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

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Biofibres and Biocomposites

The vast research area of modelling of 3D woven fabrics can be subdivided in several domains, each of them having its own challenges and difficulties, - some are already solved and implemented in software, some still wait for their solution. The paper discusses some of these problems and reviews the available solutions. − Calculate the deformation resistance of the fabric (in tension, shear and compression), based on the geometrical model and mechanical behaviour of the yarns in tension, bending and compression − The deformation modeling can be done using finite element (FE) method. Then the yarn volumes should be meshed correctly, and contacts between the yarns have to be represented in the model − Finally, if the fabric serves as reinforcement to composite, then mechanical properties of composites can be calculated based on the model of internal geometry of the fabric. This "road map" is perfectly applicable to 3D fabrics, and the present paper presents the overview of its steps.

Modelling 3d fabrics and 3d-reinforced composites: challenges and solutions

Proposes an algorithm for the computation of maximum needle penetration force; it introduces the direct dependence of penetration force on fabric structural parameters and warp and weft geometrical and mechanical properties. Uses the approach to the simulation of local deformation of woven material which accounts for the thread resistance to crimp change and friction forces when the thread is shifted from its original position in the fabric structure as the result of its interaction with a needle. The resistance of threads to tension caused by a needle pushing them from their straight‐line paths is also accounted for. The resulting formulae give the dependence of needle penetration force for a plain‐woven fabric on the following parameters: needle diameter and surface angle; warp and weft spacing, dimensions, crimp height and bending rigidity; friction coefficients thread‐thread and thread‐needle. For a non‐plain‐woven fabric the linear dependence of penetration force on the fabric tightness is suggested. The comparison with the published and specially measured penetration force data proves the predictive ability of the model to be qualitatively accurate and quantitatively reasonable.

A predictive model for the penetration force of a woven fabric by a needle

Textile composites models: integrating strategies

A software package for the prediction of woven fabrics geometrical and mechanical properties

Interlayer hybrid carbon fiber/self-reinforced polypropylene composites possess a rare combination of lightness, stiffness and ductility, but they do suffer from a catastrophic stress drop when the carbon fiber layer fractures. To promote a gradual failure of the hybrids, we introduced discontinuities in the carbon fiber layer by partially cutting it at multiple locations perpendicularly to the fiber direction. By altering characteristics of the discontinuities (their length and number over the specimen width), we were able to influence the failure mechanisms and tensile performance of these hybrid composites. When the cut length was increased to 15 mm, the carbon fiber layer fragmented and delaminated at the cut sites inducing a gradual failure development in the hybrid. The concept of fracture process zone was applied to explain the failure mechanisms in these hybrid composites.

Stepan Vladimirovitch Lomov

Papers

Modelling 3d fabrics and 3d-reinforced composites: challenges and solutions

A predictive model for the penetration force of a woven fabric by a needle

Textile composites models: integrating strategies

A software package for the prediction of woven fabrics geometrical and mechanical properties

Discontinuities as a way to influence the failure mechanisms and tensile performance of hybrid carbon fiber/self-reinforced polypropylene composites