Phase space structures governing reaction dynamics in rotating molecules

Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type equilibrium points which are characteristic for reaction type dynamics. Their construction is based on a Poincar{\'e}-Birkhoff normal form. Using tools from the geometric theory of Hamiltonian systems and their reduction we show in this paper how the construction of these phase space structures can be generalized to the case of the relative equilibria of a rotational symmetry reduced $N$-body system. As rotations almost always play an important role in the reaction dynamics of molecules the approach presented in this paper is of great relevance for applications.Comment: 28 pages, 7 figures, pdflate

Optimization of facade design based on the impact of interior obstructions to daylighting

Overcrowding in the perimeter zone is an inevitable issue in residential rooms with limited space. Obstructions, such as furniture and household items, may block the existing windows, and therefore affect interior daylight conditions. A facade design approach is needed that simultaneously takes into account daylighting and the volume of usable space for obstructions in the perimeter zone of such rooms. This study simulates daylight distributions in a typical small residential room with obstructions in front of windows. The simulation consists of two parts. First, the effects on horizontal illuminances caused by different positions and shapes of obstructions are examined under an overcast sky. Second, the maximum usable space volumes for obstructions of 51 optimized facade configurations are calculated in terms of four window-to-wall ratios (WWRs). The results of this study show that optimizing the forms of facade design can increase the usable interior space volume and meet the daylighting requirements of Chinese standards for small residential rooms. Additionally, by using the optimized facade forms, a facade with a WWR value of 50% provides the maximum usable space for obstructions. Based on the above results, this paper presents two matrices that can help architects in selecting the appropriate fenestration methods and confirming the size of usable space and allocation for residents