Rather than use inductors and capacitors to encode time dependence, it uses resistors that are negative valued in the time direction.

The link:

http://westy31.home.xs4all.nl/Electric.html#Harmonic

Gerard

I hope to say a lot more about bond graphs and the ‘signal flow diagrams’ used in control theory in a while… so stay tuned!

]]>Thanks for your reply John; I know you are hyper-busy. Bond-Graphs versus Control-System Block diagram Algebra Transfer Functions was of great interest to me after someone gave me a ‘Mechatronics’ book 20 years ago. I’m not a fan of the name Mechatronics, but is a mainstream term and curriculum at some schools. Thanks again!

]]>Sorry to take so long to reply. We discussed memristors starting here, in the comments to “week290” of This Week’s Finds, which is when I first started talking about bond graphs and analogies between different systems that could be described in terms of

At that point I just reached the point of understanding memristors as one of the natural possibilities for circuit elements that impose a relation between two of those variables

I really should get back to them… but probably when I talk about bond graphs in this network theory series!

]]>I am thinking that the low frequencies (~100 Kyears period) component of the Milankovich cycle (like thermal tides) cannot have Earth origin (geological or meteorological origin); this component (if all is true) can give an indirect measure of the change in the Sun emission for solar inner dynamics, so that can be possible to adjust the solar models to obtain the right oscillation.

]]>I obtain an approximation of the Earth temperature using a Fourier series, with free frequencies.

I init to obtain the least element of the error function.

There is a sea of relative minimun numerical values, and I init to obtain a quick program with L-BFGS that restart when there is a low error reduction, and a restart minimization of a single amplitude (minimization of a component of the gradient), and a restart in a shell neighbourhood.

The Fourier series is:

that is the solution of the differential equation

only when w_n=n w there is the usual Fourier series; when there is a free value then it is possible the forecasting of the temperature.

The free Fourier series is generally not periodic, because the angular frequencies have a irrational ratio.

The data set have a great gaussian noise, it seem me like a tide measure without stilling well, or a measure of local temperature with many local little temperature variations.

I think that can be possible a statistical mean from measure obtained in different earth places, to obtain a noiseless data set.

An analogy exist between tides (correlation with the sun position) and Milankovich cycles, and an other analogy in the measure of the data set, and an analogy in the forecasting.

My last result is (I leave the exponential notation to avoid any mistake in the transcription):

$$

T(t)=2.099191139045127e+05+2.099249038105574e+05*sin(1.164953392315472e-08*t-1.566140720103386e+00)+1.116007988528210e+00*sin(9.064747608422570e-06*t-8.959986469256902e-01)+7.754578008611679e-01*sin(2.873712764994707e-05*t-3.266007780723288e-01)+7.221259974203393e-01*sin(4.069445640197955e-05*t-6.454127975865922e-01)+4.753888139509399e+01*sin(6.005703874771750e-05*t-2.315250501098237e+00)+4.933845696193825e+01*sin(6.025121183483861e-05*t+9.150090656081382e-01)+8.851535098415111e+01*sin(7.985108823049814e-05*t+2.829017517510474e+00)+3.667553662157549e+02*sin(8.076626545516774e-05*t+6.822410238302597e-02)+2.809583376344545e+02*sin(8.105385369731186e-05*t-2.954828626960703e+00)+7.055229620573101e-01*sin(1.165965581933072e-04*t-1.815874437548951e+00)+7.019186730525050e-01*sin(1.237219351987185e-04*t-2.601845819504270e+00)+5.316781725505078e-01*sin(1.370173849863932e-04*t-2.989975152874657e+00)+1.708226369807596e+00*sin(1.548956788610667e-04*t+2.303622440814225e+00)+6.823193383445106e-01*sin(1.605838915565982e-04*t+2.477965212775418e+00)+4.966165946410211e-01*sin(2.072830247925594e-04*t+1.602643423661541e+00)+5.479294929745113e-01*sin(2.178163849748671e-04*t-2.438135638053271e+00)+7.370199085806037e-01*sin(2.680884331995166e-04*t-2.998711439306712e+00)+5.435983052457507e-01*sin(2.770240243989974e-04*t-1.052010026277807e+00)+3.408967729148522e-01*sin(4.315748228691518e-04*t+4.848673574961854e-01)+4.251840695528208e-01*sin(5.453686462715268e-04*t+2.656262240751874e+00)

$$

This is only a step, but if the forecast is optimal, then it is not necessary a Laplace transform

Thanks – fixed!

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