Simple but effective heuristics for the 2-constraint bin packing problem

The 2-constraint bin packing problem consists in packing a given number of items, each one characterised by two different but not related dimensions, into the minimum number of bins in such a way to do not exceed the capacity of the bins in either dimension. The development of the heuristics for this problem is challenged by the need of a proper definition of the criterion for evaluating the feasibility of the two capacity constraints on the two different dimensions. In this paper, we propose a computational evaluation of several criteria, and two simple but effective algorithms—a greedy and neighbourhood search algorithms—for solving the 2-constraint bin packing problem. An extensive computational analysis supports our main claim.     

Frames of exponentials and sub-multitiles in LCA groups

In this note, we investigate the existence of frames of exponentials for $L^2(\mathrm{\Omega })$ in the setting of LCA groups. Our main result shows that sub-multitiling properties of $\mathrm{\Omega }?\stackrel{?}{G}$ with respect to a uniform lattice Γ of $\stackrel{?}{G}$ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames.     

Investigation of the influence of spacer arm on the structural evolution of affinity ligands supported on agarose

The influence of the spacer arm on the interaction between agarose and a supported ligand was investigated through molecular dynamics for a combination of several spacers. The spacers differ for degree of hydrophobicity, length, and chemical composition, which was varied through insertion of thio, ether, and CH(2) groups. Agarose was modeled through a modified Glycam force field, whose parameters were determined through ab initio calculations. The structural model of agarose used for the calculations was obtained through MD studies of the conformational evolution of several agarose single and double helixes. The simulations showed that a modification of the spacer properties could determine a change of the stable structure of the ligand with respect to the support. In particular, if the spacer is hydrophilic and rigid, the favored structure is with extended spacer and solvated ligand. Either increasing the spacer length, and thus its flexibility, or decreasing its solvation free energy, which corresponds to diminishing its affinity for water, rapidly leads to a conformational change in which the ligand adsorbs on agarose. Interestingly, we found that if the spacer is long and hydrophilic, a third metastable structure, in which the spacer is sandwiched between the ligand and agarose, is possible. Simulations of several ligands adsorbed on neighboring sites on agarose showed that if the support is not held fixed through restraints, the interaction force between vicinal ligands is sufficient to determine a major conformational change of the system.     

Discrimination of active palladium sites in catalytic liquid-phase oxidation of benzyl alcohol

Knowledge of the structure of active sites is a prerequisite for the rational design of solid catalysts. Using site-selective blocking by CO and isotope labeling combined with in situ attenuated total reflection infrared (ATR-IR) spectroscopy, we were able to discriminate the different sites involved in the liquid-phase oxidation of benzyl alcohol on Pd/Al(2)O(3). The main reaction, that is, the oxidative dehydrogenation of the alcohol to the corresponding aldehyde, showed only little dependence on structure and occurred on all exposed Pd faces, whereas the undesired product decarbonylation occurred preferentially on hollow sites on (111) Pd faces. This explains why specific blocking of the latter sites, as realized in the industrially used Pd-Bi/Al(2)O(3) catalysts, leads to improved catalytic performance.     

Freezing of a Lennard-Jones fluid: from nucleation to spinodal regime

Using molecular dynamics, we investigate the crystal nucleation in a Lennard-Jones fluid as a function of the degree of supercooling. At moderate supercooling, a nucleation picture applies, while for deeper quenches, the phenomenon progressively acquires a spinodal character. We show that in the nucleation regime, the freezing is a two-step process. The formation of the critical nucleus is indeed preceded by the abrupt formation of a precritical crystallite from a density fluctuation in the fluid. In contrast, as the degree of supercooling is increased, crystallization proceeds in a more continuous and collective fashion and becomes more spatially diffuse, indicating that the liquid is unstable and crystallizes by a spinodal mechanism.     

Nonautonomous Ornstein-Uhlenbeck operators in weighted spaces of continuous functions

We consider the nonautonomous Ornstein-Uhlenbeck operator in some weighted spaces of continuous functions in $\mathbb{R}^{N}$ . We prove sharp uniform estimates for the spatial derivatives of the associated evolution operator P _s,t , which we use to prove optimal Schauder estimates for the solution to some nonhomogeneous parabolic Cauchy problems associated with the Ornstein-Uhlenbeck operator. We also prove that, for any t>s, the evolution operator P _s,t is compact in the previous weighted spaces.     

Prediction of Liner Metal Temperature of an Aeroengine Combustor with Multi-Physics Scale-Resolving CFD

Computational Fluid Dynamics is a fundamental tool to simulate the flow field and the multi-physics nature of the phenomena involved in gas turbine combustors, supporting their design since the very preliminary phases. Standard steady state RANS turbulence models provide a reasonable prediction, despite some well-known limitations in reproducing the turbulent mixing in highly unsteady flows. Their affordable cost is ideal in the preliminary design steps, whereas, in the detailed phase of the design process, turbulence scale-resolving methods (such as LES or similar approaches) can be preferred to significantly improve the accuracy. Despite that, in dealing with multi-physics and multi-scale problems, as for Conjugate Heat Transfer (CHT) in presence of radiation, transient approaches are not always affordable and appropriate numerical treatments are necessary to properly account for the huge range of characteristics scales in space and time that occur when turbulence is resolved and heat conduction is simulated contextually. The present work describes an innovative methodology to perform CHT simulations accounting for multi-physics and multi-scale problems. Such methodology, named U-THERM3D, is applied for the metal temperature prediction of an annular aeroengine lean burn combustor. The theoretical formulations of the tool are described, together with its numerical implementation in the commercial CFD code ANSYS Fluent. The proposed approach is based on a time de-synchronization of the involved time dependent physics permitting to significantly speed up the calculation with respect to fully coupled strategy, preserving at the same time the effect of unsteady heat transfer on the final time averaged predicted metal temperature. The results of some preliminary assessment tests of its consistency and accuracy are reported before showing its exploitation on the real combustor. The results are compared against steady-state calculations and experimental data obtained by full annular tests at real scale conditions. The work confirms the importance of high-fidelity CFD approaches for the aerothermal prediction of liner metal temperature.     

Generalized Complex Spherical Harmonics, Frame Functions, and Gleason Theorem

Consider a finite dimensional complex Hilbert space ${\mathcal{H}}$ , with ${dim(\mathcal{H}) \geq 3}$ , define ${\mathbb{S}(\mathcal{H}):= \{x\in \mathcal{H} \:|\: \|x\|=1\}}$ , and let ${\nu_\mathcal{H}}$ be the unique regular Borel positive measure invariant under the action of the unitary operators in ${\mathcal{H}}$ , with ${\nu_\mathcal{H}(\mathbb{S}(\mathcal{H}))=1}$ . We prove that if a complex frame function ${f : \mathbb{S}(\mathcal{H})\to \mathbb{C}}$ satisfies ${f \in \mathbb{L}^2(\mathbb{S}(\mathcal{H}), \nu_\mathcal{H})}$ , then it verifies Gleason’s statement: there is a unique linear operator ${A: \mathcal{H} \to \mathcal{H}}$ such that ${f(u) = \langle u| A u\rangle}$ for every ${u \in \mathbb{S}(\mathcal{H}).\,A}$ is Hermitean when f is real. No boundedness requirement is thus assumed on f a priori.     

Calibration of a multifactor model for the forward markets of several commodities

We propose a model for the evolution of forward prices of several commodities, which is an extension of the factor forward model in [1, 2], to a market where multiple commodities are traded. We calibrate this model in a market where forward contracts on multiple commodities are present, using historical forward prices. First, we calibrate separately the four coefficients of each individual commodity, using an approach based on quadratic variation/covariation of forward prices. Then, with the same technique, we pass to the estimation of the mutual correlation among the Brownian motions driving the different commodities. This calibration is compared to a calibration method used by practitioners, which uses rolling time series and requires a modification of the model, but turns out to be more accurate in practice, especially with a low frequency of observed transaction. We present efficient methods to perform the calibration with both methods, as well as the calibration of the intercommodity correlation matrix. Then we calibrate our model to WTI, ICE Brent and ICE Gasoil forward prices. Finally we present a method for estimating spot volatility from forward parameters, with an application to the WTI spot volatility.