Connection Definition and 520 Threads

Hello, I am trying to analyze a bolted connection. I don't remember anything about bolt connections, so I am studying at the same time ( the purpose is to actually study before actually designing a bolted connection). I designed the system itself and found the stresses on the connection and...

https://www.quantamagazine.org/20150312-mathematicians-chase-moonshines-shadow/ Sorry for the long title but ST = string theory. Just thought it was interesting news personally since string theory has been elusively hard to prove or observe(at least the particles it claims to predict, notably...

Because of drought conditions here in California, I am building a graywater collection system. One aspect of this system is the collection of water from the sink while it is running just to get hot water. So the idea is that whenever I need hot water in the bathroom (for shower or sink) I run...

The natural connection between physics,math,and geometry A – variable from 0.001mm to infinity mm ( A = diameter of circle ) B – variable from 0.0173 to zero C – constant number 0.0000003 The nature formula is ABB = C B of A = root of ( C : A ) Variable pi formula Pi of A =...

Homework Statement I have two questions. 1.The definition of binding energy is the work needed to split the nucleus into its constituent protons and neutrons. The strong nuclear force keeps the nucleus together hence is it right for me to say the binding energy is equal to the energy of the...

Some context for my question: If you have a smooth manifold \mathcal{M} you can define tangent vectors to parametrized paths in the following way: If \mathcal{P}(s) is a parametrized path, then \frac{d}{ds} \mathcal{P}(s) = V where V is the differential operator that acts on scalar fields...

Determine the tensile stress in the bolted connection shown below for the load F = 210 kN. Using a safety factor of 2, determine whether the plates will fail or not if the yield strength of the plate material is 270 MPa and the thickness of the plate is 12 mm. The nominal diameter of the bolts...

Homework Statement [/B] (a) Find christoffel symbols and ricci tensor (b) Find the transformation to the usual flat space form ## g_{\mu v} = diag (-1,1,1,1)##. Homework EquationsThe Attempt at a Solution Part(a) [/B] I have found the metric to be ## g_{tt} = g^{tt} = -1, g_{xt} = g_{tx} =...

If I understand correctly (no guarantee), the angles A and B in the generator of the three Pauli matrices (excluding the identity): cos A......exp(-iB) sin A exp(iB) sin A....-cos A refer to angles in a Hilbert space, for example the...

A simple question: If we have $$z$$ is a complex function, and we have here $$\omega_\mu^{ij}$$ represents some spin connection where $$\mu$$ is spacetime corrdinate. And say we have $$z + \omega_\mu^{12}$$ no matter for now what the metric is, if I want to take the conjugate of this, is the...

Hi, My laptop's wireless connection suprisingly weakened. I use a Windows 8.1 laptop. I thought it was related to updates but after I installed updates waiting to be installed, problem hasn't change. There is not problem for other laptops so source of wireless has not a problem. Thank you.

I'm looking at lecture notes on General Relativity by Sean M. Carroll, and after defining the Riemannanian tensor in the usual theorem, the extent to which the partial derivatives of a vector field fail to commute, it says ' having defined curvature tensor as something which characterizes the...

Conventional GR is based on the Levi-Civita connection. From the fundamental theorem of Riemann geometry - that the metric tensor is covariantly constant, subject to the metric being symmetric, non-degenerate, and differential, and the connection associated is unique and torsion-free - the...

It's kind of embarassing but I have almost finished a introductory EM class and I'm still not sure in a formal way in which cases the EMF is equal to the voltage. EMF was defined as the work done on a charge per unit of charge by any EM originated force when the charge would take a certain path...

I have read that on generating side there is star delta connection and delta-star connection on distribution side..>! I wanted to know the reason behind it..! I know in delta the line voltage =phase voltage & in star phase voltage reduces..so is this the part of the reason behind it..?? Please...

After reading these recent articles on proof of the theory that merges the "duality" of .. " The connection between uncertainty and wave-particle duality comes out very naturally when you consider them as questions about what information you can gain about a system" Can someone point me to a...

Homework Statement Is the velocity in the kinetic energy=1/2mv2 average velocity or final velocity?

As some may know, I have been studying the Morris-Thorne wormhole metric for quite some time now. ds2= -c2dt2 + dl2 + (b2 + l2)(dθ2 + sin2(θ)d∅2) Now, from this space-time interval, it is easy to see how I would deduce the following metric tensor: g00= -1 g11 = 1 g22= (b2 + l2) g33= (b2 +...

"Everyone" knows what an affine connection on a smooth manifold is a.k.a. covariant derivative. My questions are: i) Why are those connections called affine? ii) Is there a mathematical object that 'connects neighboring tangent spaces', that could be termed a 'non-affine connection'?

Hi. Say you have a canonical ensemble, and its zustandssumme is ##Z = \sum_j e^{- \beta E_j}##. Then $$d \: ln(Z) = \frac{-d\beta}{Z} \sum_j e^{- \beta E_j} E_j - \frac{-\beta}{Z} \sum_j e^{- \beta E_j} dE_j$$ Further, my book says the second term is given by the work ##dW## done on the...

Dear Readers, I'm facing a pretty interesting challenge, which is: "How to connect multiple smartphone mic's in the quickest and simplest way?" Here is a use case. I go into a meeting with a group of random (strangers) that all have smartphones, Android, iOS, Windows. Now I want to record this...

I am having some problem with this attached question. I also attached my answer... My problem is the appearence of the term: 2 e (A \cdot \partial C) |\phi|^2 which shouldn't appear...but comes from cross terms of the: A \cdot A \rightarrow ( A + \partial C) \cdot (A + \partial C) In my...

Hi there, I want to know what is the best way to connect these devices to a 3 phase power supply outlet and minimise the unbalanced load as much as possible safely? I am only worried about the single phase appliances. What type of connection would you recommend? 3x Power Supply units Single...

When is the motion sensor being connected to the brake line of the automobile?

Im a trying to understand how the string entity relates to its underlying field. Is the field a brane and the string the partice?

Homework Statement Consider the Schwarschield Metric in four dimensional spacetime (M is a constant): ds2 = -(1-(2M/r))dt2 + dr2/(1-(2M/r)) + r2(dθ2 + sin2(θ)dø2) a.) Write down the non zero components of the metric tensor, and find the inverse metric tensor. b.) find all the...

Hello, I read in an article that in GR it is possible to use a connection with torsion to model ponctual particle with spin. The connection can be decomposed in a curvatue part and a torsion part. In an other part, we know that the invariance under pointcarré group imply conservation of spin of...

I am somewhat confused with the connection between the two groups. In the text I'm reading (An Introduction to Tensors and Group theory for physicists N. Jeevanjee), there is a chapter quite early on (in the group theory part) which outlines a homomorphism from SU(2) to SO(3), however I find...

In the formulation of connections on principal bundles, one derives an expression for the covariant exterior derivative of lie-algebra valued forms which is given by $$D\alpha = d \alpha + \rho(\omega) \wedge \alpha,$$ where ##\rho: \mathfrak g \to \mathfrak{gl}(\mathfrak g)## is a...

One theory I've heard and which I find interesting is that entanglement between any pair of two-state systems could be explained deterministically by a spacelike connection which can only communicate something relative, like a phase difference, and which is essentially holding the ends...

Hello I looked for a good forum which I can use for my specific questions. I hope I am right here. English is unfortunately not my first language, but I am working on improving it. So please have understanding for it. I need help in three phase drive technology. I read in my book...

So as the title says, what are the physical reasons behind requiring the connection between tangent vector spaces to be metric-compatible? My guess is that this is desired from wanting different points in space-time to be "equivalent", in the sense that if any two vectors at a point are the...

Dear all, In my journey through learning General relativity. I have stumbled upon this problem. I have to calculate the geodesic equation for R^{3} in cylindrical polars. I am not sure how to use the metric connection. The indices confuse me. I would appreciate it if someone could shade some...

Dear All, I am teaching myself tensors for the first time. I am using D'Inverno's book and got stuck at page 73. Basically, he says: demand that the first term on the left of the equation to be a type (1,1) tensor. Then he gets the affine connection transformation. I basically wrote the...

Exist some conection between: $$\int_{0}^{+\infty} f(t) \exp(-st)dt\;\;(1)$$ $$\int_{-\infty}^{0} f(t) \exp(-st)dt\;\;(2)$$ ? The results, the transformations, are very similar, with some little difference in the signal. So, known the transformation (1), is possible to find the (2)?

If exist a connection between the infinitesimal derivative and the discrete derivative $$d = \log(\Delta + 1)$$ $$\Delta = \exp(d) - 1$$ exist too a coneection between summation ##\Sigma## and integration ##\int## ?

Hi, I have a faced a research problem where I would need to recover a frame field given its connection forms. More precisely, I begin with an orthonormal frame field (given by data) in \Re^3 written as \mathbf F=\begin{pmatrix}\vec f_1\\\vec f_2\\\vec f_3\end{pmatrix} where \vec...

Homework Statement I'm trying to bridge F =ma to m/2(dv2/dx). It was shown in the course book I have but there's a huge disconnection in the steps. The Attempt at a SolutionF =ma = m.(dv/dt) = m(dv/dx . dx/dt) = mv(dv/dx). Where do I take it from here?

I am reading up on principal bundles and currently I'm trying to get to grips with the definition of a connection on such a space. The definition is as follows: A connection on P is a unique separation of the tangent space ##T_uP## into the vertical subspace ##V_u P## and the horizontal...

So at school we had to make our own experiment, and we tried to make a loop-the-loop. We let a marble go from some height. But now we've got a problem. We had a sensor on the top of the loop, to see how long it does to go to the top of the loop. But it didn't make sense. So I had to fake the...

One of the properties of the unique Levi-Civita connection is that it preserves the metric tensor at each point's tangent space, allowing the definition of invariant intervals between points in the manifold. I'd be interested in clarifying: when the metric preserved by the L-C connection is a...

First, I'd like that you read this littler article (http://mathworld.wolfram.com/NaturalEquation.html). The solution given by Euler that coonects the system cartesian (x, y) with the curvature κ of the "cesaro system" (s, κ), is that the derivative of the cartesian tangential angle φ* wrt arc...

mathematical "connection" in the cartesian product What is the mathematical connection between elements of a cartesian product ##A\times{}B## and the elements of the sets ##A## and ##B##? In other words, what is the difference between the set ##A\times{}B## and just any set ##Z## with...

page 71 he appears to define the affine connection in terms of derivatives on the locally inertial coordinates with respect to the laboratory coordinates and then the very next page claims that all you need is the affine connection and metric tensor to determine the locally inertial...

Hello I use kubuntu on my computer. Until recently I could normally connect the internet in the university, but now it is impossible. It connects to the network but it doenst redirect to the login screen, hence turning impossible to use the internet. Can someone solve this for me? Thanks.

In flat spacetime, there exists a natural connection that allows you to compare two vectors at different events. Now, in GR the spacetime in the neighborhood of an event is flat. It therefore seems possible to define the connection between two events close to one another to simply be the...

Hellow! I want you note this similarity: \\ \int xdx=\frac{1}{2}x^2+C \\ \int x^2dx=\frac{1}{3}x^3+C \\ \sum x\Delta x=\frac{1}{2}x^2-\frac{1}{2}x+C \\ \\ \sum x^2\Delta x=\frac{1}{3}x^3-\frac{1}{2}x^2+\frac{1}{6}x+C Seems there be a connection between the discrete calculus and the...

Suppose we are given two projection operators H' and H'' such that H' + H'' = 1, i.e. that any vector can be written as V = V' + V'' = (H' + H'') V. In a formula for a projection of the Riemann tensor (see the thread "Projection of the Riemann tensor formula") I encountered the term...

Homework Statement I am tying to prove the following: \Gamma^{a}_{bc} T^{bc} =0 Homework Equations The Attempt at a Solution I approached this problem as follows: dx_{b}/dx^{c} * e^{a} (e^{b} . e^{c}) but it did not yield anything. Then I expanded the christoeffel symbols into...

I'm a physics major currently taking my first astro class. We're covering the basics at the moment but I am having trouble visualizing this question from our textbook. To preface this, I understand that declination is to the celestial sphere what latitude is to the Earth and RA is to the...