The nesting problem, also known as irregular packing problem, belongs to the generic class of cutting and packing (C&P) problems. It di↵ers from other 2-D C&P problems in the irregular shape of the pieces. This paper proposes a new mixed-integer model in which binary decision variables are associated with each discrete point of the board (a dot) and with each piece type. It is much more flexible than previously proposed formulations and solves to optimality larger instances of the nesting problem, at the cost of having its precision dependent on board discretization. To date no results have been published concerning optimal solutions for nesting problems with more than 7 pieces. We ran computational experiments on 45 problem instances with the new model, solving to optimality 34 instances with a total number of pieces ranging from 16 to 56, depending on the number of piece types, grid resolution and the size of the board. A strong advantage of the model is its insensitivity to piece and board geometry, making it easy to extend to more complex problems such as non-convex boards, possibly with defects. Additionally, the number of binary variables does not depend on the total number of pieces but on the number of piece types, making the model particularly suitable for problems with few piece types. The discrete nature of the model requires a trade-o↵ between grid resolution and problem size, as the number of binary variables grows with the square of the selected grid resolution and with board size.

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One of the major challenges to the gasoline direct injection (GDI) engine design is to understand the behaviour of fuel atomization and vaporization at a variety of chamber conditions and injection strategies. As gasoline is a volatile fuel, it is often unintentionally superheated before injection in GDI engines. This can cause significant changes in the fuel spray distribution and fuel-air mixing. To account for these situations, this paper presents a comprehensive superheat fuel spray and vaporization model. In the model, it is assumed that, under superheat conditions, a hollow cone spray sheet still forms from a pressure-swirl atomizer. The sheet flash boiling is considered to be constrained by the transient heat conduction process inside the sheet with an effective thermal conductivity. Hydrodynamic instability, cavitation and bubble growth inside the sheet eventually break up the sheet to form droplets. Models of the subsequent droplet vaporization account for heat transfer under both flash boiling and sub-boiling conditions. Simulation results have been compared with Mie scattering images of the spray in an optical engine and good agreement is found at all the operating conditions considered. Finally, changes in the spray characteristics, evolution and vaporization behaviour under superheat conditions are explored with GDI applications in mind.

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The recent increase of archaeological survey has allowed a better definition of the Acheulean techno-complex in the Iberian Peninsula, and its integration in the African and Eurasian context. This paper aims to extend the discussion around the technological features of the peninsular lithic industries of the second half of the Middle Pleistocene, through the presentation of the data from Pedreiras 2 (Monção, Alto Minho). The site excavation, on the scope of the Miño-Minho Project, allowed to recover lithic artefacts associated with the Acheulean techno-complex, testifying human occupation in a region where, until recently, only isolated remains were known, and whose chronological data fits its chronology into the second half of the Middle Pleistocene