Ref HAL: hal-03080457_v1
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Résumé:

Water transport in plant roots is of vital importance: it is a necessary transport to feed the rest of the organism in most vascular plants. To reach the xylem vessels, which ensure the long-distance transport to the aerial parts of the plant, water has first to flow across the root tissues surrounding the xylem. This flow, denoted to as radial transport, is not easily amenable to the experimentation, and has been studied mostly by measurements at a larger scale, and by models that poorly take into account cells and roots geometries. We adopted a continuous description of stationary root radial water transport to investigate how the geometry and the permeability contrasts between root compartments affect the transport of water. We experimentally modeled the root radial section as a two-dimensional and composite porous material with variable water permeabilities. It mimics the most salient water transport features of the root anatomy and allows a direct isualization of the water pathways. We also present 2D continuous numerical simulations of the water flow, in which we systematically varied the permeabilities of the different tissues. Our approach provides the physical premises to explain preferential sub-cellular radial routes from one cell to another and look for the subcellular pattern of structures or molecules involved in water transport.

Ref HAL: hal-02961331_v1
DOI: 10.1016/j.nuclphysb.2020.115176
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Free Fermions on vertices of distance-regular graphs are considered. Bipartitions are defined by taking as one part all vertices at a given distance from a reference vertex. The ground state is constructed by filling all states below a certain energy. Borrowing concepts from time and band limiting problems, algebraic Heun operators and Terwilliger algebras, it is shown how to obtain, quite generally, a block tridiagonal matrix that commutes with the entanglement Hamiltonian. The case of the Hadamard graphs is studied in detail within that framework and the existence of the commuting matrix is shown to allow for an analytic diagonalization of the restricted two-point correlation matrix and hence for an explicit determination of the entanglement entropy.

Commentaires: 24 pages, 37 ref.

Ref HAL: hal-02961322_v1
DOI: 10.1063/5.0008372
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Commentaires: 5 pages, 27 ref.

Ref HAL: hal-02961315_v1
DOI: 10.1142/9789811210679_0013
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Ref HAL: hal-02890142_v1
Ref Arxiv: 1908.04806
DOI: 10.1088/1751-8121/ab604e
Ref. & Cit.: NASA ADS
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A description of the embedding of a centrally extended Askey–Wilson algebra, AW(3), in Uq(sl2) 3 is given in terms of the universal R-matrix of Uq(sl2). The generators of the centralizer of Uq(sl2) in its three-fold tensor product are naturally expressed through conjugations of Casimir elements with R. They are seen as the images of the generators of AW(3) under the embedding map by showing that they obey the AW(3) relations. This is achieved by introducing a natural coaction also constructed with the help of the R-matrix.

Ref HAL: hal-02890130_v1
Ref Arxiv: 1909.06426
DOI: 10.1007/s11005-019-01249-w
Ref. & Cit.: NASA ADS
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Résumé:

The Bannai-Ito algebra BI(n) is viewed as the centralizer of the action of osp(1|2) in the n-fold tensor product of the universal algebra of this Lie superalgebra. The generators of this centralizer are constructed with the help of the universal R-matrix of osp(1|2). The specific structure of the osp(1|2) embeddings to which the centralizing elements are attached as Casimir elements is explained. With the generators defined, the structure relations of BI(n) are derived from those of BI(3) by repeated action of the coproduct and using properties of the R-matrix and of the generators of the symmetric group Sn.

Commentaires: 10 pages, 15 ref.