Materials Modelling and Modal Analysis of the Lighthouse in the Venetian Harbour of Chania

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On the enumeration of positive cells in generalized cluster complexes and Catalan hyperplane arrangements

Let Φ be an irreducible crystallographic root system with Weyl group W and coroot lattice Q̌, spanning a Euclidean space V. Let m be a positive integer and AΦm be the arrangement of hyperplanes in V of the form (α, x) = κ for α ε Φ and κ = 0, 1,..., m. It is known that the number N+(Φ, m) of bounded dominant regions of AΦm is equal to the number of facets of the positive part Δ+m(Φ) of the generalized cluster complex associated to the pair (Φ, m) by S. Fomin and N. Reading. We define a statistic on the set of bounded dominant regions of A Φm and conjecture that the corresponding refinement of N+(Φ, m) coincides with the h-vector of Δ+ m(Φ). We compute these refined numbers for the classical root systems as well as for all root systems when m = 1 and verify the conjecture when Φ has type A, B or C and when m = 1. We give several combinatorial interpretations to these numbers in terms of chains of order ideals in the root poset of Φ, orbits of the action of W on the quotient Q̌/ (mh - 1) Q̌ and coroot lattice points inside a certain simplex, analogous to the ones given by the first author in the case of the set of all dominant regions of AΦm We also provide a dual interpretation in terms of order filters in the root poset of Φ in the special case m = 1. © Springer Science + Business Media, LLC 2006

Shellability and higher Cohen-Macaulay connectivity of generalized cluster complexes

Let Φ be a finite root system of rank n and let m be a nonnegative integer. The generalized cluster complex Δm(Φ) was introduced by S. Fomin and N. Reading. It was conjectured by these authors that Δm(Φ) is shellable and by V. Reiner that it is (m + 1)-Cohen-Macaulay, in the sense of Baclawski. These statements are proved in this paper. Analogous statements are shown to hold for the positive part Δ + m (Φ) of Δm(Φ). An explicit homotopy equivalence is given between Δ + m (Φ) and the poset of generalized noncrossing partitions, associated to the pair (Φ, m) by D. Armstrong. © 2008 Hebrew University Magnes Press

A computational methodology for effective bioclimatic-design applications in the urban environment

In the present paper a computational methodology for assessing and improving the microclimate in the urban environment is developed. A Computational Fluid Dynamics (CFD) model is described, which accounts for the evaporation occurring on water surfaces as well as the evapotranspiration from plant surfaces and tree foliage. Solar radiation and wind effects are also taken into account. Additionally, thermal comfort indices are implemented in the model, hence local information is provided regarding thermal sensations (bioclimatic maps). Surface temperature and air temperature at pedestrian level, are also used to characterize the microclimate. The methodology is demonstrated by means of a case study, which refers to the area of Gazi in Greece. Initially, the model is applied for simulating the airflow pattern throughout the domain of interest. The numerical results reveal the problematic areas in terms of thermal discomfort and wind effects. Based on that information advanced bioclimatic techniques are suggested to reduce severe heat stresses and to eliminate these areas. The effectiveness of the architectural interventions is tested by estimating the microclimate-indices differences compared to the existing conditions. It is concluded that the proposed methodology serves adequately for applying effective bioclimatic strategies to mitigate the Urban Heat Island (UHI) effect