Delta Definition and 1000 Threads

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. Dethrone

    MHB How Do We Prove the Limit of 1/x as x Approaches 2?

    $$\lim_{{x}\to{2}}\frac{1}{x}=\frac{1}{2}$$ Here is what I have so far: For all $\delta >0$, there exists an $x$ such that $0<|x-2|<\delta $, $|\frac{1}{x}-\frac{1}{2}<\epsilon$ Cut to the chase: $$\frac{|x-2|}{|2x|}<\epsilon$$ I need to bound $\frac{1}{|2x|}$ somehow, and represent it with...
  2. Dethrone

    MHB Epsilon Delta Proof Piecewise function

    https://answers.yahoo.com/question/index?qid=20130915100124AAK4JAQ I do not understand how they got: "1 = |(1 plus d/2 - L) - (d/2 - L)| <= |1 plus d/2 - L| plus |d/2 - L| < 1/4 plus 1/4 = 1/2, " Shouldn't it be $|(1+ \frac{\delta}{2} -L) + (\frac{\delta}{2} -L)|$, not $|(1+ \frac{\delta}{2}...
  3. R

    Integration test of dirac delta function as a Fourier integral

    Homework Statement Problem: a) Find the Fourier transform of the Dirac delta function: δ(x) b) Transform back to real space, and plot the result, using a varying number of Fourier components (waves). c) test by integration, that the delta function represented by a Fourier integral integrates...
  4. I

    MHB What Is the Delta Epsilon Proof in Terms of Pizza Cooking?

    can someone explain it?
  5. sinaphysics

    A question about Dirac Delta Function

    For proving this equation: \delta (g(x)) = \sum _{ a,\\ g(a)=0,\\ { g }^{ ' }(a)\neq 0 }^{ }{ \frac { \delta (x-a) }{ \left| { g }^{ ' }(a) \right| } } We suppose that g(x)\approx g(a) + (x-a)g^{'}(a) Why for Taylor Expansion we just keep two first case and neglect others...
  6. S

    Validity of integral involving delta function

    Hi, Is the following integral well defined? If it is, then what does it evaluate to? \int_{-1}^{1} \delta(x) \Theta(x) \mathrm{d}x where \delta(x) is the dirac delta function, and \Theta(x) is the the Heaviside step function. What about if I choose two functions f_k and g_k, which are...
  7. C

    How Does the Kronecker Delta Lead to the Identity of Jacobians?

    Dear all, I was revising on a bit of tensor calculus, when I stumbled upon this: $$\delta^i_j = \frac{\partial y^i}{\partial x^\alpha} \frac{\partial x^\alpha}{\partial y^j}$$ And the next statement reads, "this expression yields: $$|\frac{\partial y^i}{\partial x^j}|...
  8. P

    Function whose Fourier transform is Dirac delta

    Is there a time domain function whose Fourier transform is the Dirac delta with no harmonics? I.e. a single frequency impulse
  9. T

    Integrating exponent to get delta function

    Something i ran into while doing hw Homework Statement starting with \int{dx} e^{-ikx}\delta(x) = 1 we conclude by Fourier theory that \int{dk} e^{+ikx} = \delta(x) Now, i try to compute \int{dk} e^{-ikx} (I've dropped the normalization factors of 2\pi. I believe no harm is done by...
  10. A

    The need for the Dirac delta function

    So part of the idea presented in my book is that: div(r/r3)=0 everywhere, but looking at this vector field it should not be expected. We would expect some divergence at the origin and zero divergence everywhere else. However I don't understand why we would expect it to be zero everywhere but...
  11. A

    Derivative of the Step Function: Exploring the Delta Distribution

    How can I find the derivative of a step function?
  12. M

    Proof? Kronecker delta is the only isotropic second rank tensor

    It is pretty straight forward to prove that the Kronecker delta \delta_{ij} is an isotropic tensor, i.e. rotationally invariant. But how can I show that it is indeed the only isotropic second order tensor? I.e., such that for any isotropic second order tensor T_{ij} we can write T_{ij} =...
  13. T

    16 bit sigma delta ADC question

    Hi every one, I am examining a prototype device that is designed to analyse current from an electrochemical O2 sensor (current source), The sensor will output 1.124 uV per PPM (cross 47 ohms @0.023 uA), and has acuracy of +- 2 PPM, with max 1000 PPM. it ueses 16 bit Sigma Delta ADC with...
  14. E

    Levi civita symbol and kronecker delta identities in 4 dimensions

    I'm trying to explicitly show that \varepsilon^{0 i j k} \varepsilon_{0 i j l} = - 2 \delta^k_l I sort of went off the deep end and tried to express everything instead of using snazzy tricks and ended up with \begin{eqnarray*} \delta^{\mu \rho}_{\nu \sigma} & = & \delta^{\mu}_{\nu}...
  15. Hepth

    Mathematica [Mathematica] Bug in Integrate with derivatives of a delta function

    Integrate[f[qs] DiracDelta'[qs (1 - 1/x)], {qs, -\[Infinity], \[Infinity]}, Assumptions -> 0 < x < 1] Integrate[f[qs] DiracDelta'[qs - qs/x], {qs, -\[Infinity], \[Infinity]}, Assumptions -> 0 < x < 1] This is on Mathematica 8 for windows. The results differ by a sign. They are effective...
  16. kq6up

    Delta Function Potential Barrier

    Homework Statement Background: The problem is to find the uncertainty relationship for the wave equation for a delta function potential barrier where ##V(x)=\alpha\delta(x)##. Check the uncertainty principle for the wave function in Equation 2.129 Hint: Calculating ##\left< p^2 \right> ##...
  17. C

    Kronecker delta symbol in calculation question

    As part of a physics calculation, I have the following integral $$\int d \bar x a^{\sigma} \left[-\partial_{\mu}\left(\frac{\delta x^{\nu}}{\delta a^{\sigma}}\right) (\partial_{\nu}\Phi )\frac{\partial L}{\partial (\partial_{\mu}\Phi)} + \partial_{\mu}\left(\frac{\delta x^{\mu}}{\delta...
  18. kq6up

    How Do Delta Functions Behave Under Scaling Transformations?

    Homework Statement Delta functions said to live under the integral signs, and two expressions (##D_1(x)## and ##D_2(x)##) involving delta functions are said to be equal if: ##\int _{ -\infty }^{ \infty }{ f(x)D_{ 1 }(x)dx } =\int _{ -\infty }^{ \infty }{ f(x)D_{ 2 }(x)dx }## (a)...
  19. S

    Solution of differential equation with Dirac Delta

    Is it possible to solve a differential equation of the following form? $$\partial_x^2y + \delta(x) \partial_x y + y= 0$$ where ##\delta(x)## is the dirac delta function. I need the solution for periodic boundary conditions from ##-\pi## to ##\pi##. I've realized that I can solve this for some...
  20. L

    How to Calculate the Integral of the Dirac Delta Function?

    How to calculate ##\int^{\infty}_{-\infty}\frac{\delta(x-x')}{x-x'}dx'## What is a value of this integral? In some youtube video I find that it is equall to zero. Odd function in symmetric boundaries.
  21. D

    Poles Arising in a Scattered Particle in a Delta Potential

    I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also like to go ahead and apologize for not knowing how to format correctly. I was given that a...
  22. D

    Cannot make sense of a derivation step involving dirac delta

    I am self studying the 17th Chapter of "Mathematical Methods for Physics and Engineering", Riley, Hobson, Bence, 3rd Edition. It is about eigenfunction methods for the solution of linear ODEs. Homework Statement On page 563, it states: "As noted earlier, the eigenfunctions of a...
  23. B

    Finding delta in terms of epsilon-delta definition

    Homework Statement If f(x) = 3x+1 en assume δ > 0. Assume ε>0. Give a δ > 0 with the following property : |x-1|< δ => |f(x) - f(1)| < ε Homework Equations The Attempt at a Solution |f(x) - f(1)| < ε <=> |3x+1-(3*1+1)| < ε <=> |3x-3| < ε <=>...
  24. Rochefort

    How can I solve this problem with Delta x?

    The question In my work \mu is the mass per unit length, therefore I believe I can say m=\mu\Delta xbecause Michael Fowler from the University of Virginia does the same at http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/AnalyzingWaves.htm (the 2nd line bellow the graph) I start...
  25. O

    How to numerically solve a PDE with delta function boundary condition?

    I have a PDE of the following form: f_t(t,x,y) = k f + g(x,y) f_x(t,x,y) + h(x,y) f_y(t,x,y) + c f_{yy}(t,x,y) \\ \lim_{t\to s^+} f(t,x,y) = \delta (x-y) Here k and c are real numbers and g, h are (infinitely) smooth real-valued functions. I have been trying to learn how to do this...
  26. M

    T type thermocouple for Delta T measurement

    I am working on an experiment where I need to measure the Delta T across a heat ex-changer. I have two independent T Type thermo couple, one at the inlet and the other at the outlet. Both tied to an Agilent data logger. I normally put the data into an excel sheet and generate Delta T = T1 - T2...
  27. L

    How can I show that the function ##\psi(x)## is continuous?

    Homework Statement ##\frac{d^2\psi}{dx^2}+\frac{2m}{\hbar^2}(E-\alpha\delta(x))\psi(x)=0## Show that ##\psi(x)## is continuous and that first derivative has discontinuity ##\frac{2m\alpha}{\hbar^2}\psi(0)##.Homework Equations The Attempt at a Solution I'm not sure how to show that function...
  28. K

    Delta-Epsilon Proof: Prove lim_{x\implies 1} \frac{2}{x-3} = -1

    Homework Statement Prove that ## lim_{x\implies 1} \frac{2}{x-3} = -1 ## Use delta-epsilon. The Attempt at a Solution Proof strategy: ## | { \frac{ 2}{x-3} +1 } | < \epsilon #### \frac{x-1}{x-3} < \epsilon ## , since delta have to be a function of epsilon alone and not include x. I...
  29. A

    Formula for delta star in capacitors

    Homework Statement How to find out the equivalent capacitance using delta star conversion? Homework Equations Delta star conversion formula of capacitors The Attempt at a Solution Using the formula of resistors but not coming.What is the formula of delta star in capacitors?
  30. Y

    Is My Acid Equilibrium Final Review Correct?

    Hello Forum! I have this review package for my final full of weird mistakes. Problem is that it is hard for me to know if the solutions are right or not: Could you please look at this problem I attached? They bizarrely switch from HA to HB. Is that just a typo? Then, the sign of DG°...
  31. M

    Is Delta H of formation the same for NH4NO3 Aqueous and in Solid Form?

    I am doing a project in Chemistry and I need to use Hess' Law to cancel two equations and if in one equation the NH4NO3 is solid and in the second one the NH4NO3 is aqueous. The equations are: 1: NH4NO3 (s) + HCl (aq) --> HNO3 (aq) + NH4Cl (aq) 2: NH4OH (s) + HNO3 (aq) --> H2O (l) + NH4NO3...
  32. karush

    MHB Delta Epsilon Proof: An Overview

    these proofs are always confusing but here's my take on it.. since $x\rightarrow +\infty$ we don't need absolute values and since $ \displaystyle \frac{1}{10^2}=0.01 $ then we could use $N=10$ letting $L=0$ since it is a horz asymptote then we have $ \displaystyle...
  33. K

    Computation about Gaussian and Dirac Delta Function

    I have a Gaussian distribution about t, say, N(t; μ, σ), and a a Dirac Delta Function δ(t). Then how can I compute: N(t; μ, σ) * δ(t > 0) Any clues? Or recommender some materials for me to read? Thanks!
  34. M

    Find Transcendental Equation for Triple Delta Potential Energy

    Homework Statement I'm looking for the bound energy of a triple delta potential: V(x) = -w \left [ \delta(x-a) + \delta(x) + \delta(x+a) \right ] What is the correct transcendental equation for kappa? Homework Equations My wave function is \psi_1(x) = A e^{\kappa x} for x < -a, \psi_2(x) =...
  35. E

    Dirac Delta Function: Is delta(x-y) the Same as delta(y-x)?

    Sorry if the question seems naive but if we have the Dirac delta function delta(x-y) is it the same as delta(y-x)?? Or there are opposite in sign? And why ? Thank you for your time
  36. G

    Understanding a problem that uses episolon delta defintion

    let E = episolon and D = delta; the problem is as follows: let f(x) = (2x^2 - 3x + 3). prove that lim as x approaches 3 f(x) = 21, we write |f(x) - 21| = |x^2 + 2x - 15| = |x + 5||x - 3| to make this small, we need a bound on the size of |x + 5| when x is close to 3. For example...
  37. U

    Delta Potential - Bound and Continuum States

    Homework Statement I am studying my lecturer's notes and in this part he uses a delta potential to illustrate a simple example of Fermi's golden rule, that the rate of excitation is ##\propto t##. Homework Equations The Attempt at a Solution I've managed to get the bound states, by solving...
  38. H

    Simplification - complicated summation involving delta functions

    Simplification -- complicated summation involving delta functions Homework Statement \frac{1}{\sqrt{(2^3)}}\sum[δ(k+1)+δ(k-1)]|k> for k=0 to 7 Homework Equations The Attempt at a Solution I am trying to simplify the above expression. I get \frac{1}{∏*\sqrt{(2^3)}} |1>, which is...
  39. T

    Proper proof of a delta function

    Prove: tδ(t) = 0 The answer our TA has given isn't doing it for me: \int dt \delta(t)f(t) = (0)f(0) = 0 I'm wanting to write: t \frac{d}{dt}\int \delta(t) dt = t \frac{d}{dt}(1) = t * 0 = 0 Am I right here? This doesn't make use of a test function. I'm very sloppy with proofs! Thanks for...
  40. M

    Proving Limit with Epsilon and Delta

    Homework Statement Prove the following sequence {an} converges to L=1/2 an = n2/(2n2+n-1) The Attempt at a Solution Given ε>0 we can determine an N∈N so that |an - L|<ε for n≥N. We have: |an-L|=|(n2/(2n2+n-1)-(1/2)| = |(-n+1)/(2(2n-1)(n+1))| I'm not sure what to do once I get to this...
  41. A

    How Does the Derivative of the Delta Function Affect y(t) in Signal Processing?

    I have an evil TA (who makes the assignments) who likes to give us torturously difficult assignments on stuff we haven't been taught (and in many cases don't even understand conceptually). Homework Statement The input signal, x(t) is a real-valued bandlimited signal with bandwidth W. Find...
  42. M

    Transition Rates / Squared Dirac Delta

    I am not understanding something from my textbook. This is related to Fermi's Golden rule. It's about what happens when the matrix element of the perturbation H' ends up being a Dirac delta for chosen normalization. Here is Fermi's Golden rule. \Gamma_{ba} = 2\pi \left|\langle b \mid H'\mid a...
  43. M

    What is the use of Dirac delta function in quantum mechanics?

    If you ask me define Dirac delta function, i can easily define it and prove its properties using laplacian or complex analysis method. But still i don't understand what is the use of DIRAC DELTA FUNCTION in quantum mechanics. As i have done some reading Quantum mechanics from Introduction to...
  44. U

    Delta wall and infinite square well potentials ,and 2 other questions

    Consider the following potential function: V=αδ(x) for x=0 and V=∞ for x>a and x<-a , solve the shroedinger equation for the odd and even solutions. solving the shroedinger equation I get ψ(x)=Asin(kx) +Bcos(kx) for -a<x<0 and ψ(x)=Asin(kx) +Bcos(kx) for 0<x<a is it...
  45. J

    Delta amplitude and nabla amplitude

    Delta amplitude and "nabla amplitude" Why all jacobi theory and all ellipitc integrals is based in ##\Delta(\theta) = \sqrt{1-m \sin(\theta)^2}## ? You already think that this definition is just midle of history, cause' you can define other elementar function: \nabla(\theta) = \sqrt{1-m...
  46. C

    Expanding delta in Field Theory Derivation of Euler-Lagrange Equations

    Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...
  47. C

    Expanding delta in Field Theory Derivation of Euler-Lagrange Equations

    Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...
  48. R

    Green function, Delta and Heaviside

    Homework Statement Show that the explicitly covariant expression: GR(x-y) = θ(x0-y0)δ((\vec{x}-\vec{y})2)/2\pi agrees with the retarded Green function: δ(x0-y0-|\vec{x}-\vec{y}|) / (4\pi|\vec{x}-\vec{y}|) Homework Equations N/A The Attempt at a Solution I know that the...
  49. E

    Dirac Delta source for vectorial equation

    Hello! By manipulating Maxwell's equation, with the potential vector \mathbf{A} and the Lorentz' gauge, one can obtain the following vector wave equation: ∇^2 \mathbf{A}(\mathbf{r}) + k^2 \mathbf{A}(\mathbf{r}) = -\mu \mathbf{J}(\mathbf{r}) The first step for the solution is to consider a...
  50. U

    Delta function potential; Schrodinger Equation

    Homework Statement Consider the TISE for a particle of mass m moving along the x-axis and interacting an attractive delta function potential at origin: Part(a): What is the difference between a bound state particle and a free particle? Part(b): Show ##\psi _{(x)} = exp (-|k|x)## is a...
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