Integrated Planning in a Steelworks: The Choice of Alternative Practices in Previous Processes to Augment Productivity at the Final Rolling Stage

The case study presented in this paper is an example in which the very different contingencies associated, on the one hand, with steel-making and, on the other hand, with cold rolling are considered together in seeking a maximum of profitability. In the works under investigation the steel-making area was a general bottleneck, while the cold mill was a bottleneck specific to the most profitable products, and the solution obtained actually involved a narrowing of the general bottleneck. The methods of calculation used in this study are not original. It is their synthesis leading to the technically important decision to create a new ingot size which deserves attention.     

Carbon-13 NMR of polyethylenes: Correlation of the crystalline component T1 with structure

The carbon-13 spin-lattice relaxation times T₁ of the crystalline portion of a set of polyethylenes have been studied. Chain structure and crystallization conditions have been varied over the widest possible extremes so that large differences are developed in the level of crystallinity, the supermolecular structure, and the crystallite thickness. Concomitantly, the observed crystalline T₁ values cover the extraordinarily wide range of about 40–4500 s. They bear a one-to-one relation with the crystallite thickness, which is found to be the key structural variable determining this property. A correlation with the temperature for the α-transition can be established, which implies a similar type of segmental motions for the two phenomena. Major changes in the interfacial structure can also have a drastic influence on the value for the crystalline T₁. Analysis of the magnetization decay curve also allows for a quantitative determination of the degree of crystallinity, which is found to be in excellent agreement with the corresponding value found from Raman spectroscopy.     

Molecule-molecule versus molecule-substrate interactions in the assembly of oligothiophenes at surfaces

In this paper we present a joint experimental and theoretical approach for the study of the assembly of end-substituted oligothiophenes at surfaces with different polarities (i.e., mica vs graphite). Scanning probe microscopy studies of (sub)monolayer deposits show various types of structures (one-dimensional fibrils, two-dimensional regular layers, and monolayers), depending on the nature of the end groups and the substrate. Using molecular modeling with an atomistic approach, we focus on the interplay between the molecule-molecule (and segment-segment) interactions and the molecule-substrate interactions and their influence on the observed morphologies and the stacking geometry. Such information is relevant for controlling the structural order in thin layers of thiophene oligomers for use in field-effect transistor applications, for example, by modifying the nature of dielectric material over which those compounds are deposited.     

Influence of chlorine substitution on the self-assembly of zinc phthalocyanine

The adsorption and ordering of zinc phthalocyanine (ZnPc) and octachloro zinc phthalocyanine (ZnPcCl(8)) on an Ag(111) surface is studied in situ by scanning tunneling microscopy under ultrahigh vacuum. Two-dimensional self-assembled supramolecular domains are observed for these two molecules. We show how substituting chlorine atoms for half of the peripheral hydrogen atoms on ZnPc influences the self-assembly mechanisms. While intermolecular interactions are dominated by van der Waals forces in ZnPc molecular networks, ZnPcCl(8) molecular packing undergoes a sequential phase evolution driven by the creation of C-Cl...H-C hydrogen bonds between adjacent molecules. At the end of this evolution, the final molecular assembly involves all possible hydrogen bonds. Our study also reveals the influence of molecule-substrate interactions through the presence of fault lines generating a stripe structure in the molecular film.     

Functional polymers: scanning force microscopy insights

Scanning force microscopy (SFM) and related techniques make it possible to visualize polymer systems with a molecular resolution. Beyond imaging, they also enable the unveiling of a variety of (dynamic) physico-chemical properties of both isolated polymer chains and their supramolecular architectures, including structural, mechanical and electronic properties. This article reviews recent progress in the use of SFM on polymers, with a particular emphasis on the mechanical properties of copolymers and single polymer chains, as well as on the bottom-up fabrication of supramolecular polymeric (helical) nanostructures in particular based upon pi-conjugated macromolecules as building blocks for nanoelectronics. Through a detailed understanding of the polymer behavior, we propose solutions for the generation of organic functional (nano)systems.     

Phase slip phenomena in superconductors: from ordered to chaotic dynamics

We consider flux penetration to a 2D superconducting cylinder. We show that in the low field limit the kinetics is deterministic. In the strong field limit the dynamics becomes stochastic. Surprisingly the inhomogeneity in the cylinder reduces the level of stochasticity because of the predominance of Kelvin-Helmholtz vortices.     

Interacting branching process as a simple model of innovation

We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/τ at each generation. In contrast with mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For τ = ∞, surviving processes exhibit a bottleneck before exploding superexponentially-a growth consistent with a law of accelerating returns. This behavior persists for finite τ. We analyze, in detail, the asymptotic behavior as p→0.     

Semidefinite and linear programming integrality gaps for scheduling identical machines

Sherali and Adams (SIAM J Discrete Math 3:411–430, 1990) and Lovász and Schrijver (SIAM J Optim 1:166–190, 1991) developed systematic procedures to construct the hierarchies of relaxations known as lift-and-project methods. They have been proven to be a strong tool for developing approximation algorithms, matching the best relaxations known for problems like Max-Cut and Sparsest-Cut. In this work we provide lower bounds for these hierarchies when applied over the configuration LP for the problem of scheduling identical machines to minimize the makespan. First we show that the configuration LP has an integrality gap of at least 1024/1023 by providing a family of instances with 15 different job sizes. Then we show that for any integer n there is an instance with n jobs in this family such that after \(\varOmega (n)\) rounds of the Sherali–Adams (\(\text {SA}\)) or the Lovász–Schrijver (\(\text {LS}_+\)) hierarchy the integrality gap remains at least 1024/1023.     

The semi-classical limit of large fermionic systems

We study a system of N fermions in the regime where the intensity of the interaction scales as 1 / N and with an effective semi-classical parameter \(\hbar =N^{-1/d}\) where d is the space dimension. For a large class of interaction potentials and of external electromagnetic fields, we prove the convergence to the Thomas–Fermi minimizers in the limit \(N\rightarrow \infty \). The limit is expressed using many-particle coherent states and Wigner functions. The method of proof is based on a fermionic de Finetti–Hewitt–Savage theorem in phase space and on a careful analysis of the possible lack of compactness at infinity.     

Reduced Dynamics of the Non-holonomic Whipple Bicycle

Though the bicycle is a familiar object of everyday life, modeling its full nonlinear three-dimensional dynamics in a closed symbolic form is a difficult issue for classical mechanics. In this article, we address this issue without resorting to the usual simplifications on the bicycle kinematics nor its dynamics. To derive this model, we use a general reduction-based approach in the principal fiber bundle of configurations of the three-dimensional bicycle. This includes a geometrically exact model of the contacts between the wheels and the ground, the explicit calculation of the kernel of constraints, along with the dynamics of the system free of any external forces, and its projection onto the kernel of admissible velocities. The approach takes benefits of the intrinsic formulation of geometric mechanics. Along the path toward the final equations, we show that the exact model of the bicycle dynamics requires to cope with a set of non-symmetric constraints with respect to the structural group of its configuration fiber bundle. The final reduced dynamics are simulated on several examples representative of the bicycle. As expected the constraints imposed by the ground contacts, as well as the energy conservation, are satisfied, while the dynamics can be numerically integrated in real time.