Random and Monte Carlo

Question 1

What is the caracteristic of pseudo-random numbers ?

Answer 1

The are determined by the previous ones

Question 2

Cite a famous pseudo-generator

Answer 2

Modulo Generator : x_i =(ax_i-1+c) mod m

Question 3

How can we generate a non uniform distribution ?

Answer 3

First by generating N unrelated random number => not efficient.
Or by creating a function to fit that distribution from random numbers

Question 4

What is proportional to the variance ?

Answer 4

The uncertainty

Question 5

What is the concept of the Monte Carlo Method ?

Answer 5

Add a weight function that acts as f does (big when big)

Question 6

Quadratic Monte Carlo Method can be demonstrated using ?

Answer 6

Variable change and limit integral<=>sum

Question 7

What should respect MD integration ?

Answer 7

Accuracy in O(\Delta t^4) and 1 force calculation only

Question 8

What is the base formula of the Verlet Method ?

Answer 8

r(t+\Delta t) = 2 r(t) - r(t-Delta t) + f(t)/m (\Delta t)^2

Question 9

What is the issue with the Verlet base method a method ?

Answer 9

Big number == acc loss

Question 10

What is the Leap-frog Vert Method ?

Answer 10

compute r(t+\Delta t)) and v(t+\Delta t/2)

Question 11

What is the Verlet Velocity Formula ?

Answer 11

v(t) = (r(t+\∆t)-r(r-∆t))/2∆t-∆t/12m*[f(t+∆t)-f(t-∆t)]+O(∆t^4)