Exploiting planarity in separation routines for the symmetric traveling salesman problem

At present, the most successful approach for solving large-scale instances of the Symmetric Traveling Salesman Problem to optimality is branch-and-cut. The success of branch-and-cut is due in large part to the availability of effective separation procedures; that is, routines for identifying violated linear constraints.

For two particular classes of constraints, known as comb and domino-parity constraints, it has been shown that separation becomes easier when the underlying graph is planar. We continue this line of research by showing how to exploit planarity in the separation of three other classes of constraints: subtour elimination, 2-matching and simple domino-parity constraints.     

Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations

In this paper we consider a class of planar autonomous systems having an isolated limit cycle x₀ of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We consider two functions, defined by means of the eigenfunctions of the adjoint of the linearized system, and we formulate conditions in terms of them in order to have the existence of two geometrically distinct families of T-periodic solutions of the autonomous system when it is perturbed by nonsmooth T-periodic nonlinear terms of small amplitude. We also show the convergence of these periodic solutions to x₀ as the perturbation disappears and we provide an estimation of the rate of convergence. The employed methods are mainly based on the theory of topological degree and its properties that allow less regularity on the data than that required by the approach, commonly employed in the existing literature on this subject, based on various versions of the implicit function theorem.     

Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1,…,n}, then with probability tending to 1 as n→∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.     

Dendriform equations

We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota–Baxter operators, e.g. the Riemann integral map or Jackson's q-integral.     

Aragonite twinning in gastropod nacre

Aragonite twinning in gastropod nacre has been investigated using scanning electron microscopy (SEM), electron back-scattered diffraction (EBSD), and transmission electron microscopy (TEM) with the focused ion beam (FIB) sample preparation technique. At the growth front of nacre, Haliotis discus hannai and Omphalius rusticus form a “stack-of-coins” structures, which consist of pseudo-hexagonal and elliptical aragonite tablets, respectively. SEM, EBSD, and TEM analyses revealed that these tablets are monolithic single crystal and almost free of the {1 1 0} twins that are common in aragonite of biotic or abiotic origin. The longest diagonal of the hexagon and the longer axis of the ellipse are parallel to the a-axis of aragonite. The crystal orientation of each tablet in a stack, measured by TEM-Kikuchi pattern analysis, is almost the same but there is occasionally {1 1 0} twin-like relationship between adjacent tablets along the stacking. On the other hand, the fibrous aragonite layer formed prior to the nacreous structure is composed of polycrystalline aragonite with high density of {1 1 0} twins. TEM observation suggests that the interlamellar organic sheet prevents the inheritance of the twins, by selecting only single domain of the twins, through the mineral bridge.     

3-list-coloring planar graphs of girth 4

In Thomassen (1995) [4], Thomassen proved that planar graphs of girth at least 5 are 3-choosable. In Li (2009) [3], Li improved Thomassen’s result by proving that planar graphs of girth 4 with no 4-cycle sharing a vertex with another 4- or 5-cycle are 3-choosable. In this paper, we prove that planar graphs of girth 4 with no 4-cycle sharing an edge with another 4- or 5-cycle are 3-choosable. It is clear that our result strengthens Li’s result.     

Poly(3-hexylthiophene-2,5-diyl) based diodes for ionizing radiation dosimetry applications

Accurate measurements of radiation dose are essential prerequisites for the safe and effective use of ionizing radiation in diagnostic and therapeutic medical applications. Recently, dosimeters based on organic polymers have been developed for this purpose. In this work, Poly(3-hexylthiophene-2,5-diyl) (P3HT) based organic diodes were evaluated as potential radiation dosimeters by quantifying the radiation-induced photocurrent under various measurement conditions. Control devices were fabricated in which the P3HT was replaced by polystyrene (PS) for the purpose of quantifying the non-photocurrent contribution to the measured signal. Net photocurrent was determined by subtracting the signal from the PS devices from the signal in the P3HT devices under identical measurement conditions. The responses of these devices were tested in various beam qualities: 100 kVp, 180 kVp, 300 kVp and 6 MV, 18 MV photons. The influences of electric field, film thickness and dose rate on dosimeter sensitivity were investigated. The diodes produced a linear increase in current with increasing dose rate. They demonstrated an increase in sensitivity with increased instantaneous dose rate and an increase in sensitivity at the lowest average dose rates studied here. The sensitivities for different energies were 22.9 nC/Gy, 21.8 nC/Gy and 21.4 nC/Gy for 100 kVp, 180 kVp and 300 kVp, respectively; and 14.5 nC/Gy, 14.7 nC/Gy for 6 MV and 18 MV, respectively for device with P3HT thickness 29 μm.     

On the Characterization of the Dynamic Performances of Planar Manipulators

The characterization of the dynamic performances of a manipulator is important both to compare different manipulators and to improve the dynamic performances of a manipulator during the design stage. In a previous paper the concepts of swiftness and of dynamic isotropy were used to characterize some dynamic performances of 3-dof manipulators. This paper analyzes the usefulness of these concepts for three-dof planar manipulators and shows that the concept of swiftness is still significant, whereas the concept of dynamic isotropy has no practical interest. Moreover, it introduces three new dynamic properties that are useful in the design of a 3-dof planar manipulator. Finally, it proposes some indices that measure both the swiftness and the three new dynamic properties and shows how to use them, both for evaluating the dynamic performances of a given 3-dof planar manipulator and for improving the dynamic performances during its design.     

Development of the large increment method for elastic perfectly plastic analysis of plane frame structures under monotonic loading

The displacement-based finite element method dominates current practice for material nonlinear analysis of structures. However, there are several characteristics that may limit the effectiveness of this approach. In particular, for elastoplastic analysis, the displacement method relies upon a step-by-step incremental approach stemming from flow theory and also requires significant mesh refinement to resolve behavior in plastic zones. This leads to computational inefficiencies that, in turn, encourage the reconsideration of force-based approaches for elastoplastic problems.One of these force algorithms that has been recently developed is the large increment method. The main advantage of the flexibility-based large increment method (LIM) over the displacement method is that it separates the global equilibrium and compatibility equations from the local constitutive relations. Consequently, LIM can reach the solution in one large increment or in a few large steps, thus, avoiding the development of cumulative errors. This paper discusses the extension of the large increment methodology for the nonlinear analysis of plane frame structures controlled by an elastic, perfectly plastic material model. The discussion focuses on the power of LIM to handle these nonlinear problems, especially when plastic hinges form in the frame and ultimately as the structure approaches the collapse stage. Illustrative planar frame examples are presented and the results are compared with those obtained from a standard displacement method.     

Creeping flow of viscoplastic materials through a planar expansion followed by a contraction

In this work, the creeping flow of a viscoplastic fluid through a planar channel with an expansion followed by a contraction is analyzed numerically. The solution of the conservation equations of mass and momentum is obtained via the finite volume method. In order to model the non-Newtonian behavior of the fluid, it was used the generalized Newtonian fluid constitutive equation. The viscosity function was the one proposed by Souza Mendes and Dutra [Souza Mendes, P.R., Dutra, E.S.S., 2004. Viscosity function for yield-stress liquids. Appl. Rheol. 14, 296–302]. The yielded and unyielded regions are obtained for several combinations of rheological parameters. The influence of these parameters on pressure drop through the cavity is also obtained and analyzed.