Hi BvU,
Thanks for your reply. Your answers really shone some light on this.
I want to be able to understand the 'steps' used in derivations, and what they mean physically, why they are done, and how you 'know' what to do and when to do it... In terms of going back to elementary level, I find...
Is there some kind of intuitive way to understand the physical meaning when mathematical operations are applied to equations in physics?
What I mean is that, say we start with a 'starting point' equation, in this example Ficks law of diffusion (wikipedia:):
J = -D \frac{\delta \phi}{\delta x}...
Hi Courtney, Andy, thanks for your replies. Some questions,
I am not 100% familiar with this term, is optical microscopy widefield imaging?
By laser light I meant very high temporally and spatially coherence lasers.
I thought speckle only comes from a coherent source interacting with a random...
I have a few questions regarding an optical microscope and their white light sources...
So white light generally first hits a diffuser, some kind of ground glass lens. What is the purpose of this?
Then the light goes through a field diaphragm, which we can open and close. I have heard that...
Thanks guys, forgot about the chain rule for differentiation.
So in general, whenever there is a \frac{d^{2}}{dx} then it can be thought of two separate derivatives, each giving their own result. But the ^2 means it skips the first result and we go right to the second?
Hello,
I am confused by the momentum version of newtons second law...
So we know
\bar{F}=m\bar{a}=m\left(\frac{d\hat{v}}{dt}\right)
and that
\bar{\rho}=m\bar{v}=m\left(\frac{d\bar{x}}{dt}\right)
so is
\frac{d\bar{p}}{dt}=m\frac{d\left(\frac{d\bar{x}}{dt}\right)}{dt}
What I mean is this...
The knife edge is just there to flatten out the transfer function. Without the knife edge the technique is known as shadography. In shadography, the samples refractive index inhomogeneities can be thought of as diffraction or phase gratings, causing the incident beam to diffract. The diffracted...
I have this expression:
f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1] where P_2 is a second order Legendre polynomial, and P(\omega) is some distribution function.
Now I am told that, given a data set of f(\tau), I can solve for P(\omega) by either...
Consider a light, an L.E.D for example, turning on and off once per second. For humans, we will look at it and think "clearly on, clearly off, clearly on, clearly off" for each 'state'.
Our view of whether it is on or off will continue like this if its 'blink frequency' is increased up to a...
Hi mate,
thanks for the reply to my very old topic hah. I had a go at that cause the original CONTIN is too complicated for me to use. rILT seems to work but its very slow. I have been using other methods in the mean time.
Thanks.
Hi, Thanks
That makes a big more sense...
So in a geometrical sense... if a rod's center of mass with fixed in a liquid somehow, but it could still rotate around that point, does this mean the distance its ends would 'trace' out on a hypothetical sphere in 1 second would equal eg 40...
When thinking of a spherical shaped particle moving about under Brownian motion, one describes its motion by Diffusion. The units being \frac{m^2}{s} I can understand this physically as a distance it will travel from a certain point in space averaged over x-y and z direction.
Now rotational...
This kind of derivation is in a lot of light scattering books and I have never understood it because they never seem to go into enough detail for me. I am beginning to 'get' it now though.
Thank you very much, that is excellent. It is details like these that books just do not say and I find them incredibly necessary for my understanding. So eqn [4] and [5] are put in as they describe how the material 'responds' to the incoming field. The one thing I still cant wrap my head around...
Thanks for your reply. This is actually from a modern book treating light scattering. I am not wondering about the original derivations Maxwell did, I am after the physical reason why the book takes this path to (eventually after 4 pages) derive an expression for the scattered field.
Can you...
I am trying to follow a Maxwell's equations derivation for light scattering but don't understand 'why' the authors do the steps they do at this start bit. Help would be greatly appreciated...
It starts with the incident electric field equation.
\textbf{E}_{0}(\textbf{r},t) = \textbf{E}_0...
Thanks, I had a look at the first few examples and got them working in MATLAB. This is definitely the kind of thing I am after. I will pick up this book so I can actually understand whats going on now lol.
Any more suggestions along the lines of this would be great, thanks.
I am looking for recommendations of books that teach physics, with an emphasis on solving real-world problems with code.
I find I can only really fully grasp a concept if I can actually program it and visualize it in MATLAB, change variables and see what effect that has on the results...
Hi Guys,
Thanks a lot for your responses. I will see if my Uni library has these books and have a flip through them. I can detect pretty quickly weather I will learn anything from a book, but these look good. That PDE book looks like a gem also. The key of 'what does it mean physically' really...
Hi Guys,
I am after recommendations of books that teach in a specific way. Basically I have come out of a 3 year physics degree with just doing the work but not really understanding the material (the mathematics) that well.
I want to re-learn a bunch of topics in a way so I will actually...
Hmm does that mean if i was trying to work out one of these equations for say a series of 5 ##t_0## values eg ##[1, 2, 3, 4, 5]##, does that mean for ##t_3## I would do
\left\langle A[q,u(3)]A^{*}[q,u(1)] \right\rangle, or
\left\langle A[q,u(3)]A^{*}[q,u(0)] \right\rangle or
\left\langle...
Hi Guys,
In a lot of books dealing with spectroscopy, correlation functions or any kind of functions involving time sometimes take the form like this:
\left\langle A[q,u(t)]A^{*}[q,u(o)] \right\rangle
Where A is some function that depends on say q and u, and u is another function that depends...
Hi Guys,
I have two questions which kind of relate. The first relates to the complex conjugate of a function. Specifically, When a function is multiplied by its complex conjugate, what does that mean physically?
For instance, I am reading a book on electromagnetic wave scattering, and often...
Hi Guys,
I am doing a bit of work with dynamic light scattering (DLS) data. It is one of the many areas of science where we encounter an inverse problem.
The forward problem is: For a known sized particle, calculate its scattered spectrum (that is easy). The inverse problem is: from the...
Hey,
You've been such a great help may I extend my question now?
I have some real data that I want to turn into the power spectrum. The data is in the form of x y where x is t, and y is S(q,t).
So I can fourier transform the theoretical equation, to obtain the answer for how we expect...
Maybe not directly related to your work, but with what I do, the FT of the autocorrelation function which obtains the power spectral density. Where the peak will be centered at the incident laser wavelength, and the line width relates to the characteristic decay time of the sample. I dont see...