Recent content by re444

I've gone a bit further to get this: (assuming τ=0.5, κ=1, β=2) [SIZE="4"]\frac{\mathrm{d} }{\mathrm{d} S} \int_{0}^{S}\frac{1}{h(x))}dx=\int_{0}^{1}\frac{1}{h(x))}dx \cdot \frac{\mathrm{d} }{\mathrm{d} S} \left ( \sqrt{\frac{K_{r}}{\sqrt{S}}} \right ) \Rightarrow...

In h(x), x is a dummy variable of integration (in calculating K , when the known relation h(S) is available, S is replaced by x in the integrands. So h(x) or h(S) is exactly what we are looking for.

The issue here is in the reverse procedure we don't have any knowledge about the relation between h and x (or in fact h and S), so the integrals could not be calculated. How about this?

Hi every one, Here is my question: In soil physics, knowing the relation between suction head, h, and the soil water content, S, one can derive the hydraulic conductivity, K, of that soil using a formula like: (ignore the superscripts "cap") where in my problem, τ=0.5, κ=1, β=2...

Yes sure, the original PDE is: in which \alpha_{i}s are medium related parameters. The formulation of the characteristic method I'm using is from here. thanks, Reza

Then How should I treat with my problem? Should I test some other methods? How about "Vanishing Viscosity method" ?

Hi everybody, I need to solve a 1st order PDE for my thesis and I'm not a specialist in this field. I've read some texts about this and know one method of solving a 1st order PDE is the method of characteristics. since my equation is nonlinear and a bit complicated, I'm going to solve it...

I want to look at it from Differential Equations point of view. Just consider the last question at the bottom of 1st post.

Hi, hope this is a right place to ask this question. I work in the soil physics field and this problem has taken lots of my energy for a while! let's state it: Unsaturated horizontal water flow in 2 layer soil: we have, M(for Moisture), K (for hydraulic conductivity), h (for hydraulic...

I have yearly rain amounts and want to estimate the rain with 100 year return period assuming different distribution. I know some ways to do with for example normal dist. but it's not general for all pdfs.

Oh ! my obvious fault: a = dV / dt = dV/ (dx / V) = V dV/dx . thanks

Hi, Is this differential equation valid for time independent acceleration" a = dV/dt = dV/ (V dx) = ( dV / dx ) * (1/V) ?

The sketch would be something like this: In each point on the plane, (x,y), there is a gradient vector as you said, 2xi - 2yj . these vectors point to the direction in the function's domain, which the main function has the greatest increase in its value.