Two-step Resolution Research Articles

Air Traffic Assignment for Intensive Urban Air Mobility Operations

In high-density urban air mobility (UAM) operations, mitigating congestion and reducing structural constraints are key challenges. Pioneering urban airspace design projects expect the air vehicles to fit into structured UAM corridor networks. However, most existing air transport networks are not capable of handling the increasing traffic demand, which is likely to cause congestion, traffic complexity, and safety issues. To adapt the increasing demand to the current airspace capacity, a novel macroscopic traffic assignment model is proposed to mitigate the congestion and organize the structure of air traffic flow. Firstly, the UAM corridor is designed and fitted into graph representation. Then, a traffic assignment problem based on linear dynamic system is formalized to minimize the congestion factors and the intrinsic air traffic complexity. A two-step resolution method based on Dafermos’s algorithm is introduced to efficiently solve this optimization problem. A case study is carried out on a two-layer air transport network with intensive UAM operations. The results demonstrate that the proposed model can successfully mitigate urban airspace congestion and organize the UAM traffic into a low-complexity flow pattern. This approach can be used as a tool to assist air navigation service provider in strategic planning for a given transportation network.

Voisin-Borcea manifolds and heterotic orbifold models

Abstract We study the relation between a heterotic ${T^6 \left/ {{{{\mathbb{Z}}_6}}} \right.}$ orbifold model and a compactification on a smooth Voisin-Borcea Calabi-Yau three-fold with non-trivial line bundles. This orbifold can be seen as a ${{\mathbb{Z}}_2}$ quotient of ${T^4 \left/ {{{{\mathbb{Z}}_3}}} \right.}\times {T^2}$ . We consider a two-step resolution, whose intermediate step is $\left( {K3\times {T^2}} \right){{\mathbb{Z}}_2}$ . This allows us to identify the massless twisted states which correspond to the geometric Kähler and complex structure moduli. We work out the match of the two models when non-zero expectation values are given to all twisted geometric moduli. We find that even though the orbifold gauge group contains an SO(10) factor, a possible GUT group, the subgroup after higgsing does not even include the standard model gauge group. Moreover, after higgsing, the massless spectrum is non-chiral under the surviving gauge group.

A partitioned resolution for concurrent fluid flow and stress analysis during solidification: application to ingot casting

In simulation of solidification processes, an open issue is the concurrent modelling of fluid flow and solid mechanics. This is critical for the prediction of cracks formed in solidified regions during the filling stage of ingot casting, or in the mould during continuous casting. The proposed approach consists of a partitioned two-step resolution strategy.

A Two-Step Resolution for Preparing Enantiopure (S)-Ethyl Nipecotate

Enantiopure nipecotic acid or ethyl nipecotate are key precursors for synthesizing a variety of pharmaceutically important compounds. In this work a two-step resolution of racemic ethyl nipecotate was developed to prepare enantiopure (S)-ethyl nipecotate. In the enzymatic resolution step, six lipases were screened for their ability to enantioselectively hydrolyze rac-ethyl nipecotate in t-butanol at 30°C and Novozym 435 was found to be the most effective. Solvent effects on the hydrolysis conversion and enantioselectivity showed that water was the optimum medium. When rac-ethyl nipecotate concentration was kept at 0.5M, the hydrolysis under optimum conditions (lipase loading 5mg/mL, phosphate buffer pH 7.0, reaction temperature 30°C, reaction time 6h) afforded 68.9% ees and 69.5% eep at 49.8% conversion. Novozym 435 preferentially hydrolyzed (R)-ethyl nipecotate over (S)-enantiomer. A parallel reaction model was suggested and found to fit the experimental initial rate data very well. (S)-enriched ethyl nipecotate was further resolved using (D)-tartaric acid and enantiopure (S)-ethyl nipecotate (98.5% ee) was acquired in 84.3% yield. The overall yield of enantiopure (S)-ethyl nipecotate by this two-step resolution was up to 36.0%.

Cyclic scheduling for F.M.S.: Modelling and evolutionary solving approach

This paper concerns the domain of flexible manufacturing systems (FMS) and focuses on the scheduling problems encountered in these systems. We have chosen the cyclic behaviour to study this problem, to reduce its complexity. This cyclic scheduling problem, whose complexity is NP-hard in the general case, aims to minimise the work in process (WIP) to satisfy economic constraints. We first recall and discuss the best known cyclic scheduling heuristics. Then, we present a two-step resolution approach. In the first step, a performance analysis is carried out; it is based on the Petri net modelling of the production process. This analysis resolves some indeterminism due to the system's flexibility and allows a lower bound of the WIP to be obtained. In the second step, after a formal model of the scheduling problem has been given, we describe a genetic algorithm approach to find a schedule which can reach the optimal production speed while minimizing the WIP. Finally, our genetic approach is validated and compared with known heuristics on a set of test problems.

Lipase-catalysed kinetic resolution in organic solvents: an approach to enantiopure α-methyl-β-alanine esters

The Candida antarctica lipase A (CAL-A) and B (CAL-B)-catalysed resolutions of α-methyl-β-alanine ethyl ester 1 with neat ethyl and butyl butanoates and with 2,2,2-trifluoroethyl butanoate in organic solvents were studied, as were the alcoholyses in neat butanol and with methanol (0.8 M) in diisopropyl ether. The two enzymes, which display opposite ( S for CAL-A and R for CAL-B) and low enantioselectivities ( E=7–10), allowed the preparation of the two enantiomers in a two-step resolution protocol. The R enantiomer (ee=97%) was first separated as its Boc-protected derivative from the CAL-A-catalysed resolution mixture of ( R)- 1 and the enantiomerically enriched N-butanoylated counterpart. The enantiopurification of the latter gave the S enantiomer (ee=96%) in the following CAL-B-catalysed ‘interesterification’ in butyl butanoate.