116 research outputs found
A compact topology for sand automata
In this paper, we exhibit a strong relation between the sand automata
configuration space and the cellular automata configuration space. This
relation induces a compact topology for sand automata, and a new context in
which sand automata are homeomorphic to cellular automata acting on a specific
subshift. We show that the existing topological results for sand automata,
including the Hedlund-like representation theorem, still hold. In this context,
we give a characterization of the cellular automata which are sand automata,
and study some dynamical behaviors such as equicontinuity. Furthermore, we deal
with the nilpotency. We show that the classical definition is not meaningful
for sand automata. Then, we introduce a suitable new notion of nilpotency for
sand automata. Finally, we prove that this simple dynamical behavior is
undecidable
On symmetric sandpiles
A symmetric version of the well-known SPM model for sandpiles is introduced.
We prove that the new model has fixed point dynamics. Although there might be
several fixed points, a precise description of the fixed points is given.
Moreover, we provide a simple closed formula for counting the number of fixed
points originated by initial conditions made of a single column of grains.Comment: Will be presented at ACRI2006 conferenc
Properties of Pseudo-Primitive Words and their Applications
A pseudo-primitive word with respect to an antimorphic involution \theta is a
word which cannot be written as a catenation of occurrences of a strictly
shorter word t and \theta(t). Properties of pseudo-primitive words are
investigated in this paper. These properties link pseudo-primitive words with
essential notions in combinatorics on words such as primitive words,
(pseudo)-palindromes, and (pseudo)-commutativity. Their applications include an
improved solution to the extended Lyndon-Sch\"utzenberger equation u_1 u_2 ...
u_l = v_1 ... v_n w_1 ... w_m, where u_1, ..., u_l \in {u, \theta(u)}, v_1,
..., v_n \in {v, \theta(v)}, and w_1, ..., w_m \in {w, \theata(w)} for some
words u, v, w, integers l, n, m \ge 2, and an antimorphic involution \theta. We
prove that for l \ge 4, n,m \ge 3, this equation implies that u, v, w can be
expressed in terms of a common word t and its image \theta(t). Moreover,
several cases of this equation where l = 3 are examined.Comment: Submitted to International Journal of Foundations of Computer Scienc
Protostellar birth with ambipolar and ohmic diffusion
The transport of angular momentum is capital during the formation of low-mass
stars; too little removal and rotation ensures stellar densities are never
reached, too much and the absence of rotation means no protoplanetary disks can
form. Magnetic diffusion is seen as a pathway to resolving this long-standing
problem. We investigate the impact of including resistive MHD in simulations of
the gravitational collapse of a 1 solar mass gas sphere, from molecular cloud
densities to the formation of the protostellar seed; the second Larson core. We
used the AMR code RAMSES to perform two 3D simulations of collapsing magnetised
gas spheres, including self-gravity, radiative transfer, and a non-ideal gas
equation of state to describe H2 dissociation which leads to the second
collapse. The first run was carried out under the ideal MHD approximation,
while ambipolar and ohmic diffusion was incorporated in the second calculation.
In the ideal MHD simulation, the magnetic field dominates the energy budget
everywhere inside and around the first core, fueling interchange instabilities
and driving a low-velocity outflow. High magnetic braking removes essentially
all angular momentum from the second core. On the other hand, ambipolar and
ohmic diffusion create a barrier which prevents amplification of the magnetic
field beyond 0.1 G in the first Larson core which is now fully thermally
supported. A significant amount of rotation is preserved and a small
Keplerian-like disk forms around the second core. When studying the radiative
efficiency of the first and second core accretion shocks, we found that it can
vary by several orders of magnitude over the 3D surface of the cores. Magnetic
diffusion is a pre-requisite to star-formation; it enables the formation of
protoplanetary disks in which planets will eventually form, and also plays a
determinant role in the formation of the protostar itself.Comment: 18 pages, 11 figures, accepted for publication in Astronomy &
Astrophysic
Basic properties for sand automata
Presented at MFCS 2005 (Gdansk, POLAND). Long version with complete proofs published in Theoretical Computer Science, 2006, under the title "From Sandpiles to Sand Automata".International audienceWe prove several results about the relations between injectivity and surjectivity for sand automata. Moreover, we begin the exploration of the dynamical behavior of sand automata proving that the property of nilpotency is undecidable. We believe that the proof technique used for this last result might reveal useful for many other results in this context
Actes du Symposium International - Le livre, la Roumanie, l’Europe / Proceedings of the International Symposium Books, Romania, Europe - 5ème édition 24-26 septembre 2012
Tome 2 des actes du Symposium International "Le livre, la Roumanie, L\u27Europe" qui s\u27est tenu les 24, 25 et 26 septembre 2012 à Mamaia, Roumanie, organisé par la Bibliothèque Métropolitaine de Bucarest. / Tome 2 of the Proceedings of the International Symposium "Books, Romania, Europe" held on 24, 25 and 26 September 2012 in Mamaia, Romania, organized by the Bucharest Metropolitan Library.
Textes réunis et présentés par :
RĂ©jean Savard
Chantal Stanescu
Hermina G.B. Anghelescu
Cristina Io
Des piles de sable aux automates de sable
In this thesis we study several discrete dynamical systems which can simulate the formation of sandpiles. The behavior of the basic models SPM and IPM(k) is well-known under specific initial conditions. We extend these results to arbitrary initial conditions. Moreover, we introduce the model SSPM which adds symmetry to these models and improves their realism. In the second part, we study another dynamical system, namely sand automata. They are defined similarly to cellular automata, with the constraint that configurations can not contain any "hole˝. These automata can simulate any locally-defined sandpile model, and their solid topological framework allows more general results. We are interested in sand automata dynamics, more precisely in the reversibility properties of sand automata. We conclude by studying the decidability of properties which characterize classical sandpile systems: grain conservation and ultimate periodicity.Dans cette thèse nous étudions différents systèmes dynamiques discrets permettant de simuler la formation des piles de sable. Le comportement des modèles de base SPM ou IPM(k) est bien connu dans des conditions initiales spécifiques. Nous étendons ces résultats à des conditions initiales plus générales, et nous introduisons le modèle SSPM qui ajoute de la symétrie à ces modèles et améliore leur réalisme. Dans un second temps, nous étudions un autre système dynamique, les automates de sable. Ils sont définis de manière analogue aux automates cellulaires, avec la contrainte supplémentaire qu'uneconfiguration n'admet pas de « trous ». Ces automates peuvent simuler tous les modèles de piles de sable définis localement, et à l'aide d'un cadre mathématique solide, ils permettent d'obtenir des résultats plus généraux. Nous nous intéressons à la dynamique des automates de sable, plus précisément aux propriétés de réversibilité d'un automate, et nous étudions la décidabilité de propriétés caractérisant les piles de sable classiques : conservation des grains et périodicité ultime
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