Showing papers by "Jean-Pierre Eckmann published in 2005"
TL;DR: In this paper, the authors consider simulations of a two-dimensional gas of hard disks in a rectangular container and study the Lyapunov spectrum near the vanishing Lipschitz exponents.
Abstract: We consider simulations of a two-dimensional gas of hard disks in a rectangular container and study the Lyapunov spectrum near the vanishing Lyapunov exponents. To this spectrum are associated “eigen-directions”, called Lyapunov modes. We carefully analyze these modes and show how they are naturally associated with vector fields over the container. We also show that the Lyapunov exponents, and the coupled dynamics of the modes (where it exists) follow linear laws, whose coefficients only depend on the density of the gas, but not on aspect ratio and very little on the boundary conditions.
46 citations
TL;DR: In this article, the authors study a few problems related to Markov processes of flipping triangulations of the sphere and show that these processes are ergodic and mixing, but find a natural example which does not satisfy detailed balance.
Abstract: We study a few problems related to Markov processes of flipping triangulations of the sphere. We show that these processes are ergodic and mixing, but find a natural example which does not satisfy detailed balance. In this example, the expected distribution of the degrees of the nodes seems to follow the power law d−4.
7 citations
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TL;DR: By explicitly constructing surrogate Hierarchical texts, it is demonstrated that the power law originates from structural organization of texts into subu nits such as chapters and paragraphs.
Abstract: Understanding texts requires memory: the reader has to keep in mind enough words to create meaning. This calls for a relation between the memory of the reader and the structure of the text. To investigate this interaction, we first identify a connectivity matrix defined by co-occurre nce of words in the text. A vector space of words characterizing the text is spanned by the principal directi ons of this matrix. It is useful to think of these weighted combinations of words as representing “concepts”. As the reader follows the text, the set of words in her window of attention follows a dynamical motion among these concepts. We observe long range power law correlations in this trajectory. By explicitly constructing surrogate h ierarchical texts, we demonstrate that the power law originates from structural organization of texts into subu nits such as chapters and paragraphs.
1 citations
TL;DR: In this article, it was shown that when the cells are weakly coupled, to a good approximation, the jump rates of particles and the energy exchange rates from cell to cell follow linear profiles.
Abstract: We consider nonequilibrium transport in a simple chain of identical mechanical cells in which particles move around. In each cell, there is a rotating disc, with which these particles interact, and this is the only interaction in the model. It was shown in \cite{eckmann-young} that when the cells are weakly coupled, to a good approximation, the jump rates of particles and the energy-exchange rates from cell to cell follow linear profiles. Here, we refine that study by analyzing higher-order effects which are induced by the presence of external gradients for situations in which memory effects, typical of Hamiltonian dynamics, cannot be neglected. For the steady state we propose a set of balance equations for the particle number and energy in terms of the reflection probabilities of the cell and solve it phenomenologically. Using this approximate theory we explain how these asymmetries affect various aspects of heat and particle transport in systems of the general type described above and obtain in the infinite volume limit the deviation from the theory in \cite{eckmann-young} to first-order. We verify our assumptions with extensive numerical simulations.