Recent content by nkinar

Thanks, I think that you are right about the notation and the substitution.

Okay, thanks Robert; I think that I understand now. Essentially what is required are four unique functions that describe some sort of physical relationship between the required quantities. The key here is that the functions must be different. Once again, thank you.

Ah, okay; what about the following. Suppose that I change the radius r_1,r_2,r_3,r_4, and take samples at four separate distances. Would this qualify as "different enough" to have a system of four non-linear equations? \Delta T(q,k,r,\alpha)= \frac{q}{4 \pi k} E_i \left(...

Okay, thanks for pointing this out, RobertT. I suppose that I have to try something else, as per post #11 or #12 above.

Similar problems for heat conduction are described in James V. Beck and Kenneth J. Arnold's 1977 book, "Parameter Estimation in Engineering and Science." On pg. 434, the authors write, "Without prior information the minimum number of measurements n needed to estimate p parameters is n = p. In...

hotvette, thank you very much for your response. Looking back at the original equation, I would like to determine {a,b,c,d} from a dataset. T(a,b,c,d)= \frac{a}{4 \pi c} E_i \left( \frac{b^2}{ 4 \frac{c}{de}t } \right) The idea that I've been toiling with for quite a...

Thanks, deluks917. I still need to explore the mathematics of this problem further, but I do agree that a root-finding algorithm such as Newton's method may be useful.

Ah, yes - that is a good example of a function where it doesn't work; thanks for posting this, LCKurtz. But I think that if the four outputs g_1,g_2,g_3,g_4 are different and unique, then perhaps optimization could be used. Perhaps uniqueness of the outputs implies that the inputs can be found.

Yeah, I was hoping for something like that as well! ;-) The variable c in the prefactor is also one of the variables. I agree that using an optimization technique seems to be the way to deal with this expression. I'll be able to explore this idea further in the following weeks as I start to...

Sure, CompuChip; thank you very much for your response. Here's an example function: T(a,b,c,d)= \frac{a}{4 \pi c} E_i \left( \frac{b^2}{ 4 \frac{c}{de}t } \right) In the above expression, a,b,c,d are the independent variables, and e,t are known constants. The E_i function is the...

Suppose that I have a function f(a,b,c,d) = g, where {a,b,c,d} are four independent variables and g is the dependent variable. Now let's say that I evaluate the function four times, each time using different inputs, and the function produces four different outputs: f(a_1,b_1,c_1,d_1) = g_1...

I've started to numerically discretize the equations that I've listed in a previous post, but I've run into a difficulty. At each timestep, I need to solve for {p_x,p_y,p_t} , but at the same time I don't know {k_x,k_y, k_t} . Is there some sort of physical basis for calculating...

Hello arildno, Many thanks for your reply! Well, from what I understand, the separation of variables approach simply produces three equations. These equations are then subjected to the application of the Convolutional Perfectly Matched Layer (CPML). So I think that the separation of...

Furthermore, for initial conditions, if p=0, then I think that it might also be possible to assume that k_x = 0, k_y=0, and k_t = 0.

Hello arildno, Looking at this again, I think that you were completely correct with your initial suggestion and I didn't really understand what you were saying. My apologies. The substitution p = p_x p_y p_t is simply a substitution which is mathematically reasonable. I believe that...