A square plate on a side is sampled at evenly spaced positions in each direction

PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Scientific programming for physicists · Scientific programming for physicists

Computational Physics, Ch Arrays: a field is a rectangle of numbers

Problem

A square plate

1.0\,\mathrm{m}

on a side is sampled at

11

evenly spaced positions in each direction,

\texttt{x = np.linspace(0.0, 1.0, 11)}

and

\texttt{y = np.linspace(0.0, 1.0, 11)}

, each of shape

(11,)

. A steady temperature across the plate is modelled as

T(x, y) = 300 + 40(x + y)

, with

T

in K and

x

and

y

in m. ((a)) Write one expression that builds the grid from

\texttt{x}

and

\texttt{y}

and evaluates

T

at every node, and state how many numbers the result holds. ((b))

\texttt{T.mean(axis=1)}

is then evaluated. State the shape of what is left and the value of its largest entry. ((c)) The part of the plate hotter than

350\,\mathrm{K}

is selected with a mask. State how many nodes the mask holds and the mean temperature over them.

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