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Team:Valencia UPV/prueba
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<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/> | ||
| - | |||
| - | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | <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>Thus, the equation reduces to the following <a class="emphasize">linear differential equation</a>:</p><br/> | ||
| + | <p></p><br/> | ||
| + | <p></p><br/> | ||
| + | <p></p><br/> | ||
| + | <p></p><br/> | ||
| + | <p></p><br/> | ||
</div> | </div> | ||
</br></br></div> | </br></br></div> | ||
Revision as of 16:55, 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:
