What is Delta: Definition and 1000 Discussions

A river delta is a landform created by deposition of sediment that is carried by a river as the flow leaves its mouth and enters slower-moving or stagnant water. This occurs where a river enters an ocean, sea, estuary, lake, reservoir, or (more rarely) another river that cannot carry away the supplied sediment. The size and shape of a delta is controlled by the balance between watershed processes that supply sediment, and receiving basin processes that redistribute, sequester, and export that sediment. The size, geometry, and location of the receiving basin also plays an important role in delta evolution. River deltas are important in human civilization, as they are major agricultural production centers and population centers. They can provide coastline defense and can impact drinking water supply. They are also ecologically important, with different species' assemblages depending on their landscape position.

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  1. Z

    Solve for Req with T to Delta Transform

    Homework Statement Find Req in the given circuit Homework Equations Series: req = r1+r2... parallel: 1/req = 1/r1 + 1/r2 ... The Attempt at a Solution Without redrawing the circuit I do: 12||60 = 10 10+20 = 30 30 || 30 = 15 15+10 = 25 25||25 = 12.5 12.5+15+5 = 32.5 = Req This is the correct...
  2. S

    Charge densities and delta functions

    Note from mentor: this thread was originally posted in a non-homework forum, therefore it lacks the homework template. I was wondering if the electric charge density ##\rho({\bf{r}})## of a point charge ##q## at position ##{\bf{r}}_{0}## is given by...
  3. A

    Delta T is making my solution come out negative

    Homework Statement Lauryl alcohol is obtained from coconut oil and is used to make detergents. A solution of 5.00 gram of lauryl alcohol in 0.100Kg of benzene freezes at 4.1 degrees Celsius. What is the molar mass of the lauryl alcohol? Kf for benzene = 5.12, Freezing point of benzene is 5.5...
  4. M

    Prove a limit using epsilon-delta definition

    Homework Statement Proof that: ##\lim_{x \to 1} \frac{1}{1+x} = \frac{1}{2}## using the epsilon-delta definition of a limit. (Problem below) Homework Equations ##\lim_{x \to 1} \frac{1}{1+x} = \frac{1}{2} \iff \forall ε>0, \existsδ>0, \forall x ∈ \mathbb{R}\backslash\{-1\}: 0 < |x-1| < δ...
  5. BjornFanden

    Circulating currents in a delta winding

    Dear PF members. I have trouble understanding how zero sequence currents circulate in a delta winding. For example zero sequence currents such as 3rd harmonics, they will circulate in the delta winding and get trapped, why? Why can they not go further? I have recently started to study...
  6. M

    I Kronecker Delta summation (easy)

    Hi PF! As outlined in my book ##\delta_{ij} \delta_{jk} = \delta_{ik}## but don't we sum over repeated indices (and the ##j## is repeated)? Can someone explain why we do not sum in this situation? Thanks!
  7. P

    Dirac Delta Function (x+a)

    Homework Statement hi i have to find the result of ##\int_{0}^{\pi}[\delta(cos\theta-1)+ \delta(cos\theta+1)]sin\theta d\theta## Homework Equations i know from Dirac Delta Function that ##\int \delta(x-a)dx=1## if the region includes x=a and zero otherwise The Attempt at a Solution first i...
  8. I

    B How does the delta ε definition prove derivatives?

    The exercises in my imaginary textbook are giving me an ε, say .001, & are making me find a delta, such that all values of x fall within that ε range of .001. The section that I'm working on is called "proving limits." Well, that is not proving a limit. All that's doing is finding values of...
  9. I

    I Is the Gradient of Dirac Delta Independent of the Coordinate System?

    Dear all, I have a quick question, is the following statement true? $$\nabla_\textbf{x'} \delta(\textbf{x}-\textbf{x'}) = \nabla_\textbf{x} \delta(\textbf{x}-\textbf{x'})?$$ I thought I have seen this somewhere before, but I could not remember where and why. I know the identity ##d/dx...
  10. F

    I Kronecker delta by using creation/annihilation operators

    Hey all, i've found the following expression: How do they get that? They somehow used the kronecker delta Sum_k exp(i k (m-n))=delta_mn. But in the expression above, they're summing over i and not over r_i?? Best
  11. Arnd Obert

    I Density of states with delta function

    Hello, I'm stuck with this exercise, so I hope anyone can help me. It is to prove, that the density of states of an unknown, quantum mechanical Hamiltonian ##\mathcal{H}##, which is defined by $$\Omega(E)=\mathrm{Tr}\left[\delta(E1\!\!1-\boldsymbol{H})\right]$$ is also representable as...
  12. J

    Help with Epsilon Delta Proof of Multivariable Limit

    Homework Statement Hey guys. I am having a little trouble answering this question. I am teaching myself calc 3 and am a little confused here (and thus can't ask a teacher). I need to find the limit as (x,y) approaches (0,1) of f(x,y) when f(x,y)=(xy-x)/(x^2+y^2-2y+1). Homework Equations...
  13. J

    I Help With Epsilon Delta Proof of multivariable limit

    I realized I placed this in the wrong forum... I will put it in coursework help
  14. Aristotle

    Question with 3 Phase Transformers Wye-Delta problem

    Homework Statement Homework Equations Wye: V_Line = sqrt(3) x V_Phase Delta: V_Line = V_Phase The Attempt at a Solution My answer doesn't quite match up with the solutions in the book, and was wondering what I went wrong here? Any help is greatly appreciated!
  15. Muthumanimaran

    Product of Dirac delta functions

    Homework Statement δ(z*-z0*)δ(z+z0)=? δ(z*+z0*)δ(z-z0)=? where 'z' is a complex variable 'z0' is a complex number Formula is just enough, derivation is not needed.
  16. Muthumanimaran

    What is the product of two Dirac delta functions

    Homework Statement What is the product of two Dirac delta functions δ(Real(z-c))δ(Img(z-c))=? 'z' and 'c' are complex numbers. This is not a problem, But I just need to use this formula in a derivation that I am currently doing. I just want the product of these two Dirac delta functions as a...
  17. Summer95

    The Dirac Delta Function

    Homework Statement Differential equation: ##Ay''+By'+Cy=f(t)## with ##y_{0}=y'_{0}=0## Write the solution as a convolution (##a \neq b##). Let ##f(t)= n## for ##t_{0} < t < t_{0}+\frac{1}{n}##. Find y and then let ##n \rightarrow \infty##. Then solve the differential equation with...
  18. GIM

    Change of the order of integration including Dirac delta

    Can somebody help me? I am studying Faddeev-Popov trick, following the Peskin and Schroeder's QFT book, but I can't understand one thing. After they inserted the Faddeev-Popov identity, $$I = \int {{\cal D}\alpha \left( x \right)\delta \left( {G\left( {{A^\alpha }} \right)} \right)\det \left(...
  19. H

    E-permutation and Kronecker delta identity

    Homework Statement \text{Show that } \epsilon_{ijk} \epsilon_{mjk} = 2\delta_{im} Homework Equations \begin{equation*} \epsilon_{ijk} \epsilon_{mnp} = \left| \! \begin{array}{ccc} \delta_{im} & \delta_{in} & \delta_{ip} \\ \delta_{jm} & \delta_{jn} & \delta_{jp} \\ \delta_{km} &...
  20. S

    I Fourier transform of Dirac delta

    In lectures, I have learned that F(k)= \int_{-\infty}^{\infty} e^{-ikx}f(x)dx where F(k) is the Fourier transform of f(x) and the inverse Fourier transform is f(x)= \frac{1}{2\pi}\int_{-\infty}^{\infty} e^{ikx}f(k)dk . But on the same chapter in the lecture notes, there is an example solving...
  21. X

    Question about the Dirac Delta Function

    Homework Statement Find the Fourier spectrum of the following equation Homework Equations ##F(\omega)=\pi[\delta(\omega - \omega _0)+\delta(\omega +\omega_0)]## The Attempt at a Solution Would the Fourier spectrum just be two spikes at ##+\omega _0## and ##-\omega _0## which go up to infinity?
  22. Kevin McHugh

    I Question regarding the Dirac delta function

    Given the definition: δ(x) = 0 for all x ≠ 0 ∞ for x = 0 ∫-∞∞δ(x)dx = 1 I don't understand how the integral can equal unity. The integral from -∞ to zero is zero, and the integral from 0 to ∞...
  23. ELB27

    Product of a delta function and functions of its arguments

    Homework Statement I am trying to determine whether $$f(x)g(x')\delta (x-x') = f(x)g(x)\delta (x-x') = f(x')g(x')\delta(x-x')$$ where \delta(x-x') is the Dirac delta function and f,g are some arbitrary (reasonably nice?) functions. Homework Equations The defining equation of a delta function...
  24. DrPapper

    Finding the Delta Function of a Thin Ring

    Homework Statement [/B] A very thin plastic ring (radius R) has a constant linear charge density, and total charge Q. The ring spins at angular velocity \omega about its center (which is the origin). What is the current I, in terms of given quantities? What is the volume current density J in...
  25. N

    (Hard QM) Consider the double well potential with delta func

    Homework Statement Consider the double well potential with two wells separated by delta function in middle. V(x) = V0 > 0 for x<-a and x>a 0 for -a<x<0 and 0<x<a αδ for x =0 1. Find Bound state energies 2. Find odd solns and their eigenvalue equation. Give solns in...
  26. F

    Double delta well separated by a delta barrier

    Homework Statement Consider a one-dimensional time-independent Schrodinger equation for an electron in a double quantum well separated by an additional barrier. The potential is modeled by: V (x) = -γδ(x - a) -γδ(x + a) + βδ(x) Find algebraic equations which determine the energies (or...
  27. Nasbah BM

    I Why we use Dirac delta function? (in 1 Dimension & 3 Dimesions)

    I want to understand why and where exactly we use dirac delta function? what is its exact use?
  28. M

    MHB Proving F=-constant*(delta y) for delta y < d

    I need to prove that F=-constant*(delta y) if delta y < d I have no idea how to go about this. Please help!
  29. R

    I General Solution of Dirac Delta Potential Well

    We know that the solutions of time-independent Dirac delta potential well contain bound and scattering states: $$\psi_b(x)=\frac{\sqrt{mu}}{\hbar}e^{-\frac{mu|x|}{\hbar^2}}\text{ with energy }E_b=-\frac{mu^2}{2\hbar^2}$$ and $$ \psi_k(x)= \begin{cases} A(e^{ikx}+\frac{i\beta}{1-i\beta}e^{-ikx})...
  30. R

    Delta Function Graphs: Formula, Derivative, and Anti-Derivative with Examples

    Homework Statement For each of these sketch and provide a formula for the function (i.e. in terms of ##u(t)##, ##\delta(t)##) and its derivative and anti-derivative. Denote the ##\delta## function with a vertical arrow of length 1. (a) ##f(t)=\frac{|t|}{t}## (b) ##f(t)=u(t) exp(-t)##...
  31. Kara386

    Tricky integration (maybe delta function)

    Homework Statement I need to integrate ##\frac{A}{2a\sqrt{2\pi}} \int_{-\infty}^{\infty} \frac{e^{ik(x+x')}}{(b^2+k^2)}dk## I have tried substitution and integration by parts and that hasn't worked. I can see that part of it is the delta function, but I don't really know how to use that fact...
  32. F

    Quantum Mechanics: Delta Potential Sudden Change

    Homework Statement I have a particle which is initially in a bound state for a given voltage in the form of a delta function at the origin, V = -αδ(x) initial state is ψα = (√αm)/h2*exp(-m*α*|x|/(h2) At t=0, voltage is changed to V = -βδ(x) both α and β are greater than zero. Right now I'm...
  33. R

    Dirac Delta Function in Differential Equation

    Homework Statement Find the solution to: $$\frac{d^2}{dt^2} x + \omega^2 x = \delta (t)$$ Given the initial condition that ##x=0## for ##t<0##. First find the general solution to ##t>0## and ##t<0##. Homework Equations The Attempt at a Solution This looks like a non-homogeneous second...
  34. Danny Boy

    I Delta fuction potential general solution

    Hi, in the book 'Introduction to Quantum Mechanics' by Griffiths, on page 71 in the section 'The Delta-Function Potential' he states that the general solution to time independent Schrodinger Equation is $$\psi(x) = Ae^{-\kappa x} + B e^{\kappa x}$$ he then notes that the first term blows up as...
  35. A

    Calculating Delta P in Vacuum Chambers: P1 or 0?

    in calculating the delta p in vacuum chambers do we substitute p1 with 0 or the whole equation doesn't exist if air doesn't exist?
  36. Y

    Three-Phase Delta Network: Not all Voltage Sources are 120V?

    Using the Delta Netowrk from this image: http://www.belden.com/images/B23_WyevsDelta.jpg Between Y-X, there should be 120V. Between Y-Z, there should be 120V. Between X-Z, there should be 120V. But wait! If we assign values to make the above statements true... Call X = 0V, and Y = 120V, so...
  37. DavideGenoa

    Commutations and delta in deriving Ampère's law

    Hi, friends! I have been able to understand, thanks to Hawkeye18, whom I thank again, that, if ##\mathbf{J}## is measurable according to the usual ##\mathbb{R}^3## Lebesgue measure ##\mu_{\mathbf{l}}## and bounded, a reasonable hypothesis if we consider it the density of current, if...
  38. F

    Summation Convention – Substitution Rule

    Hello. I'm new to this forum. I'm starting a PhD – it's going to be a big long journey through the jungle that is CFD. I would like to arm myself with some tools before entering. The machete is Cartesian Tensors. I know the rules regarding free suffix's and dummy suffixes, but I'm having...
  39. A

    Bessel functions and the dirac delta

    Homework Statement Find the scalar product of diracs delta function ##\delta(\bar{x})## and the bessel function ##J_0## in polar coordinates. I need to do this since I want the orthogonal projection of some function onto the Bessel function and this is a key step towards that solution. I only...
  40. J

    A Separating the Dirac Delta function in spherical coordinates

    The following integral arises in the calculation of the new density of a non-uniform elastic medium under stress: ∫dx ρ(r,θ)δ(x+u(x)-x') where ρ is a known mass density and u = ru_r+θu_θ a known vector function of spherical coordinates (r,θ) (no azimuthal dependence). How should the Dirac...
  41. I

    Given Epsilon > 0, come up with a delta? Limit problem.

    Lim as x approaches 4 of 1/x = 1/4 Given epsilon > 0, come up with a delta, d?Limits have been introduced. So far my instructor has had us make tables to see what value x was approaching. Although I don't understand exactly how limits are EVALUATED (different from looking at a chart & saying...
  42. L

    Integration over delta distribution

    Homework Statement a) ∫δ( x² cos x) dx with x from -∞ to +∞ b) Integral over C, with C = unit circle ∫C δ(α-α0) a ds a =(1,1) Homework Equations a) δ(g(x)) =∑δ(x-xi)/|g'(xi)| b)? The Attempt at a Solution a) g(x) = x² cosx g'(x) = 2x cos x - x² sin x xi = 0 and (2n+1)π/2...
  43. AutumnWater

    Epsilon Delta proof of a 2variable limit. Is my proof valid?

    Homework Statement Use the epsilon delta definition to show that lim(x,y) -> (0,0) (x*y^3)/(x^2 + 2y^2) = 0 Homework Equations sqrt(x^2) = |x| <= sqrt(x^2+y^2) ==> |x|/sqrt(x^2+y^2) <= 1 ==> |x|/(x^2+2y^2)? The Attempt at a Solution This limit is true IFF for all values of epsilon > 0, there...
  44. AutumnWater

    Will epsilon delta test fail if curve changed direction?

    Will epsilon delta test fail if curve changed direction within the +/- delta of the limit point? Is there a scenario where no matter how small we pick delta to be, the frequency of the graph changing directions is always going to be a higher than delta's distance? In that scenario the limit...
  45. Domenico94

    How do you apply the wye delta transformation in complex electrical circuits?

    Homework Statement What can be special cases, in the study of electrical circuits, in which one can not apply wye delta transformation? Can someone graph them in some way? Homework EquationsThe Attempt at a Solution
  46. chi_rho

    Delta Function Identity in Modern Electrodynamics, Zangwill

    I am currently reading Modern Electrodynamics by Andrew Zangwill and came across a section listing some delta function identities (Section 1.5.5 page 15 equation 1.122 for those interested), and there is one identity that really confused me. He states: \begin{align*} \frac{\partial}{\partial...
  47. KostasV

    Delta function and dirac notation

    Hello there ! I found this discussion http://physics.stackexchange.com/questions/155304/how-do-we-normalize-a-delta-function-position-space-wave-function about dirac notation and delta function . The one that answers to the problem says that ##<a|a>=1## and ##<a|-a>=0## . As far as i know: 1)...
  48. j3dwards

    Average of function (using dirac delta function)

    Homework Statement Compute the average value of the function: f(x) = δ(x-1)*16x2sin(πx/2)*eiπx/(1+x)(2-x) over the interval x ∈ [0, 8]. Note that δ(x) is the Dirac δ-function, and exp(iπ) = −1. Homework Equations ∫ dx δ(x-y) f(x) = f(y) The Attempt at a Solution Average of f(x) = 1/8 ∫from...
  49. A

    Why is flow unsymmetric over a delta wing?

    I understand that there are vortices formed on the delta wing for moderate angles and low speeds. I observed recently 2 asymmetric vortices forming on a small delta wing model for a moderate angle and a low speed. But, why would there be asymmetriic flow over a delta wing? If the flow is...
  50. Julian102

    How to calculate the equivalent resistance using wye delta ?

    Homework Statement https://z-1-scontent-sin1-1.xx.fbcdn.net/hphotos-xtf1/v/t34.0-12/12435980_942112312550457_1708451532_n.jpg?oh=b29a5e9b2ff96bbf0e11932d081eb25e&oe=568A9B79 [/B] We need to find the equivalent resistance along A to B ie AB Homework Equations R=(1/R1 + 1/R2+...+1/Rn)^-1 ...
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