Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof

In this paper, we prove the off-shell equation satisfied by the transfer matrix associated with the XXZ spin-$\frac12$ chain on the segment with two generic integrable boundaries acting on the Bethe vector. The essential step is to prove that the expression of the action of a modified creation operator on the Bethe vector has an off-shell structure which results in an inhomogeneous term in the eigenvalues and Bethe equations of the corresponding transfer matrix.Comment: V2 published version, 16 page

Highest coefficient of scalar products in SU(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various different representations for the highest coefficient in terms of sums over partitions. We also obtain multiple integral representations for the highest coefficient.Comment: 17 page

An eco-geomorphic model of tidal channel initiation and elaboration in progressive marsh accretional contexts

The formation and evolution of tidal networks have been described through various theories which mostly assume that tidal network development results from erosional processes, therefore emphasizing the chief role of external forcing triggering channel net erosion such as tidal currents. In contrast, in the present contribution we explore the influence of sediment supply in governing tidal channel initiation and further elaboration using an ecogeomorphic modeling framework. This deliberate choice of environmental conditions allows for the investigation of tidal network growth and development in different sedimentary contexts and provides evidences for the occurrence of both erosional and depositional channel-forming processes. Results show that these two mechanisms in reality coexist but act at different time scales: channel initiation stems from erosional processes, while channel elaboration mostly results from depositional processes. Furthermore, analyses suggest that tidal network ontogeny is accelerated as the marsh accretional activity increases, revealing the high magnitude and prevalence of the depositional processes in governing the morphodynamic evolution of the tidal network. On a second stage, we analyze the role of different initial topographic configurations in driving the development of tidal networks. Results point out an increase in network complexity over highly perturbed initial topographic surfaces, highlighting the legacy of initial conditions on channel morphological properties. Lastly, the consideration that landscape evolution depends significantly on the parameterization of the vegetation biomass distribution suggests that the claim to use uncalibrated models for vegetation dynamics is still questionable when studying real cases

Évolution à long terme du peuplement piscicole du bassin de la Seine

Des données anciennes issues de la littérature sont utilisées pour apprécier les conséquences des activités humaines sur l'évolution de la structure des communautés piscicoles du bassin de la Seine

On factorizing FF-matrices in Y(sln)Y(sl_n) and Uq(sln^)U_q(\hat{sl_n}) spin chains

We consider quantum spin chains arising from $N$-fold tensor products of the fundamental evaluation representations of $Y(sl_n)$ and $U_q(\hat{sl_n})$. Using the partial $F$-matrix formalism from the seminal work of Maillet and Sanchez de Santos, we derive a completely factorized expression for the $F$-matrix of such models and prove its equivalence to the expression obtained by Albert, Boos, Flume and Ruhlig. A new relation between the $F$-matrices and the Bethe eigenvectors of these spin chains is given.Comment: 30 page

Quantifying the physical alterations of river reaches using a regional river morphology reference model. A step towards river restoration.

River engineeringRiver habitat management and restoratio

Mangroves as nature-based mitigation for ENSO-driven compound flood risks in a large river delta

Densely populated coastal river deltas are very vulnerable to compound flood risks coming from both oceanic and riverine sources. Climate change may increase these compound flood risks due to sea level rise and intensifying precipitation events. Here, we investigate to what extent nature-based flood defence strategies, through the conservation of mangroves in a tropical river delta, can contribute to mitigate the oceanic and riverine components of compound flood risks. While current knowledge of estuarine compound flood risks is mostly focussed on short-term events such as storm surges (taking 1 or a few days), longer-term events, such as El Niño events (continuing for several weeks to months) along the Pacific coast of Latin America, are less studied. Here, we present a hydrodynamic modelling study of a large river delta in Ecuador aiming to elucidate the compound effects of El Niño-driven oceanic and riverine forcing on extreme high water level propagation through the delta and, in particular, the role of mangroves in reducing the compound high water levels. Our results show that the deltaic high water level anomalies are predominantly driven by the oceanic forcing but that the riverine forcing causes the anomalies to amplify upstream. Furthermore, mangroves in the delta attenuate part of the oceanic contribution to the high water level anomalies, with the attenuating effect increasing in the landward direction, while mangroves have a negligible effect on the riverine component. These findings show that mangrove conservation and restoration programmes can contribute to nature-based mitigation, especially the oceanic component of compound flood risks in a tropical river delta.</p

On Form Factors in nested Bethe Ansatz systems

We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and we establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the "magnonic form factors", which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity) we obtain explicit solutions for the recursion relations.Comment: 34 pages, v2 (minor modifications

Central extension of the reflection equations and an analog of Miki's formula

Two different types of centrally extended quantum reflection algebras are introduced. Realizations in terms of the elements of the central extension of the Yang-Baxter algebra are exhibited. A coaction map is identified. For the special case of $U_q(\hat{sl_2})$, a realization in terms of elements satisfying the Zamolodchikov-Faddeev algebra - a `boundary' analog of Miki's formula - is also proposed, providing a free field realization of $O_q(\hat{sl_2})$ (q-Onsager) currents.Comment: 11 pages; two references added; to appear in J. Phys.

Generalized q-Onsager Algebras and Dynamical K-matrices

A procedure to construct $K$-matrices from the generalized $q$-Onsager algebra \cO_{q}(\hat{g}) is proposed. This procedure extends the intertwiner techniques used to obtain scalar (c-number) solutions of the reflection equation to dynamical (non-c-number) solutions. It shows the relation between soliton non-preserving reflection equations or twisted reflection equations and the generalized $q$-Onsager algebras. These dynamical $K$-matrices are important to quantum integrable models with extra degrees of freedom located at the boundaries: for instance, in the quantum affine Toda field theories on the half-line they yield the boundary amplitudes. As examples, the cases of \cO_{q}(a^{(2)}_{2}) and \cO_{q}(a^{(1)}_{2}) are treated in details