Please help with this paragraph of the article, i dont understand

[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)

1- Would someone please help me understand this paragraph of the article?

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

 

[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

 

[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 π/200 of a radian.
http://en.wikipedia.org/wiki/Gradian

Hope this helps.

 

[dextercioby]

Pocket smart calculators have the functions/keys "deg", "grad" and "rad". "Grad" comes from "gradian" which is ... (see above post).

 

[eaboujaoudeh]

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

 

[nrqed]

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

Wait...where is the word "gradian" or "gradient" mentioned in the text?

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!

 

[D H]

nrqed has it right. The article uses the gradient of the repulsive potential between pairs of pedestrians to determine the repulsive "force". To model this behavior in a computer program, you will develop this potential and its gradient. This is just a model of the interaction between pairs of pedestrians. You will need to sum the forces generated by all nearby pedestrians to determine what happens to any particular pedestrian.

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: $\Nabla V_{\alpha\beta}(b) = dV/db\;\nabla b(\vec r_{\alpha\beta})$.