Expansion Definition and 1000 Threads

Homework Statement This is from Griffith's Introduction to Electrodynamics, where the book is deriving the magnetic dipole moment from multipole expansion of the vector potential The vector potential of a current loop can be written as $$\mathbf{A(r)}=\frac{\mu_0 I}{4\pi} \left[ \frac{1}{r}...

So I was doing some studying and got a question on why the rate of expansion of the universe was increasing, and it got me thinking. Newton's first law states that an object in motion will remain in motion with a constant speed unless an external force acts upon it. If the expansion of the...

Gravitational waves are quadrupoles, they bend and stretch spacetime. Does the expansion of spacetime due to gravitational waves exceed flat (Minkowski) spacetime or is flat spacetime it's limit?

I learn quantum field theory using the book of " quantum field theory in a nutshell" by A. Zee. But I am confuse when I read the content about the "baby problem" at the beginning of "1.7 Feynman Diagrams". In that section, author get the term of order λ and [J][/4] by -(λ/4!)[(d/dJ)][/4]...

What is the deviation in the expansion of the universe exactly quantified, when I would assume general relativity and project it backwards? As a statistician I am asking for data, for either the backwards projected general relativity case and either the real expansion case, as it is...

The question is whether or not expansion in flat, matter-only universes (no lambda) has any effect whatsoever - no matter how negligible - on dynamics of small-scale systems. Context: It's a variation on the 'is Brooklyn expanding?' type of questions. My understanding has always been that...

In a physics video on YouTube it's told that moving away from an object causes eextension of the length. (Link: from 6:00, but video is Norwegian) Imagine: From planet B to planet C, the distance is 20 light years. And from planet A to planet B the distance is 20 light years. We are on...

Homework Statement A steel container is filled with alcohol. For how much kelvins we have to raise the temperature for the pressure to be raised by 6 bar? Compressibility of alcohol is \kappa=1.15 \cdot 10^{-4} bar^{-1} temperature coefficient of volume expansion of alcohol is \beta_a=...

Pipe loops are used to accommodate thermal expansion. I have seen many types and lengths but here is one example: https://www.engineeringtoolbox.com/steel-pipe-expansion-loop-d_1069.html I am a little unclear on why they can work. With any thermal expansion the stresses on the elbow joints...

I've read that until 5 billion years ago the rate of expansion of space was decreasing. How do we know that it was slowing down? Does the uniformity of the CMB mean that the rate of expansion is identical throughout the entire universe - or does it just mean that the average rate of expansion...

Imagine that the CMB did not exist. What observational evidence exists to support the theory of the metric expansion of spacetime, as opposed to having a static spacetime and it's the matter distribution that is expanding - as it would in an explosion?

Hi, I have a vessel/chamber filled partially (25%) with silicon fluid (coefficient of thermal expansion is 0.00096 cm^3/cm^3/ °C) and the rest is filled with nitrogen gas at a certain pressure (P1) and temperature (T1). my question is, how to predict the final pressure (P2) If I increased the...

nmh{898} 311 Determinants And Cofactor Expansion (3.1.1) a. Compare the determinants using a cofactor expansion across the first row. b. compute the determinant by a cofactor expansion down the second column. $$\left| \begin{array}{rrr} 3&0& 4\\ 2&3& 2\\ 0&5&-1\\ \end{array} \right|$$ ok I...

I've written a short text adapted from a previous post by Count Iblis. I'll append it below. It shows that irreversible PV-work is always smaller than reversible, which fits very nicely with W = Pext ΔV. I'd be interested if there's a way to show that W is exactly equal to Pext ΔV for all...

Can anyone tell me how if the derivative of n(n') is quadratic the second term in the taylor series expansion given below vanishes. This doubt is from the book Classical Mechanics by Goldstein Chapter 6 page 240 3rd edition. I have attached a screenshot below

Homework Statement A part of a circular ring is missing .What happens to the angle when temperature is increased ? 1) θ increases 2) θ decreases 3) θ remains same 4) θ increases initially but becomes constant after a particular temperature . Homework EquationsThe Attempt at a Solution As...

For thermal expansion in a bottle - is there a theoretical model on the pressure exerted on the inside of the bottle due to the air inside expanding when the bottle heats up. The air will be expanding randomly in all directions so the pressure exerted at any point on the inside of the bottle...

MODERATOR'S NOTE: Moved from other forum, so no template @Chestermiller I am still having trouble figuring out if a given process is Quasi-static or not. Consider the following case. The cylinder consists of an ideal gas at the bottom and a liquid of density ρ at the top separated by a piston...

From our perspective the Universe is expanding faster the further away things get, correct? Given that we are measuring further and further back in time my question is this. If you were at the furthest known point in the Universe looking back at our galaxy and attempting to measure the expansion...

Hi everybody. In Python there is a library called chaospy. One useful command is cp.orth_ttr which generates a polynomial expansion, e. g. a series of orthogonal polynomials or orders zero, one, two... for a random variable e.g normal, uniform... For more information see...

I already learn to use Taylor series as: f(x) = ∑ fn(x0) / n! (x-x0)n But i don´t see why the serie change when we use differents x0 points. Por example: f(x) = x2 to express Taylor series in x0 = 0 f(x) = f(0) + f(0) (x-0) + ... = 0 due to f(0) = (0)2 to x0=1 the series are...

- check if right check if right Now, 2 seems to be the right answer for A yet when i made x=5 and subtracted new form form the old one I got a difference of ~$\frac{4}{9}$ (should be 0 obviously) I got A=2 B=$\frac{45}{21}$ C=2 How to calculate $\lim_{{x}\to{\infty}}(- e^{-x})$

Homework Statement Air with an initial volume of 0.12m³, pressure 1 bar and temperature 18°C is compressed according to the law pV1.3 = c through an 8:1 compression ratio. It is then allowed to expand isothermally back to its initial volume. Determine: i) the pressure and temperature after...

If a big bang could occur at a point in space-time, couldn't we at least speculate that many big bangs could have occurred at many other points in space time, and could have resulted in many parrelel universes evolving far away or in close neighborhood of our own one? And then, could it not be...

What is the dark energy which apparently is causing the expansion of the universe to accelerate?

As we know the universe is expanding. Could this accelerating expansion contribute or cause black hole evaporation given that the strength of the gravitational force does not depend directly on time, while the distance of two given points in space increases with time? Sorry if my approach is...

Homework Statement Prove that ##\vec {a} \cdot (\vec {b} \wedge \vec {C_r}) = \vec {a} \cdot \vec {b} \vec {C_r} - \vec {b} \wedge (\vec {a} \cdot \vec {C_r})##. Note that ##\vec {a}## is a vector, ##\vec {b}## is a vector, and ##\vec {C_r}## is an r-blade with ##r > 0##. Also, the dot...

Hi, I'm reading about the wave packet solution to the dirac equation but in the book I'm reading it states that \int \frac {d^3p} {(2\pi)^3 2E} [a u e^{-ipx} + b^\dagger \bar{v} e^{ipx} The normalisation constant confuses me. I guess the 2pi^3 is reasonalbe. However, the 1/2E seems a bit...

1. Homework Statement order of zero of a modular form ? 2. Homework Equations 3. The Attempt at a Solution Apologies if this is a stupid question but I'm pretty confused. So, a modular form ##f(t) \in M_k ## is usually given by it's expansion about ##\infty## expressed in the variable...

The attached pic is from Schwartz. Can someone explain the second equality sign in (2.72)?

We did an activity today in class where we placed an empty 2L bottle in the Freezer, let it contract, then calculated the coeffcient of volumetric expansion using ΔV = VoβΔT. We got pretty close to the accepted value. The question is... Does the coefficient of thermal expansion only work for...

I have 1" aluminum rod and I want to dril a hole in a steel structure for the bolt. If I have a 1" drill and take .001" inches off of it at the machine shop, so that it is now 0.998 inches, there will have to be about a 200°C difference in temperature between the two articles (aluminum...

Homework Statement question concerning part c. Homework Equations The question is pretty simple if there is no zero of order ##N## at infinity, such that it does not cancel the pole of ##f(t)## at infinity of order ##N##. In this case it follows that ## f(t) g(t) \in M^{!}_2 ## and so we...

Hi everyone, I'm currently working through Mathematical Methods for Physicists 7th ed. by Arfken/Weber/Harris and there's one question that's been giving me some difficulty. I would appreciate any feedback if possible. Thanks! Chris Homework Statement The relativistic sum w of two...

Is there any relationship between the Speed of gravitational waves and the Universe's "local" expansion rate? Speed of gravitational waves is supposed to be equal to the speed of light. Gravitational waves don't travel faster than light. But we can observe far galaxies moving away from us with...

Why is it written that enthalpy (##H##) is constant for Joule-Thompson expansion? It seems the essence of this process is to convert from one pressure to another with no heat loss. How does that connect with enthalpy being constant? When I learned about enthalpy it seemed to be most relevant to...

In the universe, there are several celestial bodies, all of which attract each other. Then why is it so that they do not collapse towards each other. Is it a consequence of expansion. If so, will a change in acceleration of expansion have any effect on it.And can then this be considered a...

Homework Statement [/B] A bimetallic strip is made of metal which has coefficient of thermal expansion is equal to α1 and the other's is equal to α2 at the temperature of T0. The temperature is increased to T0 + ΔT (ΔT > 0). The strip curves as shown in the figure. If both strip have the same...

I am a little confused by the following; When an isothermal expansion takes place there is negative work done on the gas by the pressure, this I understand. Now by the first law the change in internal energy is equal to the heat transferred to the gas plus the work done it. So now in my script...

I was thinking about the expansion of space. It seems clear that objects that are bound by gravitation or the strong nuclear force do not experience an increase in size as the universe continues it's expansion. However, such systems do contain abundant space. It is argued that gravitation and...

I'm not quit sure whether we had this paper here already, since it is a couple of weeks old. I've seen it here https://phys.org/news/2017-12-dark-energy-mathematicians-alternative-explanation.html and I'm somehow fascinated by the idea to get rid of dark energy as only explanation of current...

Hi PF! Regarding matched asymptotic expansions, given an ODE BVP, I have learned a boundary layer can arise, where we need to stretch the independent variable through carefully selection i.e. if ##x## is the independent variable, perhaps ##\phi = (1-x)/\epsilon : \epsilon \ll 1##. Would we...

I’ve understood that within the theory of Eternal Inflation the Bubble Universes that form from a drop of “vacuum” energy expand at the Speed of Light. My question is: Why would expansion be at the speed of light and not at a speed proportional to the level of vacuum energy still present in...

Homework Statement There is a sawtooth function with u(t)=t-π. Find the Fourier Series expansion in the form of a0 + ∑αkcos(kt) + βksin(kt) Homework Equations a0 = ... αk = ... βk = ... The Attempt at a Solution After solving for a0, ak, and bk, I found that a0=0, ak=0, and bk=-2/k...

"For simplicity, let us assume the flow turns around a corner downstream of the throat, where the Mach number is M0 > 1, to an angle θ1, and let us indicate just three of an infinite number of waves making up the "expansion fan". Since the centerline is an axis of symmetry, the waves must...

Homework Statement I do not know if I am allowed to have two question in one post, so forgive me if I am breaking a rule. These two are frustrating me as I cannot see where the error in my process is. 1) A 1.00-mol sample of an ideal diatomic gas, originally at 1.00 atm and 10 ∘C, expands...

This may sound like a noob question but please help me out guys.Will universal acceleration ever retard ? And if it continues to accelerate for all eternity, where is it getting this never ending energy from ?

Before I get to a question that's been on my mind for a while, I would like to make it clear that I am a high school student with no understanding of physics beyond my school's curriculum and some books that I've read, so excuse me if this sounds rather absurd. I know that the expansion of...

Hello guys, every "scientist" I have talked to say the universe is "expanding" at an ever increasing rate. then I tell them the following: "hey man, you say the farther away the galaxies you see, the quicker away from us they are moving, right ? (redshift, etc)" they say: "yeah" then I say...

Homework Statement Steam is expanded from 90 bar, 412°C to 4.0 bar saturation in a high pressure turbine, after-which a certain percentage of the steam is bled off to a feed heater. The remaining steam is then expanded through a low pressure turbine to 1.0 bar and dryness fraction of 0.93. All...