Connection Definition and 498 Threads

A (3-d or higher) metric which is flat except for one non-trivial metric function of a different coordinate - eg changing dx2 to f(y)dx2 in Euclidean or Minkowski metric [but not f(x)dx2] - is curved if f(y) has a non-zero second derivative; there is no way to make the f(y) 'disappear', ie to...

Hi. I have been looking at differential forms, and that inspired me to consider a partial derivative as a ratio between cross products. Please tell me if the following makes sense. Say we have cartesian coordinates (x,y) and polar coordinates (\rho, \phi). I want to calculate...

I am familiar with changes that occur with capacitance and ESR when you connect supercapacitors in series or in parallel. My question is along those lines, but the answer is elusive to me... From schematics I have seen about supercapacitors imbedded in circuitry, the supercaps always have...

As it suggests, the problem I face is to how I carry about an Earth connection (for an AM radio transmitter set I made) instead of burying it into the ground? Of course, if I make a radio set, I simply can't carry it about making an Earth connection into the ground. I have provided a solution...

First off, let me say that while I am an avid astronomer, I know very little about the mathematics of astrophysics. My specialty falls more under mechanical engineering. While initially they may not seem all that related, history shows that the mixing of varying disciplines often sparks...

In a few days, people from my ISP are coming to my house to install super-fast fiber optic internet. Right now, I am using a DSL, or about a 3-meg connection speed. According to what I've heard, a fiber-optic network connection can give up to 20 megs. I use my computer for gaming, especially...

Hi all! Anyone knows where to find, online or on a book, the affine connection for the schwarzschild metric? Thanks

Homework Statement A 10 cm * 10 cm * 10 cm box contains .01 mol of nitrogen at 20 degrees C. What is the rate of collisions (collisions/s) on one wall of the box? Homework Equations \frac{N_{coll}}{t}=\frac{NAv_{x}}{2V} v_{rms}=\sqrt{\frac{3k_{B}T}{m}}The Attempt at a Solution I'm really...

Let E = span{v1, v2} be the linear subspace of R3 spanned by the vectors v1 = (0,1,-2) and v2 = (1, 1, 1). Find numbers a, b, c so that E = {(x, y, z) of R3 : ax + by + cz = 0} I tried doing this question, but I am totally lost. I know that any vector in E can be represented as a linear...

I have posted a similar problem not long ago.This time, I am trying to find a connection between 3 concepts that would possibly lead to the answer to the problem. I have heard that there is a way to find the probability of getting a particular sum by rolling multiple six-sided dice at the...

I'm reading about emission spectrums, and my text says that when an iron bar is heated until it's hot and glowing, the "warmth of the glowing bar represents the infrared portion of its emission spectrum". Is it true that radiating heat is associated only with infrared EM waves? ~Jules~

How well off are you in physics if you're pretty good at math? This is probably an attempt to rouse my self-esteem but it seems like I'm pretty good at math (doing an introductory analysis/calculus course, think Courant and Spivak) but I really, really suck at physics.. How can this be? maybe I...

Hello, I was curious about the following point. I know that if a function is monotone, then it is one to one (meaning for x1 != x2, then f(x1) != f(x2) ). But what about the converse? I can't seem to think of a counter-example.

Homework Statement Capacitors of 11.1uF and 1.9uF are charged as a parallel combination across a 333V battery. The capacitors are disconnected from the battery and from each other. They are then connected positive to negative plate and negative to positive plate. Find the resulting charge on...

What is the connection between spherical packing and lattice structures of atoms or molecule? For example, i can't see any relationship between spherical packing and the structure of graphite..

I wonder how much information about metic tensor of Riemmanian manifold can be extracted if only the Levi-Civita connection is given. Conversly, if the metric on manifold is given there is formula for Christoffel symbols which define connection so there exists only one symetrical metric...

I have to determine the 18 connection coefficients \Gamma_{ij}^{k} for spherical coordinates. I know how to calculate said coefficients, but I'm not sure what all 18 are. Can anyone clarify what the possible combinations could be?

Can anyone help me on this question: Under what relation between vector fields X and Y, the Levi-Civita connection of X with respect to Y, \nabla_{Y}X is 0? Any answers or suggestion will be highly appreciated.

Hello Friends I need little help pleasezz :redface: How Can I solve this circuit? Which things first I have to find. And how. Problem Statement is. A. Average power of each phase load and total Load. B. Determine the reactive power of each phase and total reactive power C. Find the...

Getting "connection reset" errors Today I've had several errors when following links around the forums, but refreshing the page works immediately. The error occurs immediately (not like a timeout) and the "errors details" say that the connection was reset by the server. Here's what Google...

As of today, every time that I hit the 'edit' button on one of my posts, Safari crashes. Is anyone else experiencing such annoyance? This has never happened before, but I just downloaded the Safari 4 upgrade. Any connection that anyone knows of?

Hi! I'm having kind of a "little" problem. I got an old program written in Fortran77 and I want to implement some functionality from Fortran90 routines. The routines are quite long, so I'm not able to rewrite them in F77... Is there a possibility to connect the routines so that they can...

Good afternoon! To build a serial connection of two transformers, four coils are used: Two of this coils have n1 turning, two of them have n2 turnings. The coils are built together in the way, you can see on this picture: http://img197.imageshack.us/img197/2698/transformer.jpg The...

two AC power sources -- connection? i am working on a control system for a compressed air energy storage system for a wind turbine (generates ac). the goal is to shave peak power consumption, so at night the compressor will charge (either by the wind or by the grid), and during peak hours, it...

who can help me with this: on an ellipsoid most points are not umbilic, but there are some special places that are. Discuss how to find these points and their connection to lines of curvature.

In covariant derivative, we have a quantity called affinity. The book says: When defining an affine connection, a coordinate frame must first be selected and the choice of the components of the affinity is then arbitrary within this frame. However, when these are all determined, the component...

Hi all, 1. the max. speed of waves in the air is the speed of sound. it's caused by the physical limitation - changes in the air fabric (particles) can't propagate faster in it. 2. so I was wondering, whether the max. speed in our space isn't limited by the max. (indivisible/atomic) change...

Homework Statement I'm supposed to make a connection between SU(2) and SO(3), by using U=\frac{a_0+i\vec{\sigma}\vec{a}}{a_0+i\vec{\sigma}\vec{a}}, where \sigma are the usual 2 dimensional Pauli matrices. I need to find the corresponding axis and angle of rotation in three dimensions, in...

My (new*) linux system is having trouble connecting to most websites. Originally I thought it was a DNS issue, because I can connect to some websites (Google, thanks goodness, and physicsforums of course), but now I'm not sure. What do you think this is? Is it me, my connection, or an...

I wasnt quite sure where to put this thread. This question occurred to me while I was looking at the group theory of standard model groups so I thought I'd put it here. Anyway, here is my question: One can define the Killing form for a group by taking the trace of two generators. One can...

I am reading a book which says that if the components of the connection vanishes then the torsion and curvature tensors vanish. Now, I understand how this happens with curvature tensor, but I don't see how torsion tensor would vanish. Torsion tensor: \tau (X,Y) = D_X (Y) - D_Y (X) - [X,Y]...

I wanted to ask if there is any connection between the SU(2) group for the spin 1/2 and the gauge group of weak interactions. I feel there isn't much of a connection other than the fact that they share the same group properties, but I am not sure. Thanks to anyone in advance that can clarify...

Searching for the "Human Connection"--Physics and Music. Hello everyone! I'm currently a senior in high school (going off to study architecture at either Rensselaer Polytech Ins., Marywood U, or Philadelphia U) and am doing an independent research project on the topic of relating acoustic...

I have read several books on relativity and find the subject fascinating. But there are a couple of things that I hope someone can help me understand. The big question on my mind is "why is light always associated with time"? It seems to my simple mind that light just portrays a visual...

I currently have 2 computers (laptop running ubuntu, desktop running vista) connected to the internet, through a "Linksys 5-port workgroup switch", which my cable modem is also plugged into (my internet gives me 2 IP's, so I don't need an additional router). This arrangement works perfectly, no...

Hi everyone -- I have a question about the relation between the spin connection and the Christoffel connection. The spin connection comes from the local (gauge) Lorentz symmetry of how we orient vielbeins at each point in space, it contains a manifold index and two tangent space indices. The...

Dear PF, What does this mean? .. Bayonet connection. It is used in cryostats..If anyone have some experience with such things..please explain me in details.. how does it work? etc... thanks

It seems to be true, that if some eigenvalue of a Hamilton's operator is an isolated eigenvalue (part of discrete spectrum, not of continuous spectrum), then the corresponding eigenstate is normalizable, and on the other hand, if some eigenvalue of a Hamilton's operator is not isolated, then the...

Could anyone tell me about the covariant derivative with respect to the connection?

hallo, i now spent an hour looking for a formula connecting the modified bessel functions I_n and K_n to the hypergeometrical series F(a,b;c;z). has somedoby an idea? thank you

I quote http://en.wikipedia.org/wiki/Torsion_tensor#Affine_developments": I try to apply this to the natural connection on the tangent bundle of M = S2 (or more intuitively, of the surface of the Earth) I mean here natural connection the connection which defines the parallel transport so...

I'm building a tank circuit and I need to know if a ground connection is needed.

Hi I've just started a new Electrical Course and have been working through an old exam paper but i got a bit lost when doing the star connection question - see attached for question and work done would just like someone to tell me if any of what I've done is correct and where I've gone...

Is there some mathematician who knows the "core reason" why exp() is connected with cos()? I mean I'm confident with "advanced maths for physicists", but maybe some abstract theory gives an answer to this. I was think of something like: |e^{i\phi}|=1 therefore it's a unit circle. But also...

Im sorry to bother you, but I am trying to understand one thing about embedding. Consider you have sphere embedded in the R^3, so you have a flat metrik. Otherwise you could describe the same sphere without embedding but with an induced metric. My problem is to make clear that the Lie-Brackets...

Homework Statement I have to prove in a conservation of energy question T-W =(mv^2)/L mgL(1-cosO)=(mv^2)/2 mg=W T=W(3-2Cos0) How could I go about starting this?

I have to prove in a conservation of energy question T-W =(mv^2)/L mgL(1-cosO)=(mv^2)/2 mg=W T=W(3-2Cos0) How could I go about starting this?

Stock market - no connection company/share - money isn't lost?!? I've spoken to some hobby stock market "users" but none of them could convincingly explain the basic share system without ending up in circular arguments. 1) My impression is that there is no logical connection at all between...

Hi guys! Today I remembered that I used to have a fantastic image (like a flow chart) about different parts of mathematics and how they are connected. In the final stage (at the top), they were connected to QFT and GR. It's down->top, at the lower end were basic mathematics (sets, boolian...

How do I obtain the Levi-Civita connection from the concept of parallel transport? So Do Carmo asks to prove that for vector fields X, Y on M, and for c(t) an integral curve of X, i.e. c(t_0) = p and X(c(t)) = dc/dt, the covariant derivative of Y along X is the derivative of the parallel...