Expansion Definition and 1000 Threads

I pulled this quote from an article on the Hubble Constant: "...for example, if the Hubble Constant was determined to be 50 km/s/Mpc, a galaxy at 10 Mpc, would have a redshift corresponding to a radial velocity of 500 km/s." In this illustration provided from the article, if this was the...

Hello guys I struggle since yesterday with the following problem I am reading the book "Elements of applied bifurcation theory" by Kuznetsov . At one point he has the following Taylor expansion of a nonlinear system with respect to x=0 where ##x\in \mathbb(R)^n## $$\dot{x} = f(x) = \Lambda x +...

I read in a so called sci-fi website from my country that as the universe is expanding we may not be able to get to certain galaxies in a possible interstellar travel. That information seems ok for me. But then there was a comment by a reader concluding from the website post that there is coming...

Just a thought I had today. I read an article that mentioned how the universe is expanding faster and faster and how dark energy may be the cause for this, but I wondered, what if the accelerating expansion of the universe is not caused by dark energy but simply by the gravitational attraction...

I came across the following working in my notes and would like some help understanding how the step was done. Many thanks in advance! The following is the working, and we assume that ##\beta## is small $$\frac{1}{1+ \beta \hbar \omega /2 + (7/12)(\beta \hbar \omega)^2 +...} \approx 1 - (\beta...

I seek a little help in understanding why we can see so far into the past to be able to view events where the light from these events should have long ago overtaken wherever the masses ended up. I get it that there was a considerable time during which the limits of the space expansion exceeded...

1) space is expanding at an increasing rate, therefore things are getting farther from each other and therefore increasing in velocity. 2) the faster an object moves relative to another, the more mass it has 3) supermassive objects can turn into neutron stars, black holes, etc. Therefore, will...

I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/4}\sigma^{3/2}}\text{exp}\left[ -\frac{(\textbf{r} - \textbf{r}_0)^2}{4\sigma^2} + i\textbf{k}_0...

Homework Statement Consider the isentropic expansion of air from a fixed given reservoir (i.e. total pressure and temperature). Investigate the behaviour of the value of the Reynolds number of the flow, as a function of the Mach Number M of the expanded flow. For small values of M, the...

Bessel function using g(x,t)=g(u+v,t)=g(u,t)g(v,t) to show that J_{0}(u+v)=J_{0}(u)J_{0}(v)+2\sum_{s=1}^{\infty}J_{s}(u)J_{-s}(v) ___________________________________________________________________________________________ my solution g(u+v,t)=e^{\frac{u+v}{2}(t-\frac{1}{t})}...

I am looking at a couple of very interesting papers, published in MNRAS, that deduce, that the accelerated expansion of the Universe we observe can be attributed to gravitational waves, produced by a very distant merger of two or more universe-mass-scale black holes. The last one is on the...

How does the expansion of space cause light to lose energy?

This idea has always bugged me: If we are looking at the past when observing the redshift of far away galaxies (ex: 10 billions light years).. then how can we tell that the universe at the present time is still expanding at same rate, deaccelerated, or stopped expanding?

My discussion of the Friedmann metric comes from the derivation presented in section 4.2.1 of the reference: https://www1.maths.leeds.ac.uk/~serguei/teaching/cosmology.pdf I have a couple of simple questions on the derivation. The are placed at points during the derivation.I note the...

Homework Statement An iron ring of radius 2.1 m is to be fitted on the rim of a wheel of radius 2.121 m. The coefficient of volume expansion for iron is 3.6 x 10-5 K-1. By how much should the temperature of the ring be increased? (a) 532 °C (b) 833 °C (c) 278 °C (d) 378 °C Homework Equations...

Homework Statement Expand ##(1+3x-4x^2)^{0.5}/(1-2x)^2## find its convergence valueHomework EquationsThe Attempt at a Solution on expansion ##(1+3/2x-3.125x^2+4.6875x^3+...)(1+4x+12x^2+32x^3+...)## ##1+5.5x+14.875x^2+42.1875x^3+... ## how do i prove for convergence here?

The definition of the angular diameter distance is the ratio of an object's physical transverse size to its angular size. However when I was reading my textbook, *Astrophysics in a Nutshell by Dan Maoz pp.220-221*, I am having some trouble trying to understand the notion of **angular diameter...

Homework Statement Consider a perfect monoatomic gas at pressure $p_i$ 1.2 atm and temperature $T_i$ 300K, that is in equilibrium inside a cylinder having a volume $V_i=1L$ and which piston has a mass of 1kg and is at an height of 50 cm. Admit that a mass M=3.13kg is over the piston. When that...

In case of isobaric expansion, the system expands at constant pressure(the external pressure i.e. the resistance is constant.).In case of flow work, the fluid trying to exit the control volume, pushes against the pressure at the exit of the control volume or when entering the control volume, the...

In an isothermal expansion of an ideal gas, can the piston be made to expand isothermally if the initial system pressure is equal to the initial surrounding pressure?(In most of the books and video lectures whenever they explain isothermal expansion, they assume initial system pressure to be...

Initially, the pressure of the gas inside the cylinder is higher than the atmospheric pressure and the piston is held in the contracted position by some means.When the piston is released, it expands and the pressure and temperature of the system decreases but the volume increases.In order to...

Hi, Joule's original gas expansion experiment is often presented like in the following link: http://demonstrations.wolfram.com/JouleExperimentOnFreeExpansion/ The apparent lack of temperature change in this experiment is often used in textbooks to demonstrate that the energy of an ideal gas is...

Hey everyone 1. Homework Statement I want to compute the Taylor expansion (the first four terms) of $$f(x) =x/sin(ax)$$ around $$x_0 = 0$$. I am working in the space of complex numbers here. Homework Equations function: $$f(x) = \frac{x}{\sin (ax)}$$ Taylor expansion: $$ f(x) = \sum...

Homework Statement Homework EquationsThe Attempt at a Solution Coefficient of volume expansion γ = ∆V/V∆T VT2 = constant Differentiating we get , T2∆V + 2VT∆T = 0 ∆V/V∆T = -2/T So , option 2) looks right . Is that correct ? How do I interpret the answer ? Does that mean the...

I was just curious because if space can expand faster than light, doesn't that mean there will be a lot of space that we just can't see? Do objects just vanish because we can't see them? For instance, if a hypothetical alien lived in MACS0647-JD galaxy which is 13.3 billion light years away...

Homework Statement A rod of length ##L_o## is kept on a friction-less surface. The coefficient of linear expansion for the material of the rod is ##\alpha##. The the temperature of the rod is increased by ##\Delta T## the strain developed in the rod will be? Homework Equations $$ \Delta L=...

I am extremely confused by the use of the term coefficient of increase of something. For example , if it is stated that the index of refraction varies linearly with a coefficient of 2.5×10^-5, how is this coefficient defined? Is it simply the slope of the line plotted with index of refraction on...

Question about accelerating expansion Why do I see everything backwards? Here is a paragraph from Bernard Schutz’s excellent book on General Relativity, p. 352: (referring to the famous plot from the High-Z Supernova Search Team: Riess, et al, 1998) The top diagram shows the flux (magnitude)...

Homework Statement Adiabatic expansion of an ideal gas is carried out in a steady flow process. The initial pressure of the gas is 2.5 bar. The volume is expanded from 1.2m3 to 3.8m3. Heat capacity ratio (γ) = 1.42. Calculate enthalpy change of the process. Homework Equations PV = nRT W = ∫...

Hello everyone. I am trying to generate the KL expansion of a stochastic process. I use a Monte Carlo sampling method to generate the process, which involves two random variables and I compare it with it's theoretical mean for 50 values of time and they look quite similar. Then, I calculate the...

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...