Diffusion

Question 1

Diffusion equation

Answer 1

dP/dt = Dgrad^2(P)

Question 2

What is diffusion

Answer 2

a kinetic process that leads to homogenization of a solution

Question 3

Laplace operator

Answer 3

grad^2

Question 4

covariance of noise

Answer 4

= 2Ddelta(ab)delta(t-t’)

Question 5

brownian motion exact form and forces

Answer 5

m(d^2x/dt^2) = -(1/mu)(dx/dt)-(dV/dx)+fr(t)

3 forces

1) friction force in low reynold number limit (mu = 6pi(specific viscosity)*R)^-1
2) force due to external potential V
3) random force (fr) due to particle impacts

Question 6

brownian motion, simplified

Answer 6

usually overdamped

dx/dt = -v(x)+nu(t)

v = -mu*dV/dx
nu= mu*fr(t)

Question 7

einstein relation for diffusion

Answer 7

D =kbTmu

mu = dynamic viscosity

Question 8

markov process

Answer 8

random process where future is independent of past

Question 9

markov chain

Answer 9

the future state only depends upon the current state (it’s a probability calculation

Question 10

ergodic

Answer 10

will reach all points in the system

Question 11

bayes theorem

Answer 11

P(A|B) = P(B|A)*P(A)/P(B)

Question 12

basic def of a random walk

Answer 12

can travel in all directions with equal probability