Mode Definition and 295 Threads

What is the commutator between a^2 (lowering operator squared) and the squared mode expansion from QFT (the integral of a^2e^2ikx, the conjugate, and the cross term I don't feel like writing out)? My instinct is to try and divide the mode expansion into its two parts since integration is linear...

Suppose we can boost from a frame ##S## to another frame ##S'## by using a Lorentz transformation ##\Lambda##. Also, ##\phi(x^\mu;\omega,\mathbf k)## is a mode function of a scalar field in frame ##S##. Then, how do we express this mode function in frame ##S'##? Here is my attempt. First, the...

I have watched a few videos about how to use a 3 ball incentive spirometer for lung rehabilitation. Most of them are about inhalation, which you exercise with the device held right side up. I also saw a couple of videos where they hold the device upside down to test and strengthen exhalation...

Attached is my reference on the literature. My question is; ' are there cases where we may have a continuous distribution that has no Mode value? or is it that the Mode will always be there due to the reason that any given function will have a maximum at some point. Cheers.

I am currently reading about small signal analysis of a MOSFET differential amplifier. The text I am using has the below two figures for a common-mode equivalent circuit for the amplifier. The first makes sense to me except where it calls it a "Norton equivalent circuit", whereas I thought a...

If a Hookean spring-mass system is made from one mass and a spring, to produce a system with a particular oscillation frequency, it's not a problem to use the propagation of errors concept to find how this frequency responds to small errors in the mass and spring constant. If a chain of...

My new Lenovo tablet has a "battery protection mode". This is useful for example when you want to leave it on charge almost permanently, in which case the protection mode will charge and discharge between 40% and 60% in order to maximize battery life. Is there an API that can enable/disable...

I recall, about 30 years ago, seeing the eight mode shapes (and eigenvalues) of a single plane stress (or strain) finite element. Also, years ago, I wrote a FORTRAN code to obtain them (using IMSL libraries) I know there are eight (because the plane quad element had 8 degrees of freedom) I...

ρ_kdk = k^2/π^2 dk is the density of field modes (what we are trying to solve for here), and as ρ_kdk = ρ_λdλ, and k=2π/λ, we can rearrange this to get ρ_λdλ = 8π/λ^4dλ This is where my confusion lies. I am not sure what to do next. I know this equation physically means the number of modes per...

Known: 1) The mass of the ball is ##m## (constant ##\frac{dm}{dt} = 0##) 2) ##v(0) = v_{0}## 3) Air drag force magnitude ##| \vec F_{D} | = B \cdot | \vec v(t) |## (##B \in R##) 4) The ramp is frictionless. 5) The magnitude of Earth's acceleration = ##g## I'm not sure if θ is known or not, and...

See attached question and markscheme. Solutions Now they give the Mode as ##1## i am not getting this... My understanding 'maybe its the English used' is that we have ##0## children living in 3 houses, 7 houses have ##1## kid each bringing total number of kids to 7!, 5 houses have ##2##...

Hello, it may be a little bizarre but I've a question: is there a significant figures mode on AUKORZ AK-991EX calculator? Or in a general CASIO fx-991EX?

I have a 6 years old MacBook air, still running the OS of a couple of years ago. Lately, battery life is going down (around 4.5 hours of light/medium use) so I mainly use it as a desktop computer, connected to an external monitor. However, when I leave it in sleep mode (still on, but shell...

Hello! I'm trying to model common mode current with LTSpice, but there is a problem with my simulation. Someone else tried on an other software and got the expected result, but I can't explain why. When going through the capacitor, square signals should become pulses, but that's not the case...

Hello! I've obtained common mode choke from detached pieces, so I don't know anything about them, exept for their inductance/resistance. I'd like to know how could I determine the rated current of these coilsthank you in advance for your help

Hello! I'm currently working on a project which aims to study common mode current filters. What I'd like to know is how can I generate enough common mode current in order to be able to make experiment on my filter ( its efficiency to reduce it for example) I have some constraints: -the current...

Hello! What is the best way to mode match a cavity in practice? I know the laser spot size before it enters the cavity, but I don't know what the beam spot size should be inside the cavity, so I am not sure how I should adjust the size of the laser spot such that it matches the one that builds...

The first method doesn't work. The second method does work but I can't run avira and malware bytes. Can someone help? First method I hold the shift button and click the restart button. I click on troubleshoot then click on advance objects then I click on see more recovery options. The problem...

I am just reading Carroll's textbook on GR, where at the end of chapter 7.4 Gravitational Wave Solutions he discuss how rotational symmetries in polarization modes are related to spin of massless particles. He then explains that we could expect associated spin-2 particles to gravity - gravitons...

I was reading some articles about buying an air humidifier when I stepped into an "anion mode" which, if present, makes the divide much more expensive. It's supposed to release negative ions along with the water vapor that will bond to dust and other impurities in order to "trap" those. I...

I am trying to understand what happens in the engine (especially gasoline vehicles) during coasting (in drive mode) and engine braking. It looks like both mechanisms shut off the fuel injectors. Then how is the former (coasting in drive mode) able to use the momentum while the latter (engine...

I heard there is a saying that photon and light in a certain wave mode are equivalent. Is it so ?

What you think about this question? Seems a little strange to me, that is, it considers the maximum kinetic energy when the displacement of the oscillators is maximum, i don't think this is right.

Dear All, I'm confused after reading of some chapter in a book, in which equations related to TEM mode have been derived. I want to prove mathematically, that Electric and Magnetic fields are ortogonal to each other. Thus, I use well known Maxwell equation: $$\nabla \times \overrightarrow{E} +...

In Feynman's lectures, he explained the ##TE_{10}## mode of waveguide by considering a line source in the middle of waveguide as below: since the adjacent sources are all out-of-phase, which means to have interference, the adjacent optical path would be about half of wavelength as below: where...

Summary:: Differential amplifier common mode gain derivation of forumlas I'm having a hard time deriving for equations 10-8 -10-9. I tried adding equation's 18-6 and 18-7 but cannot proceed with the derivation. I need help on this. Thank you!

Suppose I prepare an experiment where I excite a single mode of oscillation of the lattice, that is something like ##u(x, t) = Ae^{i(kx-\omega t)} ## (in the classical limit). The energy corresponding to that mode should be ##E = \frac 1 2 \rho L^3 A^2 \omega^2 ##. If I equate this equation to...

Im unsure if I am on the correct track or have gone off on a tangent. Any help or guidance would be appreciated. CMRR=20log10(Adiff/Acm) 120=20log10(10^5/Acm) 120/20=log10(100,000/Acm) 6=log10(100,000/Acm) taking antilogs 1,000,000=100,000/Acm Acm=100,000/1,000,000 Acm=0.1Max amplified...

I know how to calculate the power output and input by analyzing the current in put and output with multimeters and using the formula P=VI. But P_out is obviously incomparably smaller than P_in so the efficiency would suck this way. Is there a better way to do this??

Zpinch works by running a strong current through the plasma which sets up a field that tends to confine the plasma, so if the current is switched on rapidly the resulting temperature increase and B field increase tends to compress the plasma channel rapidly, at least this is how I understand the...

If i have a thermal shock in a thermo-elastic material with crack mode I propagated ? what are the stress-strain relations in this case? or what is the factor K relation? "sorry if the question is not true, but i hope you understood what i mean"

I just saw a video about an electric car which has an ECO mode. In ECO mode the car has less power. So let's say in normal mode the car has 100 kW and in ECO mode 60 kW. But why should the range of the car be greater if it has less power? Because as far as I know to reach a speed of v it...

Hey there, the task I'm working on is written below. Find the quadrature distribution ρ(q), for an optical mode being in the coherent state |α>. Hint: use ∑Hn(x)*(t^n)/(n!) I really am struggling with this type of tasks :D I tried to follow a solved example that I found in my workbook, but...

Source: fobasics.blogspot.com Source: scirp.org As it is shown in the first pic above that the mode field diameter is defined as the mode field decreases to 1/e (in intensity 1/e^2), if I take the mode field and subtract the core's diameter then I divide it by 2, should I get the penetration...

$$\frac{dP_{flow}}{dA} = \frac{1}{2} Re \{\vec{E} \times \vec{H^*} \} \cdot \hat{z}$$ since ##E_z = 0## everywhere ##\vec{E} = \vec{E_t}##$$\frac{dP_{flow}}{dA} = \frac{1}{2} Re \{\vec{E_t} \times \vec{H^*} \} \cdot \hat{z}$$ $$\frac{1}{2} Re \left\{\mp Z_{TE} \left[ \left(\hat{z} \times...

In nuclear magnetic resonance, when should one process spectra in absorption mode and when - in magnitude mode? What is benefit of using the first one and the second one? For example, I need to integrate spectrum. In this case, what should I use - absorption or magnitude mode?

First I worked out the dispersion relations, which is pretty easy: ##M \ddot x_j = K x_{j-1} + K x_{j+1} - 2K x_j -mg \frac {x_j} {l} ## (All t-derivatives) We know ##x_j## will be in the form ##Ae^{ijka}e^{-i\omega t}## so the above becomes: ## -\omega^2M = K (e^{-ika}+e^{ika}-2)-\frac {g}...

https://arstechnica.com/science/2019/03/physicists-flip-the-d-in-tokamak-get-unexpectedly-good-result/ I wonder if it'll fit into a Tesla and then we can remake the Back to the Future with a Tesla movie.

Hi, We talk about single-mode and multi-mode fiber and I assume they talk about the way of sending just one modes (TEM or TMmn or TEmn). Which mode is generally used for single-mode fiber? Is this set by the geometry of the single-mode fiber (especially the opening)? Also, this means that the...

The outdoor fan on heat pumps always runs when the compressor is pumping refrigerant when the heat pump is in heating mode unless the heat pump has defect(s). I don't understand why the outdoor fan on a split system heat pump needs to run when the heat pump is in heating mode. When a split...

In Numerical methods for computing Casimir interactions, we have this expression for the Casimir force between two plates: where I am trying to interpret this physically on a per-frequency and per-mode basis, before actually looking at the complete integral. If we focus on a single...

what is 1^21 + 2^21 + 3^21 + ... + 18^21 in mode 19? i can only think about individually calculating equivalents in mode 19 and then adding them up but there must be a better way then finding equivalents of exponentials of numbers from to 1 to 18, as this question is expected to be solved in...

Hello! I am reading some QFT and at a point I read that any vector field (here we are working with massive spin 1 particles) can be written as: $$A_\mu(x)=A^T_\mu(x)+\partial_\mu\pi(x)$$ with $$\partial_\mu A^T_\mu(x)=0$$ They don't talk about notation, but from the context I understand that...

I have a Samsung Galaxy On7, Android 6.0.1. On my computer (Windows 7, 32-bit), I have adb and fastboot installed. I can work on my phone properly from adb. But the problem starts in fastboot mode. When I put my phone in bootloader mode, the computer takes the phone to be a modem. There are...

I would like to know if there are any general equations (such as the AC transformer equations) that describe a switch mode DC transformer. By this i mean a constant frequency DC signal (50% duty cycle) that ranges from 0V to some max voltage on the primary coil and outputs some higher voltage on...

I know that there are some cases where the mode just isn’t very helpful for finding central tendency, but I have never heard any real specific reason why other than it isn’t too reliable.

Homework Statement Consider non-decreasing series of numbers: 1, 8, 8, 13, 14, 14, x, y, 18, 20, 31, 34, 38 and 40. Median is 15 Calculate mode Homework Equations Median is middle term for odd number of terms and it's average of middle 2 terms for even number of terms. 3 Median = Mode + 2 Mean...

Hi, this message "You can't use `\eqno' in math mode." appears frequently in a sharelatex document I am working on. How can it be fixed? Thanks!

Homework Statement I am having trouble connecting the expectation value of ##\hat a^\dagger \hat a## to the prediction from statistical mechanics for the state $$\hat \rho = \sum_n \frac{\bar n^n}{(1 + \bar n)^{n+1}} |n\rangle \langle n|$$ Homework EquationsThe Attempt at a Solution [/B]...

Hi, I have a 2nd order of sliding mode observer of the form: \dot{\hat{x}} = \hat{f}(x,t) + \delta f + \Psi(u,y) +[ \frac{d \Omega}{dx}]^{-1} \upsilon where ##\upsilon##: \upsilon_1= \alpha_1 \lambda_1^{1/2} | y_1 -\hat{x}_1|^{1/2}*sign(y_1 -\hat{x}_1) \upsilon_2= \alpha_2...