Eric Goles
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Eric Goles has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Ha Duong Phan
LIAFA Université Denis Diderot, Paris 7 - Case 7014-2, Place Jussieu- 75256 Paris Cedex 05-France and Institute of Mathematics, 18 Hoang Quoc Viet, Hanoi, Vietnam
4 shared publications - Michel Morvan
LIAFA, Université Denis Diderot Paris 7 and Institut Universitaire de France, Case 7014-2, Place Jussieu-75256 Paris Cedex, France , FR
4 shared publications - Ivan Rapaport
Universidad de Chile, Santiago, Chile
3 shared publications - Mario Markus
Max-Planck-Institut für molekulare Physiologie, Postfach 500247, 44202 Dortmund, Germany
3 shared publications - Christoph Durr
Laboratoire de Recherche en Informatique Université Paris-Sud 91405 Orsay France
2 shared publications - Eric Rémila
Laboratoire de l'Informatique du Parallélisme, UMR 5668 CNRS-INRIA-ENS Lyon-Univ. Lyon 1, 46 Allée d'Italie, 69364 Lyon Cedex 07, France
2 shared publications
Latest Publications
- 3 January 2003
- Published by Elsevier in Theoretical Computer Science
- Vol. 290 (3) , 1317-1329
Tiling with bars under tomographic constraints
- 3 January 2003
- Published by Elsevier in Theoretical Computer Science
- Vol. 290 (3) , 1317-1329
Tiling with bars under tomographic constraints
- 20 December 2002
- Published by American Physical Society (APS) in Physical Review E
- Vol. 66 (6) , 066214
On-off intermittency and intermingledlike basins in a granular medium
Molecular dynamic simulations of a medium consisting of disks in a periodically tilted box yield two dynamic modes differing considerably in the total potential and kinetic energies of the disks. Depending on parameters, these modes display the following features: (i) hysteresis (coexistence of the two modes in phase space); (ii) intermingledlike basins of attraction (uncertainty exponent indistinguishable from zero); (iii) two-state on-off intermittency; and (iv) bimodal velocity distributions. Bifurcations are defined by a cross-shaped phase diagram.
- 20 December 2002
- Published by American Physical Society (APS) in Physical Review E
- Vol. 66 (6) , 066214
On-off intermittency and intermingledlike basins in a granular medium
Molecular dynamic simulations of a medium consisting of disks in a periodically tilted box yield two dynamic modes differing considerably in the total potential and kinetic energies of the disks. Depending on parameters, these modes display the following features: (i) hysteresis (coexistence of the two modes in phase space); (ii) intermingledlike basins of attraction (uncertainty exponent indistinguishable from zero); (iii) two-state on-off intermittency; and (iv) bimodal velocity distributions. Bifurcations are defined by a cross-shaped phase diagram.
- 1 December 2002
- Published by Springer Nature in Annals of Combinatorics
- Vol. 6 (3) , 327-335
Lattice Structure and Convergence of a Game of Cards
- 1 December 2002
- Published by Springer Nature in Annals of Combinatorics
- Vol. 6 (3) , 327-335
Lattice Structure and Convergence of a Game of Cards
- Open Access
Tiling with bars under tomographic constraints
We wish to tile a rectangle or a torus with only vertical and horizontal bars of a given length, such that the number of bars in every column and row equals given numbers. We present results for particular instances and for a more general problem, while leaving open the initial problem.
Open AccessTiling with bars under tomographic constraints
We wish to tile a rectangle or a torus with only vertical and horizontal bars of a given length, such that the number of bars in every column and row equals given numbers. We present results for particular instances and for a more general problem, while leaving open the initial problem.
- Open Access
The structure of Chip Firing Games and related models
In this paper, we study the dynamics of sand grains falling in sand piles. Usually sand piles are characterized by a decreasing integer partition and grain moves are described in terms of transitions between such partitions. We study here four main transition rules. The more classical one, introduced by Brylawski (1973) induces a lattice structure $L_B (n)$ (called dominance ordering) between decreasing partitions of a given integer n. We prove that a more restrictive transition rule, called SPM rule, induces a natural partition of L_B (n) in suborders, each one associated to a fixed point for SPM rule. In the second part, we extend the SPM rule in a natural way and obtain a model called Chip Firing Game (Goles and Kiwi, 1993). We prove that this new model has interesting properties: the induced order is a lattice, a natural greedoid can be associated to the model and it also defines a strongly convergent game. In the last section, we generalize the SPM rule in another way and obtain other lattice structure parametrized by some t: L(n,t), which form for -n+2 <= t <= n a decreasing sequence of lattices. For each t, we characterize the fixed point of L(n,t) and give the value of its maximal sized chain's lenght. We also note that L(n,-n+2) is the lattice of all compositions of n.Open AccessThe structure of Chip Firing Games and related models
In this paper, we study the dynamics of sand grains falling in sand piles. Usually sand piles are characterized by a decreasing integer partition and grain moves are described in terms of transitions between such partitions. We study here four main transition rules. The more classical one, introduced by Brylawski (1973) induces a lattice structure $L_B (n)$ (called dominance ordering) between decreasing partitions of a given integer n. We prove that a more restrictive transition rule, called SPM rule, induces a natural partition of L_B (n) in suborders, each one associated to a fixed point for SPM rule. In the second part, we extend the SPM rule in a natural way and obtain a model called Chip Firing Game (Goles and Kiwi, 1993). We prove that this new model has interesting properties: the induced order is a lattice, a natural greedoid can be associated to the model and it also defines a strongly convergent game. In the last section, we generalize the SPM rule in another way and obtain other lattice structure parametrized by some t: L(n,t), which form for -n+2 <= t <= n a decreasing sequence of lattices. For each t, we characterize the fixed point of L(n,t) and give the value of its maximal sized chain's lenght. We also note that L(n,-n+2) is the lattice of all compositions of n. - Open Access
Lattice Structure and Convergence of a Game of Cards
This paper is devoted to the study of the dynamics of a discrete system related to some self stabilizing protocol on a ring of processors.
Open AccessLattice Structure and Convergence of a Game of Cards
This paper is devoted to the study of the dynamics of a discrete system related to some self stabilizing protocol on a ring of processors.
- 1 July 2000
- Published by American Physical Society (APS) in Physical Review E
- Vol. 62 (1) , 397-401
Intermingled basins due to finite accuracy
We investigate numerically first a chaotic map interrupted by two small neighborhoods, each containing an attracting point, and secondly a periodically tilted box within which disorderly colliding disks can reach different attracting configurations, due to dissipation. For finite, arbitrarily small accuracy, both systems have basins of attraction that are indistinguishable from intermingled basins: any neighborhood of a point in phase space leading to one attractor contains points leading to the other attractor. A bifurcation destabilizing the fixed points or the disk configurations causes on-off intermittency; the disks then alternate between a “frozen” and a gaslike state.
- 1 July 2000
- Published by American Physical Society (APS) in Physical Review E
- Vol. 62 (1) , 397-401
Intermingled basins due to finite accuracy
We investigate numerically first a chaotic map interrupted by two small neighborhoods, each containing an attracting point, and secondly a periodically tilted box within which disorderly colliding disks can reach different attracting configurations, due to dissipation. For finite, arbitrarily small accuracy, both systems have basins of attraction that are indistinguishable from intermingled basins: any neighborhood of a point in phase space leading to one attractor contains points leading to the other attractor. A bifurcation destabilizing the fixed points or the disk configurations causes on-off intermittency; the disks then alternate between a “frozen” and a gaslike state.
- 1 February 2000
- Published by Elsevier in Theoretical Computer Science
- Vol. 233 (1-2) , 287-295
Source reversal and chip firing on graphs
- 1 February 2000
- Published by Elsevier in Theoretical Computer Science
- Vol. 233 (1-2) , 287-295
Source reversal and chip firing on graphs
- 1 January 2000
- Published by Springer Nature
- p. 214-225
About the Dynamics of Some Systems Based on Integer Partitions and Compositions
- 1 January 2000
- Published by Springer Nature
- p. 214-225
About the Dynamics of Some Systems Based on Integer Partitions and Compositions
- 1 December 1999
- Published by American Physical Society (APS) in Physical Review E
- Vol. 60 (6) , 7182-7185
Shell structures with “magic numbers” of spheres in a swirled dish
Molecular dynamic simulations of a low number of spheres in a swirled dish yield solidlike shell structures with stable rings. In contrast to known granular media, solidification occurs only at singular values of N: 7, 8, 12, 14, 19, 21, 30, 37, 40. Otherwise, we obtain intermittent switching of particles between rings — the average switching time scaling exponentially with a control parameter — or fluidlike disorder. Stable shell structures can be classified by particular geometrical arrangements (one-centered hexagonal, one-centered “quasicircular,” three centered, and four centered).- 1 December 1999
- Published by American Physical Society (APS) in Physical Review E
- Vol. 60 (6) , 7182-7185
Shell structures with “magic numbers” of spheres in a swirled dish
Molecular dynamic simulations of a low number of spheres in a swirled dish yield solidlike shell structures with stable rings. In contrast to known granular media, solidification occurs only at singular values of N: 7, 8, 12, 14, 19, 21, 30, 37, 40. Otherwise, we obtain intermittent switching of particles between rings — the average switching time scaling exponentially with a control parameter — or fluidlike disorder. Stable shell structures can be classified by particular geometrical arrangements (one-centered hexagonal, one-centered “quasicircular,” three centered, and four centered).