## Plural Form

Take a figure of a historical patent, meticulously drawn before there was software. It’s a Plural Grating Spectrograph. Wonder about the appeal of antique technical drawings. So modest, so sublime. Copy it, multiply it. Slowly rotate the color wheel, until the purples meet the reds again. This is an impossible spectrum. There are no purples…

## Tribute to a Pragmatic Swiss Solar Pioneer – Who Called to Action in 1989

He is called a pragmatic doer, knowing his physics and engineering, devoid of ideology. This is how Josef Jenni is introduced in the preface to his document called How can we achieve the energy transition (Wie erreichen wir die Energiewende). It’s a manifesto and a technical overview – by the pioneer whose company had built…

## Jellyfish of Diffraction

Diffraction patterns, again. But this time I tack them to an imaginary semi-circular screen. Screens grow bigger in radius with increasing wavelength – growing more reddish. If every wavelength would be diffracted in the same way, all peaks would lie on a radius of the circle. But as red is diffracted more, maxima move to…

## Creative Process. Evolution.

My creative process has been evolving gradually in the past year. ~ I am thinking about a little piece of physics, and how it is described with math. ~ Then I am creating a SageMath notebook (plus custom code) that outputs a set of functions as parametric curves in a three-dimensional space. Here, diffraction patterns…

## Newton’s Space Probes Investigate my Ribbons of Diffraction

I have been calculating diffraction patterns for visible light. Curves are displaced to turn the whole structure into a wavy ribbon built from colored wires or threads. I have turned these images into collages, adding Isaac Newton’s drawings from Opticks (1704). The more I moved Newton’s figures around, and the more I twisted the ribbons…

## Vintage Covectors

Covectors in the Dual Space. This sounds like an alien tribe living in a parallel universe hitherto unknown to humans. In this lectures on General Relativity, Prof. Frederic Schuller says: Now comes a much-feared topic: Dual vector space. And it’s totally unclear why this is such a feared topic! A vector feels familiar: three numbers…

## Dirac’s Belt Trick

Is classical physics boring? In his preface to Volume 1 of The Feynman Lectures on Physics, Richard Feynman worries about students’ enthusiasm: … They have heard a lot about how interesting and exciting physics is—the theory of relativity, quantum mechanics, and other modern ideas. By the end of two years of our previous course, many…

## Motivational Function

Deadly mutants are after us. What can give us hope? This innocuous-looking function is a sublime light in the dark. It proves you can always recover. If your perseverance is infinite. As x tends to zero, the exponent tends to minus infinity. The function’s value at zero tends to zero. It is a zero value…

## Heat Conduction Cheat Sheet

I am dumping some equations here I need now and then! The sections about 3-dimensional temperature waves summarize what is described at length in the second part of this post. Temperature waves are interesting for simulating yearly and daily oscillations in the temperature below the surface of the earth or near wall/floor of our ice/water…

## Consequences of the Second Law of Thermodynamics

Why a Carnot process using a Van der Waals gas – or other fluid with uncommon equation of state – also runs at Carnot’s efficiency. Textbooks often refer to an ideal gas when introducing Carnot’s cycle – it’s easy to calculate heat energies and work in this case. Perhaps this might imply that not only must the…

## Computers, Science, and History Thereof

I am reading three online resources in parallel – on the history and the basics of computing, computer science, software engineering, and the related culture and ‘philosophy’. An accidental combination I find most enjoyable. Joel on Software: Joel Spolsky’s blog – a collection of classic essays. What every developer needs to know about Unicode. New terms…

## Tinkering, Science, and (Not) Sharing It

I stumbled upon this research paper called PVC polyhedra: We describe how to construct a dodecahedron, tetrahedron, cube, and octahedron out of pvc pipes using standard fittings. … In particular, if we take a connector that takes three pipes each at 120 degree angles from the others (this is called a “true wye”) and we…

## Spheres in a Space with Trillions of Dimensions

I don’t venture into speculative science writing – this is just about classical statistical mechanics; actually about a special mathematical aspect. It was one of the things I found particularly intriguing in my first encounters with statistical mechanics and thermodynamics a long time ago – a curious feature of volumes. I was mulling upon how…

## You Never Know

… when obscure knowledge comes in handy! You can dismantle an old gutter without efforts, and without any special tools: Just by gently setting it into twisted motion, effectively applying ~1Hz torsion waves that would lead to fatigue break within a few minutes. I knew my stint in steel research in the 1990s would finally…

## Ploughing Through Theoretical Physics Textbooks Is Therapeutic

And finally science confirms it, in a sense. Again and again, I’ve harping on this pet theory of mine: At the peak of my immersion in the so-called corporate world, as a super-busy bonus miles-collecting consultant, I turned to the only solace: Getting up (even) earlier, and starting to re-read all my old mathematics and…

## Simulating Peak Ice

This year ice in the tank was finally melted between March 5 to March 10 – as ‘visual inspection’ showed. Level sensor Mr. Bubble was confused during the melting phase; thus it was an interesting exercise to compare simulations to measurements. Simulations use the measured ambient temperature and solar radiation as an input, data points…

## Earth, Air, Water, and Ice.

In my attempts at Ice Storage Heat Source popularization I have been facing one big challenge: How can you – succinctly, using pictures – answer questions like: How much energy does the collector harvest? or What’s the contribution of ground? or Why do you need a collector if the monthly performance factor just drops a…

## On Photovoltaic Generators and Scattering Cross Sections

Subtitle: Dimensional Analysis again. Our photovoltaic generator has about 5 kW rated ‘peak’ power – 18 panels with 265W each. Peak output power is obtained under so-called standard testing condition – 1 kWp (kilo Watt peak) is equivalent to: a panel temperature of 25°C (as efficiency depends on temperature) an incident angle of sunlight relative to…

## Learning General Relativity

Math blogger Joseph Nebus does another A – Z series of posts, explaining technical terms in mathematics. He asked readers for their favorite pick of things to be covered in this series, and I came up with General Covariance. Which he laid out in this post – in his signature style, using neither equations nor…

## Re-Visiting Carnot’s Theorem

The proof by contradiction used in physics textbooks is one of those arguments that appear surprising, then self-evident, then deceptive in its simplicity. You – or maybe only: I – cannot resist turning it over and over in your head again, viewing it from different angles. tl;dr: I just wanted to introduce the time-honored tradition…

## Rowboats, Laser Pulses, and Heat Energy (Boring Title: Dimensional Analysis)

Dimensional analysis means to understand the essentials of a phenomenon in physics and to calculate characteristic numbers – without solving the underlying, often complex, differential equation. The theory of fluid dynamics is full of interesting dimensionless numbers –  Reynolds Number is perhaps most famous. In the previous post on temperature waves I solved the Heat…

## Temperature Waves and Geothermal Energy

Nearly all of renewable energy exploited today is, in a sense, solar energy. Photovoltaic cells convert solar radiation into electricity, solar thermal collectors heat hot water. Plants need solar power for photosynthesis, for ‘creating biomass’. The motion of water and air is influenced by the forces caused by the earth’s rotation, but by temperature gradients…

## Lest We Forget the Pioneer: Ottokar Tumlirz and His Early Demo of the Coriolis Effect

Two years ago I wrote an article about The Myth of the Toilet Flush, comparing the angular rotation caused by the earth’s rotation to the typical rotation in experiments with garden hoses that make it easy to observe the Coriolis effect. There are several orders of magnitude in difference, and the effect can only be…

## An Efficiency Greater Than 1?

No, my next project is not building a Perpetuum Mobile. Sometimes I mull upon definitions of performance indicators. It seems straight-forward that the efficiency of a wood log or oil burner is smaller than 1 – if combustion is not perfect you will never be able to turn the caloric value into heat, due to…

## How to Evaluate a Heat Pump’s Performance?

The straight-forward way is to read off two energy values at the end of a period – day, month, or season: The electrical energy used by the heat pump and the heating energy delivered. The Seasonal Performance Factor (SPF) is the ratio of these – the factor the input electrical energy is ‘multiplied with’ to…

## A Sublime Transition

Don’t expect anything philosophical or career-change-related. I am talking about water and its phase transition to ice because … …the fact that a process so common and important as water freezing is not fully resolved and understood, is astonishing. (Source) There are more spectacular ways of triggering this transition than just letting a tank of water…

## Being Creative with What Is Available

This is a quote from Simon Dale’s website who has built several eco-friendly ‘Hobbit’ houses. It reminded me of the cave house built into lava bubbles by Lanzarote’s most famous artist César Manrique: Being creative with what is available has an appeal beyond economical necessities. As a teenage hobby astronomer I built a mounting for…

## On Learning

Some years ago I was busy with projects that required a lot of travelling but I also needed to stay up-to-date with latest product features and technologies. When a new operating system was released a colleague asked how I could do that – without having time for attending trainings. Without giving that too much thought, and having my…

## What Learning about Feynman’s Path Integrals Was Good for

I have gone to great lengths on this blog in order to explain how and why a degree in physics prepares you for seemingly different careers, or at least does not hurt. But it would have been so simple. I will now illustrate this – using just two incomprehensible images. Actually, I have a hidden…

## Grim Reaper Does a Back-of-the-Envelope Calculation

I have a secondary super-villain identity. People on Google+ called me: Elke the Ripper or Master of the Scythe. [FAQ] No, I don’t lost a bet. We don’t have a lawn-mower by choice. Yes, we tried the alternatives including a reel lawn-mower. Yes, I really enjoy doing this. It is utterly exhausting – there is no…