EXISTENCE OF A CUSP POINT ON A FOLD BIFURCATION CURVE AND STABILITY OF THE ASSOCIATED FIXED POINT: CASE OF AN n-DIMENSIONAL MAP

Considering an n–dimensional map T, a necessary and sufficient condition for the existence of a cusp point on a fold bifurcation curve in a parameter plane of T is proposed. In the case of a nondegenerated cusp point, a necessary and sufficient condition for the stability of the associated nonhyperbolic fixed point is established. These conditions, obtained using the classical methods (center manifold, normal form), are expressed in an explicit algebraic well adapted for numerical computing. </jats:p

APPEARANCE AND DISAPPEARANCE OF A DOVETAIL STRUCTURE IN THE PARAMETER PLANE OF AN n-DIMENSIONAL MAP

A dovetail structure is made up of two cusp points located on a same fold bifurcation curve in a parameter plane of a discrete dynamical system defined by a differentiable map. When a third parameter varies, an existing dovetail structure may disappear by the merging of the two cusp points, or a dovetail structure may appear by the creation of two cusp points on a locally smooth fold bifurcation curve. This paper presents a method permitting to determine the value of the third parameter at which a dovetail structure may appear or disappear in n-dimensional systems. The exposed method is based on the definition of a new singular point, called E-point, belonging to a fold bifurcation curve. </jats:p

Experimental investigation of the variability of concrete durability properties

International audienceOne of the main objectives of the APPLET project was to quantify the variability of concrete properties to allow for a probabilistic performance-based approach regarding the service lifetime prediction of concrete structures. The characterization of concrete variability was the subject of an experimental program which included a significant number of tests allowing the characterization of durability indicators or performance tests. Two construction sites were selected from which concrete specimens were periodically taken and tested by the different project partners. The obtained results (mechanical behavior, chloride migration, accelerated carbonation, gas permeability, desorption isotherms, porosity) are discussed and a statistical analysis was performed to characterize these results through appropriate probability density functions