Timeline for What is the most appropriate mathematical theory for electrical circuits?
Current License: CC BY-SA 4.0
18 events
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| Aug 12, 2023 at 14:19 | comment | added | Nabla | Still you are Not getting what I say but I really have No time to discuss it further. My only advice to you would be, try telling the same theory here: electronics.stackexchange.com :) Have a nice day and thanks for deep discussion! | |
| Aug 12, 2023 at 13:59 | comment | added | Yvan Velenik | @Nabla Actually, the title also changed. The original title was "From a mathematical point of view, what are electrical circuits?". This is the question I provided one possible answer to (resistor networks can be essentially identified with reversible Markov chains). | |
| Aug 12, 2023 at 8:01 | comment | added | Nabla | Please read the original post again. | |
| Aug 12, 2023 at 7:57 | comment | added | Yvan Velenik | @Nabla The tags in the original version of the OP included Mathematical-Physics. This includes the theoretical aspects of equilibrium statistical physics, where reversible Markov chains and this particular relation between the latter and resistor networks are important. In fact, there are many papers in Communications in Mathematical Physics on this topic. | |
| Aug 12, 2023 at 7:55 | comment | added | Nabla | In your original post, you are interpreting electrical circuits as a probability theory problem this was my objection. Original poster asked "how can we think electrical circuits in terms of a mathematical model". If you are talking about probability theory since all this time, then your answer is Not related to the original post. | |
| Aug 12, 2023 at 7:53 | comment | added | Yvan Velenik | @And where exactly have I said that it was about EE? My point was, and still is, that resistor networks can be reinterpreted in terms of Markov chains, which is one of the possible answers to the OP. That's all. If you're not interested in it, so be it, but the answer is still perfectly valid in my opinion. | |
| Aug 12, 2023 at 7:51 | comment | added | Nabla | @YvanVelenik Exactly. I was trying to tell this all the time. Your references are meant for Probability Theory and has no practical meaning from Electrical Engineering side. | |
| Aug 12, 2023 at 7:49 | comment | added | Yvan Velenik | @Nabla "what is the practical side of it" The importance of this mapping between resistor networks and Markov chains (as I already mentioned elsewhere in the comments) is mostly of interest in the study of Markov chains. It allows to import intuition from resistor networks (notion of energy, variational problems, effective resistance, the series/parallel/Y-$\Delta$ laws, etc.). This plays a very important role in the theory of reversible Markov chains. As you can see, all the references I mention are books in probability theory, not in EE. | |
| Aug 11, 2023 at 21:43 | comment | added | Nabla | Again, I read it. The distinction must be made. If we are talking about "the probability that the random walk hits some set before some other set." it is not about circuits properties (voltage, current, resistance in this case) but mesh properties. If resistive circuits are deterministic, as you say, then there is no probability about its "electrical" properties but as you are talking "the mesh." I just wanted to clarify this. So a mathematical interpretation of a resisitive circuit cannot be "probabilistic" but its mesh can be. | |
| Aug 11, 2023 at 21:39 | comment | added | Yvan Velenik | @Nabla They are deterministic. The voltage for instance, is directly related to the probability that the Markov chain hits some set before some other set. Once more, please read iinstead of trying to guess… | |
| Aug 11, 2023 at 20:45 | comment | added | Nabla | "In particular, current and voltage acquire natural probabilistic interpretations." if there is no "active" element in a circuit (like a diode), on what sense can resistor, current and voltage be probabilistic? | |
| Aug 11, 2023 at 20:34 | comment | added | Nabla | I have checked it but i still did not understand its practical side. It seems like applying random walk theory to electrical mesh but again what is the practical side of it? That is what i meant by "in practice has no meaning" | |
| Aug 11, 2023 at 20:31 | comment | added | Yvan Velenik | @Nabla I am not talking about a probabilistic approach to resistor networks. Please have a look at the first book I refer to. It’s very easy. | |
| Aug 11, 2023 at 19:18 | comment | added | Nabla | resistor networks are highly deterministic, so a probabilistic approach can be useful in "theory" but in "practice" has no meaning. | |
| Aug 10, 2023 at 19:50 | comment | added | Yvan Velenik | @RayButterworth You're right, that was lazy. I have updated my answer. | |
| Aug 10, 2023 at 19:49 | history | edited | Yvan Velenik | CC BY-SA 4.0 |
References written down explicitly (title + authors)
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| Aug 10, 2023 at 18:12 | comment | added | Ray Butterworth | "this book", "here", "here", and "here" won't be very useful when those links go away, especially as the links themselves don't provide any useful information about title or author. | |
| Aug 10, 2023 at 8:16 | history | answered | Yvan Velenik | CC BY-SA 4.0 |