Derivation Definition and 1000 Threads

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.

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  1. simonjech

    I Schwinger-Dyson equations derivation

    This is the part of Schwinger-Dyson equations derivation. I did not understand how can we obtain the commutator in the last line of the picture. I understand why the delta functions appeared from Heaviside functions but there is no minus sign in any term so how can we get the commutator...
  2. M

    I Derivation of two-electron density operator

    Hello, I am going over the derivation for two-electron density. I am having a hard time understanding how the second term in 2.11a seen below is derived. I know this term must eliminate the i=j products but can't seem to understand how. Thanks for the help.
  3. Twigg

    A Lame parameter mu = shear modulus derivation (rogue factor of 2)

    Hello, I am trying and failing to derive that the shear modulus ##G## is equal to the Lame parameter ##\mu##. I start with the linear, symmetric, isotropic stress-strain formula: $$\sigma = \lambda \mathrm{tr}(\epsilon) \mathrm{I} + 2\mu \epsilon$$ I then substitute a simple (symmetric) shear...
  4. F

    Looking for a particular function

    TL;DR Summary: I want to find a function with f'>0, f''<0 and takes the values 2, 2^2, 2^3, 2^4,..., 2^n Hello everyone. A professor explained the St. Petersburgh paradox in class and the concept of utility function U used to explain why someone won't play a betting game with an infinite...
  5. P

    I Derivation of SR's time-dilatation in 1d?

    Hey, I am looking for a derivation of time-dilatation or some trivially equivalent formulas (Lorentz-transformation, conservation of 4-distance (edit: invariance of spacetime interval) etc) in 1 dimension, using that c is observer independent. I only can find the one that uses a light-clock...
  6. M

    Derivation for capacitance of cylindrical capacitor

    I don't understand how they got from the previous step to the next step of the derivation circled in red: Many thanks!
  7. M

    The direction of flux vectors in derivation of conservation of mass

    In the derivation of the conservation law of the conservation of mass, the flux on one side enters and the flux on the other side leaves the control volume. I presume this is due to the assumption that the volume is infinitesimally small and hence v(x,y,z,t) will not change directions...
  8. P

    Lienard-Wiechert Potential derivation, chain rule

    I want to follow the Lienard-Wiechert potential derivation in Robert Wald's E-M book, page 179. I do not understand $$dX(t_\text{ret})/dt$$ on the right side. I assume the chain rule is applied, but I can't see how. $$ \frac{\partial[x'^i - X^i(t - |\mathbf x - \mathbf x'|/c)]}{\partial x'^j} =...
  9. PeterDonis

    A Landau's Maximum Mass Limit Derivation in Shapiro & Teukolsky (1983)

    In Section 3.4 of Shapiro & Teukolsky (1983), a simple derivation, due to Landau, of the maximum mass limit for white dwarfs and neutron stars is given. I will briefly describe it here and then pose my question. The basic method is to derive an expression for the total energy (excluding rest...
  10. J

    I Best Derivation of E=mc^2 - Fdx = V^2 dm

    F= V dm/dt = V (dm/dx)(dx/dt) = V^2 (dm/dx) Fdx = V^2 dm E = m v^2. ,mass flowing with constant velocity If velocity is changing rather than mass, then E = 1/2 m V^2 Ok, joking aside, what is the best derivation of E= mc^2 ?
  11. James1238765

    I How Is the Matrix V Related to Dirac Spinors and Tensor Products?

    Could anyone help with some of the later parts of the derivation for Dirac spinors, please? I understand that an arbitrary vector ##\vec v## $$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} $$ can be defined as an equivalent matrix V with the components $$ \begin{bmatrix} z & x - iy \\ x + iy...
  12. C

    I Annoying detail in derivation of Compton scattering

    In Compton's 1923 paper on X-rays scattering from light elements, he presents the following diagram: Here, ## h\nu_0/c ## is the momentum of the incident photon, ## h\nu_\theta/c ## is that of the scattered photon and ## mv/(1-\beta^2)^{1/2} ## is that of the recoiled electron. He uses this to...
  13. Halc

    I Einstein's Derivation of Elapsed Time for Remote Comoving Object

    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...
  14. U

    A Question about dilaton monopole interaction derivation

    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...
  15. M

    I Principle of Physics: Derivation of -dU/dx=F

    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...
  16. mr_sparxx

    I Kepler's second law derivation from angular momentum conservation

    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...
  17. Dario56

    I Derivation of the Canonical Ensemble

    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...
  18. Dario56

    I Boltzmann Entropy Formula – Derivation

    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...
  19. WMDhamnekar

    A Derivation of P.D.F. from distribution function

    Author computed ##f_{X_k}(x)## as follows but I don't understand it. Would any member explain me the following computations?
  20. mgong21

    I Derivation of Voigt's Shear Modulus

    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...
  21. B

    B Derivation for Aphelion and Perihelion Distances

    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.
  22. E

    I On the derivation of Child-Langmuir law

    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##...
  23. W

    How Do You Derive Electron Energy in Physics Equations?

    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...
  24. A

    I Derivation of the magnetic flux in coaxial cable

    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}##?
  25. A

    I Derivation of induced voltage in loop

    ##\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...
  26. E

    I How can the dual tensors derivation be achieved using rotation matrices?

    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...
  27. M

    I Neutrinoless double beta decay derivation

    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!
  28. Dario56

    Derivation of McCabe - Thiele Method

    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...
  29. K

    A Microscopic derivation of Josephson effect

    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...
  30. N

    A Derivation of Statistical Mechanics

    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##.
  31. E

    I Schwartz derivation of the Feynman rules for scalar fields

    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 $$...
  32. B

    A Help needed with derivation: solving a complex double integral

    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...
  33. steve1763

    A Integrating the Stokeslet: Solving Expression 7 from ResearchGate Publication

    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...
  34. A

    I Conversion factors derivation.

    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 ?
  35. B

    The Traditional Bernoulli Eqn Derivation of Rocket Exhaust Velocity

    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...
  36. T

    A Derivation of Equation 26 in Bardeen's Four Laws of Black Hole Thermodynamics

    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...
  37. yucheng

    Derivation of Boltzmann Factor via Reservoir Method (canonical ensemble)

    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...
  38. R

    I Kinetic Energy derivation assumption?

    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...
  39. just NOTHING

    B Question in the momemtum-impulse theorem derivation

    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?
  40. S

    When it states "in terms of a, b, c" do you need to use all variables?

    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...
  41. Hamiltonian

    I Derivation of Schrodinger equation (chicken and egg problem?)

    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...
  42. Garlic

    I Cyclic rotation of the cross product involving derivation

    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...
  43. U

    Help in derivation of Birkhoff's theorem

    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*}...
  44. Dario56

    I Bernoull's Equation Derivation From Work - Energy Principle

    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...
  45. S

    Derivation of single slit diffraction formula

    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...
  46. K

    I Assumption in the derivation of the Lorentz transformation

    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...
  47. Father_Ing

    Torque formula derivation for a particle moving in circular

    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)
  48. U

    I Phase Speed of Wave in non-relativistic Doppler Shift Derivation

    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...
  49. Ale_Rodo

    What's the derivation of the 'Kinetic Equation' in Chemical kinetics?

    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...
  50. Philip Koeck

    A Volume constraint in micro-canonical derivation of statistical physics

    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...
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