324 research outputs found
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- 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 -matrices in and spin chains
We consider quantum spin chains arising from -fold tensor products of the
fundamental evaluation representations of and .
Using the partial -matrix formalism from the seminal work of Maillet and
Sanchez de Santos, we derive a completely factorized expression for the
-matrix of such models and prove its equivalence to the expression obtained
by Albert, Boos, Flume and Ruhlig. A new relation between the -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 , 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
(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 -matrices from the generalized -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 -Onsager algebras. These dynamical -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
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