Electromagnetic wave-based analogue computing has become an interesting computing paradigm demonstrating the potential for high-throughput, low power, and parallel operations. In this work, we propose a technique for the calculation of derivatives of temporal signals by exploiting transmission line techniques. We consider multiple interconnected waveguides (with some of them being closed-ended stubs) forming junctions. The transmission coefficient of the proposed structure is then tailored by controlling the length and number of stubs at the junction, such that the differentiation operation is applied directly onto the envelope of an incident signal sinusoidally modulated in the time domain. The physics behind the proposed structure is explained in detail and a full theoretical description of this operation is presented, demonstrating how this technique can be used to calculate higher order or even fractional temporal derivatives. We envision that these results may enable the development of further time domain wave-based analogue processors by exploiting waveguide junctions, opening new opportunities for wave-based single operators and systems.
I am happy to announce that I have been awarded a new EPSRC grant – technically it is UKRI & RCN (Research Council of Norway) project – UKRI-RCN: Exploiting the dynamics of self-timed machine learning hardware (ESTEEM).
I am very excited to work on it with my two Newcastle colleagues Rishad Shafik and Domenico Balsamo, Uni of Agder colleague Ole-Christoffer Granmo, and in close collaboration with PragmatIC, Mignon and CFT.
I had a pleasure to present a keynote talk at the 13th International Conference Dependable Systems, Services and Technologies (DESSERT 2023), held in Greece, Athens, October 13-15, 2023, in a hybrid mode.
Victor Ilyich Varshavsky was born today, on 23rd February, 90 years ago. Victor Varshavsky is a pioneer of automata theory, aperiodic (aka self-timed) circuits and systems https://en.wikipedia.org/wiki/Asynchronous_circuit, and collective behaviour of automata. In the 1960s, being a close colleague and friend of Mikhail Tsetlin, Victor laid foundation to the theory of learning automata and machine intelligence, which find their way today to modern methods of machine learning – such as Tsetlin Machine: https://en.wikipedia.org/wiki/Tsetlin_machine
Last week I gave a public lecture “”Data-driven computing (or Liberating computing from memory walls)”, at Technical University of Vienna, Austria, where I am acting as Guest Professor for 2022.
The lecture was on my relatively recent ideas of bringing machine learning into computing at different scales and levels of abstraction, basically making it a commodity that can be introduced for improving the quality of computing from many aspects, in particular performance and use of energy.
Together with Alex Ventisei and Victor Pacheco-Pena, we recently published a paper that for the first time connects the world of electromagnetic waves with the graphical modelling language of Petri nets. https://onlinelibrary.wiley.com/doi/10.1002/adts.202100429
Petri nets are known to capture in a very natural for comprehension form ideas of causality, concurrency and choice. The way how the Petri nets primitives – transitions (bars or boxes), places (circles), flow relation between them (arcs between places and transitions and between transitions and places), and marking of places (tokens) – can ‘speak’ in the languages of EM pulses propagating in transmission lines and interacting in their cross-points is quite interesting. For example, firstly, due to the fact that EM or to be precise TEM pulses cannot wait for each other in the points of crossing, is expressed in the corresponding Petri nets by the fact that we have not multiple incidence of flows on the same transition. In other words, we cannot have AND causality in TEM switching structures. On the other hand, secondly, due to the physical superposition of TEM pulses travelling from different sources, we have a pure effect of OR causality, manifested itself in the Petri nets having multiple incidence of flows of tokens on the same place. Thirdly, the fact that pulses are propagated and reflected in the points of crossing according to the proportions dictated by the impedance rations, represented by the scattering matrices, is manifested in the Petri net model by the corresponding fractioning and additions of tokens in places standing for these pulse interactions.
The type of Petri nets characterising TEM pulse interaction is fairly unique and is worthy separate investigation. For example, the EM nature of information flow in such structures has the property of reciprocity, i.e. the ‘execution runs’ in these processes can be played back to the original states, and hence the modelling Petri nets possess a certain notion of reversibility. In his PhD study, Alex Ventisei, is planning to advance this modelling work further to capture more complex structures of TEM pulse interactions, and complement the existing methods of modelling based on scattering matrices with graphical models using such Petri nets, as well as develop some simulation and analysis tools.
About a year or so ago, I had an interesting email exchange with Dave Walton about photon size and how photon can be seen as a form of energy current extracted from an atom, much like a pulse or pulse train is generated when we discharge a capacitor …
An example of the demonstration that quantum physics is NOT the way to explain physics. Here is a story about lasers from Electronics Weekly:
+++++++++++++++++++++++++++++++++++ “Markus Pollnau, Professor in Photonics at the University of Surrey, said: “Since the laser was invented in 1960, the laser spectral linewidth has been treated as the stepchild in the descriptions of lasers in textbooks and university teaching worldwide, because its quantum-physical explanation has placed extraordinary challenges even for the lecturers.
“As we have explained in this study, there is a simple, easy-to-understand derivation of the laser spectral linewidth, and the underlying classical physics proves the quantum-physics attempt of explaining the laser spectral linewidth hopelessly incorrect. This result has fundamental consequences for quantum physics.””
++++++++++++++++++++++++++++++++++
Dave Walton:
I have puzzled for some time over two simple questions:
1. How long is a photon?
2. Why is the wavelength of light so much longer than the physical size of an atom.
As far as question 1 is concerned, the authors of this paper seem to be seeing the photon as a truncated sine wave which leads to its finite spectral width when expressed as a Fourier transform. This can lead directly to a calculation of photon length.
Question 2 is a puzzle to me. As engineers we are familiar that the size of an effective antenna must be of the order of the radiated wavelength. (1/4 wave or 5/8 wave etc). But the atom is much smaller than the wavelength of emitted light. The type size of an atom is 5×10^-10 m, but the wavelength of light is of the order of 5 x 10^-7 m, which is a factor of 1000 times larger. So how does it succeed in being such an efficient radiator?
Of course, Quantum Theory does not address these questions at all. It simply states that the ‘Quantum Jump’ happens, and we cannot dissect it any further.
Alex Yakovlev:
I like both of your questions a lot.
Questions about real physical size dimensions are most pertinent if we think about energy current propagating in space (but how else to think?!).
Quantum Theory does not seem to address the dynamics of energy in real space, succumbing to abstract transitions between states in phase (state) space.
Reading your points regarding these questions is fascinating. Re: Q2, in particular, it begs for something like the sine wave period (i.e., wavelength) can only be 1000 longer than the atom IFF this sine wave is constructed of many (order of 1000 or so) steps, each the size of the atom, and each such step is the time of flight of the ExH current travelling between the ‘walls of the atom’. Pretty much like we have the time constant of the capacitor charge (discharge) exponential via resistor R, where the cap is a TL.
Isn’t it?
So, generally all these different wavelengths, can they be the result of the epsilon/mu (i.e. characteristic impedance of the medium) plus sizes of the unit of space that generates the light producing the sine wave in a manner similar to an L&C TL?
Perhaps, we can derive the period of the sine wave for the case of the L&C pair of TL? and this way determine the length of photon?
Dave Walton:
Very Interesting Alex.
It is amazing how the obvious can escape one for so long, but I had honestly never considered a transmission line model for the atom (!!).
Given the factor of 1,000 between the atomic diameter and the wavelength of the photon, this would suggest about 1000 transitions before all of the energy current escapes. This suggests a reflection coefficient of the same order, i.e., 1/1000.
The next questions would seem to be,
1. What is the energy current arrangement in the atom?
2. How exactly do these arrangements change during the process of emission?
I would be very interested to hear your thoughts on these and other issues which arise.
Alex Yakovlev:
Just to clarify, if we have 1000 steps for one swing of the wave (or exponential) between High and Low, should not the reflection be a complement, i.e., 999/1000.
That is basically to say that the characteristic impedance of the internals of the atom is 1000 times smaller than the ohmic impedance of the interface, right?
Shows quite an opposite effect where the TL is so long that the time of flight in TL is twice that of the time constant of the equivalent RC circuit. Here, despite the fact that the reflection coefficient is even negative, the step is commensurate with the time constant. So, this is probably the effect of the capacitance of the TL being relatively small.
So, we somehow, need to take into account not only the Z0 vs R ratios, but also C as a function of the length and epsilon, which in the atomic case needs to be relatively large compared to ordinary coax like TLs. For the atom, we probably talk about much higher C per size unit, i.e., very high epsilon, right?
Incidentally, can we also calculate the frequency/clock period of the TL-based LC circuit? Was it your or Mike Gibson’s derivation of the sinewave for the TL-based LC oscillator? In Ivor’s Electromagnetics 1 book, I cannot find the frequency-period parameters of the sine wave, so we could work out some likely L and C values for the atom.
Your Qs:
1. What is the energy current arrangement in the atom?
That is a good question. If we think about 3D this might be some kind of cube with the Poynting vector rotating around the nucleus, with E directed radially and H azimuthally?
2. How exactly do these arrangements change during the process of emission?
What would trigger emission? some sort of window opening so that the sine wave will be radiate out?
Alex Yakovlev, continued:
Just played a bit with numbers.
Suppose we play with a cap model of the atom, and we’d like to find the length unit C, bearing in mind that the exponential’s time constant tau should be 1000 that of the step.
The key equation is
RC*l = 1000*l/c
R is the resistance of discharge
C is unit length cap
l is length
c is speed of light in the medium, let’s say 2*10^8 m/s
eliminating l, we have
RC=1000/c,
suppose R=1000Ohm.
We have C=1/c=5nF/m
Does it sound reasonable?
Suppose we use the parallel plate cap model:
C=eps*(w/a), where w is width and a is distance between the plates.
What should they be?
Suppose the ratio between w and a, w/a is 5000.
This means that our eps then must be 10^(-12), does it sound realistic?
In vacuo, I think eps0 is about that order, 8.85*10^(-12).
Dave Walton:
Yes, the numbers do seem reasonable, but would you agree that the real challenge is to understand (or at least model) how the energy current distribution changes when a photon is emitted. This should ultimately lead to the undemanding of the probability distribution in the orbitals.
This is tough.
Alex Yakovlev:
Dave,
This is puzzling.
Assuming that the atom is an LC loop with distributed parameters and a normally closed door, then it emits a photon in the form of an exponential/sine wave section. What then happens? My knowledge of atomic physics is rusty and weak. But presumably the aperture and interval of door opening depends on some external factors, right?
It’s a bit like we control the switch (externally) for a TL when the energy current comes out during the discharge process. Can we extract energy from Capacitive or LC-ive by portions – sections of exponential or chunks of sine wave?
I am pretty sure there should be a deterministic model – or at least one based on some sort of histograms of frequencies of spending time in different states – rather than purely stochastic probability model.
On a slightly different yet related side:
It seems that with energy current trapped in units like atoms or TLs, we have to deal with the two levels of dynamics:
1) higher frequency one – which is concerned with the vacillating TEM inside the atom or TL – basically where the step or period is determined by the eps and mu parameters and the geometry of the atom/TL
2) lower frequency one – which is concerned with some macro-elements – like resistors and switches that are controlled outside – these are parameters like time constants of charge/discharge exponentials or periods of sine waves.
Interestingly, that (1) is about the level of 100s of THz – that close to infrared and higher frequency light – people seem to know how to sense it at the level of photonic materials
(2) is the modern analogue electronics – with lumped LC loop antennas – somewhere up to 100 GHz.
What’s between is some sort of dead zone – a gap (between materials level and circuits level), where not much can be done.
This is my own perception, maybe I am wrong. I wonder what you think about it.
Some people object the idea of reciprocating ExH waves in a charged capacitor because they claim that then we should have ohmic losses. Why?
Why should we associate the emergence of ohmic losses with the basic ExH energy current propagation. At this level there is no point to talk about ohmic losses because at this level we have no idea about any charge movement, i.e. no electric current is defined here. It’s all about EM energy current. Ohmic losses need only be considered at the level of the superposition of Electric and Magnetic fields, i.e. at the level of V and I values in a particular place in space and a particular point in time. If we take any of Wakefield experiments, we can find in them an interval of time at a certain place where the odds of overlap of two reciprocating waves are such that they produce no current (i.e. the cumulative effect on magnetic field is zero), so there are ohmic losses here and then. This does not however preclude the two ExH waves to move in opposite directions.
With fervent drive for neuromorphism in computing and generally in science, the whole engineering science seems to follow human-centric views upon many natural phenomena. There is a tremendous shift towards pretending that we should see the world from the so called bio-inspired position. Models are increasingly been selected as to their applicability to explaining experimental evidence on the principles of human-oriented ‘voting mechanism’.
That can only get worse as people are increasingly living in virtual reality.
With the massive advent of AI and ML we are rapidly moving towards the society where quick pattern recognition (according to the accepted canons, textbooks and all kinds of lookup tables) is trained, tested and rewarded.
Engineers are commonly regarded as good if they can quickly look up the bag of available models and tools and identify the right one to apply.
Any attempt to be doubtful or suspicious, or even discard the canon for a completely new way of expression is penalised by the Pharisees of the society appointed by the society to be its so called “Scientific Advisors”.
Anglo-American culture is particularly characteristic of that – with its love for all kinds of pub quizzes, TV game shows, praising for quickly detecting and nodding to quick recognition of soup opera catch-phrases, quoting Bob Hope or aphorisms and what not. Including of course, pretence to be intellectual by showing off in using Latin or French expressions … As long as nothing is going deep into understanding of the English or let alone any foreign language grammar (why bother with that if you can simply build your sentences out of phrasal verbs of which English is so rich), or even deeper learning and thinking in different languages.
So, whether the members of this society want to be unique or original when moving into science or other intellectual activity forms, they remain apples that don’t fall far from their trees.
