wall kind tube#
Describes the entry tube at version 0.1.0, registered by mime.walls.TubeWall.
At a glance#
wall kind
tube, version0.1.0, namespacemimeDerivative:
piecewise_kinkValidity: 3 declared lines
What it models, and when not to use it#
tube#
A straight circular tube with a no-slip wall, the medium filling its lumen. The method of regularised Stokeslets adds the tube’s
image system to the free-space kernel: the flow a point force makes inside the tube, less the free Stokeslet
[@LironShahar1978]. It is read from one table of the unit tube’s image system, which the tube’s radius and the
fluid’s viscosity scale to any tube, a file fetched into the assets cache (mime assets fetch unit_tube_R0.997) and
read when an experiment with the wall kind is planned; a file that is not there is refused by name, never downloaded.
What it reads. The tube’s centre, axis and radius, from the cylinder region the medium fills.
Where it reads. Within the table’s readable range: from the axis to the last radial knot of the file, and a few
radii apart along the axis (the file’s reach). A body whose samples leave that range is refused: the plan refuses a
body longer than the table reaches along the axis, and a run that leaves the range publishes wall_accepted false. The
numbers, the read’s accuracy and the table’s gate are MIME-ANO-117’s.
When not to use it. For interactions between bodies several radii apart along the axis: from there the read’s error exceeds the tube’s whole Green’s function, which is fine for a body’s drag and not for a long-range interaction.
The gradient. The derivative is continuous except where a sample crosses the tube’s axis: the read is continuous
through the axis and its derivative across it is not (tube.axis, a kink).
Versions. The first.
Settings#
none: the entry takes no setting, so its setting_roles declares none.
Nodes it builds#
Builds no node of its own.
Gradient status#
The derivative through this entry is piecewise_kink: not the exact derivative of what it computes everywhere.
Switches the law evaluates, each declared once by its owner:
Switch |
Indicator |
Orders, per output group |
Route to exact |
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a query’s offset from its nearest knot on a table axis, in that axis’s units (the tube’s radius for a radius or an axial offset, radians for the angle) |
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none needed: the table is read by a cubic, continuously differentiable across every knot inside the readable range; a read past the range stops the run (wall_accepted false) |
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the sine of the angle from one sample to another about the tube’s axis |
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none needed: the table is mirrored past its first and last angle knots with the slope of the symmetric extension, and the odd components are zero there, so the folded read is continuously differentiable across them |
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the axial offset between two samples, in the tube’s radius |
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none needed: as tube.angle’s, the table is mirrored past its first axial knot, a zero offset |
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a sample’s distance from the tube’s axis, in the tube’s radius (a pair’s: the root of the mean of its two samples’ squared distances) |
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a table read that is smooth in the square of the distance from the axis, for instance one mirrored past the axis knot with the slope of the symmetric extension; the read is continuous through the axis and, being cubic in the distance, has a different slope on its two sides |
Validity#
Declared validity lines: free text, not parsed, and not yet checked against the operating point or the region each one describes.
a straight circular tube of no-slip wall, infinitely long, the medium filling its lumen; the body’s samples read within the table’s readable range, from the axis to its last radial knot and as far apart along the axis as its file reaches, a read outside refused (wall_accepted false, and the plan refuses a body longer than the table reaches)
the read’s accuracy against the builder’s image, and the table’s gate, are MIME-ANO-117’s
from several radii along the axis the read’s error exceeds the tube’s whole Green’s function: use it for a body’s drag, not for interactions between bodies that far apart
References#
[@LironShahar1978]
Other declarations#
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