On birational transformations of pairs in the complex plane

This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of the art and provide some new results on this subject.      

A refined cohesive zone model that accounts for inertia of cohesive zone of a moving crack

Existing cohesive zone models assume that actual fracture zone of non-zero mass can be modeled by a line segment (cohesive zone) with no mass and inertia. In the present work, a simplified mass-spring model is presented to study inertia effect of cohesive zone on a mode-I steady-state moving crack. It is showed that fracture energy predicted by the present model increases dramatically when a finite limiting crack speed is approached. Reasonable agreement with known experiments indicates that the present model has the potential to catch the inertia effect of cohesive zone which has been ignored in existing cohesive zone models and better simulate dynamic fracture at high crack speed.     

Distribution of the inter and intra inertia in conditional MCA

Conditional Multiple Correspondence Analysis (MCA), where a control variable plays the role of a partition model, allows us to decompose global inertia into between inertia and within inertia. The problem is to assess when the conditioning variable gives different results with respect to the unconditional analysis. In this paper, we study the asymptotic distribution function of these inertias, which can allow us to determine whether conditioning is significant. Some simulations were performed to corroborate the established results.     

Mathematical Modeling and Parameter Identification of a Planar Servo-Pneumatic Test Facility. Part II: Experimental Identification

The main objective of this paper is the identification of the inertia parameters of a rigid body under planar motion using a planar servo-pneumatic test facility designed for vibration tests. The hardware realization of the test facility used is discussed. The pneumatic components as well as the mechanical components of the test facility are described by linear and by nonlinear mathematical models, derived in Part I [1] of this paper. These model equations are used as identification hypotheses in the identification process. A comparison of time histories obtained by computer simulations of the nonlinear test facility model and by laboratory experiments shows that this nonlinear test facility model provides a realistic identification hypothesis for the estimation experiments. Based on different model hypotheses the inertia parameters of the test table and of the payload have been successfully identified from laboratory experiments. The relative estimation errors of the identified parameters are less than 10%.     

Locating the Eigenvalues of Trees

e give an O(n) method that computes, for any tree T and interval (α,β), how many eigenvalues of T lie within the interval. Our method is based on Sylvester’s Law of Inertia. We use our algorithm to show that the nonzero eigenvalues of a caterpillar are simple. It follows that caterpillars having b back nodes, where , are not integral. We also show that among the regular caterpillars C(b,k) formed by adjoining k legs to each of b back nodes, all positive roots are in the interval , and C(b,k) is not integral if b>2.     

Sparse inertially arbitrary patterns

An n-by-n sign pattern is a matrix with entries in {+,-,0}. An n-by-n nonzero pattern is a matrix with entries in {*,0} where * represents a nonzero entry. A pattern is inertially arbitrary if for every set of nonnegative integers n₁,n₂,n₃ with n₁+n₂+n₃=n there is a real matrix with pattern having inertia (n₁,n₂,n₃). We explore how the inertia of a matrix relates to the signs of the coefficients of its characteristic polynomial and describe the inertias allowed by certain sets of polynomials. This information is useful for describing the inertia of a pattern and can help show a pattern is inertially arbitrary. Britz et al. [T. Britz, J.J. McDonald, D.D. Olesky, P. van den Driessche, Minimal spectrally arbitrary sign patterns, SIAM J. Matrix Anal. Appl. 26 (2004) 257–271] conjectured that irreducible spectrally arbitrary patterns must have at least 2n nonzero entries; we demonstrate that irreducible inertially arbitrary patterns can have less than 2n nonzero entries.     

Characterizing the constitutive response and energy absorption of rigid polymeric foams subjected to intermediate-velocity impact

As an optimum energy-absorbing material system, polymeric foams are needed to dissipate the kinetic energy of an impact, while maintaining the impact force transferred to the protected object at a low level. Therefore, it is crucial to accurately characterize the load bearing and energy dissipation performance of foams at high strain rate loading conditions. There are certain challenges faced in the accurate measurement of the deformation response of foams due to their low mechanical impedance. In the present work, a non-parametric method is successfully implemented to enable the accurate assessment of the compressive constitutive response of rigid polymeric foams subjected to impact loading conditions. The method is based on stereovision high speed photography in conjunction with 3D digital image correlation, and allows for accurate evaluation of inertia stresses developed within the specimen during deformation time. Full-field distributions of stress, strain and strain rate are used to extract the local constitutive response of the material at any given location along the specimen axis. In addition, the effective energy absorbed by the material is calculated. Finally, results obtained from the proposed non-parametric analysis are compared with data obtained from conventional test procedures.     

Computing the inertia from sign patterns

A symmetric matrix A is said to be sign-nonsingular if every symmetric matrix with the same sign pattern as A is nonsingular. Hall, Li and Wang showed that the inertia of a sign-nonsingular symmetric matrix is determined uniquely by its sign pattern. The purpose of this paper is to present an efficient algorithm for computing the inertia of such symmetric matrices. The algorithm runs in time for a symmetric matrix of order n with m nonzero entries. In addition, it is shown to be NP-complete to decide whether the inertia of a given symmetric matrix is not determined by its sign pattern.     

Deactivation of glass capillary columns by silylation. Part 1: Principles and basic technique

A deactivation procedure is described based on a published method using hexamethyldisilazane in the gas phase. In addition to unusually high inertia and thermostability, the method produces truly neutral columns which allow simultaneous analysis of moderately strong free acids and bases. The silylated columns show their full potential only with on-column injection. Preliminary experimental directions are given; more elaborate directions will become available after extended optimization work.     

Modelling of dynamic ductile fracture and application to the simulation of plate impact tests on tantalum

A model of dynamic damage by void nucleation and growth is proposed for elastic-viscoplastic materials sustaining intense loading. The model is dedicated to ductile materials for which fracture is caused by microvoiding. The material contains potential nucleation sites where microvoids are generated when the local pressure overcomes the nucleation pressure. A probability density function is adopted to describe the fluctuation of the nucleation pressure within the material. The void growth is described by using a hollow sphere model where micro-inertia effects are accounted for. The matrix weakening due to void growth is also included.The model has been first tested under uniaxial deformation. When the strain rate is assumed constant, the pressure inside the material has nearly a linear response up to a maximum. An analytical expression for the maximum pressure is proposed.Finite element simulations of plate impact tests have been carried out and compared to experiments on tantalum. From simulations based on the proposed model, an increase of the spall strength is observed with higher shock intensities. Therefore, the relationship between the velocity pullback and spall strength usually assumed in the literature (based on the acoustic approach) seems to be inadequate. Velocity profiles are simulated for different flyer thicknesses and different impact velocities with close agreement with experiments.