Marc Monticelli

Conférence "Multidimensional symbolic dynamics and lattice models of quasicrystals"

marc — 2024-04-01T07:03:00Z

(Participants)

"The aim of this meeting is to bring together researchers from three a priori distinct fields that have come closer in recent years, but probably not sufficiently so:statistical physics on the lattice Zd and multidimensional symbolic dynamics, which has a strong link with theoretical computer science.
This rapprochement began with the study of the convergence, or the non-convergence of Gibbs and equilibrium measures, when the temperature tends to zero. This work has provided some surprises and raised many questions.
A major goal is to demonstrate the existence of freezing phase transitions giving rise to quasicrystals that are modeled, when d ě 2, by aperiodic Wang tilings, i.e., subshifts of finite type having no periodic configuration. When d “ 1, the subshifts modeling quasicrystals are not of finite type because they cannot be aperiodic. When d “ 2, only numerical experiments attest to the existence of freezing phase transitions.
There are of course other questions that arise, for example the robustness of quasicrystals. We formulate some of them in the main document about scientific content, and one of the goals of this meeting is certainly to bring out new ones.
We believe that the interaction between the three areas mentioned below will feed each of them with new questions.
Keywords:Zd-subshifts in dimension greater than one, Wang tilings, quasicrystals, freezing phase transitions, Gibbs measures, equilibrium states, ground states, Turing machines."

Voir en ligne : https://conferences.cirm-math.fr/30...

Computer experiments and visualization in mathematics and physics. A subjective short walk among some historical examples

marc — 2022-03-22T09:11:00Z

- Articles de culture scientifique

Connaît-on toutes les suites de Barker ?

marc — 2022-03-21T08:54:19Z

Modèles simples du climat (II)

marc — 2020-05-06T14:43:00Z

Modélisation d'une épidémie (partie 2)- Comment les maths aident à la prise de décision

marc — 2020-04-09T08:06:00Z

Modélisation d'une épidémie (partie 1)- Comment les maths aident à la prise de décision

marc — 2020-04-09T07:30:00Z

Nos neurones se synchronisent-ils ?

marc — 2017-07-10T17:02:00Z

Voir en ligne : https://images-des-maths.pages.math...

Automates cellulaires et corrections d'erreurs

marc — 2016-08-26T10:29:00Z

Les neurophysiologistes sont aujourd'hui capables d'enregistrer simultanément l'activité de plusieurs neurones. À partir de ces enregistrements, des méthodes statistiques permettent de détecter les moments où les neurones se synchronisent. Nous présentons succinctement l'une d'entre elles dans cette première partie.

- Articles de culture scientifique

DIFFERENTIAL EQUATIONS - An invitation through embedded visual interactive digital experiments

marc — 2016-07-25T10:32:00Z

http://www.generative-ebooks.com

Extrait de la préface de Cédric Villani :
« ... Going through all these jewels, tapping and stroking the pad as I was testing this ebook, I felt some jealousy for the students who would enjoy this experience and see differential equations coming into life ; a little bit as I felt jealous for my kids when they were discovering classical geometry with GeoGebra. Indeed, this is exactly the same kind of experience that Chazottes and Monticelli are offering you : no magical recipe to make you an expert, but a way to feel and grasp the concepts in a beautifully interactive, flexible and playful way. »

This is the first eBook with embedded interactive digital experiments. They will allow you to visualize the behavior of the equations and models we will study, and to experiment with them. A unique feature of this eBook is that you won't have to write any computer program, nor to install any software, since the digital experiments are embedded into the text.

This eBook focuses on processes that can be mathematically idealized as differential equations. Such equations continue to be a major tool with which scientists make mathematical models of real systems in physics, biology, ecology, chemistry, economy, etc. Even if you can reduce the description of a real system to the mathematical study of a differential equation, this will not be the end of the story because most interesting differential equations are nonlinear. This implies that, most of the time, we are not able to write down the solutions in terms of elementary functions.

Fortunately, qualitative methods were developed, yielding a general idea of how all the solutions behave without actually knowing them explicitly. Such methods were initiated by Henri Poincaré at the end of the 19th century. The main idea is to visualize all solutions of a differential equation at once by considering an appropriate abstract space, to get what is called a 'phase portrait'. The full power of this approach was revealed with the advent of graphics software packages which became widely available from the 1980's onward.

The consequence in teaching differential equations was tremendous since students could see the solutions of a differential equation, thus grasping the overall behavior of the associated model. In particular, using graphics software packages has made possible to teach differential equations to nonmathematically-oriented students primarily interested in modeling.

This revolution has also impacted modern textbooks on differential equations that contain many eye-catching graphics and snapshot views of computer experiments. In some of them, the reader is invited to buy and install a computation package on his/her computer, and use the worksheet files given by the authors.

What we propose here is a major step forward : you simply read the text and interactively experiment with the models within the eBook. We hope you will enjoy this new experience !

Voir en ligne : http://www.generative-ebooks.com

Des canards dans mes neurones

marc — 2015-03-25T09:13:00Z