Geometrical Folding Transitions of the Triangular Lattice in the Face-Centred Cubic Lattice

We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional Face-Centred Cubic lattice, a discrete model for the crumpling of membranes. Possible folds are complete planar folds, folds with the angle of a regular tetrahedron (71 degrees) or with that of a regular octahedron (109 degrees). We study this model in the presence of a negative bending rigidity K, which favours the folding process. We use both a cluster variation method (CVM) approximation and a transfer matrix approach. The system is shown to undergo two separate geometrical transitions with increasing |K|: a first discontinuous transition separates a phase where the triangular lattice is preferentially wrapped around octahedra from a phase where it is preferentially wrapped around tetrahedra. A second continuous transition separates this latter phase from a phase of complete folding of the lattice on top of a single triangle.Comment: 25 pages, uses harvmac(b) and epsf, 14+1 figures include

Discrete Folding

Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a face-centered-cubic lattice are treated. The 3d-folding problem corresponds to a 96-vertex model and exhibits a first-order folding transition from a crumpled phase to a completely flat phase as the bending rigidity increases.Comment: LaTeX, 13 pages, 11 eps/ps figures: To appear in the Proceedings of the 4th Chia Meeting on "Condensed Matter and High-Energy Physics" (World Scientific, Singapore

The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics

The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by Bethe ansatz. Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and J. Feinberg editor

A new gene involved in coenzyme Q biosynthesis in Escherichia coli: UbiI functions in aerobic C5-hydroxylation

International audienceCoenzyme Q (ubiquinone or Q) is a redox-active lipid found in organisms ranging from bacteria to mammals in which it plays a crucial role in energy-generating processes. Q biosynthesis is a complex pathway that involves multiple proteins. In this work, we show that the uncharacterized conserved visC gene is involved in Q biosynthesis in Escherichia coli, and we have renamed it ubiI. Based on genetic and biochemical experiments, we establish that the UbiI protein functions in the C5-hydroxylation reaction. A strain deficient in ubiI has a low level of Q and accumulates a compound derived from the Q biosynthetic pathway, which we purified and characterized. We also demonstrate that UbiI is only implicated in aerobic Q biosynthesis and that an alternative enzyme catalyzes the C5-hydroxylation reaction in the absence of oxygen. We have solved the crystal structure of a truncated form of UbiI. This structure shares many features with the canonical FAD-dependent para-hydroxybenzoate hydroxylase and represents the first structural characterization of a monooxygenase involved in Q biosynthesis. Site-directed mutagenesis confirms that residues of the flavin binding pocket of UbiI are important for activity. With our identification of UbiI, the three monooxygenases necessary for aerobic Q biosynthesis in E. coli are known

Transitions de phase dynamique dans des modeles de spins et d'automates

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : TD 78166 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Physics of integer-spin antiferromagnetic chains: Haldane gaps and edge states

International audienceThe antiferromagnetic Heisenberg spin chain with integer spin has short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling J of the Heisenberg chain. We discuss recent results about the spin dependence of the Haldane gap and conjecture an analytical formula valid asymptotically for large spin values. We next study the robustness of the edge states of the spin one chain by studying by the DMRG algorithm a spin one ladder. We show that the peculiar hidden topological order of the spin one chain disappears smoothly by increasing the ladder rung coupling without any intervening phase transition. This is evidence for the fragile character of the topological order of the spin one chain

Hamiltonian cycles on bicolored random planar maps

International audienceWe study the statistics of Hamiltonian cycles on various families of bicolored random planar maps (with the spherical topology). These families fall into two groups corresponding to two distinct universality classes with respective central charges c=−1 and c=−2. The first group includes generic p-regular maps with vertices of fixed valency p≥3, whereas the second group comprises maps with vertices of mixed valencies, and the so-called rigid case of 2q-regular maps (q≥2) for which, at each vertex, the unvisited edges are equally distributed on both sides of the cycle. We predict for each class its universal configuration exponent γ, as well as a new universal critical exponent ν characterizing the number of long-distance contacts along the Hamiltonian cycle. These exponents are theoretically obtained by using the Knizhnik, Polyakov and Zamolodchikov (KPZ) relations, with the appropriate values of the central charge, applied, in the case of ν, to the corresponding critical exponent on regular (hexagonal or square) lattices. These predictions are numerically confirmed by analyzing exact enumeration results for p-regular maps with p=3,4,…,7, and for maps with mixed valencies (2,3), (2,4) and (3,4)

Exponents for Hamiltonian paths on random bicubic maps and KPZ

38 pages, 19 figuresWe evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exact enumeration results for finite sizes and compared with their theoretical predictions based on the KPZ relations, as applied to their regular counterpart on the honeycomb lattice. We show that a naive use of these relations does not reproduce the measured exponents but that a simple modification in their application may possibly correct the observed discrepancy. We show that a similar modification is required to reproduce via the KPZ formulas some exactly known exponents for the problem of unweighted fully packed loops on random planar bicubic maps

Exponents for Hamiltonian paths on random bicubic maps and KPZ

We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exact enumeration results for finite sizes and compared with their theoretical predictions based on the Knizhnik, Polyakov and Zamolodchikov (KPZ) relations, as applied to their regular counterpart on the honeycomb lattice. We show that a naive use of these relations does not reproduce the measured exponents but that a simple modification in their application may possibly correct the observed discrepancy. We show that a similar modification is required to reproduce via the KPZ formulas some exactly known exponents for the problem of unweighted fully packed loops on random planar bicubic maps