Interior symmetry and local bifurcation in coupled cell networks

A coupled cell system is a network of dynamical systems, or 'cells', coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells and edges that preserves all internal dynamics and all couplings. It is well known that symmetry can lead to patterns of synchronized cells, rotating waves, multirhythms, and synchronized chaos. Recently, the introduction of a less stringent form of symmetry, the 'symmetry groupoid', has shown that global group-theoretic symmetry is not the only mechanism that can create such states in a coupled cell system. The symmetry groupoid consists of structure-preserving bijections between certain subsets of the cell network, the input sets. Here, we introduce a concept intermediate between the groupoid symmetries and the global group symmetries of a network: 'interior symmetry'. This concept is closely related to the groupoid structure, but imposes stronger constraints of a group-theoretic nature. We develop the local bifurcation theory of coupled cell systems possessing interior symmetries, by analogy with symmetric bifurcation theory. The main results are analogues for 'synchrony-breaking' bifurcations of the Equivariant Branching Lemma for steady-state bifurcation, and the Equivariant Hopf Theorem for bifurcation to time-periodic states.     

Modeling aviation baggage screening security systems: a case study

Aviation security protects vital national interests, as well as passengers and aircraft. Key components of an aviation security system include baggage and passenger screening devices and operations. Determining how and where to assign (deploy) such devices can be quite challenging. Moreover, even after such systems are in place, it can be difficult to measure their effectiveness. This paper describes how discrete optimization models can be used to address these questions, based on three performance measures that quantify the effectiveness of airport baggage screening security device systems. These models are used to solve for optimal airport baggage screening security device deployments considering the number of passengers on a set of flights who have not been cleared using a security risk assessment system in use by the Federal Aviation Administration (i.e., passengers whose baggage is subjected to screening), the number of flights in this set, and the size of the aircraft for such flights. Several examples are provided to illustrate these results, including an example that uses data available from the Official Airline Guide.     

Trajectory control of incompletely restrained parallel-wire-suspended mechanism based on inverse dynamics

This paper discusses parallel wire mechanisms where an end-effector of the mechanism is suspended by multiple wires. The mechanisms enable not only three-dimensional (3-D) positioning but also 3-D orienting of the end-effector, unlike typical wire suspension-type mechanisms such as overhead crane. To discuss the parallel-wire-suspended mechanisms generally, two forms of basic dynamic equations are presented. Then the parallel wire mechanisms are classified into two types based on the basic equations. Dynamical properties of the two types of wire-suspended positioning mechanism are discussed. In this paper, one of the wire-suspended mechanism, incompletely restrained-type parallel wire mechanism, is mainly discussed on its inverse dynamics problem and its trajectory control problem. The inverse dynamics problem for the incompletely restrained-type mechanism plays an important role on its control problem, because the mechanism has low stiffness based on incomplete constraints on the suspended object which is governed by its dynamics. The paper proposes an antisway control method for the suspended object. In the method, the inverse dynamics calculation is used for nonlinear dynamics compensation to control the suspended object of the incompletely restrained parallel wire mechanism.     

The Soft-Contact Method and Instruments for Measuring the Surface Temperature of Solids

A method and instruments based on it are proposed for the contact measurement of surface temperature when carrying out industrial experiments and when monitoring technological parameters.     

Magnetotransport Calculations for Two-Dimensional Electrons with Spin-Orbit Interaction

We present calculations of the magnetoconductivity in a two-dimensional electron system including the Rashba spin-orbit interaction. Essential for these calculations is an extension of the self-consistent Born approximation which takes into account the electron spin degree of freedom. The calculated magnetoconductivity exhibits, besides the beating in the Shubnikov-de Haas oscillations, a modulation related to the spin-orbit induced crossings of Landau levels, as a consequence of spin-conserving scattering between spin-orbit coupled states.     

A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind

A fast and efficient numerical method based on the Gauss-Jacobi quadrature is described that is suitable for solving Fredholm singular integral equations of the second kind that are frequently encountered in fracture and contact mechanics. Here we concentrate on the case when the unknown function is singular at both ends of the interval. Quadrature formulae involve fixed nodal points and provide exact results for polynomials of degree 2n − 1, where n is the number of nodes. Finally, an application of the method to a plane problem involving complete contact is presented.     

Segmented polymer networks containing amino‐dendrimers

Polymer networks in which poly(propylene imine) dendrimers (Astramol?) are connected to each other by linear polytetrahydrofuran (polyTHF) segments, were prepared by two methods. The first method was a one‐step procedure in which bifunctionally living polyTHF, obtained by initiation of the THF polymerization with trifluoromethane sulfonic anhydride (triflic anhydride), was reacted with an amino‐dendrimer. This reaction was very fast but did not allow formation of the end products. The second method was a two‐step procedure. In a first step, living polyTHF, prepared with acryloyloxybutyl triflate as initiator, was grafted on an amino‐dendrimer, to form a star‐like, acrylate‐terminated polyTHF multi‐macromonomer with the dendrimer as core. In a second step, networks were obtained by Michael addition between the acrylate end‐groups and unreacted amino‐groups of the dendrimer. This cross‐linking reaction occurred spontaneously upon heating of the solution of the multi‐macromonomer with gelation times varying from a few minutes to a few hours, depending on the temperature and the composition of the prepolymers. With this method it was possible to prepare networks in the form of coatings or films. © 2003 Society of Chemical Industry     

Teaching robust programming

Robust programming aims to prevent abnormal termination or unexpected actions and requires code to handle bad (invalid or absurd) inputs in a way that is consistent with the developer's intent. For example, if an internal error occurs, the program might terminate gracefully rather than simply failing, providing enough information for the programmer to debug the program and avoiding giving the user additional access or information. This article focuses on teaching these principles.