How to reproduce this tensor calculation with Mathematica

The tensor operation shown in the red box is used in the textbook to prove that there are only 9 independent constants for orthotropic materials:

Enter the image description here

I want to use MMA to reproduce the operation of $ C_ {pqmn} = l_ {ip} ; l_ {jq} ; l_ {km} ; l_ {ln} ; C_ {ijkl} $ (Where $ C_ {ijkl} $ is the stiffness tensor), but currently I have no specific idea. I will continue to update the details to make them perfect.

Additional details:

Details will be added …

dnd 5e – How do daemons / yugoloths reproduce (make more of themselves)?

As far as I know, the Lawful Evil Devils primarily continue their race by doing business with mortals in exchange for their souls. A mortal who accepts this arrangement will be resurrected as a lemur in the Nine Hells (or sometimes a more powerful type of devil, depending on the arrangement) after his death. Teufel also offers these offers to souls who have reached the joint level after their death. A soul who takes advantage of such a deal is likely trying to avoid punishment in the afterlife and thinks that damnation is better for some reason. It's all well and good.

Chaotic Evil Demons raid the fugue level and capture souls that Kelemvor's servants cannot save, or simply tear some souls off the wall of the unbelievers. These souls become manes in the abyss. I can't find a mention of how demons rank up, but I may be missing some information.

How do the neutral evil yugoloths make more yugoloths? Nowhere can I mention that they interact in any way with the joint plane or the hereafter. Where devils embody tyranny and structure (deals) and demons take on anarchy and willful destruction (raids), Yugoloths stand for selfishness and sociopathy, and it seems unclear how they come about.

How can you reproduce § on ESC?

I want to picture that § on a Macbook with system-level touchbar.

I need that at least for the use of the Esc while using vim (I want to feel the keystroke).

I'm using a keyboard layout created with Ukelele and I've tried to change it to fit the map §Escbut it does not seem to work.

How can I do that?

dnd 5e – Can a simulacrum reproduce itself?

The Simulacrum spell begins as follows:

They form an illusory duplicate of an animal or humanoid that is within range of the spell casting time. The duplicate is a creature that is partly real and made of ice or snow. It can take actions and otherwise be affected like a normal creature. It seems to be the same as the original, but it has half the creature's maximum hit point maximum and is formed without any gear. Otherwise, the illusion uses all the stats of the creature it is duplicating.

As far as I know, the simulacrum is treated just like the original creature, except for the exceptions listed in the spell. It is also explicitly referred to as a creature in the spell. Would the simulacrum retain the reproductive ability of the original creature? As a DM, I imagined a sorcerer running a business where Simulacra is made up of wealthy women as a substitute for high profits. I wanted to know the RAW interpretation of this topic to better know if or what I would accommodate if I did.

I think that's possible, but I wanted to make sure I did not miss something.

Which JS framework would be useful to reproduce this Facebook game? [on hold]

I want to reproduce this game:

  • Look at the rocket effect, which points to the button on the upper left and the astronauts

  • Buttons and texts as well as future input text:

but I'm not sure which js framework would be better to do these things quickly and robustly. Phaser 3 would be difficult to do these things? I also want to use Facebook instant games.

Can you reproduce the appearance of an orthochromatic film with a blue filter on a panchromatic film?

In the past, films reacted to a limited range of the visible light spectrum. These orthochromatic films were very sensitive to blue light, in contrast to the more common panchromatic films used today, had an accurate color representation of yellow and green light, but were hardly sensitive to orange. The films could be exposed to red light, barely (or rather not) sensitizing the emulsion of the film.
The latter is also the reason why darkrooms use red lights to this day, as in black and white orthochromatic photo paper.

Panchromatic film, which today mostly displaces orthochromatic films, does respond to higher (red) wavelengths and some films even cover the infrared spectrum.

Considering how the orthochromatic films responded mainly to blue light, would the use of a blue filter on modern panchromatic films replicate the sound representation of ortho films? The use of a blue filter would prevent (most of) the red light from getting onto the film.
I could not find the answer to this question online, but have my doubts about my own theory. Mainly, the use of a blue filter would also mean a reduced sensitivity to yellow / green. Since I have limited knowledge of which filters are out there, is there perhaps a filter (a combination) that would approximate if it were not perfectly replicated?

Debugging – Mathematica deletes all definitions or crashes with the following code. Can someone reproduce the mistake?

I'm working on a simple code, but Mathematica crashes every time or deletes all definitions when I try to do anything with Matrix B, Even if I print it out right now. The code that causes the problem is:

Cs = With({aT = {0., 98., 201., 316., 428., 571.}, 
    Cp = {917., 978., 1028., 1078., 1133., 1230.}}, 
   Interpolation(Transpose@{aT, Cp}));

Capp(T_) := 
 With({T1 = 582., T2 = 652., Tm = 617., A = 11371.42}, 
  A Cos((Pi) (T - Tm)/(T2 - T1))^2)

Cn(T_) := 
 With({C1 = 1180., T1 = 582., T2 = 652., Tm = 617.}, 
  Cs(T) + 0.5 (C1 - Cs(T)) (1. + Tanh(8. (T - Tm)/(T2 - T1))))
Ct(T_) := 
 With({T1 = 582., T2 = 652.}, 
    Piecewise({{Cn(#), # <= T1}, {Cn(#) + 
        Capp(#), # >= T1 && # <= T2}, {Cn(#), True}})) & /@ T

(Rho) = With({T = {0., 98., 201., 316., 428., 571., 600., 610., 
      720.}, (Rho) = {2705., 2685., 2670., 2640., 2620., 2575., 
      2550., 2375., 2300.}}, 
   Interpolation(Transpose@{T, (Rho)}, InterpolationOrder -> 1));

k = With({T = {0., 98., 201., 316., 428., 571., 600., 700., 800.}, 
    k = {162., 177., 192., 207., 223., 253., 210., 90., 100.}}, 
   Interpolation(Transpose@{T, k}, InterpolationOrder -> 1));

ra(T_) := 1./((Rho)(T) Ct(T))

L = 2.; (*domain length*)
Ts = 50.; (*simulation time*)
Tm = 700.; (*max temperature*)
a = 3.;
T(t_, x_) := 0.5 (Tm Exp(-a x) Cos(t - a x) + Tm)
Plot(Evaluate@Table(T(t, x), {t, 0, Ts, Ts/10}), {x, 0, L}, 
 PlotRange -> All, AxesOrigin -> {0, 0})
Plot({T(t, 0), T(t, L)}, {t, 0, Ts}, PlotRange -> All, 
 AxesOrigin -> {0, 0})
Plot(T(0, x), {x, 0, L}, PlotRange -> All, AxesOrigin -> {0, 0})

kxx(x_) := k(x)

(Phi)(t_, x_) = 
  Simplify(D(T(t, x), t) - 
    ra(T(t, x)) D(kxx(T(t, x)) D(T(t, x), x), x));
eq = D(u(t, x), t) - 
    ra(u(t, x)) D(kxx(u(t, x)) D(u(t, x), x), x) == (Phi)(t, x);

maxIter = 50;

Nx = 21;
Nt = 100;
dt = Ts/Nt;
dx = L/(Nx - 1);
(Omega) = 0.7;
(Theta) = 0.50;
(Epsilon)T = 0.001;

X = Join(Range(0, L/2, L/2/IntegerPart@(4/5 Nx)), 
   2^Table(i, {i, Log(2., L/2 + dx), 
      1, (1 - Log(2., L/2 + dx))/(IntegerPart@(Nx/5) - 1)}));
DX = Differences(X);
T0 = T(0, X);

A = ConstantArray(0, {Nx, Nx});
A((1, 1)) = 0.5 (Omega) DX((1)); 
A((1, 2)) = 0.5 (1. - (Omega)) DX((1));
For(i = 2, i <= Nx - 1, i++,
  A((i, i - 1)) = 0.5 (1. - (Omega)) DX((i));
  A((i, i)) = (Omega) DX((i));
  A((i, i + 1)) = 0.5 (1. - (Omega)) DX((i));
A((Nx, Nx - 1)) = 0.5 (1. - (Omega)) DX((-1)); 
A((Nx, Nx)) = 0.5 (Omega) DX((-1));
A = SparseArray(A);

Kxx = kxx(T0)*ra(T0);
avgK = 0.5 Table(Kxx((i)) + Kxx((i + 1)), {i, Nx - 1});

B = ConstantArray(0, {Nx, Nx});
B((1, 1)) = avgK((1))/DX((1)); B((1, 2)) = -avgK((1))/DX((1));
For(i = 2, i <= Nx - 1, i++,
  B((i, i - 1)) = -avgK((i - 1))/DX((1)); 
  B((i, i)) = (avgK((i - 1)) + avgK((i)))/DX((i)); 
  B((i, i + 1)) = -avgK((i))/DX((i)););
B((Nx, Nx - 1)) = -avgK((Nx - 1))/DX((-1)); 
B((Nx, Nx)) = avgK((Nx - 1))/DX((-1));
B = SparseArray(B);

Now it's enough to write B in the cell and hit Shift+Enter to crash or delete all variables. Can someone tell me if this is also the case in your environment? My is Windows 10, Mathematica 12.

opengl – How do I reproduce examples of ShaderToy on my computer?

I am a beginner with computer graphics. I have some experience with drawing polygons, shaded surfaces, using geometry shaders, etc. I am trying to make such a volumetric cloud / volume shader using techniques like raymarching. The problem is that I've understood that rendering graphics in a pipeline (creating vertex information with CPU, storing in buffer objects, processing with the vertex shader, and then rendering the image with the fragment shaders) clearly states in which Stage of the pipeline volumetric rendering is performed because the cloud is generally not made up of polygons or vertices. My first step would be to reproduce the same rendering of Shadertoy, to better understand the technique, to add parameters, lighting, and so on. What kind of shader is that? How do I write a program to use it? I use OpenGL on Linux. Thank you in advance!

film – How do I reproduce the Velvia 50 look with RAW processing?

Note: Even the most accurate representation of the actual film will not be able to reproduce all of its characteristics. Therefore, film behaves very differently than sensors or digital images If you really want the Velvia 50 look: shoot Velvia. Although I'm 90% digital myself, I find it still fun to make movies from time to time.

RawTherapee offers a feature called film simulation:

With the film simulation tool, you can associate the colors of a photo with a single click to a reference image. This tool requires the use of reference images in the HaldCLUT pattern in PNG or TIFF format. Each HaldCLUT image corresponds to a "look". Although the look may be based on anything, most reference pictures we send are based on classic footage, which is the name of the tool.

They even offer a download with many movie simulations – including Velvia 50 and 100. And although they are not able to reproduce 100% of the Velvia look, as I've already mentioned, I still think presets are pretty good :


Just one random image I took one day – "Stock" is the edited version of the RAW, "RT Velvia 50" is the same as the left, but with the added movie simulation. The upper part shows the HaldCLUTs for both.

The difference between profiles and these CLUTs is simple: a profile overrides your settings, while a CLUT adds appearance after the changes. You still have control over curves and all functions.

You can even create your own presets relatively easily:

  • Use RawPedias HaldCLUT or create your own ImageMagick: magick convert hald: 12-deep 16-color space sRGB hald12_16bit.tif
  • Take a picture and make the desired changes. Save these changes as a profile or save the changes made manually.
  • Take the HaldCLUT from above and apply the changes.
  • Render the edited HaldCLUT as TIF or PNG (8 bits are enough)

In general, with most CLUTs (including the Velvia console), different channels are compressed (SCurves and / or H / S / V changes (per channel). Local settings, such as For example, the contrast is generally rejected by the tool:

To create a "look", the identity image is opened in an image editor – any image editor – and the Colors are changed in a global way, eg. Using layers, curves, adjusting hue and saturation, etc. Only make global adjustments such as those listed. Local customizations are not compatible with the functionality; For example, you can not give a HaldCLUT image a true-to-life appearance, it can not snap or sharpen, but skin tones may look tanned and leaves become more vibrant.

The tool simply compares your CLUT image with the original. The original has certain color values ​​(eg. R250 G130 B110on certain pixels – on your CLUT, this pixel has a value of R110 G130 B250Then R and B are inverted for all pixels that provide a value of R250 G130 B110, Since the CLUT image is not large enough to hold one pixel per value (that would be 16.8 MP for 8 bits – and 68.7 GP for 16 bits!), The values ​​in the environment are interpolated.

After editing: Capture One offers the option for user styles, which are text files for which the parameters are set. Phase One itself sells something for C1 (aka "Film Styles"), as does Really Nice Images (RNI). The latter also offers this for Lightroom. Note that all of these options for Velvia movies are different, albeit similar.