To be used for questions on geometry closely pertaining to physics. Includes differential geometry and euclidean geometry.

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2
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2answers
274 views

Finding the illuminance from a triangular light source

Since most light sources in games are point-like, it's pretty difficult to approximate area light sources with point sources. As triangles are a universal form to represent 3D models (thus area light ...
5
votes
1answer
138 views

Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle ...
1
vote
1answer
95 views

Structure factor of crystals (X-ray crystallography)

How can one prove that the degree of each node in a distance graph must be at least four in order to obtain a unique solution to an exact distance geometry problem with sparse distance data? The ...
0
votes
1answer
228 views

Tensor of inertia

The tensor of inertia of a solid sphere is $I_{ii}=\frac{2}{5}MR^2$ about an axis passing through its CM. Why would the tensor of inertia of each hemisphere about that axis be ...
0
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1answer
52 views

Geometric Interpretation of Rotated basis of Hamiltonian and collective Dicke states

Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, ...
3
votes
0answers
50 views

Rigid rectangle in Schwarzschild

Say I build a perfect rectangle. Side lengths $l_1$ and $l_2$ and perfect right angles. I am on earth and the metric is given by the Schwarzschild metric. Setting $dt=0$ leads to the spatial ...
3
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0answers
124 views

Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
3
votes
0answers
77 views

Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
2
votes
0answers
34 views

T duality for lower codimension branes or ALF spaces

These are purely mathematical questions in some sense but I believe this is relevant in string theory as the title says. I wonder if it is possible to perform T-duality of Taub-NUT space not along ...
2
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0answers
80 views

Can we derive the relation between proper time and the spacetime interval?

In GR, it's usually taken for granted - or as a definition - that the time measured by an observer's clock is related to the geometry in a very simple way, $d\tau^2 = |ds^2|$. This is easy enough to ...
2
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0answers
60 views

Dirichlet's work on gravity in non-Euclidean space?

In the book The Norton History of Astronomy and Cosmology by the late John North I have found the following statement (page 514): "The German mathematician Lejeune Dirichlet studied the law of ...
2
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0answers
145 views

Getting the AdS metric from maximally symmetric spaces

I am familiar with the way we derive the form of the FRW metric by just using the fact that we have a maximally symmetric space i.e the universe is homogeneous and isotropic in spatial coordinates. ...
2
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0answers
91 views

Self-organizing maps

I'm currently interested in this subject but all I can see is about neural networks and I'm more interested on the Theoretical point of view: "how can a system (Lagrangian/Hamiltonian) alter it's ...
1
vote
0answers
43 views

Bending of a pipe filled with sand

There is this industrial pipe made out of steel that is 1 meter in diameter and 6 meters long (and volume 4,71 cubic meters). The thickness of the pipe "wall" is 4 centimeter. The pipe is filled ...
1
vote
0answers
37 views

Could a fourth dimension be “spatially simulated” one point at a time by using movements?

I wonder if time and movement can be translated into a simulation of an extra spatial dimension. At least in one point at a time. I'll try to explain. Imagine a fixed probe which measures the ...
1
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0answers
115 views

How far is the horizon, if a 2m tall man watches to the sea?

How far is the horizon, if a $r=2 m$ tall man watches to the sea? I have calculated that it would be even just about 6 km. if R = radius of earth( $6370 \cdot10^3$ m ). By pythagorean theorem we ...
1
vote
0answers
102 views

Does the measure of proximity of two theories in “theory space” run?

From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the ...
0
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0answers
11 views

What are some structures which minimize surface stress upon expansion

Intro I am currently researching into a problem involving the cyclical expansion and contraction of a 3 layered structure comprised of an internal metal encased by another metal encased in an outer ...
0
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0answers
39 views

Close-packing of equal spheres - one sphere in a pyramid with a square base and four equilateral trianglular faces

I'm trying to determine the "packing efficiency" of fitting on sphere into a square based pyramidal container with four equilateral triangular faces. In other words, how much space within the pyramid ...
0
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0answers
71 views

Transforming components of the angular momentum operator

Let me introduce the problem: In a two electron fixed nucleus problem the "body" is the atom, whose electrons are located relative to the nucleus by the coordinates $r_1$ and $r_2$, and the angle ...
0
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0answers
13 views

Did a racer on a “restless” course race at some particular average velocity? (2: Starting gate and finish line being rigid to each other)

Consider two participants, a starting gate ($A$) and a finish line ($B$), in a (sufficiently) flat region, both undergoing uniformly accelerated motion, such that $A$ finds constant ping duration ...
0
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0answers
20 views

Did a racer on a “restless” course race at some particular average velocity? (1: Starting blocks, finish line moving uniformly wrt. each o.)

Consider two participants, $A$ and $B$ moving uniformly wrt. each other; first having approached each other, then having met and passed each other, and eventually having separated from each other such ...
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0answers
111 views

Electric Potential of a Cube Made of Point Charges

I'm trying to find the potential energy of multiple geometric shapes made entirely out of point charges. This particular shape is a cube made out of two different point charges, A and B, each ...
0
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0answers
42 views

How to express “curvature scalars” in terms of "discrete curvature values $\kappa_n$?

We know from MTW [1] and Synge [2] how, for participants who were (pairwise) rigid to each other, it may be determined whether or not they were straight to each other, plane to each other, or ...
0
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0answers
68 views

Water Stream from a Horizontal Surface

If water was projected from a flat surface where gravity was equal all over the surface. What would happen when the water fell in on itself? The water is in a continuous stream and is perfectly ...
0
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0answers
219 views

Extrinsic curvature versus Intrinsic curvature (Euclidean versus Riemannian)

Do we believe the universe has any extrinsic curvature at all? As far as I'm aware extrinsic curvature is only used in geometry/math to model the intrinsic curvature, correct? From the answers to ...