"
Team:Valencia UPV/prueba
From 2014.igem.org
| Line 8: | Line 8: | ||
<p>The <strong>diffusion equation</strong> is a <a class="emphasize">partial differential equation</a> which describes density dynamics in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive-like behavior, like in our case.</p><br/> | <p>The <strong>diffusion equation</strong> is a <a class="emphasize">partial differential equation</a> which describes density dynamics in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive-like behavior, like in our case.</p><br/> | ||
| + | |||
<p>The equation is usually written as:</p><br/> | <p>The equation is usually written as:</p><br/> | ||
| Line 15: | Line 16: | ||
<p>where ϕ(r, t) is the density of the diffusing material at location r and time t and D(ϕ, r) is the collective <a class="emphasize">diffusion coefficient</a> for <a class="emphasize">density</a> ϕ at location r; and ∇ represents the vector <a class="emphasize">differential operator del</a>.</p><br/> | <p>where ϕ(r, t) is the density of the diffusing material at location r and time t and D(ϕ, r) is the collective <a class="emphasize">diffusion coefficient</a> for <a class="emphasize">density</a> ϕ at location r; and ∇ represents the vector <a class="emphasize">differential operator del</a>.</p><br/> | ||
| + | |||
<p>If the diffusion coefficient does not depend on the density then the equation is linear and D is constant.</p> | <p>If the diffusion coefficient does not depend on the density then the equation is linear and D is constant.</p> | ||
<p>Thus, the equation reduces to the following <a class="emphasize">linear differential equation</a>:</p><br/> | <p>Thus, the equation reduces to the following <a class="emphasize">linear differential equation</a>:</p><br/> | ||
| + | |||
| + | |||
| + | <p>also called the <a class="emphasize">heat equation</a>.</p><br/> | ||
| + | |||
| + | <p>Making use of this equation we can write pheromones chemicals diffusion equation with no wind effect consideration as:</p><br/> | ||
| + | |||
| + | |||
| + | <p>Where C is the pheromone concentration, ∇ is the Laplacian operator, and D is the pheromone diffusion constant in air.</p><br/> | ||
| + | |||
| + | <p>If we consider the wind, we face a diffusion system with drift and an advection term is added to the equation above.</p><br/> | ||
| + | |||
| + | |||
| + | <p><a class="vectorial">v</a> is the average <a class="emphasize">velocity</a> that the quantity is moving. Thus, <a class="vectorial">v</a> would be the velocity of the air flow.</p><br/> | ||
| + | |||
| + | |||
| + | <p></p><br/> | ||
| + | <p></p><br/> | ||
| + | <p></p><br/> | ||
| + | <p></p><br/> | ||
<p></p><br/> | <p></p><br/> | ||
<p></p><br/> | <p></p><br/> | ||
Revision as of 17:09, 24 September 2014
Diffusion
The diffusion equation is a partial differential equation which describes density dynamics in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive-like behavior, like in our case.
The equation is usually written as:
where ϕ(r, t) is the density of the diffusing material at location r and time t and D(ϕ, r) is the collective diffusion coefficient for density ϕ at location r; and ∇ represents the vector differential operator del.
If the diffusion coefficient does not depend on the density then the equation is linear and D is constant.
Thus, the equation reduces to the following linear differential equation:
also called the heat equation.
Making use of this equation we can write pheromones chemicals diffusion equation with no wind effect consideration as:
Where C is the pheromone concentration, ∇ is the Laplacian operator, and D is the pheromone diffusion constant in air.
If we consider the wind, we face a diffusion system with drift and an advection term is added to the equation above.
v is the average velocity that the quantity is moving. Thus, v would be the velocity of the air flow.
