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. A

    Verifying the integral of a dirac delta function

    Homework Statement I'll post it as an image since the notation will be tricky to type out. It's problem 4. http://img29.imageshack.us/img29/1228/307hw3.jpg Homework Equations Not sure this really applies hereThe Attempt at a Solution This is for a physics course but as you can see it's...
  2. J

    Epsilon Delta Limits: Finding \delta

    Homework Statement Suppose |f(x)-5|<0.1 when 0<x<5. Find all values \delta>0 such that |f(x)-5|<0.1 whenever 0<|x-2|<\delta Homework Equations The Attempt at a Solution I know that 0<|x-2|<\delta 2-\delta<x<2+\delta \delta=2 but how does this part of the equation help me find...
  3. N

    Why Does the Integration of exp[abs(x)+3]*delta(x-2) from -1 to 1 Equal Zero?

    Homework Statement Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 2. The attempt at a solution f(x)=exp[abs(x)+3]*delta(x-2) f(2)=148.4 Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 = 0 [b]3. Why is the answer 0?
  4. N

    Solving Poissons Eqn w/ Delta Fn in RHS using Separation of Vars

    Hi Everyone, I am trying to solve the partial differential equation given below: \Delta^2\phi(x,y,z)=\frac{qf(x,y,z)}{\epsilon} where f(x,y,z)=1 at one point and zero elsewhere. This is the poisons equation for a point charge inside a conducting box. Can this be solved using the...
  5. R

    Covariant vector differentiation problem with kronecker delta?

    I'm having trouble understanding the proof/solution below (please see photo, I also wrote out the problem below). I highlighted the part of my problem in red (in the picture attached). Basically I'm not sure what identity they use to get the Kronecker delta after differentiating or whether they...
  6. B

    How do I handle Kronecker Delta in my homework?

    Homework Statement I am a bit confused with how to deal with Kronecker Delta. I need to show that P,i = ( P*δij ),j The i and j are subscripts. Homework Equations The Attempt at a Solution P,i = ( P*δij ),j = P,j*δij + P*δij,j I assumed I could get rid of P*δij,j leaving...
  7. A

    Convolution of two delta functions in frequency domain

    Apparently, when convolving, for example: [δ(ω-π) - δ(ω+π)] * (δ(ω+50π)-δ(ω-50π)) the result is δ(ω+49π)-δ(ω-51π)-δ(ω+51π)+δ(ω-49π) where δ() is the Dirac delta function, * the convolution operator and ω the frequency variable How do we get to this? Can you help me on the intuition in...
  8. F

    Is Dirac delta function dimensionless?

    Probably a trivial question, but does Dirac delta function has (to have always) a physical dimension or is it used just as a auxiliary construct to express e.g. sudden force impulse, i.e. Force = Impulse \times \delta, where 'Impulse' carries the dimension? Any comments would be highly...
  9. F

    Dirac Delta: Finite Height in Fourier Analysis

    Hi, if the definition of a dirac delta (impulse) function is just a sinc function with an infinite height and 0 width, why is it that they are shown and used in Fourier analysis as having a finite height? for example g(t) = cos(2*PI*f0*t) has two impulses of height = 1/2 at f=+/-f0
  10. W

    Proofs with epsilon delta (real analysis)

    Hello, I have stumbled upon a couple of proofs, but I can not seem to get an intuitive grasp on the what's and the whys in the steps of the proofs. Strictly logical I think I get it. Enough talk however. Number 1. "Let f be a continuous function on the real numbers. Then the set {x in R ...
  11. Q

    Why does the Kronecker delta interchange with itself when j equals l?

    does anyone know why djmdkl = dkm when j = l thanks! can i interchange it to djmdkl = dkldjm ? since l = j do the "j" in dkjdjm signify summation? so i get dk1d1m + dk2d2m + dk3d3m ?
  12. I

    Dirac Delta Integral Homework: Proving Equations

    Homework Statement For some reason these are just messing me up. I need to prove: 1. \delta(y)=\delta(-y) 2.\delta^{'}(y) = -\delta^{'}(-y) 3.\delta(ay) = (1/a)\delta(y) In 2, those are supposed to be first derivatives of the delta functions Homework Equations Use an integral...
  13. A

    How can you derive the regularization of a product with a delta function?

    Hi, I was wondering about something a friend told me. He said that we can regularize this product in this form sgn(x)^2 \delta(x)=\frac{\delta(x)}{3} Any guess on how to derive it Thanks.
  14. L

    Covariant and Contravariant Kronecker Delta operating on Tensor

    I am aware that the following operation: mathbf{M}_{ij} \delta_{ij} produces mathbf{M}_{ii} or mathbf{M}_jj However, if we have the following operation: mathbf{M}_{ij} \delta^i{}_j will the tensor M be transformed at all? Thank you for your time.
  15. V

    Why is delta used in the equation for the discriminate?

    Homework Statement With the discriminate, why is delta sometimes used? Homework Equations \Delta = b2 - 4ac The Attempt at a Solution I get the logic behind what the discriminate is and how and why it works, but I don't understand why delta is used in the equation. What change is...
  16. N

    Why there is 2[itex]\pi[/itex] in every dirac delta function

    in QF, every dirac delta function is accompanied by 2\pi,i.e.(2\pi)\delta(p-p_0) or (2\pi)^3\delta(\vec{p}-\vec{p_0}) the intergral element in QF is \int\frac{d^3p}{(2\pi)^3}\frac{1}{2E_P}, it comes from the integral element \int\frac{d^4p}{(2\pi)^4}(2\pi)\delta(p^2-m^2),I want to know why...
  17. A

    How to derive Relation between Levi-civita Density and Kronecker's Delta?

    The Relation between Levi-Civita Density and Kroneckers Delta as follows \sum^{3}_{k=1} \epsilon_{mnk} \epsilon_{ijk} = \delta_{mi} \delta_{nj} - \delta_{mj} \delta_{ni} Logically we can satisfy both sides of the expression but Can anyone tell me how to derive this analytically ?
  18. N

    Infinite potential well- Delta potential inside

    Hello again. Thank you guys. You have been great help... I have another one: Given a potential well- 2a is it's width, and in the middle - there is a delta potential: V(x)= \frac {\hbar^2} {2m} \frac {\lambda} {a} \delta(x) I am looking for the odd solution to this problem. I thought...
  19. A

    Is f(x)δ(x) Equal to f(2)δ(x)?

    Homework Statement Homework Equations The Attempt at a Solution Can I write, say, f(x) \delta(x)=f(2)\delta(x)? Since \delta(x) =0 for x\neq0
  20. D

    Prove that derivative of the theta function is the dirac delta function

    let θ(x-x') be the function such that θ = 1 when x-x' > 0 and θ = 0 when x-x' < 0. Show that d/dx θ(x-x') = δ(x - x'). it is easy to show that d/dx θ(x-x') is 0 everywhere except at x = x'. To show that d/dx θ(x-x') is the dirac delta function i also need to show that the integral over the...
  21. L

    Index Notation and Kronecker Delta

    Homework Statement Simplify the following expressions involving the Kronecker delta in N dimensions. Where possible, write the final result without indices. C_{ns}\delta_{rn} Homework Equations The Attempt at a Solution I know Kronecker delta is symmetric but that doesn't seem to help. Is...
  22. A

    The difference between big delta and small delta?

    Could anybody explain me what's the difference between \delta\Gamma^{\rho}_{\mu\nu} and \Delta\Gamma^{\rho}_{\mu\nu}? Thank you
  23. D

    Help on epsilon delta proof of discontinuity

    Homework Statement Prove the function f(x)= { 4 if x=0; x^2 otherwise is discontinuous at 0 using epsilon delta. Homework Equations definiton of discontinuity in this case: there exists an e>0 such that for all d>0 if |x-0|<d, |x^2-4|>e The Attempt at a Solution I'm confused...
  24. J

    Dirac Delta Integration for Exponential Functions

    Homework Statement find \int_{-\infty}^{+\infty} x(t) \delta (\beta t - t_{0}) dt for x(t) = e^{a t} u(t) there is no information conserning a, β, or t_{0}... The Attempt at a Solution assuming that t_{0} is a constant\int_{-\infty}^{+\infty} x(t) \delta (\beta t - t_{0}) dt =...
  25. M

    A balanced wye delta connection

    Homework Statement A balanced delta load having 18ohm resistance and 24 capacitive reactance in series in each phase is supplied through lines each having 1 ohm resistance and 2 ohm inductive reactance. If the line to line voltage at the sending end is 250 V, find the phase current and line...
  26. M

    Question about balanced wye - delta connection

    i am confused on how to find the line currents when there is a line impedance in between the wye source and delta load... is it wrong to directly add the line impedance and the delta load without converting first the delta load to wye...? is there a way that i can find the line currents and...
  27. Rasalhague

    Exploring Dirac Delta Functions in QM Theory

    I'm reading Daniel T. Gillespie's A QM Primer: An Elementary Introduction to the Formal Theory of QM. In the section on continuous eigenvalues, he admits to playing "fast and loose" with the laws of calculus, with respect to the Dirac delta function. I'd like to understand it better, or, if such...
  28. P

    Solve Dirac Delta Function IVP: y''-2y'-3y=2\delta (t-1)-\delta (t-3)

    Homework Statement Solve the given symbolic initial value problem: y''-2y'-3y=2\delta (t-1)-\delta (t-3) ;y(0)=2,y'(0)=2 The attempt at a solution Let Y(s):= L{y(t)}(s) Taking laplace transform of both sides: [s^{2}Y(s)-2s-2]-2[sY(s)-2]-3Y(s)=2e^{-s}-e^{-3s}...
  29. Z

    Zeta regularization and product of dirac delta distribution

    using the convolution theorem with power functions x^{m} we may define via the convolution theorem the product of 2 dirac delta distribution then main idea is to consider the convolution integral \int_{R}dt(x-t)^{m}t^{n} and then apply the Fourier transform with respect to variable 'x'...
  30. A

    A problem with a Dirac delta function potential

    Homework Statement An ideal particle of energy E is incident upon a rectangular barrier of width 2a and height V_{0}. Imagine adjusting the barrier width and height so that it approaches V(x)=\alpha \delta(x). What is the relationship between V0, alpha and a? Homework Equations The...
  31. L

    Calculating Delta for Red & Violet Light in a Rainbow

    Hi everyone Homework Statement Let's say we observe a rainbow. We know the refraction index of the red and violet light, let's call them n_{1}=1.46 and n_{2}1.47 Now I want to calculate the angle \delta Homework Equations In a square the total angle is 360°, so we have...
  32. F

    Delta vs simplicial complexes

    What is the difference between a delta-complex and a simplicial complex? Hatcher's book says that simplicial complexes are uniquely determined by their vertices. Could someone clarify this? Thanks.
  33. L

    Difference Equation and Dirac Delta

    Homework Statement y[n] - (2/3)y[n-1] = x[n] what is y[n] if x[n] = diracdelta[n] The Attempt at a Solution for some reason, i argued that y[n-1] = diracdelta[n-1] so y[n] = diracdelta[n] + (2/3)diracdelta[n-1] Im pretty sure this is wrong, anybody can help?
  34. L

    Simple Integral: Complex exp -> delta function

    Simple Integral: Complex exp --> delta function My Professor has written this down but I'm having some trouble of precisely where this is coming from: \int\psi^*_{f}(\boldsymbol k')\psi_{f}(\boldsymbol k) d^3\boldsymbol r = (2\pi)^3\delta(\boldsymbol k- \boldsymbol k') where \psi_{f} =...
  35. S

    Convolution with an delta function

    Homework Statement Convolve an arbitary function f(t) with comb(t) [a sum of delta functions that run from -infinity to infinity with spikes at t = nT]. Is the convolution an array of copies of f(t) or is it a set of discrete points such that f(t) is returned at every t = nT? Homework...
  36. S

    Fourier Transform of Delta Function: Solving Homework Statement

    Homework Statement Show that \int^{\infty}_{-\infty} e^{-ipt} dt = \delta(t). Homework Equations The Attempt at a Solution I know that I must Fourier transform \delta(t), but not sure how.
  37. D

    Calculating CFM hole size and delta P known

    I'm looking to fabricate a small version of this device http://energyconservatory.com/products/products7.htm , which is used to measure airflow through a typical residential bath fan. It adjusts to three different known hole sizes, and typically connects to a manometer that has algorithms built...
  38. R

    Finding values of delta that correspond with M=Any Number

    Homework Statement For example you have a limit approaching 0 from the right cot x=infiniti m=1000 Homework Equations The Attempt at a Solution
  39. T

    Scaling Property of the Dirac Delta Function

    Homework Statement Prove that \displaystyle \int_{-\infty}^{\infty} \delta (at - t_0) \ dt = \frac{1}{ | a |} \int_{-\infty}^{\infty} \delta (t - \frac{t_0}{a}) \ dt For some constant a. The Attempt at a Solution Edit: Looking at this again, I really don't understand where this is coming...
  40. R

    Finding Values of Delta that correspond to epsilon

    Homework Statement #8 (4x+1)/(3x-4)=4.5 Homework Equations The Attempt at a Solution 4<(4x+1)/(3x-4)<5 What do I have to do next?
  41. W

    Delta H of formation for diatomic molecules.

    I just finished up my first class of chemistry, and have a question on something that I just can't figure out. The delta H of formation for diatomic molecules is 0. I just don't understand why this is. If there is a reaction, and O2 is one of the products, why is there no heat released when...
  42. jfy4

    Definition of the Derivative using delta and epsilon

    Hi, I have a question about the formulation of the derivative. The definition is f'(x_0)=\lim_{x\rightarrow x_0}\frac{f(x)-f(x_0)}{x-x_0}[/itex] Lets say this limit exists. Can I write the limit in the typical \epsilon-\delta method as such Given the limit exists, then for all...
  43. V

    Solving a Delta Connected Induction Machine Homework Problem

    Homework Statement A \Delta connected induction machine is to start from a source of 480V, 60 Hz. The motor ratings are : 4 poles, \Delta connected, 480V, 60 Hz, X_{ls}\,=\,X_{lr}\,=\,4\,\Omega, X_m\,=\,50\,\Omega, R_s\,=\,0.25\,\Omega, R_r\,=\,0.4\,\Omega. Find the current in the...
  44. A

    Understanding Delta & Star Load Connections

    why do we require delta and star load connection ? thanks.
  45. R

    Mathematica Mathematica Plotting Delta Function

    Hi All, I'm trying to plot some DiscreteDelta functions in mathematica but unfortunately since the points are singular nothing shows up in the plot. Usually when this comes up I replace the delta functions with very narrow gaussians, graphically it looks even nicer (I'm plotting absorption...
  46. L

    Proof of Dirac delta sifting property.

    Homework Statement Prove the statement http://www.mathhelpforum.com/math-help/vlatex/pics/60_32c8daf48ffa5f233ecc2ac3660e517e.png The Attempt at a Solution I am clueless as to how I would go about doing this, I know the basic properties. I think it has to do with using epsilon...
  47. C

    Calculating Delta Free Energy

    Homework Statement At 699 K, DeltaG (degree)=-23.25kJ for the reaction H2(g) + I2(g) <-> 2HI(g). Calculate DeltaG for this reaction if the reagents are both supplied at 10.0 atm pressure and the product is at 1.97 pressure. Homework Equations I believe this is the relevant equation G=G(degree)...
  48. K

    Prove that delta G = delta G^o + RTlnQ

    Please show me the derivation for the formula relating Gibbs free energy change and the reaction quotient. I didn't find it on Google, so I decided to turn here. Is it really that hard? Thanks for any help.
  49. S

    Difference between delta H and q?

    what is the difference between delta H and q? delta H = delta U + P(delta V) so, delta H = delta U -W delta U=q + W so, q=delta U - W So now is there a difference between the two at all? Why then 2 separate quantities? Thank You
  50. S

    Is delta H a state function?(Hess Law?)

    is delta H a state function??(Hess Law?) Is delta H a state function? We know that delta H=delta U+W (at const P) so, we also know that W is path dependent function.So delta H being a sum of delta U and a path dependent function must not be a state function.(point 1) But there is this Hess...
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