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M3P2
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b9d63285
Commit
b9d63285
authored
Feb 10, 2026
by
Claude Meny
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Update cheatsheet.en.md
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@@ -80,33 +80,34 @@ of the pond.
*
A field is
**uniform**
if
*its value is the same at every point*
in space at a given
instant or over a specified time period.
<br>
_
*Example:*
E
ven without ripples, the depth of a pond varies from one point to another._
_The water height field beneath the surface is
**not uniform**
._
_
*However,*
in an Olympic swimming pool where the water depth is the same everywhere,_
_the water height field
**is uniform**
at the surface._
_
For example, e
ven without ripples, the depth of a pond varies from one point to another._
_The water height field beneath the surface is
not uniform._
_
However,
in an Olympic swimming pool where the water depth is the same everywhere,_
_the water height field
is uniform
at the surface._
*
A field is
**stationary**
if
*its values*
—which may vary in space—
*do not change over time*
.
_
*Example:*
In a calm, windless pond where the water surface is "at rest," perfectly still,_
_the water height field is
**stationary**
._
*
A field is
**stationary**
if
*its values*
—which may vary in space—
*do not change over time*
.
<br>
_In a calm, windless pond where the water surface is "at rest," perfectly still,_
_the water height field is stationary._
*
A field is
**homogeneous**
if
*its propagation properties*
(the shape of the perturbation
for a given impact and its propagation speed in a given direction)
*are identical at every point*
in space, even if the field’s values vary spatially.
<br>
_
*Example:*
The speed of ripples depends on depth—shallow water slows propagation due to friction_
_with the bottom, while deep water allows faster wave movement._
_
*Thus,*
since a pond’s depth varies, its water height field is
**not strictly homogeneous**
._
_
*However,*
in an Olympic pool with constant depth, the field
**is homogeneous**
._
_The speed of ripples depends on depth—shallow water slows propagation due to friction_
_with the bottom, while deep water allows faster wave movement._
_
Thus, since a pond’s depth varies, its water height field is not strictly homogeneous
._
_
However, in an Olympic pool with constant depth, the field is homogeneous
._
*
A field is
**isotropic**
if, regardless of the impact point,
*the propagation of the perturbation*
(its speed, shape, and attenuation)
*does not depend on direction*
, even if the
induced perturbation varies from one point to another for the same impact.
<br>
_
*Example:*
If raindrops in a pond always create perfectly circular ripples that propagate_
_If raindrops in a pond always create perfectly circular ripples that propagate_
_outward, it means each ripple spreads at the same speed in all directions._
_
*Furthermore,*
if the height of a ripple remains constant at equal distances from_
_the impact point, then the water height field is
**isotropic**
._
_
Furthermore,
if the height of a ripple remains constant at equal distances from_
_the impact point, then the water height field is
isotropic
._
*
A field is
**linear**
if, for a point-like and instantaneous impact,
*the amplitude of the perturbation is proportional to the energy of the impact*
,
...
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