Dispersion Definition and 284 Threads

I have synthesized nano-hydroxyapatite particles via wet chemistry precipitation of a Ca-PO4 solution. In water and PBS, these crystals tend to clump together in aggrigates up to 20-30 microns. The only way that I can get them to disperse is to sonicate them in either Hexafluoro-2-propanol or...

In some textbooks ##\Delta \hat{x}## is called dispersion of coordinate ##\Delta \hat{x}=(\langle \hat{x^2} \rangle-\langle \hat{x} \rangle ^2)^{\frac{1}{2}}##. For me that is standard deviation. What do you think?

Hello everyone I need to know why is it so important to use anomalous dispersion in FWM which four wave mixing and is there any experiment using HNLF high nonlinear fiber ?? Any papers about that I tried. To look but nothing

Homework Statement Using the Debye dispersion approximation, calculate the heat capacity of a harmonic, monatomic, 1D lattice. Next, find the temperature dependence in the low temperature limit. (Assume that the longitudinal mode has spring constant CL = C, and the two transverse modes both...

Sorry if it's a silly question but I was trying to find such an experiment and wasn't successful. What I am thinking is, in the standard delayed choice quantum eraser, the dispersion pattern on the screen correlates to whether or not we can detect which path the electron took. What if the...

Hi guys, I'm currently working on a project related to Faraday instability, and I of course came across the dispersion relation for capillary-gravity waves, i.e. ω² = tanh(kh)(gk + σk³/ρ) . Now I would need to numerically solve this relation for the wavenumber k as a function of depth h...

If different frequencies of light have different refractive indices for the same material and travel at different speed in the same material, isn't it inaccurate to say that the speed of light through a certain material is c/n, where n is the "standard" refractive index?

Hi, Homework Statement I have two questions, in fact, both involving 2D graphene: (1) How may I determine the number of nearest neighbours in a primitive cell of graphene? (2) Given that graphene has linear energy dispersion near the fermi level and the dispersion is given by E=(hbar)vF|k|...

Homework Statement : The dispersion relation for long-wavelength surface waves in deep water is ω=(gk)^1/2 . Waves of a fixed wavelength (or period) travel at their group velocity. Surface waves generated by a storm in the mid-Atlantic and having a period of 15 seconds arrive at the...

I want to ask how does the wave keep the same amplitude if the wave broadens ? Thank you for your time

Homework Statement If light moves from a medium with a refractive index that is a function of wavelength, [\itex]n_1(\lambda)[/itex], to vacuum n_2=1, then dispersion will occur. Find the incident angle \theta_1 that will maximize dispersion. The Attempt at a Solution I'm interpreting...

I'm trying to get my head around quantum mechanics with the help of Sakurai "Modern Quantum Physics". It's been good so far, but I came across a formula I don't really understand. When discussing uncertainty relation (in 1.4) the author begins with defining an "operator": \Delta A \equiv A -...

Hey! Two questions: 1) How exactly does the proof go for the formula for the group-velocity: v_g = \frac{d \omega}{dk} Is it something along the line of using the superposition principle to add all the (arbitrarily numerous) wave-functions making up the wave-packet together, then using...

Hi, I just got a small bottle of graphene dispersion (not GO) on ebay and put a small drop on a ciruit board as shown in the pic. I expected to measure a finite resistance because graphene is a conductor as much as I know. But it seems to have zero conductance from what I read on the...

Homework Statement problem statement is attached as problem.pdf Homework Equations eqn are given in the pdf file The Attempt at a Solution I have tried in vain to connect Fermi energy with dispersion relation. I just don't have any clue ,I also tried to determine the effective...

Why is V=fl a "dispersion relationship"? I've heard of V=fλ being referred to as "the simplest dispersion relationship", however it seems to be used to describe non dispersive traveling and standing waves, where the wave velocity is determined by the medium (fixed) and either f is a dependent...

I read some papers on astrophysics and they discussed dispersion measure. Is there any theoretic meaning of dispersion measure? And what does the unit pc/cm^3 mean?

Hi everyone Homework Statement The frequence for phonons between two atoms with mass M1 and M2 is given by: \Omega^2 = C (\frac{1}{M_1} + \frac {1} {M_2}) \pm C*[(\frac{1}{M_1} + \frac {1} {M_2})^2 - \frac {4} {M_1 M_2} sin^2(\frac {Ka}{2})]^{\frac 1 2} Show that for Ka <<1 the...

Hi. is there anyone who is familiar with surface wave plasma discharges? I want to solve dispersion equation of surface waves in cylindrical plasma column,numerically,to obtain "phase diagram" and "attenuation diagram" from dispersion equation solving. But this dispersion equation include...

Hi, I am trying to implement phase dispersion in a retarded time frame. c_{phase}(ω) = c_{0} + c'(ω) where c'(ω) is a small deviation from the reference phase speed c_{0}. In the frequency domain, the propagation term appears as an exponent: e^{-(\alpha + iω/c_{phase}(ω))z} where z is...

Hi Guys, I am learning some solid state physics. I see a lot of pictures with Phonon Dispersion Relation, with \omega (\vec{k}) on the y-axis and \Gamma, X, M, \Gamma, R on the x-axis. I don't understand, why the angular frequenzy \omega (\vec{k}) is important. Or why is this...

IR and NIR spectroscopy usually employ Fourier transformation to separate the signal into individual wavelength, UV and Vis spectroscopy normally apply gratings for light dispersion (into individual wavelength). What is the cutoff wavelength, and why is so?

Homework Statement I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation \omega = c_sk. It is said that for temperatures much less than the Debye temperature, the heat capacity at constant volume C_V\sim T^3...

When making the transition from the dispersion relation for a beaded string to the relation for a continuous string, I'm confused about the following issue. Take a to be the spacing between beads, m the mass of each bead, and T the tension in the string. We assume these to be constant. For the...

Hi everybody, I would like to use the 'cauchy dispersion formula', ie (http://en.wikipedia.org/wiki/Cauchy's_equation"]http://en.wikipedia.org/wiki/Cauchy's_equation):[/PLAIN] eta = A + B / w² Where : eta is the resulting IOR A is the base IOR B is the dispersion coefficient expressed...

I want to define (and find the sound velocity i iron). can i read it through the dispersion curves of iron? I am trying to see it through the group propagation velocity, vg = dw/dk, i. e the slope of the dispersion relation w(k). am i on the right track? thanks

From the elementary texts, dispersion is the phenomenon where the refractive index of a medium depends on the wavelength of electromagnetic radiation through it. From what I've read, it is the wavelength of the radiation in vacuum. Also, it is said that the refractive index increases with...

Homework Statement Calculate the spin wave dispersion relation Ek for the ferromagnetic Heisenberg model with jtot = 1/2 Assume a 1d square lattice and interactions of strength J between nearest neighbours and zero elsewhere Homework Equations H|k> = [E0 +2jtot\sum J(r)(1-Exp(ik.r) ]...

Homework Statement Hi, dispersion force exists in non-polar molecules due to instantaneous dipole. In polar molecule,the intermolecular force is the sum of dipole-dipole force and dispersion force. Polar molecules have permanent dipoles,this enables the oppositely charged end of molecules...

Hello, I have several question in this thread which is related to velocity dispersion as well as some other areas of galaxy formation and super massive black holes (SMBH) (1) The sigma is used to calculate the speed of the star at the edge of the galaxy and there is a direct relationship...

May I know what is the difference between the dispersion relation for 100 and 001 on the E-K diagram? Can i say 001 has lesser dispersion? But why is it so?

During refraction the different colors that white light is composed of are dispersed but does this happen during reflection or total internal reflection?

Hello people, I think the problem what I have is well known in experimental physics. Hope, somebody can helps me, thanks in advance. Here is: There is a source of neutrons with a flux of λ neutrons per minute, which you do not know and want to estimate. You open the detector for one minute...

While practicing for an upcoming exam, i ran into this question that has truly got me stumped. A phonon dispersion graph is given for NiAl (attached), and then they ask you to schematicaly plot the density of modes graph. I have the result of what is should look like, but i do not understand how...

1. Homework Statement Determine the dispersion (dn/d lambda) at a wavelength of 800 nm from fitting equation. 2. Homework Equations Fitting equation from graph of n vs 1/lambda^2 y = 7e-15 x + 1.60 3. The Attempt at a Solution Since it is a plot of n vs 1/lambda^2 I...

Homework Statement Determine the dispersion (dn/d lambda) at a wavelength of 800 nm from fitting equation. Homework Equations Fitting equation from graph of n vs 1/lambda^2 y = 7e-15 x + 1.60 The Attempt at a Solution Since it is a plot of n vs 1/lambda^2 I thought that...

A wave travels through a (homogeneous) medium at a given velocity, the velocity depends on the frequency of the energy... why?

When white light passes through a rectangular prism, will dispersion occur? Will emerging light ray comes out as a single white light ray or as seven different colors?

Hello, Can anyone explain to me why, concept wise (not from calculations that I get it), is the dispersion relation of magnons (spin waves) quadratic in k for small wavelengths? Also, can you give me other examples where such behavior appears? Thank you

Hi, I've been reading a QM book and it mentions that particles can be represented as a wave packet, which provides a description for particles simultaneously as a wave and particle. It also mentions that the wave packets disperse, and the width becomes extremely large for free microscopic...

Hello All, My question is "What is the relationship between nonlinearity and dispersion?" I know that all materials are dispersive in nature, but keeping that aside for a moment and thinking of an ideal material, can I have a nonlinear (2nd order to be exact) material which is...

Light gets dispersed into different colors in a window glass, just like in a glass prism, but the different colors exit the glass at the same angle. We can't see this phenomenon in a glass window because the distance between the different color lightrays is too small for our eyes to detect, or...

Hey guys, stupid question probably, but I somehow don't get it. I'm just reading an article about dark matter in elliptical galaxies. They mention at a certain point that while for the detection of DM in spiral galaxies we measure the rotational velocity of its stars around the center, for...

Hi there, Could anybody explain how the free electron dispersion relation would be modified by the presence of a periodic potential..? I'm struggling to get my head around it. Thanks!

So the problem I am having is I have no idea what I am supposed to do. I read the chapter on spatial pattern in JD Murrays Math Bio Vol 2 and looked through Strogatz Nonlinear Dynamics and Chaos but I am not sure how to solve anything with these modes. I have no idea what to start doing. $$...

I understand that the relationship between the phonon frequency and its wavenumber is the phonon dispersion. But is there a much more indepth definition of phonon dispersion and if i was asked to explain in a few lines (and in english not mathematical equations) what the phonon dispersion...

I have derived 2D dispersion relation which has the same atoms. But I also need to calculate this 2D dispersion relation with two different atoms. One atom is located at the center and the other type of atoms surrounds this atom. But I am not sure how ı should calculate it because only...

hello I am new in this forum.. and i would like to ask first this is statement that i confused about 'At low values of k (i.e. long wavelengths), the dispersion relation is almost linear, and the speed of sound is approximately ω a, independent of the phonon frequency. As a result, packets of...

Hi, I am a postgraduate environmental science student (NOT a mathematician!) struggling through some necessary maths. Any help with the following (which I suspect will be relatively straight foward) would be very much appreciated. Please ask questions if I have not made myself clear. Homework...

Hi I have two books about electrodynamics that solve Maxwell's Equations. The first one uses the assumptions 1) Linear regime (i.e. not strong fields) 2) Isotropic medium (so disregard tensor nature of ε) 3) Transparent medium (i.e. a real ε) 4) No dispersion of ε In the second book, they use...