Enhanced transport of flexible fibers by pole vaulting in turbulent wall-bounded flow

Long, flexible fibers transported by a turbulent channel flow sample non-linear variations of the fluid velocity along their length. As the fibers tumble and collide with the boundaries, they bounce off with an impulse that propels them toward the center of the flow, similar to pole vaulting. As a result, the fibers migrate away from the walls, leading to depleted regions near the boundaries and more concentrated regions in the bulk. These higher concentrations in the center of the channel result in a greater net flux of fibers than what was initially imposed by the fluid. This effect becomes more pronounced as fiber length increases, especially when it approaches the channel height.Comment: 5 pages, 5 figure

Free quasi-symmetric functions, product actions and quantum field theory of partitions

We examine two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender's QFT of partitions. We end by exploring possibilities to construct noncommutative analogues.Comment: Submitted 28.11.0

The sparse Blume-Emery-Griffiths model of associative memories

We analyze the Blume-Emery-Griffiths (BEG) associative memory with sparse patterns and at zero temperature. We give bounds on its storage capacity provided that we want the stored patterns to be fixed points of the retrieval dynamics. We compare our results to that of other models of sparse neural networks and show that the BEG model has a superior performance compared to them.Comment: 23 p

Gradation of Algebras of Curves by the Winding Number

We construct a new grading on the Goldman Lie algebra of a closed oriented surface by the winding number. This grading induces a grading on the HOMFLY-PT skein algebra and related algebras. Our work supports the conjectures of B. Cooper and P. SamuelsonComment: Changed acknowledgments and Definition 2.

Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization

In this work, an effective construction, via Sch\"utzenberger's monoidal factorization, of dual bases for the non commutative symmetric and quasi-symmetric functions is proposed

Combinatorics of ϕ\phi-deformed stuffle Hopf algebras

In order to extend the Sch\"utzenberger's factorization to general perturbations, the combinatorial aspects of the Hopf algebra of the $\phi$-deformed stuffle product is developed systematically in a parallel way with those of the shuffle product