xmax = max(xg.flat)
ymin = min(yg.flat)
ymax = max(yg.flat)
x = xg
y = yg
# Potential inside a conducting cylinder (or sphere) by method of images.
# Charge 1 is placed at (d1, d1), with image charge at (d2, d2).
# Charge 2 is placed at (d1, -d1), with image charge at (d2, -d2).
# Also put in smoothing term at small distances.
eps = 2.
q1 = 1.
d1 = rmax/4.
q1i = - q1*rmax/d1
d1i = rmax**2/d1
q2 = -1.
d2 = rmax/4.
q2i = - q2*rmax/d2
d2i = rmax**2/d2
div1 = sqrt((x-d1)**2 + (y-d1)**2 + eps**2)
div1i = sqrt((x-d1i)**2 + (y-d1i)**2 + eps**2)
div2 = sqrt((x-d2)**2 + (y+d2)**2 + eps**2)
div2i = sqrt((x-d2i)**2 + (y+d2i)**2 + eps**2)
zg = q1/div1 + q1i/div1i + q2/div2 + q2i/div2i
zmin = min(zg.flat)
zmax = max(zg.flat)
ug = -q1*(x-d1)/div1**3 - q1i*(x-d1i)/div1i**3 \
- q2*(x-d2)/div2**3 - q2i*(x-d2i)/div2i**3
vg = -q1*(y-d1)/div1**3 - q1i*(y-d1i)/div1i**3 \
- q2*(y+d2)/div2**3 - q2i*(y+d2i)/div2i**3
umin = min(ug.flat)
umax = max(ug.flat)
vmin = min(vg.flat)
vmax = max(vg.flat)
plenv(xmin, xmax, ymin, ymax, 0, 0)
pllab("(x)", "(y)", "#frPLplot Example 22 - potential gradient vector plot")
# Plot contours of the potential
dz = (zmax-zmin)/float(nlevel)
clevel = zmin + (arange(20)+0.5)*dz
du = (umax-umin)/float(nlevel)
clevelu = umin + (arange(20)+0.5)*du
dv = (vmax-vmin)/float(nlevel)
clevelv = vmin + (arange(20)+0.5)*dv
plcol0(3)
pllsty(2)
plcont(zg,clevel,pltr2,xg,yg)
pllsty(1)
plcol0(1)
# Plot the vectors of the gradient of the potential
plcol0(2)
scaling = 25.0
plvect(ug,vg,scaling,pltr2,xg,yg)
plcol0(1)
# Perimeter
t = (2.*pi/(nper-1))*arange(nper)
px = rmax*cos(t)
py = rmax*sin(t)
plline(px,py)
# main
#
# Does a series of vector plots
#
def main():
circulation()
narr = 6
fill = 0
# Set arrow style using arrow_x and arrow_y then
# plot using these arrows.
plsvect(arrow_x, arrow_y, fill)
constriction()
# Set arrow style using arrow2_x and arrow2_y then
# plot using these filled arrows.
fill = 1
plsvect(arrow2_x, arrow2_y, fill)
constriction()
potential()
# Vector plot of the circulation about the origin
main()
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