What is Derivation: Definition and 1000 Discussions
In cryptography, a key derivation function (KDF) is a cryptographic hash function that derives one or more secret keys from a secret value such as a main key, a password, or a passphrase using a pseudorandom function. KDFs can be used to stretch keys into longer keys or to obtain keys of a required format, such as converting a group element that is the result of a Diffie–Hellman key exchange into a symmetric key for use with AES. Keyed cryptographic hash functions are popular examples of pseudorandom functions used for key derivation.
This is a question on Einstein's 1907 paper first discussing equivalence principle and uniform acceleration.
Picture a rigid accelerating object of length £ with a clock at each end. The rear accelerates for time τ (measured by the clock there) at a proper acceleration γ. The clock at the front...
I am trying to understand how one derives the dilaton monopole interaction. In "Black holes and membranes in higher-dimensional theories with dilaton fields", Gibbons and Maeda mentioned that one could obtain the dilaton monopole interaction as such:
where the action is given by
However, I...
Hi, Everyone! This is the page(first image) from Principle of physics by resnik.
I want to ask the definition of work(##W=F(x) \Delta x##) by variable force here is somewhat different from the usual integral version. I don't understand how is this valid definition?
Secondly, how did they reach...
Many texts state that in an elliptic orbit you can find angular momentum magnitude as
$$ L = r m v = m r^2 \frac {d \theta} {dt} $$
I wonder if
$$ v = r \frac {d \theta} {dt} $$
is valid at every point. I understand this approximation in a circumference or radius r but what about an arc...
One of the common derivations of the canonical ensemble goes as follows:
Assume there is a system of interest in the contact with heat reservoir which together form an isolated system. Heat can be exchanged between the system and reservoir until thermal equilibrium is established and both are...
Boltzmann entropy definition is given by: $$ S = k_B lnW $$ where ##W## is the weight of the configuration which has the maximum number of microstates.
This equation is used everywhere in statistical thermodynamics and I saw it in the derivation of Gibbs entropy. However, I can't find the...
How did Voigt derive the average shear modulus of an anisotropic material, G=1/5 (A-B+3C), where 3A=c11+c22+c33, 3B=c12+c13+c23, 3C=c44+c55+c66?
The original text is published in German about 100 years ago. I looked for other papers explaining this, but none has explained the derivation. They...
I know the formulas for perihelion and aphelion distances in an orbit with SMA a and eccentricity e are a(1-e) and a(1+e), respectively. However, why is this? I can't seem to find any derivations for this anywhere and also cannot figure this out myself.
This problem is from Griffiths' book Introduction to Electrodynamics [Problem 2.53 in 4th edition].
It considers that electrons are emitted from the cathode and move to the anode. This establishes a constant current between the parallel plates. It asks to show that the constant current ##I##...
I am having trouble understanding this derivation and need some guidance.
1) I tried solving the algebra from the first equation to the second equation circled in red. Can someone please help with what algebra steps, I cannot solve to the circled solution.
2) What does Ee stand for? Is it...
The magnetic flux ##\phi_m = \int{BdA}##
The magnetic field of the coaxial cable B = ##\frac{I_{enc} \mu_0}{2\pi r}##
since surface area of a cylinder = ##2\pi rdr L, dA = 2\pi L dr## where L is the length of the coaxial cable
so ##\phi_m = \int{\frac{I_{enc} \mu_0}{2\pi r}2\pi L dr}##?
##\phi_m = Blwcos\theta##
voltage = ##\frac{-d\phi_m}{dt} = Blwsin\theta\frac{d\theta}{dt}## where l is the length of the loop and w is the width of the loop
The top and bottom of the loop have magnetic forces perpendicular to the loop. My book says that means that there is no current through...
Hello,
I'm reading Group Theory in a nutshell for physicist by A Zee. When he introduced Dual tensors (pp 192), he made a claim with a light hint, and I have had great trouble deriving this claim, any help would be appreciated -
Let ##R \in SO(N)## be an ##N##-dimensional rotation, then the...
Hello! Can someone point me towards a derivation (whether with Fermi Golden rule, or full QFT calculations) of the decay rate for the neutrinoless double beta decay:
$$\Gamma_{\beta\beta}^{0\nu} = G^{0\nu}|M^{0\nu}|^2<m_{\beta\beta}>^2$$
Thank you!
McCabe - Thiele method is used to find minimum number of separation stages or theoretical plates for a given efficiency of separation in distillation for two - component mixture if components have similar enthalpy of vaporization.
If components have similar enthalpy of vaporization ,than on...
In section 18.7 of Bruus & Flensberg the authors provide a microscopic derivation of the Josephson effect.
The hamiltonian on both sides of the tunnelling junction is just the typical BCS hamiltonian, on one side (with fermion operators ##c##)
$$
H_c = \sum_{k,\sigma} \epsilon_k...
Moderator's note: Spin-off from previous thread due to topic change.
Because it doesn't work. Bohmian time evolution doesn't involve the coarse graining steps that are used in his calculation. A delta distribution remains a delta distribution at all times and does not decay into ##|\Psi|^2##.
Hi everyone,
In his book "Quantum field theory and the standard model", Schwartz derives the position-space Feynman rules starting from the Schwinger-Dyson formula (section 7.1.1). I have two questions about his derivation.
1) As a first step, he rewrites the correlation function as
$$...
I need help with a derivation of an equation given in a journal paper. My question is related to the third paragraph of this paper: https://doi.org/10.1007/BF00619826. Although it is about fibre coupling my problem is purely mathematical. It is about solving a complex double integral. The...
https://www.researchgate.net/publication/301874096_Emergent_behavior_in_active_colloids/link/5730bb3608ae08415e6a7c0a/download (expression 9 on this document derivation). I understand the need for substitution etc into the integral. What puzzles me is how the integral equals what it does. If...
Queries regarding MKS to CGS system for the following formulas.
Force - Newton (MKS), Dynes (CGS)
Work - Joule (MKS), Ergs (CGS)
1N = 10^5 dynes.
1J = 10^7 ergs.
How the above unit conversion formulas are derived ?
If you've seen it, they chose one point in the combustion chamber and the other in the exhaust nozzle. I think they're assuming that we have a gas both places. They say that the pressure in the nozzle is atmospheric pressure, or it you're in outer space, zero. That makes perfect sense...
Hi all,
I am currently reading Bardeen's Paper on The Four Laws of Black Hole Thermodynamics: https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-31/issue-2/The-four-laws-of-black-hole-mechanics/cmp/1103858973.pdf
and am struggling with the derivation of equation 26...
https://scholar.harvard.edu/files/schwartz/files/7-ensembles.pdf
https://mcgreevy.physics.ucsd.edu/s12/lecture-notes/chapter06.pdf
On page 3 of both the notes above, the author merely claims that $$P \propto \Omega_{\text{reservoir}}$$
But isn't $$P \propto...
The classical definition to the Kinetic Energy equation is KE=integral of F*dx where F=d(m*v)/dt. When mass is constant, KE=(1/2)m*v^2.
I am working on a vibration problem at work and having to review my Lagrangian Dynamics books from 30 years ago. So my question is about all of the authors...
when the net force is constant then
Q1. rate of change of momentum (dp/dt) is zero or constant
Q2. assuming dp/dt is constant we replaced it with ----> p2-p1(total change in momentum ) ? how?
This is a spring problem
From this, it says I need to answer in terms of kinematic friction which to me doesn't make much sense. I also looked at similar questions online to the "in terms of" problems and they don't use all four variables in their derived equation. Do I not need to use all...
The classical wave equation in 1-D reads:
$$\frac{\partial^2 u}{\partial x^2}(x,t) = \frac{1}{v^2}\frac{\partial^2 u}{\partial t^2}(x,t)$$
The D'alembert solution to the wave equation is:
$$u(x,t) = f(x+vt) + g(x-vt)$$
so a allowed wave function solution to the 1-Dimensional classical wave...
Dear PF,
so we know that cross product of two vectors can be permutated like this: ## \vec{ \alpha } \times \vec{ \beta }=-\vec{ \alpha} \times \vec{ \beta} ##
But in a specific case, like ## \vec{p} \times \vec{A} = \frac{ \hbar }{ i } \vec{ \nabla } \times \vec{A} ## the cyclic permutation of...
Using the transformation for ##t##, I obtained
$$\mathrm{d}t'=\left(1+\frac{\partial f}{\partial t}\right)\mathrm{d}t+\frac{\partial f}{\partial r}\mathrm{d}r$$.
Using this equation, I substituted it into the general line element to obtain
\begin{align*}...
Work - Energy principle states that work of resultant force or sum of work of all forces acting on some system equals change in kinetic energy of the system.
For inviscid fluid flowing in a pipe such theorem can be used to derive Bernoulli's equation because as fluid flows it is subjected to...
I want to ask several questions regarding to the text:
1) Why do we find the minima of the diffraction? Why not the maxima?2) "Figure 25.32b shows two rays that represent the propagation of two wavelets: one from the top edge of the slit and one from exactly halfway down"
Why do we take point...
In the special theory of relativity, it seems impossible to derive the lorentz transformation without assuming that the lorentz factor is independent of the sign of the relative velocity. For some reason, I can't get my head around why this assumption is so easily made, as if it's trivial. Can...
Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin.
I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)
Consider the situation where an observer at rest on the ground measures the frequency of a siren which is moving away from the observer at speed ##v_{Ex}##. Let ##v_w## be the speed of the sound wave. Let ##\lambda_0##, ##f_0##, ##\lambda_D##, and ##f_D## be the wavelengths and frequencies...
Hi,
I'm following an introduction course to chemistry and I am reviewing the chapter on Chemical kinetics.
It's shown that the reaction speed for a certain component of a general chemical equation such as aA +bB <-> cC + dD , might be expressed as v = k[A]m[ B]m.
I was wondering where it does...
Another question about the use of the micro-canonical ensemble in deriving distributions.
On the Wikipedia-page the authors mention that the total volume of the system has to be constant.
See...
Sorry if there are other threads on this, but after a discussion with a friend on this (im in the mountains, so no books, and my googlefu isn't helping), I realize that my understanding of the variational principles arent exactly... great! So, maybe some one can help.
Start with a functional...
The total energy of the particle is ##u^2 / 2 - k/R##. When ##u^2 \gg 2k/R##, we take the total energy to be ##u^2/2## only. By the conservation of energy, we have:
$$
\frac{u^2}{2} = \frac{w^2}{2} - \frac{k}{p}
$$
Take the angular momentum expression ##l = bu##, we can replace ##u## with...
Can somebody please derive for me an example of the Binding energy from the Semi Empirical mass formula? I am trying myself but always there is a difference between the database binding energy and my own result. I am calculating the BE of Niobium 93. For the mass formula I used the coefficients...
The covariant form for the Levi-Civita is defined as ##\varepsilon_{i,j,k}:=\sqrt{g}\epsilon_{i,j,k}##. I want to show from this definition that it's contravariant form is given by ##\varepsilon^{i,j,k}=\frac{1}{\sqrt{g}}\epsilon^{i,j,k}##.My attemptWhat I have tried is to express this tensor...
I am trying to understand the Helmholtz equation, where the Helmholtz equation can be considered as the time-independent form of the wave equation. It seems to me that the Helmholtz equation can be derived from the Fourier transform, such that it is part of a larger set of equations of varying...
Summary:: According to Yale’s University PHYS: 200:
v*(dv/dt) = d(v^2/2)/dt
Could someone explain how has he reached that conclusion? He claims to be some standard derivation rules, but I can’t find anything about it.
As much as I can tell: (dv/dt)* v = v’ * v = a* v
thanks!
[Moderator's...
In the screenshots below there are the equations (11.49) and (11.53).
I don't understand how did he derive equation (11.53) from Eq.(11.49)?
From (11.49) I get: ##d\phi/dy= d\phi/du du/dy = (1/b^2-u^2+2Mu^3)^{-1/2}(1+2My)##.
It seems he neglected the ##2Mu^3## since ##Mu\ll 1##, so ##y\approx...
In general, if R is the recovery channel of an error channel ε, with state ρ, then
and according to these lecture slides, we get the final result highlighted in red for a bit flip error channel. I am simply asking how one reaches this final result. Thank you (a full-ish derivation can be found...
Hello! I found this formula in several places for the total angular momentum of a particle with intrinsic spin 1/2 and angular momentum l=1 in the non-relativistic limit:
$$\frac{1}{\sqrt{4 \pi}}(-\sigma r /r )\chi$$
where ##\sigma## are the Pauli matrices and ##\chi## is the spinor. Can someone...
I've been noodling around with derivations of the relativistic energy and momentum, and I almost got it down to just a few lines. But not quite.
I'm going to work in one spatial dimension, for simplicity (even though some derivations require a second spatial dimension)
Let's assume that there...