09 Feb 2016
Today I read an interesting article that I am delighted to share with you. These thoughts are written by a prominent (Argentine-American) computer scientist - Gregory Chaitin. It is published by Inference Review:
It is devoted to Author’s baby - the Algorithmic Information Theory (AIT). The issues discussed there should be of interest for any working mathematician. Perhaps, this is my favourite passage from the aforementioned article:
What if we take Gödel incompleteness very seriously and throw away rigor? Suppose you have a property of the prime numbers which has been checked on the computer. You graph it and there is a beautiful curve, and it is fit beautifully by a very simple equation. What if you cannot prove it? A physicist would publish anyway. But a pure mathematician does not care how much empirical evidence there is, or how accurately this simple formula fits the curve. You need a proof!
09 Feb 2016
Today I put on my repository at Github the Matlab sources of a pseudo-spectral full Euler solver on general (smooth) bottoms in 2D. It is based on the method of dynamic conformal mappings proposed by Ovsyannikov in early 70’s. More details can be found at the following URL:
30 Jan 2016
A few days ago, with Delia Ionescu-Kruse (IMAR, Bucharest, Romania) we submitted a study of solitary and cnoidal wave solutions in three different two-component systems:
- The classical Green-Naghdi (GN) model
- A new variant of GN equations (proposed by Delia a couple of years age)
- The two-component Camassa-Holm equations
In our study we describe all possible travelling gravity waves which may arise in that systems:
However, my dear co-author Delia strongly forbade me to share the preprint before it gets accepted to a peer-reviewed Journal. So, please, be patient to see these results.
19 Jan 2016
In this brief post I would like to advertise the notes that I made available recently. In these notes we attempt to introduce the reader to pseudo-spectral methods. The main applications include the heat conduction problems (i.e. parabolic PDEs) since initially the notes were intended for a PhD school on thermal modelling in buildings. The notes cover some other topics such as stochastic approaches (Feynman-Kac) and Trefftz methods which are put into Appendix. If you are interested, you can download the document at this URL address:
12 Dec 2015
I would like to advertise here a general audience article devoted to tsunami waves, which was written by with a modest input from me. You can consult it here:
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