Elliptic Quantum Group U_{q,p}(\hat{sl}_2) and Vertex Operators

Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we investigate the vertex operators of the elliptic quantum group U_{q,p}(\widedhat{sl}_2) defined as intertwining operators of infinite dimensional U_{q,p}(\widedhat{sl}_2)-modules. We show that the vertex operators coincide with the previous results obtained indirectly by using the quasi-Hopf algebra B_{q,\lambda}(\hat{sl}_2). This shows a consistency of our H-Hopf algebroid structure even in the case with non-zero central element.Comment: 15 pages. Typos fixed. Version to appear in J.Phys.A :Math.and Theor., special issue on Recent Developments in Infinite Dimensional Algebras and Their Applications to Quantum Integrable Systems 200

Air entrainment and energy dissipation on porous pooled stepped spillways

The hydraulics of stepped spillways with flat steps is well documented and some design guidelines exist for typical embankment dam slopes. On the other hand, alternative stepped designs are poorly understood. In the present study, some porous pooled stepped spillways were investigated with two different porosities of the pooled weir. The air-water flow patterns, air-water flow properties and the energy dissipation rate were observed and compared to the corresponding flat and pooled stepped spillways. The comparative study highlighted a larger interfacial velocity for the pooled step configurations. The largest residual energy at the downstream end was observed for the porous pooled steps which was associated with reduced cavity recirculation and form drag. Overall the porous pooled stepped design exhibited some more stable flow patterns than the pooled stepped design, but it was characterised by a lesser rate of energy dissipation than the flat step design for the investigated slope (θ = 26.6°)

Air-water flow in hydraulic jumps on macro-roughness

Hydraulic jumps are highly complex three dimensional flows with strong energy dissipation and air bubble entrainment associated with intense mixing. To date turbulence and air-water flow observations in hydraulic jumps have been limited to smooth rectangular channels. Herein novel experiments were conducted on a channel with bed macro roughness to characterise the effect of boundary roughness on the air-water flow properties. The results showed distinctive differences including a reduction in hydraulic jump length and upward shift of the roller toe for a rough bed jump. The air-water flow profiles were comparable with larger aeration downstream of the jump toe for the rough bed and a reduction in aeration and interfacial velocity compared to a smooth bed flow towards the downstream end of the jump. The present study highlighted the potential to use macro roughness boundaries to manipulate the flow performance and the re-aeration capabilities of turbulent hydraulic jumps

Infinite Hopf family of elliptic algebras and bosonization

Elliptic current algebras E_{q,p}(\hat{g}) for arbitrary simply laced finite dimensional Lie algebra g are defined and their co-algebraic structures are studied. It is shown that under the Drinfeld like comultiplications, the algebra E_{q,p}(\hat{g}) is not co-closed for any g. However putting the algebras E_{q,p}(\hat{g}) with different deformation parameters together, we can establish a structure of infinite Hopf family of algebras. The level 1 bosonic realization for the algebra E_{q,p}(\hat{g}) is also established.Comment: LaTeX, 11 pages. This is the new and final versio

Note on the Algebra of Screening Currents for the Quantum Deformed W-Algebra

With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W-algebra W_{q,p}(g) can be put together to form a single algebra which can be regarded as an elliptic deformation of the universal enveloping algebra of \hat{g}, where g is any classical simply-laced Lie algebra.Comment: LaTeX file, 9 pages. Errors in Serre relation corrected. Two references to Awata,H. et al adde

Structure Constants of the Fractional Supersymmetry Chiral Algebras

The fractional supersymmetry chiral algebras in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents. We show that associativity and closure of these algebras determines their structure constants in the case that the Virasoro algebra is extended by precisely one current. We compute the structure constants of these algebras explicitly and we show that correlators of the currents satisfy non-Abelian braiding relations.Comment: 44 page

SOS model partition function and the elliptic weight functions

We generalize a recent observation [arXiv:math/0610433] that the partition function of the 6-vertex model with domain-wall boundary conditions can be obtained by computing the projections of the product of the total currents in the quantum affine algebra $U_{q}(\hat{\mathfrak{sl}}_{2})$ in its current realization. A generalization is proved for the the elliptic current algebra [arXiv:q-alg/9703018,arXiv:q-alg/9601022]. The projections of the product of total currents are calculated explicitly and are represented as integral transforms of the product of the total currents. We prove that the kernel of this transform is proportional to the partition function of the SOS model with domain-wall boundary conditions.Comment: 21 pages, 5 figures, requires iopart packag

Predicting flow resistance in open-channel flows with submerged vegetation

In vegetated flows, hydrodynamic parameters, such as drag coefficient, frontal area and deflected canopy height, influence velocity distributions, mean velocity and flow resistance. Previous studies have focused on flow–structure interaction in sparse vegetation, dense vegetation or transitional canopies, respectively. To date, a unifying approach to estimate hydrodynamic properties of submerged vegetated flows across the full vegetation density spectrum is missing. Herein, published data sets across a wide range of vegetation conditions were re-analysed using a previously proposed four-layer velocity superposition model. For the investigated vegetation conditions, the velocity model was able to match measured velocity distributions and depth-averaged mean velocity. The contribution of each velocity layer to the mean velocity was analyzed, showing that the mixing layer is dominant in transitional canopies with shallow submergence, and that the log-law layer is dominant in denser canopies with deeper submergence. Based upon velocity distributions, an explicit equation for the Darcy–Weisbach friction factors was deduced that is able to predict flow resistance as function of relative submergence. While each velocity distribution could be well described with the four-layer model across the range of vegetation conditions, some data scatter in model parameters was observed. To improve predictive capabilities of the model, future research should focus on detailed velocity measurements with high spatial resolution

Cosmology in Nonlinear Born-Infeld Scalar Field Theory With Negative Potentials

The cosmological evolution in Nonlinear Born-Infeld(hereafter NLBI) scalar field theory with negative potentials was investigated. The cosmological solutions in some important evolutive epoches were obtained. The different evolutional behaviors between NLBI and linear(canonical) scalar field theory have been presented. A notable characteristic is that NLBI scalar field behaves as ordinary matter nearly the singularity while the linear scalar field behaves as "stiff" matter. We find that in order to accommodate current observational accelerating expanding universe the value of potential parameters $|m|$ and $|V_0|$ must have an {\it upper bound}. We compare different cosmological evolutions for different potential parameters $m, V_0$.Comment: 18 pages, 18 figures, some references added, revised version for Int.J.Mod.Phys.A, appeared in Int.J.Mod.Phys.