Recent content by James Brady

the thickness of the line segment represent a faster fluid. wouldn’t all of these be positive divergence just in different directions?

When I apply the Taylor series about x = 0: ##\frac{f(0)}{0!}0^0:## ##z_0 \sqrt{1 + (0-s/2)^2/z_0^2} = z_0 \sqrt{1 + (-s/2)^2/z_0^2}## ##\frac{f^{(1)}(0)}{1!}0^1:## ##\frac{0-s/2}{z_0 \sqrt{1 + (0-s/2)^2/z_0^2}}## = ##\frac{-s/2}{z_0 \sqrt{1 + (-s/2)^2/z_0^2}}## Adding these values...

Electrons are shot thru two slits separated by a distance s at a screen a distance ##z_0## away. The wave function for the particles is proportional to ## e^{ik \sqrt{(x-s/2)^2+z_0^2}} +e^{ik \sqrt{(x+s/2)^2+z_0^2}}## Taking the first one, we can manipulate the square root algebraically...

##u_t + t \cdot u_x = 0## The equation can be written as ##<1, t, 0> \cdot <d_t, d_x, -1>## where the second vector represents the perpendicular vector to the surface and since the dot product is zero, the first vector must necessarily represent the tangent to the surface. We parameterize this...

Ah gotcha, I guess that makes sense now.

I'm working with the Nernst equation with pressure differences right now: ## E = E_t + \frac{RT}{nF}ln ((P/P_0)^{\Delta \eta_G})## I'm assuming pure reactants here so, so I'm omitting the product terms: ##\frac{\Pi_{products} x_i ^{\nu_i}}{\Pi_{reactants} x_i ^{\nu_i}}## which would normally...

@Tom G Thanks much, really good video. In case you're interested, the instructor was modeling a heat map in excel and I couldn't find a chart feature which did that. Turns out he used each individual cell as a colored pixel with 24 rows and 365 columns.

The attached Image is a for some kind of heat map of temperature with the y-axis corresponding to the time of day and the x-axis corresponding to the time of year. It was generated in Excel from weather data files. What is this type of data representation called? I've seen the same type of...

@Nidum looks like that'll be a lot of fun :ok:. Thanks, appreciate it.

I've been playing with that solution for the past couple of days, a couple insights: The method of separation of variables as described here won't work. The solution you provided has an x component in the imaginary exponential term as well as a time component, so it's not two independent...

Hello, I am attempting to solve the 1 d heat equation using separation of variables. 1d heat equation: ##\frac{\partial T}{\partial t} = \alpha \frac{\partial^2 T}{\partial x^2}## I used the standard separation of variables to get a solution. Without including boundary conditions right now...

@mfb That's completely made up. I'm just trying to get a grasp on how to work with the numbers.

Oh... So I would formulate it as P(IQ>0.88|M)?

So it looks like I'm having to mix binary (male vs female) and continuous (percentile) probabilities and I'm not sure where to starts.

I scored in the 88th percentile in a certain personality trait and am trying to figure out the probability of that given that I'm male. I'm trying the likelihood that I would land in the 88th percentile given that I'm male. Definitions: T = trait, M = males, F = female. Given: P(T|M) = 0.3...