1. Dec 11, 2006

### wmac

Hello,

- I am a CS student and I am trying to simulate movements of people using a theory described in Helbing's paper.

I have put the paragraph in below address:

www.host111.com/question/helbing.jpg[/URL]

- The problem is that I have passed college physics and math about 10 years ago ! :) and now need to understand above paragraph to be able to find a numerical solutions for it. (unfortunately I have been a software developer since then and shame that I have forgotten most of the things)

2- What that Gradian mathematically and physically mean?

3- Would you please introduce me some quick references for a) physical side of it i.e potential functions b) mathematical side ie gradian etc?

Thank you very much in advance.

Mac

Last edited by a moderator: Apr 22, 2017
2. Feb 23, 2007

### eaboujaoudeh

i think the paper is missing some explanations. Gradian or gradient? i never heard of gradian, but gradient is a difference between values of the same constant. like the velocity gradient would be the difference between two velocities in a certain amount of time. Potentiality is the ability to impose work or force on an object. like the repulsive potential is a potential that can impose a force, example: A potential difference in voltage will result in an electric current, here a repulsive potential might result in the pedestrian not stepping. if there is a continuity of the explanation it would be better. i hope i'm correct in this explanation

3. Feb 23, 2007

### demo

gradian is a unit of measure for angles. one gradian equals to 1/400 of a full circle.
math.comsci.us/trig/glossary.html

The gradian is a measurement of plane angles, corresponding to 1/400 of a full circle, thus dividing a right angle in 100. The unit is also known as the grad, grade or gon. One gradian is equal to 9/10 of a degree or Ï€/200 of a radian.

Hope this helps.

Last edited: Feb 23, 2007
4. Feb 23, 2007

### dextercioby

5. Feb 23, 2007

### eaboujaoudeh

oh my god !! i forgot about that !! thnx for the refreshing course guys

6. Feb 23, 2007

### nrqed

I *think* that you are referring to the operator $\vec{\nabla}$ which when applied to a scalar function (like a potential) is called the gradient of that function. This is more than a simple difference. It tells you in what direction the scalar function is increasing the fastest! I think this is what you are looking for, in order to understand that text!!
The article (you did not post the full article) talks about but does not describe the scalar function $V_{\alpha\beta}(b)$. Note that $V$ is a scalar function of a scalar variable $b$, but that $b$ is a scalar function of the vector toward a nearby pedestrian $\vec r_{\alpha\beta}$. The chain rule gives the gradient of V: $\Nabla V_{\alpha\beta}(b) = dV/db\;\nabla b(\vec r_{\alpha\beta})$.