Line Integral of a Scalar Field
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Get ready everyone (Desmos graph credit to u/scalar-field)
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Animation of Line Integrals of Scalar Fields with 3b1b's manim. I've also made a video on it (Link in the comments), would be glad to receive any feedback. v.redd.it/uawlrhek8q961
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Animation of Line Integrals of Scalar Fields. I've also made a video on it (Link in the comments), would be glad to receive any feedback. v.redd.it/xn79674poq961
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I made an animation on Line Integrals of Scalar Fields & also made a video (Link in comments) sharing my perspective regarding the transition from integrating with "ds" to integrating with "dt" , which is essentially just rescaling the riemann sum. I'd be glad to hear your thoughts on this, thanks! v.redd.it/k15pbfkjsq961
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Animation of Line Integrals of Scalar Fields made with manim. I've also made a video on it (Link in the comments), would be glad to receive any feedback. v.redd.it/t72b8p8ugq961
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Animation of Line Integrals of Scalar Fields made with manim. I've also made a video on it (Link in the comments), would be glad to receive any feedback. v.redd.it/5qt636o1nq961
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Line Integrals of 2D Scalar Fields, made with 3b1b's shaders youtu.be/G28aYRu9aZI
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Animation of Line Integrals of Scalar Fields made with manim. I've also made a video on it (Link in the comments), would be glad to receive any feedback. v.redd.it/w107bdrtdq961
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Why does an electric field have a scalar potential, while a magnetic field has a vector potential?
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How to interpolate a 3d scalar field from discrete measurement points to a cut of an object?

Hello Mayans, sorry for a total newb question .... I'd like to spice an animated section up with a display of interpolated color-coded temperature values on the section plane. A little more precisely, my data are a surface object, and the temperature values on some discretely spaced point cloud that fills the interior of the object in a not very regular fashion. Now, instead of just slicing the object and displaying the section contour as usual, I'd like Maya to generate a mesh of the slicing contour on the slicing plane, and interpolate the temperature values on the vertices of that mesh from the closest points with known temperature, or maybe in a more advanced fashion using some inverse distance weighting or whatever. So far, I have imported the object and can animate the section, but I have no clue how to import the point cloud, how to import the temperature values on these points , how to make Maya mesh the slicing contour and interpolate the temperatures and color the slices meshes accordingly. Hope this is a clear description.

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Scalar and Vector Fields youtube.com/watch?v=ybNSE…
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Is the line integral of a scalar field a vector?

Hi, I'm studying line integrals of a scalar field and I find two definitions:

https://preview.redd.it/4247aqb80rb51.png?width=570&format=png&auto=webp&s=df742d9382f6f1ed6bac17757be67098a193b6e6

and

https://preview.redd.it/ela59ui5zqb51.png?width=338&format=png&auto=webp&s=4c2832d637878c38deb875d316b789b7a723e5b4

The first is a vector and the second is a scalar. I'm confused. Are they both correct? Why are they different?

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Star CCM field function for passive scalar location

Hi I’m trying to define a passive scalar location for my tank (which has no inlet) as a spherical ball (equation x^2 + y^2 + z^2 = 0.1). Essentially a sphere of radius sqrt(0.1) at origin. What would be the syntax for this?

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Scalar function too slow - Calculated field in column based on another columns

I have a big query, (really big, 800+columns - can't really make it smaller) that I'm trying to build in the most efficient way.

I have some fields like this:

SELECT distinct(td.EVENT_ID), 
       td.MENU_HINT, 
       td.EVENT_NAME, 
       td.EVENT_DT AS Expr1003, 
       COUNT(td.EVENT_NAME) AS [Total Runners], 
       -- AS [WinnerPrice], 
       -- COUNT(td.ID) AS [WinnerCount],
       SUM(CASE WHEN td.BSP >= 1 AND td.BSP < 2 THEN td.BSP END) AS Sum1to2, 
       count(CASE WHEN td.BSP >= 1 AND td.BSP < 2 THEN td.BSP END) AS count1to2, 
       avg(CASE WHEN td.BSP >= 1 AND td.BSP < 2 THEN td.BSP END) AS average1to2,
       dbo.FN_SumWinnerRunners(td.EVENT_ID,34,55,0,7,12) AS [TEST FUNCTION],
       SUM(CASE WHEN (td.BSP >= 2 AND td.BSP < 3) AND td.WIN_LOSE =1 THEN td.BSP END) AS SumWinnerPrice2to3, 
       count(CASE WHEN (td.BSP >= 2 AND td.BSP < 3) AND td.WIN_LOSE =1 THEN td.BSP END) AS CountWinnerPrice2to3
       FROM tblData td 
GROUP BY td.EVENT_ID, 
         td.MENU_HINT, 
         td.EVENT_NAME, 
         td.EVENT_DT
ORDER BY [Total Runners] DESC;

And here a graphical one (click to enlarge):

https://preview.redd.it/5xpivq1wvum41.png?width=1039&format=png&auto=webp&s=c77b04efb616ad4c7909da16b8c39ace75ba429e

if you notice, I've tried, as I have several queries that are fairly similar, to use a function (dbo.FN_SumWinnerRunners(td.EVENT_ID,34,55,0,7,12)

the definition for it below:

CREATE FUNCTION [dbo].[FN_SumWinnerRunners](
                                @event_id    INT,   
                                @BSPFrom     SMALLINT, 
                                @BSPTo       SMALLINT, 
                                @Win_Lose    SMALLINT, 
                                @RunnersFrom SMALLINT, 
                                @RunnersTo   SMALLINT)
RETURNS FLOAT
AS
     BEGIN
         DECLARE @result FLOAT=
         (
             SELECT SUM(CASE
                            WHEN(td.BSP >= @BSPFrom
                                 AND td.BSP < @BSPTo)
                                AND td.WIN_LOSE = @Win_Lose
                            THEN td.BSP
                        END)
             FROM tblData td
             WHERE td.EVENT_ID = @event_id
             HAVING COUNT(td.EVENT_NAME) > @RunnersFrom
... keep reading on reddit ➑

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Happiness is a scalar field

Happiness is a scalar field in the many dimensional phase space representing the state of the universe. Finding the point at which your happiness is maximum is very hard, taking infinite computation time in the general case. Instead, the best way to find happiness is to perform gradient descent. Looking at every small step you could take in the phase space from where you currently are, pick the one which changes your happiness the most. If you continue to do so, eventually you'll find a local maximum of your happiness field. This may not be the global maximum of the happiness function but at the very least it's a local maximum with the added benefit of being able to find it in finite time. Although if you're going to take this advice, remember time is also a dimension of the phase space and you are constantly taking steps through time so make sure to adjust for those.

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Is Ohm's law still valid if the Electric field isn't uniform through a conductor? Is it possible to prove that vector and scalar form of Ohm's law are equivalent with this condition? How?

As this website and other textbooks shows, to pass from the microscopic to macroscopic version of Ohm's law, these assumptions are made:

β€’ E=βˆ†V/L which is only true if the field through the conductor is uniform.

β€’ J=I/A that due to its definition implies that the direction of the drift speed of electrons is the same as the normal vector of the conductor's surface.

But this can't be true considering we are assuming pJ=E and E, since the conductor isn't in electrostatic equilibrium anymore, is the field inside of the conductor generated by the current. So it makes sense for me that E can be considered uniform because is almost always tangencial to the path, but then again, the direction of J and E can't be the same to make these 2 assumption simultaneously, am I right? What am I missing in this analysis?

Also, I couldn't find anything mathematically rigorous on this particular issue, like how is it possible that we can have a vector and scalar form of Ohm's law that are equivalent? Is the law actually the module of J and E or why is the vector form which is correct?

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People that say there are only 2 genders are the same people that would forget the Higgs field is a complex scalar field
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More of a physics question, but do you think there a typo in this question? I know a scalar field multiplied by a vector field returns a vector field, and the gradient of a vector field is a tensor, which we never covered in class. Am I missing something?
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A fluffy forest made entirely out of a scalar field! No SDFs for this one! ;) https://www.shadertoy.com/view/Wt2SRm v.redd.it/ru224r0s17g31
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tf is a Power energy scalar quantum bio science negative ions pendant necklace electromagnetic field protection necklace?
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Is there a systematic way of getting all feynman diagrams in scalar field theory?

Often our exam questions say something like 'draw all irreducible feynman diagrams with one loop'. I could just learn all the possibilities but we get questions that include phi-fourth, phi-third, mix them together etc.

Obviously one alternative is to expand the exponential and use wicks theorem and then remove any that don't fit the criteria, however this feels like a long way round

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Majestic and exotic-tech [CERN] scalar-based laser-drive interference-pattern future-proves-past [HAARP] Chemtrailing and Mandela Effecting Zero Point Energar-field weighs in on those [Dummy Dems] [LOL]
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Given a vector field F, find scalar functions u and v to decompose F into u grad(v) and v grad(u).

Is it always possible to find a pair of functions that satisfy this condition? And if so how can I find them?
This question popped up when watching Introducing Green's Functions for Partial Differential Equations (PDEs) 3:15.
Any guidance would be greatly appreciated, thanks in advance.

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What are the fundamental differences between the concept of an Aether and the idea of a vacuum being a scalar field?
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how can I prove this. if ΓΈ scalar field
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