Bathtub´s and cellular glass

logo_smallThe bathtub curve is used for many subjects where an estimation of the remaining life is needed. It was used to estimate the best time to change an air conditioning or even to estimate the creep of steel. The last application was the motivation to try this concept on the creep of cellular glass. It was brought to my attention by G. Crevecoeur.

350px-Bathtub_curve.svgThe creep of cellular glass can be very sensitively monitored with the acoustic emission technique (AE) like shown in this paper. There we mentioned that creep on cellular glass can be described with a bathtub curve. We were combining Omori’s law (power law in time) with an exponential, which describes the damage already done in the foam due to the creep and so increasing the load. We found that if we fit the AE-signals with this simple bathtub curve, we can safely describe the mechanical stability of the cellular glass on the long term. Twenty years back, this statement was not really accepted.


godinBut recently, a book appeared on the market about estimating lifetime with AE, with a reference to our paper. Googling the authors brought me to a PhD thesis  about this subject, applied on composite materials. In this thesis, I found power laws and bathtub curves. The bathtub curve was also inspired on Omori´s law for earthquakes but the exponential is rather complicated.

aebath  aepower

220px-Didier_SornetteIn the references, I found also Prof. Didier Sornette. Didier became an expert in the prediction of catastrophes, like earth quakes and financial bubbles. I know him because he was the one who downgraded the above paper from Physical Review Letters to Physical Review. The reason was that we had written in the original paper title “self organized criticality”. Later on, he recognized that earthquakes are self organized critical due to the fractal nature of the tectonic plates like we had argued for the microscopic defects in cellular glass, showing exactly the same statistics.

bakDidier was not really a friend of Per Bak, the inventor of self organized criticality. In fact, Per had a lot of discussions with theoretical physicists like him but he loved experimental guys, which are testing (and hopefully) confirming his theory. When I informed Per about our results, he kindly asked me to publish the data in a high level magazine. Per passed away much too early but he left us a fantastic book: How Nature Works: The Science of Self-socOrganized Criticality. Like acoustics, you need a logaritmic scale to describe the intelligence of people. Per has a few octaves more than most other people.


weversI learned once the tool AE from Prof. Wevers, KU Leuven during a workshop, organized by my (ex-)father in law, Jules Heirman. We collaborated in a few papers about this technique on cellular glass. She was well informed about our interpretation of AE with bathtub curves. Great was my surprise when I discovered the following paper about AE on creep of masonry, interpreted by the bathtub curve, published ten years later than ours. The following picture says everything.


godinThere are generally two kind of bright scientists. The one who recognizes the work of less intelligent industrial scientists and the one who seems to have a blackout about this. Prof. Godin, AE expert in composite materials at Mateis, Lyon, does not know me but refers to our work twenty years later. I must be honnest, my ego got a boost.



Open source software: Python

logo_smallWe are still selecting the right replacement for FORTRAN, because we like to work with a graphical interface (GUI) and to develop new programs in an efficient way. The current speed of ordinary PC’s allow us to work with a script language. In this case, an interpreter reads, translates and executes line by line. Declarations of variables is not needed anymore and debugging is much easier.

pythonOne of the most popular languages today is beyond any doubt Python. It is a 27 years old language, which is object oriented and procedural. In our case, we just want a FORTRAN equivalent. Python is written by  Guido van Rossum, a mathematician from the Netherlands. The blocks in the programs are created with indentation to improve readability of the programs. But on top of that, the Python community has written a huge amount of external commands for mathematics, science, data-mining, etc … . The intelligent language, easy to learn, together with the large amount of external commands makes the language extremely attractive.

220px-Guido_van_Rossum_OSCON_2006The language runs on Windows, Linux, Unix, Android and probably more operating systems. The Internet is full of tutorials and examples with this language. It seems that almost every programmer is a fan.

The language allows to export (import) data to (of) other programs with all kind of file formats. For the physicsts, there are the following exceptional possibilities:

  • SciPy, a package for scientist with plotting possibilities
  • SfePy, a package to solve differntial equations with finite elements.
  • and much more … . We think the best way to start as a scientist is Anaconda.

anacondaWe wish you a nice adventure with Python. And it is true, the writer Guido answers all emails.

Open source software: octave

logo_smallOpen source software was always a point of interest for BELGLAS. Semi professionals work together and generate an equivalent of commercial software. In this case, we discuss GNU Octave, which is an alternative of MATLAB.

100px-Gnu-octave-logo.svgBoth products are used to solve mathematical problems with numerical methods. Everything is based on matrices but standard programming, like done with C and FORTRAN is also included. It is a script language, which means that every command is first interpreted and then executed , contrary to FORTRAN or C, where compiled programs are executed.

downloadDeveloping a solution for a problem goes much faster with this software but execution is slower than with FORTRAN. If a certain solution works well with Octave but execution is too slow, reprogramming partially or completely is an option. The plotting software is also very easy to use and writing or reading data to/from a file is straightforward. A lot of Octave programs are already available in all kind of technical disciplines.

For the interest reader, there is the official website, where you can download the program and I found a tutorial on the internet. Even a more complete handbook could be found next to the official octave manual.

Acoustic absorption with cellular glass

logo_smallAcoustic absorption is a typical open cell foam application like nicely explained in this handbook for acoustics or in this wikibook. In some cases, fibrous materials like mineral wool are not allowed and an open cell foam is chosen. But if also combustibility is an issue, we have to work with a mineral foam. A typical example (and maybe the only one today on the market) is Reapor.

In the datasheet, I found the following absorption spectrum.


absorberThis means that 1m² of this material is equivalent with an open window of 1m² for the noise in a room, which is almost perfect. In another post, we found what was already possible in 1963. In this case, we reach 70% to compare with 100% for the Reapor product.  This means we the 1963 product, you have to install 30% more to obtain the same result. The composition on the Reapor datasheet discloses that the material is in fact foamed bottle glass.

Both products are two steps process. Reapor starts from foamed glass granules, which are sinterd to obtain a irregular structure of small and larger pores. The 1961 process starts from closed cell cellular glass. The cells are opened with hydro-static pressure and the holes are introduced on both sides to improve the absorption.

If a material could be foamed in large boards with 100% open cells and an irregular hole pattern could be introduced during the finishing, we have a one step process, which should be competitive. But today, such a process is still not public domain. Typical (one step) open cell foams have about 70% open cells.