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. M

    Calculating phase currents from line currents in an unbalanced delta

    In an unbalanced delta system, I can calculate the line currents given the phase currents. However, I seem to be unable to go the other direction and cannot find sufficient resources to do so. Looking at the phasor diagrams it seems like this should be possible, but my math (or understanding of...
  2. Justforthisquestion1

    Solving for Speed & Revolution: F * delta t = p

    Honestly i have very little idea. F * delta t = p F * delta t /m = v So i know the speed of the rod And i know that however high the rod is supposed to go, when its back down it should have done excactly one revolution. I have the feeling that I should So probably i have to use something like...
  3. S

    I What kind of differential does the small Greek delta letter represent?

    δ I had always thought that it represents a differential element for a parameter that it is not supposed to be a well-defined function - e.g., for a differential or heat or work in thermodynamics - as opposed to a regular Latin d, which is supposed to be such a well-defined function. However...
  4. yucheng

    I Fermi's golden rule: why delta function instead of density states?

    Sakurai, in ##\S## 5.7.3 Constant Perturbation mentions that the transition rate can be written in both ways: $$w_{i \to [n]} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \rho(E_n)$$ and $$w_{i \to n} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \delta(E_n - E_i)$$ where it must be understood that this expression is...
  5. H

    Kramers-Kronig, parity and delta function

    Hi, First of all, I'm not sure to understand what he Kramers-kronig do exactly. It is used to get the Real part of a function using the imaginary part? Then, when asked to add a peak to the parity at ##\omega = -\omega_0##, is ##Im[\epsilon_r(\omega)] = \delta(\omega^2 - \omega_0 ^2)## correct...
  6. Delerion24

    Help with the derivative of the Dirac delta

    My goal is to develop the equation 21. You should asume that \delta(r_2-r_1)^2 =0. These is named renormalization. Then my question is , do my computes are correct with previous condition ?
  7. H

    I ##\epsilon - \delta## proof and algebraic proof of limits

    It occurred to me that I should ask this to people who passed the stage in which I’m right now, being unable to find anyone in my milieu (maybe because people around me have expertise in other fields than mathematics) I reckoned to come here. Let’s see this sequence: ## s_n =...
  8. Jim Lai

    I Kronecker Delta: Order of Indices Explained

    Hi everyone, I am a new member and would like to ask a naive simple (my guess) question. I am reading Weinberg’s Gravitation and Cosmology. On page 59, Eq. 2.12.10 therein reads $$ \begin{aligned} \left[\sigma_{\alpha \beta}\right]_{\gamma \delta}{}^{\varepsilon \zeta} &=\eta_{\alpha \gamma}...
  9. wruehl1

    Calculating fill rate if pressure delta, volume, and time are known?

    I am looking for an equation that I can use to compute L/min or mL/min for a 480cc vessel going from 150bar to 250bar with a fill time of 6min. Sensors for flow rate at these pressures are hard to find, but I thought there might be a way to work this out with the parameters known. An equation...
  10. M

    B Why is Delta y not equal to dy for infinitesimally dx on the graph?

    Hello! As is known, \Delta y = dy for infinitesimally small dx. It's true. But if we have graph we may see that \Delta y isn't equal to dy even for infinitesimally small dx. Why is that so? Thanks!
  11. P

    A Time dependent problem with a delta function

    Hello, I try to solve a time dependent problem described by a Hamiltonian of the type $$ \mathcal{H}(t) = H_0 + V \delta(t) .$$ I started by trying to solve the Schrödinger equation with ##H_0 = p^2 / 2m##, but I'm getting a bit stuck. I would like to know if you know of any books that deal...
  12. H

    Sifting property of a Dirac delta inverse Mellin transformation

    Hi, I have to verify the sifting property of ##\frac{1}{2\pi i} \int_{-i\infty}^{i\infty} e^{-sa}e^{st} ds## which is the inverse Mellin transformation of the Dirac delta function ##f(t) = \delta(t-a) ##. let ##s = iw## and ##ds = idw## ##\frac{1}{2\pi} \int_{-\infty}^{\infty} e^{-iwa}e^{iwt}...
  13. H

    Mellin transform of Dirac delta function ##\delta(t-a)##

    Hi, I found Laplace transform of this Dirac delta function which is ##F(s) = e^{-st}## since ##\int_{\infty}^{-\infty} f(t) \delta (t-a) dt = f(a)## and that ##\delta(x) = 0## if ##x \neq 0## Then the Mellin transform ##f(t) = \frac{1}{2 \pi i} \int_{\gamma - i \omega}^{\gamma +i \omega}...
  14. Astronuc

    New SARS-Cov-2 variant, "Deltacron" = Delta + Omicron variants

    https://www.msn.com/en-us/health/medical/there-may-be-a-new-covid-variant-deltacron-heres-what-we-know-about-it/ar-AAUSuZi So there appear to be subvariants, or different combinations of Delta+Omicron.
  15. Salmone

    A Prove a formula with Dirac Delta

    Why is the Laplacian of ##1/r## in spherical coordinates proportional to Dirac's Delta, namely: ##\left(\frac{\partial^2 }{\partial r^2}+\frac{2}{r}\frac{\partial }{\partial r}\right)\left(\frac{1}{r}\right)=-\frac{\delta(r)}{r^2}## I get that the result is zero.
  16. P

    Scattered State Solutions of a Repulsive Dirac Delta Potential

    I feel that this problem can be directly answered from the E>0 case of the attractive Dirac delta potential -a##\delta##(x), with the same reflection and transmission coefficients. Can someone confirm this hunch of mine?
  17. R

    Driven oscillator amplitude steady state X(t) = ##Asin(\omega t + \delta)##

    I found ## \frac{\gamma}{2} = 7##, ##\gamma = 14## ##\omega_0^2 = \omega_d^2 + \frac{\gamma^2}{4} = 25## ##\omega_0 = \omega = 25##, thus ##\delta = \frac{\pi}{2}## ##A = \frac{\frac{F_0}{m}}{\sqrt((\omega_0^2 - \omega^2)+ \gamma^2\omega^2)} = 0.04## Thus, ##X(t) = 0.04sin(25t + \frac{\pi}{3} -...
  18. bhobba

    With Delta Attending School A Difficult Dilemma

    See: https://www.medrxiv.org/content/10.1101/2021.08.10.21261726v1 'Without interventions in place, the vast majority of susceptible students among K12 schools will become infected, and school absences will increase, followed by additional cases in communities as infected students transmit to...
  19. Leo Liu

    I What is the Definition of the Delta Function?

    I came across it in the derivation of Gauss' law of electric flux from Coulomb's law. I did some research on it, but the wikipedia page about it was slightly confusing. All I know about it is that it models an instantaneous surge by a distribution. However I am still perplexed by this concept...
  20. F

    Conservation of charge with Dirac delta

    Hello, I was reviewing a part related to electromagnetism in which the charge and current densities are defined by the Dirac delta: ##\rho(\underline{x}, t)=\sum_n e_n \delta^3(\underline{x} - \underline{x}_n(t))## ##\underline{J}(\underline{x}, t)=\sum_n e_n \delta^3(\underline{x} -...
  21. A

    MHB Proof that lim loga_n/n = 0 in epsilon delta language

    Let $\,a>0\,,\,a\neq1\,$ be a real number. We can prove by using the continuity of $\ln n$ function that $\;\lim\limits_{n\to\infty}\dfrac{\log_an}n=0\;$ However, this problem appears in my problems book quite early right after the definition of $\epsilon$-language definition of limit of a...
  22. Evo

    COVID Get Vaccinated Against the Covid Delta Variant

    Get vaccinated! https://www.yahoo.com/news/the-covid-19-delta-variant-what-you-need-to-know-151035628.html...
  23. U

    A question on the Dirac delta distribution

    Is it correct to say that $$\int e^{-i(k+k’)x}\,\mathrm{d}x$$ is proportional to ##\delta(k+k’)##?
  24. A

    Writing the charge density in the form of the Dirac delta function

    Hey guys! Sorry if this is a stupid question but I'm having some trouble to express this charge distribution as dirac delta functions. I know that the charge distribution of a circular disc in the ##x-y##-plane with radius ##a## and charge ##q## is given by $$\rho(r,\theta)=qC_a...
  25. Istiak

    Is My Delta to Wye Conversion Calculation Correct?

    I was following these [steps](https://www.allaboutcircuits.com/textbook/direct-current/chpt-10/delta-y-and-y-conversions/). I was calculating resistance for left side circuit. $$R_1=\frac{2 × 2}{2+2+4}=0.5\Omega$$ $$R_2=\frac{2 × 4}{2+2+4}=1\Omega$$ $$R_3=\frac{2 × 4}{2+2+4}=1\Omega$$ Then...
  26. F

    I Understand the delta rule increment in gradient descent

    Hello Everyone, I have a question about the gradient descent algorithm. Given a multivariable function ##f(x,y)##, we can find its minima (local or global) by either setting its gradient ##\nabla f = 0## or by using the gradient descent iterative approach. The first approach (setting the...
  27. Haorong Wu

    I Could this function be approximated by Dirac delta function?

    hi, there. I am doing some frequency analysis. Suppose I have a function defined in frequency space $$N(k)=\frac {-1} {|k|} e^{-c|k|}$$ where ##c## is some very large positive number, and another function in frequency space ##P(k)##. Now I need integrate them as $$ \int \frac {dk}{2 \pi} N(k)...
  28. L

    Delta potential problem - bound states problem

    I am confused here. For ##x>0## particle is free and for ##x<0## particle is free. That I am not sure how we can have bond states. If particle is in the area ##x>0## why it feel ##\delta## - potential at ##x=0##. Besides that, I know how to solve problem. But I am confused about this. If we...
  29. L

    I Double delta potential -- Degeneracy of bound states in one dimension?

    I have a question from the youtube lecture That part starts after 42 minutes and 47 seconds. Balakrishnan said that if delta barriers are very distant (largely separated) then we have degeneracy. I do not understand how this is possible when in 1d problems there is no degeneracy for bond states.
  30. eradan

    Double Delta Potential: Solving Particle Scattering Problem

    Summary:: I have a problem with a particle, which gets scatterd at a double delta-potential Hello, I am really stuck with the floowing problem: A particle moves from the left along the x-axis and gets scatterd at a one-dimensional potential V(x)=a[dirac delta of x) +b [dirac delta of x-c]...
  31. M

    I Probability: why can we use the Dirac delta function for a conditional pdf?

    Hi, I have a quick question about something which I have read regarding the use of dirac delta functions to represent conditional pdfs. I have heard the word 'mask' thrown around, but I am not sure whether that is related or not. The source I am reading from states: p(x) = \lim_{\sigma \to...
  32. M

    A sudden change in the depth of delta function potential well

    is it correct that the continuum states will be free particle states? and the probability will be |< Ψf | ΨB>|^2 . Where Ψf is the wave function for free particle and ΨB is the wave function for the bound state when the depth is B.
  33. A

    Chemistry Delta H Calculation: 7.455 + 94 + 8.4

    -(7.455 so,94+8,4) Delta T
  34. Frabjous

    I Representations of a delta function

    There are many representations of the delta function. Is there a place/reference that lists AND proves them? I am interested in proofs that would satisfy a physicist not a mathematician.
  35. redtree

    I Integrating with the Dirac delta distribution

    Given \begin{equation} \begin{split} \int_{y-\epsilon}^{y+\epsilon} \delta^{(2)}(x-y) f(x) dx &= f^{(2)}(y) \end{split} \end{equation} where ##\epsilon > 0## Is the following also true as ##\epsilon \rightarrow 0## \begin{equation} \begin{split} \int_{y-\epsilon}^{y+\epsilon}...
  36. Z

    Delta function for \nabla(log s), where s = \sqrt{x^2+y^2}

    My intuition for this problem is to use divergence theorem: ## \int_V \nabla^2 u dV = \int_S \nabla u \cdot \vec{n} dS## But note that ##\vec{n}## is perpendicular to x-y plane, and makes ##\int_S \nabla \ln s \cdot \vec{n} dS = 0## If we take laplacian in polar coordinate directly, then...
  37. Antarres

    A Dirac delta function confusion

    As a part of a bigger problem, I was trying to evaluate the D'Alambertian of ##\epsilon(t)\delta(t^2-x^2-y^2-z^2)##, where ##\epsilon(t)## is a sign function. This term appears in covariant commutator function, so I was checking whether I can prove it solves Klein-Gordon equation. Since there's...
  38. rannasquaer

    MHB Dirac Delta and Fourier Series

    A beam of length L with fixed ends, has a concentrated force P applied in the center exactly in L / 2. In the differential equation: \[ \frac{d^4y(x)}{dx^4}=\frac{1}{\text{EI}}q(x) \] In which \[ q(x)= P \delta(x-\frac{L}{2}) \] P represents an infinitely concentrated charge distribution...
  39. karush

    MHB How do I find the value of delta in a delta epsilon proof using a graph?

    Find a graph to a number $\delta$ such that $$\textit{if } |x-1|<\delta \textit{ then } \left|\dfrac{2x}{x^2+4}-0.4\right|<0.1 $$ ok I always had a very hard time doing these I did look at some examples but still ? did a ibispaint drawing to start basically it looks like we are finding the...
  40. brotherbobby

    Product of two Kronecker delta symbols as a determinant

    I don't have a clue as to how to go about proving (or verifying) the equation above. It would be very hard to take individual values of i,j and k and p,q and r for each side and evaluate ##3^6## times! More than that, I'd like a proof more than a verification. Any help would be welcome.
  41. C

    A Evaluation of an improper integral leading to a delta function

    Hi, I have pasted two improper integrals. The text has evaluated these integrals and come up with answers. I wanted to know how these integrals have been evaluated and what is the process to do so. Integral 1 Now the 1st integral is again integrated Now the text accompanying the integration...
  42. MathematicalPhysicist

    I Kronecker's delta from the solution to the final project in Peskin's and Schroeder's book

    My problem is on page 194 of the solution, where he writes: ##\frac{1}{2}\delta^{ab}\frac{1}{2}\delta^{ab}=2##. I assume there are three colours and thus ##a,b \in \{ 0,1,2 \}##. So I get: ##\delta^{ab}\delta^{ab} =...
  43. P

    Neural Networks Question about the Hebbs and Delta Rule

    Good afternoon, I am currently working on Neural Networks and I am reading an introduction by Jeff Heaton (Neural Networks in Java). Now there are two tasks there whose solutions interest me. The first task is about applying the Hebbs rule. In the book it is given wrong because of a typo but I...
  44. M

    Kronecker Delta & Levi Civita manipulation

    εikl εjmngkmMkn = εikl εjknMkn = (in book it changed sign to -εikl εjknMkn - Why? ) By identity εikl εnjkMln = (δinδkj - δijδkn)Mkn = ? I then get .. Mji - δij Mnn ( is this correct ?) There 's more to the question but if can get this part right, I should be able to complete the...
  45. lalo_u

    A Delta Baryon Quartet: Constructing from SU(2) Symmetry

    In ##SU(2)## symmetry, we can define a triplet as ##2\otimes 2^*=3\oplus 1## with a tensor representation like this: $$q_iq_j^*=\left(q_iq^j-\frac{1}{2}\delta_j^iq_kq^k\right)+\frac{1}{2}\delta_j^iq_kq^k.$$ The upper index denotes an anti-doublet and the traceless part in parentheses represents...
  46. N

    Chemistry Calculating delta H of reaction using bond energies?

    Hi, I have been stuck for hours, i do not understand how i am supposed to use bond energy values for this question like it asks when bond energy values are for molecules in the gas state. The first molecule reactant is a liquid and the second reactant has resonance. I have 0 idea how to approach...
  47. J

    Scattering amplitude in scattering from a delta function

    I tried to calculate the Fourier transform to get the amplitude, but I got lost
  48. giveortake

    Engineering Dirac Delta Function in an Ordinary Differential Equation

    1.) Laplace transform of differential equation, where L is the Laplace transform of y: s2L - sy(0) - y'(0) + 9L = -3e-πs/2 = s2L - s+ 9L = -3e-πs/2 2.) Solve for L L = (-3e-πs/2 + s) / (s2 + 9) 3.) Solve for y by performing the inverse Laplace on L Decompose L into 2 parts: L =...