1
vote
0answers
15 views

Derivation of the advection equation

Is there a good derivation of the advection equation available online? By that I mean the equation $\partial_t u = -\nabla( \vec{v} u)$ I know a good explanation for the one-dimensional case ...
-2
votes
2answers
64 views

mathematical biology (steady-states)

non-dimensionalisation equation: \begin{equation} \frac {du}{d\tau}=\frac{\overline{\lambda}_{1} u}{u+1} -\overline{r}_{ab}uv -\overline{d}u \end{equation} where $\overline{\lambda}_{1}= \frac ...
0
votes
0answers
52 views

Mathematical Biology and modelling

Consider the two species competition model given by $$ \frac{da}{dt }= \frac {λ_1 a} {a+K_1} - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= λ_2 b (1-\frac{b}{K_2}) - ...
0
votes
1answer
89 views

Mathematicals biology

Consider the two species competition model given by $$ \frac{da}{dt }= [λ_1 a /(a+K1)] - r_{ab}\cdot ab - da, \ \ \ \ \ \ \ \ \ \ (1)$$ $$\frac{db}{dt }= [λ_2 b *(1-b/K2)] - r_{ba}\cdot ab , \ ...
2
votes
2answers
84 views

Why don't elliptic PDE's have a time coordinate?

Usually second-order linear PDE's are classified as elliptic, parabolic, or hyperbolic (or ultrahyperbolic) depending on the eigenvalues of the coefficient matrix. The three cases correspond to the ...
3
votes
0answers
121 views

How to solve the advection equation with spiral motion

The advection equation is : $$\frac{\partial f(x,y,t)}{\partial t} + \nabla_{(x,y)} \cdot (A f)= 0$$ With initial condition $f(x,y,0) = f_0(x,y)$. If the vector $A$ is constant, ie. $A = ...
0
votes
1answer
228 views

Relationship between Turing bifurcation, saddle-node bifurcation, and Hopf bifurcation?

Quoting from http://jxshix.people.wm.edu/2009-harbin-course/mississippi-bifurcation-2.pdf a Turing bifurcation occurs when for an ODE and related PDE $u' = f(u,v), v' = g(u,v)$ $u_t = d_1 \nabla ...
1
vote
0answers
118 views

Should I get the absolute value of the result of the inverse discrete fourier transform?

The result of equation 36 can be positive and negative.And if I don't get the absolute value of it,the ocean surface tend to be very regular.But according to the paper,the author never get the ...
1
vote
1answer
312 views

Complex results in inverse Fourier transform for simulating ocean water

I don't understand the equation37 in simulate ocean water by Jerry Tessendorf.The result is all complex number, how to be the slope.Even if I compute the magnitude of it,the result is just positive ...
2
votes
2answers
338 views

How to determine units in a partial differential equation

How do we determine the units used in a differential equation? Yes, in theory a PDE has nothing to do with units, but I'm interested in this question from a modeling point of view. By units, I mean ...
1
vote
1answer
282 views

Heat Equation Derivation and Mean Value Theorem

Farlow book PDEs for Scientists and Engineers pg. 27 shows derivation for Heat Equation. It starts by stating Net change of heat inside $[x,x+\Delta x]$ = Net flux of heat across boundaries + Total ...
1
vote
2answers
142 views

How to model multi-step cell differentiation

Can I better explain cell lineages using PDEs or stochastic?