Distribution between non-linear branches

In summary, the conversation discusses how to calculate currents in circuits with non-linear resistances, specifically in a network with 3 low-value linear resistances and two 3rd order polynomial devices. The question is whether there is a mathematical solution or if a successive approximation approach is necessary. The suggested solution involves using two cubic functions and a constant to solve for x, with the result being a polynomial with powers of 6.
  • #1
Roger44
80
1
Hello

My question could be about bars and litres/sec but I'll express it as volts and ampères, mathematically it's the same puzzle for me. How do you calculate the currents in circuits when there are devices whose resistances are not linear?
In the following network there are 3 low value linear resistances and two 3rd order polynomial devices whose functions are :

V1 = 0.24 x I1^3 - 0.3 x I1^2) + 0.98 x I1 + 3.72
V2 = 0.07 x I2^3 - 0.02 x I2^2) + 0.16 x I2 + 1.57

No mathematical solution other than a successive approximation approach?

Thanks for your help.

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  • #2
You have two cubic functions f and g, and two constant R and V, and you wish to solve
f(i1)=g(i2), f(i1)+R(i1+i2) = V. Yes?
Writing x = i1,
f(x) = g(V/R-f(x)/R-x)
Expanding that will give a polynomial with powers of 6.
 

FAQ: Distribution between non-linear branches

What is distribution between non-linear branches?

Distribution between non-linear branches refers to the allocation of resources or data between different branches or paths in a non-linear system. This can include distribution of information, materials, or energy.

Why is distribution between non-linear branches important?

Distribution between non-linear branches is important because it allows for efficient utilization of resources in a complex system. It ensures that each branch receives the necessary resources to function properly and prevents one branch from becoming overloaded while others are underutilized.

How is distribution between non-linear branches determined?

The distribution between non-linear branches is typically determined through mathematical models and simulations. These models take into account various factors such as the capacity of each branch, the flow of resources, and the desired output of the system.

What are some examples of non-linear systems with distribution between branches?

Some examples of non-linear systems with distribution between branches include computer networks, transportation systems, and biological organisms. In these systems, information, goods, or nutrients are distributed between different branches to achieve a specific goal or function.

What challenges can arise in distribution between non-linear branches?

Some challenges that can arise in distribution between non-linear branches include imbalances in resource allocation, unexpected changes in the system, and difficulties in accurately modeling the system. These challenges can lead to inefficiencies, delays, and even system failures.

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