Expansion Definition and 1000 Threads

Homework Statement Prove that, if x is so small that x^6 and higher powers of x may be neglected, then \frac{e^{2x}-1}{e^{2x}+1}\approx x-\frac{x^3}{3}+\frac{2x^5}{15} Homework EquationsThe Attempt at a Solution [/B] \\...

I'm trying to derive Feynman rules for massive vector boson and its antiparticle. It all boils down to plane wave expansion of the bosons which atm is a little bit confusing. Should I account for two different set of ladder operators (as in the case of complex KG or spinors, cf Peskin&Schröder...

Hey. I am writing my master thesis, and I really need to find the temperature dependent heat capacity and expansion coffient for Cobalt. I have tried searching the internet, whitout luck. Please, can anybody help me. It is really important!

I've been trying to find the latest, best guess, as to how long ago the universe's expansion began to accelerate (post-inflation). I've seen various estimates on websites from 5 billion to 8 billion years ago. Is there any kind of consensus in the community that studies these things as to a...

Are there any expansion joints (for example between two beams) which can carry a shear force?

Looking for some information on how a shrink fit collar actually works. I get the basic principle that you heat it, it expands, fit the collar, let it cool and it contracts and grips as a collar. However, if you heat a material am I right in saying that it expands in all direction. If this is...

Homework Statement Find the coefficient of x^3 in the binomial expansion of (2/x - 3x^4)^12 Homework EquationsThe Attempt at a Solution Expanding this out would take too long and I cannot use a calculator to find the coefficient I know the formula for the expansion summation (12 choose k)...

Homework Statement Basically I wanted to see if anyone would be willing to give me the solution to the 4th problem of the Weinberg textbook on quantum field theory. The exact question in the book is "Derive the perturbation expansion (3.5.8) directly from the expansion (3.5.3) of old-fashioned...

Homework Statement Consider the infinite series $$\frac{x}{e^x - 1} = A_o + A_1 x + \frac{A_2}{2!}x^2 + ... + \frac{A_n}{n!}x^n + ...$$ Determine that ##1 = A_o,\,\,\,\,\,0 = A_o/2! + A_1,\,\,\,\,\,0 = A_o/3! + A_1/2! + A_2/2!##. Show that for ##n > 1##, one can write the relations as $$(A+1)^n...

Homework Statement IF e^{m \arctan x}=a_0 + a_1x + a_2x^2 + a_3x^3...+a_nx^n+... prove that (n+1)a_{n+1} + (n-1)a_{n-1}=ma_n and hence obtain the expansion of e^{m \arctan x} . Homework Equations The Attempt at a Solution $$e^{m \arctan x} = 1+m \arctan x + (m \arctan x)^2/2! + (m...

The Friedmann equation states that $$(\frac{\dot a}{a}) = \frac{8\pi G}{3} \dot \rho + \frac{1}3 \Lambda - \frac{K}{a^2},$$ where ##a, \rho, \Lambda, K## respectively denotes the scale factor, matter density, cosmological constant and curvature. Now, I'm trying to get at an intuition on...

I have been wondering for a few years if the current equations for the expansion of the universe have ever been used to extrapolate back in time, to determine how many years ago, the rate of expansion was zero. I believe this amount of time will not agree with the accepted age of the universe...

Hey guys, I've been doing a lot of research looking for a fluid that has a high expansion ratio that does not leave the liquid state. the idea is that the fluid could either: - using heat will expand and contract using hot and cold cycles - using electricity (not necessarily needing...

Can someone please explain to me why the universe must be expanding and not contracting? Here is my take on this. The Doppler Effect tells us that we are moving faster than objects. "Behind" us, and objects "ahead" of us are moving faster still. Hence the inference of expansion. But , if...

I attached an image of two expansion cases I am analyzing. Both cases involve an insulated cylinder that is divided by a separating element (diaphragm for case A and piston for B). The portion on the right is evacuated. The left contains a calorically perfect gas with an initial pressure and...

Homework Statement "see attachment" "q1" Homework Equations V=\frac{-A}{r}+\frac{B}{r^{10}} A=5*10^-30 B=8*10^-121 V=potential energy r=interatomic separation distance Coefficient of thermal expansion = \frac{change in L}{L*change in T} The Attempt at a Solution I have...

I am absolutely dying with this question. Ok so referring to the attached image; we can re-iterate the given equation in SL-Form. so $(1-x^2)u'' - xu' + 2u =0 $ divide everything by $\sqrt{1-x^2}$ so we get $\sqrt{1-x^2}u'' - \frac{x}{\sqrt{1-x^2}} u' + \frac{2}{\sqrt{1-x^2}}u=0$ which...

Hi everyone. I'm new to this forum...I just want to make it clear that I'm an engineering student, thus I don't want to look conceited with what I'm going to say. Some day ago, I was watching a documentary talking about the universe ( its expansion in particular), in which it was shown that (...

Homework Statement If the compressability factor is given at a certain temperature as a function of pressure: Z(T) = 1+αP+βP2 find α and β in the form α(a, b, T) and β(a, b, T) where a and b are the van der waals coefficients. Homework Equations nRT=(P+a(n/V)2))(V-nb) Z=PV/nRT The Attempt...

Homework Statement This is a paraphrase, since this is only part of a 3 part question. A sample of 1.00 mol perfect gas molecules with C_{p,m}=7/2*R and initial pressure of 1.00 atm undegoes constant-volume heating to twice its initial pressure. Find q, w, ΔU, and ΔH.Homework Equations PV=nRT...

Homework Statement Two interconnected tanks are of equal volume. One is filled with methane at 500bar and 293K, the other is initially evacuated. A valve connecting the two tanks is opened only long enough to allow the pressures to equilibrate. If there is no heat transfer between the gas and...

Homework Statement Hi, I did a lab experiment where I took a 5L vessel made of some material that isolates gas inside and thus behaves like an isolated system (adiabatic). I then pumped gas from ~90kPa to up to 150 kPa... recorded the temperature, then let the gas 'expand' by opening the...

I know the universe doesn't expand at a speed but rather a rate over distance but if we take two objects on opposite sides of the observable universe, would they be moving away from each other at a greater rate than light? IE if object A was a star and object B was a planet, would the light...

Hi people, I just found out that the famous Feynman Lectures on Physics are now online, so I'm going through them just for fun (I took Physics in College a long long time ago, but was too much content with too little time to actually understand it for real, so here I'm again learning it)...

Is it possible that our universe is just one of more universes and that our universe just appears to be expanding because we are actually merging with another universe? Just wondering if it would be a plausible explanation. Maybe the pull from the other universe against the pull from ours...

Hello all, so I've always wondered about the expansion of the universe as indicated by the observed doppler (red) shift... i get the observed spectrum change and how this can be credited to the stretching of electromagnetic waves... what doesn't make sense to me is that if this is due to a...

Apparently, f \nabla^2 f = \nabla \cdot f \nabla f - \nabla f \cdot \nabla f where f is a scalar function. Can someone please show me why this is step by step. Feel free to use suffix notation. Thanks in advance.

Homework Statement Many hot-water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has 63.1 m of copper pipe whose inside radius is 7.69 x 10^-3 m. When the water and pipe are heated...

Please help me with this, In Reheat Rankine cycle, we first Expand the steam partially in a high pressure turbine and then reheat it again . How is this partial expansion in high pressure turbine done ? in the sense, what is the procedure followed to have only partial expansion of steam...

This expression: \Gammaavc\Gammacab Can someone please show me how to multiply the two Christoffel symbol formulas for these Christoffel symbols without overloading any indices?

I have been thinking for the past couple months on how the expansion of the universe effects the matter and energy within it. Please read every line, skipping any part of this thread will lead to confusion. Hopefully someone can shed some light on this amazing new question of universal expansion...

Hi All, I would like to ask if what supplier's fabricate Low Coefficient of Thermal Expansion (CTE) glass tubing for Fiber Optics application. or What type of glass do we need in Low CTE? It will serve as the packaging for DWDM components. Hoping for your response. Thank you.

We know that a function f(x) over an interval [a, b] can be written as an infinite weighted sum over some set of basis functions for that interval, e.g. sines and cosines: f(x) = \alpha_0 + \sum_{k=1}^\infty \alpha_k\cos kx + \beta_k\sin kx. Hence, I could provide you either with the function...

find the taylor series for $f(x)=x^4-3x^2+1$ centered at $a=1$. assume that f has a power series expansion. also find the associated radius of convergence. i found the taylor series. its $-1-2(x-1)+3(x-1)^2+4(x-1)3+(x-1)^4$ but how do i find the radius of convergence?

The 3 nonlinear differential equations are as follows \begin{equation} \epsilon \frac{dc}{dt}=\alpha I + \ c (-K_F - K_D-K_N s-K_P(1-q)), \nonumber \end{equation} \begin{equation} \frac{ds}{dt}= \lambda_b P_C \ \epsilon \ c (1-s)- \lambda_r (1-q) \ s, \nonumber \end{equation}...

Hi all. I'm working on a project that requires me to perform calculations in Fermi normal coordinates to certain orders, mostly 2nd order in the distance along the central worldline orthogonal space-like geodesics. In particular I need a rotating tetrad propagated along the central worldline...

Hi, I just read a physics paper and there it expands signum of a sine function as below: sgn(sin(wt))=(4/pi)*{sin(wt)+(1/3)*sin(3wt)+(1/5)*sin(5wt)+...} How can we expand sgn(sin(wt)) like this? Thanks.

[SIZE="4"]Definition/Summary The Expansion Postulate is a fundamental postulate in the formalism of quantum mechanics which states that any wavefunction that describes a possible state of a quantum system can be written as a linear combination of the eigenfunctions of a linear hermitian...

Homework Statement Find the coefficient of x^n in the expansion of each of the following functions as a series of ascending powers of x. \frac{1}{(1+2x)(3-x)} Homework Equations The Attempt at a Solution (1+2x)^{-1} = 1 + (-1)2x + \frac{(-1)(-2)}{2!}(2x)^2 +...

I've often read posts where the conservation of energy is questioned regarding redshift due to expansion. The question arises because the energy level of photons is directly related to the light's frequency, and this alludes to photons "losing" energy as the frequency lowers. The reasoning I've...

Expand the following functions as a series of ascending powers of x up to and including the term x^3. In each case give the range of values of x for which the expansion is valid. (1+(1/x))^(-1) The Attempt at a Solution 1 + (-1)(1/x) + (-1)(-2)(1/x^2)/2 + (-1)(-2)(-3)(1/x^3)/3! = 1 -...

As far as I know, the main argument for the statement that the universe is expanding is that the velocities of galaxies increase proportional to the distance. This together with the cosmological principle indicates that every point in the universe observes the same thing, something that is...

I am puzzled by the following example of the application of binomial expansion from Bostock and Chandler's book Pure Mathematics: If n is a positive integer find the coefficient of xr in the expansion of (1+x)(1-x)n as a series of ascending powers of x. (1+x)(1-x)^{n} \equiv (1-x)^{n} +...

Homework Statement From a journal I read that the cobalt-based perovskite cathode usually has better ionic and electrical conduction but higher TEC compare to Maganite-based perovskite cathode. Because of the Co-O bond is weaker than Mn-O bond. e.g. Cobalt-based perovskite cathode...

So I know \cos n \theta + i \sin n \theta = (\cos \theta + i \sin \theta)^n and by applying binomial to the RHS and taking the real part gives you: \cos n \theta = \sum_{k=0}^{\lfloor {n \over 2} \rfloor} C^n_{2k} (\cos^2 \theta - 1)^k \cos^{n - 2k} \theta . I have come across another...

Hello everyone, I am currently reading chapter two, section 3 of Griffiths Quantum Mechanics textbook. Here is an excerpt that is giving me some difficulty: "Formally, if we expand V(x) in a Taylor series about the minimum: V(x) = V(x_0) + V'(x_0) (x-x_0) + \frac{1}{2} V''(x_0)(x-x_0)^2...

Homework Statement Use the power series for e^z and the def. of sin(z) to check that sum ((-1)^k z^(2 k+1))/((2 k+1)!) Homework Equations The Attempt at a Solution I apologize, but I am not particularly good with latex. Therefore, I attached a picture of my solution thus far...

After some thinking, I have concluded that the expansion of the universe must have started at the speed of light or greater than the speed of light but not less than speed of light. I say this because if the expansion of the universe at the instant of the big bang was less than the speed of...

Hello everyone, I'm studying the finite strain theory and have come across the maximum dissipation principle. It implies a dissipation function defined as D=\tau:d-\dfrac{d\Psi}{dt} \tau denotes the Kirchhoff stress tensor, d the eulerian deformation rate and \Psi=\Psi(b_e,\xi) the free...

The following is what I call an expansion info-representation: ... _ _ _ _ _4.3 _ _ _ _ _ ... A) Each of the underscores represent placeholders for digit selection. (Psst: a whim) B) The decimal can be arbitrarily adjustable or fixed for the purpose of experiment. I'm going to try...