Connection Definition and 498 Threads

I have question about the proof of Cartan's structure equation in the context of pincipal bundle in Nakahara's book. The attached image is taken from the book. To show that the curvature two-form ##\Omega ## satisfies ##\Omega (X,Y) = {d_P}\omega (X,Y) + [\omega (X),\omega (Y)]## The author...

Hi guys, I'm struggling to understand why an increase of entropy is directly linked with a decrease of total (stagnation) pressure. I have an idea, but I'm not sure if this is right. My understanding of the problem is as follows: Shear stress (friction) is a part of the entropy production term...

Hello, What is the fastest connection method (i.e. type of cabling) to transfer images from a video camera to a computer, i.e. what type of connection gives the highest frame per minutes? Is a USB connection fast? If not, why not? Should I look at a camera that connects in a different way...

I have been having trouble getting the calculation of energy for a chain of coupled oscillators to come out correctly. The program was run in Matlab and is intended to calculate the energy of a system of connected Hooke's law oscillators. Right now there is only stiffness and no dampening...

I am at the stage of my education where I am seeing calculus (mainly differential equations) popping up in my engineering courses. However, I have just started multi-variable calculus, so I have not taken differential equations yet. My professors basically show us how certain equations are...

Hi, I am creating a netbeans application. I am trying to handle square root exception. If the argument to sqrt is positive it should display its result in the text area otherwise, it would display a message that square not possible. Its displaying the result. For instance if the argument is...

Hello, is there an official word that describes the connection (or "information exchange") between a receptor (or effector) and the neurons that they touch? I know that between neurons, there is a synaptic connection, and between muscles, that would be kinesthetic connection (I am guessing) but...

are gravitational waves somehow connected with dark matter??

Dear All in the idea of gauging Poincare group i am trying to find the equation of motion of the spin connection w_mu^ab using Euler Lagrange equation. but it seems that i am not getting the same terms can i have a help. I know that this equation is equivalent to the torsionless condition, but...

http://arxiv.org/abs/1105.3735 I have a question about the paper that haushofer mentioned. In the paper, the author states that Moving on to helicity 2, the required gauge symmetry is linearized general coordinate invariance. Asking for consistent self interactions leads essentially uniquely...

Dear All I am trying to find the equation of motion of the spin connection out of the einstein hilbert action written in terms of the vielbeins. Can anyone help me to do? Thank you

Homework Statement Homework Equations Ohm's Law R = V/I V = IR The Attempt at a Solution here is my answer, i have a feeling I am missing something, any help would be appreciated.[/B] The graph represents a linear relationship between the potential difference (V) and the current (A). By...

If my understanding is correct, with respect to dry-type building power transformers, due to the virtues of the transformer as a dumb machine it really doesn't care which side of itself is the primary versus the secondary. In other words a 480D-208Y tranformer can be correctly connected such...

I have been reading Nakahara's book "Geometry, Topology & Physics" with the aim of teaching myself some differential geometry. Unfortunately I've gotten a little stuck on the notion of a connection and how it relates to the covariant derivative. As I understand it a connection ##\nabla...

Does a router tells a slave device to close a TCP connection, if the router loses connect from the master device ? So, I have a Qterm-g72 HMI and I am trying to connect it to a Moxa over TCP Modbus. This only works if a Computer or a router is between the Moxa and the HMI. I am trying to found...

So the electric and magnetic fields are linked, when they're at 90 degrees and self propagating they're a photon. I sort of know you can have TE and TM propagation. But I'm having trouble seeing how the electric field link is maintained with magnetism; can someone explain to me where the...

Say we have this scenario, we have two bodies (big rocks, asteroid etc), existing in the vacuum of space, both are in perfect sync with each other (distance between them remains static) and are 1 light second apart in distance. Bob is standing on one rock and Mary on the other. Each has a radio...

Dear Group, I have 1 tablet and 1 desktop, I am trying to use tablet with putty.exe to remote a desktop without internet connection, My goal is creating bat file on the tablet, edit file such as: "start putty.exe -v -ssh %finderunit% -l FINDER -pw finder -m calibrate_commands.txt" . Means...

Hello, I've noticed that Planck's constant h and the action of a particle S both share the units of Joule-second. I was wondering if there were a connection between the two, but my Modern Physics textbook (Harris) doesn't say anything about it. Wikipedia's definition of Planck's constant says...

What is the connection between complex numbers, chaos theory, fractals, and power laws? By connection i mean, does one require the other in order to exist? For example, from my readings, complex numbers gave rise to the chaotic system, that proceeded to create the Mandelbrot set. So the...

In cumulative cascade connection of two induction motors, why does the net speed reduce? Also, how are the torques of the two motors in the same direction?

Hi, some one know the expression of the affine connection Γ in terms of tetrad formalism? I would like also some references if it's possible, i found a hit but i think that is wrong... please help me it's so important!

I'm not perfectly clear on the connection between Poisson brackets in classical mechanics and commutators in quantum mechanics. For any classical mechanical system, if I can find the Poisson bracket between two physical observables, is that always the value of the corresponding commutator in the...

I now study general relativity and have a few questions regarding the mathematical formulation: 1) What ist the relation between an connection and a covariant derivative? Can you explain the exact difference? 2) One a lorentzian manifold, what ist the relation between the...

I'm stuck on a relation issue if there is a direct relation at all. If I were to verify that a subset is a subspace of a vector space V, would it then be correct to check that subset for linear independence to verify that the subset spans the subspace? I'm not sure if I'm following the...

I've run into a couple of problems with exercise 12.6 in MTW (attached). At this stage, all I'm asking is for someone to give me answers to the following questions: 1. What are the Rα'β'γ'δ' in the primed co-ordinate system? and 2. What are the non-zero connection coefficients in the...

Hi all, Hope this is not a " where do I buy the latest version of the interweb " question. How does one send a file from a PC ( win 8.1 ) to a smart phone, knowing only the phone number? What info do I need in order to send it? Thanks. EDIT: Never mind, DUH. If I received a file in my email...

I have a DC source. then I connect a capacitor from the +ve to ground. if all connection are made from ordinary , copper for example, wires then electrons flow from negative to positive terminals.So electrons from the negative side of the capacitor would flow to the positive. I wonder what...

I have a question about the directional derivative of the Ricci scalar along a Killing Vector Field. What conditions are necessary on the connection such that K^\alpha \nabla_\alpha R=0. Is the Levi-Civita connection necessary? I'm not sure about it but I believe since the Lie derivative is...

The Einstein-Cartan theory is, to my mind, a completely straightforward generalization of General Relativity, and indeed seems like a necessary generalization if we are to accommodate particles with intrinsic spin. (The mathematics for this claim is beyond me, but the layman's summary is this...

I am studying connections on abstract manifolds. So far, I have read several equivalent definitions but I can't establish the equivalence between them on my own. The first definition is the Ehresmann connection that defines a connection on a manifold as a distribution of vector spaces...

I am building a system which uses multiple components, each has varying voltage. The large motors use a voltage of 14-16 Volts, thus there are several batteries wired in series, providing this voltage. Now, there are other components such as microcontrollers, multiple sensors and smaller servos...

Hello everyone. The physics forum is a great online community, and I used to spend a lot of time browsing the philosophy pages. But now I've had to register and post, because I've got a very specific problem with regards mechanical engineering. My problem is relating to torque transmission...

Hello, I've worked through most of Carroll's appendix on the non-coordinate basis. I see and agree how the spin connection and tetrad one-forms are useful while calculating. However as an example he sets out to apply the formalism to a spatially flat, expanding universe. ds^2 = -dt^2...

Hey guys What's the connection between an increase in pressure and the melting point of ice? Ice contracts as it melts so does an increase in pressure reduce or increase the melting point?

Hi dear friends. I have a big problem and I need your help, I've realized that the joint connection I've drawn (and it is made already) was (most probably) wrong. There is a plate that is bolted to two U beams and the plate is welded to a horizontal I beam at the top. Please take a look at the...

Hello everyone :) I came across a strange situation today when I was listening to my music with my headphones on. When I pressed play to a song, the instrumental intro started off fairly normally (although the audio sounded a little "thinner" than usual, as if compressed), and then, when...

Hello, We know that light get bent near stars (because of its gravitational force), and in fact it cannot escape the gravitational forces of black holes. We also know from Newton's laws of gravity that the gravitational attraction between any two objects is ZERO if any mass is ZERO. We also...

Hello all, I have two rollers that will be rotated which will in turn rotate another tube on top of them. The connection will be made with a drive chain between the motor sprocket and the roller sprocket(s). My question is, would it be better to connect the chain to one roller, or to both? I'd...

this is maybe one basic question, i drew 2 connections of capacitors, the left : connected in series. the right : connected in parallel ??

Hi, So in an informal sense, we hear about string theory requiring small, curled up dimensions locally at every point of spacetime. In my very, very limited knowledge of geometry, I would like to think of this as a fibre bundle structure over each point of Minkowski space. However, analogous...

I wish to imagine Spin connection on a 2-sphere. Now, I am reading Carroll's http://arxiv.org/abs/gr-qc/9712019. He begins to write about spin connections in page 88. Calculations of ##\Gamma## on sphere are evident in page 84. Can you help me, how spin connection on a 2-sphere look like and...

Hello, Just as the title asks, what sort of applications would series and parallel connections of Direct Methanol Fuel Cell suit the best? Based from my understanding of Fuel Cells and experimental results, one cell is not enough to power anything, hence they are used in stacks, in addition...

Let's say I got a nerve electrical signal running in one direction "/" and when the signal gets to the middle of that path I poll for that signal and shoots out a electrical current in the other direction "\" not the electrochemical current, so now I have a shape that looks like "y", does it...

s2 = t2 - x2 - y2 - z2 This equation is covariant (Lorentz covariance). The interval "s" is invariant (Lorentz invariance). Can you derive everything in special relativity from these facts? Or am I mistaken about that?

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...