There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

http://mech.spbstu.ru/images/b/bd/Potyondy_Cundall_2004_A_bonded-particle_model_for_rock.pdf

A bonded-particle model for rock

Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

Preface (P.-G. de Gennes). Foreword. 1. Introduction to basic notions and facts (H.J. Herrmann). 2. Experimental evidences for various materials. 2.1 Rupture and deformation of ceramics (J.-L. Chermant). 2.2 Failure mechanisms of composite materials (D. Baptiste). 2.3 Concrete: Large-scale heterogeneyies and size effects (P. Acker). 2.4 Fracture mechanisms of metals (D. Francois). 2.5 Mechanical properties of polymeric materials (L. Monnerie). 2.6 Viscous fingering and viscoelastic fracture in clays (H. van Damme and E. Lemaire). 3. Continuum and discrete description of elasticity and other rheological behavior (S. Roux). 4. Disorder (A. Hansen). 5. Modelization of fracture in disordered systems (H.J. Herrmann and S. Roux). 6. Breakdown of diluted and hierarchical systems (P.M. Duxbury). 7. Randomness in breaking thresholds (L. de Arcangelis). 8. Dielectric breakdown and single crackmodels (J. Kertesz). 9. Simple kinetic models for material failure and deformation (P. Meakin). 10. Fragmentation (S. Redner).

Statistical Models for the Fracture of Disordered Media

The current development of digital image correlation, whose displacement uncertainty is well below the pixel value, enables one to better characterise the behaviour of materials and the response of structures to external loads. A general presentation of the extraction of displacement fields from the knowledge of pictures taken at different instants of an experiment is given. Different strategies can be followed to achieve a sub-pixel uncertainty. From these measurements, new identification procedures are devised making use of full-field measures. A priori or a posteriori routes can be followed. They are illustrated on the analysis of a Brazilian test.

Digital Image Correlation: From Displacement Measurement to Identification of Elastic Properties - A Review

https://hal.archives-ouvertes.fr/hal-00013816/document

Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties – a Review

A new methodology is proposed to estimate displacement fields from pairs of images (reference and strained) that evaluates continuous displacement fields. This approach is specialized to a finite-element decomposition, therefore providing a natural interface with a numerical modeling of the mechanical behavior used for identification purposes. The method is illustrated with the analysis of Portevin–Le Châtelier bands in an aluminum alloy sample subjected to a tensile test. A significant progress with respect to classical digital image correlation techniques is observed in terms of spatial resolution and uncertainty.

/pdf/finite-element-displacement-fields-analysis-from-digital-30ph6qjmd3.pdf

"Finite-Element" Displacement Fields Analysis from Digital Images: Application to Portevin-Le Châtelier Bands

Relying on contact dynamics simulations, we study the statistical distribution of contact forces inside a confined packing of circular rigid disks with solid friction. We find the following: (1) The number of normal and tangential forces lower than their respective mean value decays as a power law. (2) The number of normal and tangential forces higher than their respective mean value decays exponentially. (3) The ratio of friction to normal force is uniformly distributed and is uncorrelated with normal force. (4) When normalized with respect to their mean values, these distributions are independent of sample size and particle size distribution.

/pdf/force-distributions-in-dense-two-dimensional-granular-i4e17tkuvg.pdf

Stéphane Roux

Papers

Statistical Models for the Fracture of Disordered Media

Digital Image Correlation: From Displacement Measurement to Identification of Elastic Properties - A Review

Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties – a Review

"Finite-Element" Displacement Fields Analysis from Digital Images: Application to Portevin-Le Châtelier Bands

Force Distributions in Dense Two-Dimensional Granular Systems