Peeling of an elastic membrane tape adhered to a substrate by a uniform cohesive traction

An analytical model is provided for the peeling of a tape from a surface to which it adheres through cohesive tractions. The tape is considered to be a membrane without bending stiffness and is initially attached everywhere to a flat rigid surface. The tape is assumed to deform in plane strain, and finite deformations in the form of elastic strains are accounted for. The cohesive tractions are taken to be uniform when the tape is within a critical interaction distance from the substrate and then to fall immediately to zero once this critical interaction distance is exceeded. When the distance between the tape and the substrate is zero, repulsive and attractive tractions balance to zero; in this segment, sliding of the tape relative to the substrate is forbidden when we pull the tape up somewhere in the middle, though we permit such sliding when the tape is peeled from one end. In the cohesive zone and where the tape is detached, the interaction of the tape with the substrate is frictionless. Results are given for the force to peel a neo-Hookean tape at any angle up to vertical when one end of it is pulled away from the substrate, as well as for scenarios when the tape is lifted somewhere in the middle to form a V shape being pulled away from the substrate.     

Simultaneous column-and-row generation for large-scale linear programs with column-dependent-rows

In this paper, we develop a simultaneous column-and-row generation algorithm that could be applied to a general class of large-scale linear programming problems. These problems typically arise in the context of linear programming formulations with exponentially many variables. The defining property for these formulations is a set of linking constraints, which are either too many to be included in the formulation directly, or the full set of linking constraints can only be identified, if all variables are generated explicitly. Due to this dependence between columns and rows, we refer to this class of linear programs as problems with column-dependent-rows. To solve these problems, we need to be able to generate both columns and rows on-the-fly within an efficient solution approach. We emphasize that the generated rows are structural constraints and distinguish our work from the branch-and-cut-and-price framework. We first characterize the underlying assumptions for the proposed column-and-row generation algorithm. These assumptions are general enough and cover all problems with column-dependent-rows studied in the literature up until now to the best of our knowledge. We then introduce in detail a set of pricing subproblems, which are used within the proposed column-and-row generation algorithm. This is followed by a formal discussion on the optimality of the algorithm. To illustrate our approach, the paper is concluded by applying the proposed framework to the multi-stage cutting stock and the quadratic set covering problems.     

A Contact Homogenization Framework for Granular Interfaces

A computational contact homogenization framework is developed for contact interfaces with dry granular third bodies. The micro-to-macro transition procedure that forms the basis of this framework consists of projecting the macroscale contact pressure and slip velocity to the observable test surface of a representative contact element. The solution of the local microscale problem reveals a macroscale friction coefficient where inelastic effects are taken into account in a finite deformation setting. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Unprecedented Domino Double Allylsilane [3+2] Cycloaddition/Wagner–Meerwein Rearrangement/Friedel–Crafts Alkylation/Elimination Reaction Sequence Leading to a Novel Pentacyclic Ring System

A stereoselective synthesis of the disilyl derivatives 3 is achieved by the title reaction, an unprecedented Lewis acid promoted domino reaction, between the cross-conjugated dienone 1 and the allylsilanes 2 . The configurations of the five stereogenic centers of this novel ring system are established in the first step of the reaction sequence, the double [3+2] cycloaddition.     

Optical dephasing of the S1 ← S0 transition of free-base porphin in an n-decane host studied by photochemical hole-burning: a case of slow exchange

The homogeneous width and frequency of S₁ ← S₀ 0-0 transitions of free-base porphin in site B of n-decane are studied by photochemical hole-burning (T = 1.2–4.2 K). A localized phonon mode of 7 cm^?1 is identified as a phonon sideband and holes burnt into it yield a lifetime of 115 ± 20 ps. The results are consistent with the exchange model for slow exchange.     

Precision laser spectroscopy of highly charged ions

Recently, intense beams of highly charged ions have become available at heavy ion cooler rings. The obstacle for producing these highly interesting candidates is the large binding energy of K-shell electrons in heavy systems in excess of 100 keV. One way to remove these electrons is to strip them off by passing the ion through material. In the cooler ring, the ions are cooled to a well defined velocity. At the SIS/ESR complex it is possible to produce, store, and cool highly charged ions up to bare uranium with intensities exceeding 10⁸ atoms in the ring. This opens the door for precision laser spectroscopy of hydrogenlike-heavy ions, e.g.²⁰⁹Bi⁸²⁺, and allows to examine the interaction of the single electron with the large fields of the heavy nucleus, exceeding any artificially produced electric and magnetic fields by orders of magnitude. In the electron cooler the interaction of electrons and highly charged ions otherwise only present in the hottest plasmas can be studied.