Kashiwara's crystal graphs have a natural monoid structure that arises by identifying words labelling vertices that appear in the same position of isomorphic components. The celebrated plactic monoid (the monoid of Young tableaux), arises in this way from the crystal graph for the q-analogue of the general linear Lie algebra gln, and the so-called Kashiwara operators interact beautifully with the combinatorics of Young tableaux and with the Robinson–Schensted–Knuth correspondence. The authors previously constructed an analogous ‘quasi-crystal’ structure for the related hypoplactic monoid (the monoid of quasi-ribbon tableaux), which has similarly neat combinatorial properties. This paper constructs an analogous ‘crystal-type’ structure for the sylvester and Baxter monoids (the monoids of binary search trees and pairs of twin binary search trees, respectively). Both monoids are shown to arise from this structure just as the plactic monoid does from the usual crystal graph. The interaction of the structure with the sylvester and Baxter versions of the Robinson–Schensted–Knuth correspondence is studied. The structure is then applied to prove results on the number of factorizations of elements of these monoids, and to prove that both monoids satisfy non-trivial identities.

Abstract This paper addresses the durability of bond between concrete and carbon fibre reinforced polymer (CFRP) strips installed according to the near-surface mounted (NSM) technique (NSM CFRP-concrete systems) under the effects of two main groups of environmental conditions: (i) laboratory-based ageing conditions; (ii) real outdoor ageing conditions. The bond degradation was evaluated by carrying out direct pullout tests on aged specimens that were previously subjected to distinct environmental conditions for different periods of exposure. Moreover, the degradation of the mechanical properties of the involved materials was investigated. The digital image correlation (DIC) method was used to document the evolution of the deformation fields at the surface over the whole region of interest consisting of concrete and epoxy adhesive at the ligament region. This information supported the discussion about the evolution of the bond resistant mechanism developed in \{NSM\} CFRP-concrete specimens during testing, as well as the assessment of the bond quality of the system. In general, the results obtained from the durability tests conducted have shown that the different exposure environments, which may be considered as quite severe, did not result in significant damage on \{NSM\} CFRP-concrete system. The maximum decrease of about 12% on bond strength was obtained for real outdoor environments. Conversely, a maximum increase of 8% on bond strength was obtained on the specimens exposed to the temperature cycles between -15��C and +60��C. \{DIC\} allowed to document the stress transfer mechanisms established between the \{CFRP\} and the concrete substrate, revealing the crack patterns and the influence widths of the \{CFRP\} reinforcement strips, which were shown to be important for avoiding group effect when using multiple parallel strengthening \{CFRP\} strips.

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This paper considers whether non-trivial identities are satisfied by certain ‘plactic-like’ monoids that, like the plactic monoid, are closely connected with combinatorics. New results show that the hypoplactic, sylvester, Baxter, stalactic, and taiga monoids satisfy identities. The existing state of knowledge is discussed for the plactic and Bell monoids.

{We consider a velocity tracking problem for the Navier-Stokes equations in a 2D bounded domain. The control acts on the boundary through an injection-suction device, and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations, and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.}

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The paper presents a nonlinear analytical solution for the prediction of the full-range debonding response of mechanically-anchored FRP composites from the substrate. The nonlinear analytical approach predicts, for any monotonic loading history or bonded length the relative displacements (or slips) between materials, the strains in the FRP composite, the bond stresses within the interface and the stresses developed in the substrate. The load-slip responses FRP-to-substrate interfaces with a short and a long bonded lengths are motive of analysis and discussion. The solutions obtained from the proposed approach are also compared with other experimental results found in the literature.

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https://docentes.fct.unl.pt/lblm/files/electroanalysis-2018-30-2485.pdf