# Simple 2D random diffusion question (collisions with wall)

• O2F
In summary, the conversation is discussing the process of finding the expectation value for the time it takes for an object to reach the edge of a circular plane while diffusing randomly. The speaker mentions finding the radius and diffusion rate of the plane and suggests looking into the Wiener process for help.
O2F
I am looking at an object that diffuses randomly inside a circular plane.
What is the easiest way to find the expectation value for how long would it take on average to reach the wall if it was initially placed at a random position?

If it is easier: what if the initial position were the center of the circle?

I can find the radius of the plane and the diffusion rate.

The object in reality diffuses continuously, not in discrete steps.

This is quite an annoying recurring problem for me at the moment, any help would be greatly appreciated.

You should have a look on the Wiener process.

## 1. What is simple 2D random diffusion?

Simple 2D random diffusion is a type of motion in which a particle moves randomly in two dimensions due to collisions with other particles or boundaries, such as walls. It is a fundamental process that occurs in many physical and biological systems.

## 2. How does simple 2D random diffusion occur?

In simple 2D random diffusion, particles move in a straight line until they collide with another particle or the boundary of the system. Upon collision, the particle changes direction and continues to move in a new random direction until the next collision occurs.

## 3. What factors influence the rate of simple 2D random diffusion?

The rate of simple 2D random diffusion is influenced by several factors, including the size and shape of the particles, the temperature of the system, and the presence of any obstacles or barriers.

## 4. How is simple 2D random diffusion different from other types of diffusion?

Simple 2D random diffusion differs from other types of diffusion, such as Brownian motion, in that it only occurs in two dimensions and does not involve any specific interactions between particles.

## 5. What are the real-world applications of simple 2D random diffusion?

Simple 2D random diffusion has many real-world applications, including in the study of gas and liquid dynamics, the diffusion of molecules in biological systems, and the movement of particles in aerosols and colloidal suspensions.

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