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 implementation of mathematical models of ballistic impact on textile structures revealed some computational problems, arising from the complex wave structure of transversal impact on an orthotropic plate, and also from an empirical nature of deformation rapture criteria. The dependence of modelling results on computational options is discussed. A comparison between onedimensional, two-dimensional isothropic (circular symmetry) and twodimensional orthotropic impact problems is given.

/pdf/computational-aspects-of-modelling-of-ballistic-impact-on-2kpjqcob93.pdf

Computational aspects of modelling of ballistic impact on woven structures

Mathematical simulation of the high-velocity impact on woven targets

Variability in textile composites is substantial. A full characterisation of the internal geometry supports material design and increases the reliability of numerical simulations. An approach is presented and tested to obtain a full statistical description of the internal structure of a carbon-epoxy 2/2 twill woven composite, produced using resin transfer moulding. In a first step experimental data are collected using micro-CT to characterise the short range, i.e. within unit cell dimensions, and optical imaging for the long range, spanning several unit cells. The statistical information of the tow reinforcement is quantified per tow type, warp and weft direction, in terms of standard deviation and correlation length. The largest variation is found for the in-plane tow centroid coordinate with a significantly different behaviour in warp and weft direction. Tow cross-sectional properties such as area and aspect ratio vary within the unit cell size with limited scatter. Cross-correlation between neighbouring tows is only observed for the in-plane position. In a second step the statistical data are the input for a multi-scale modelling strategy to generate virtual specimens with random tow reinforcement. While the mean trends of each tow property are directly taken from the experiments, the deviations are generated by two different geometry generators. The properties without cross-correlation are produced using a Markov Chain algorithm, while the cross-correlated in-plane coordinate is generated using the Karhunen-Loève series expansion. Virtual specimens are obtained which possess the same statistical information as present in the experimental samples.

https://lirias.kuleuven.be/bitstream/123456789/459727/1/Eurodyn2014_paper_Vanaerschot.pdf

Stochastic multi-scale modelling of composite materials based on experimental data

A general approach to 3-D progressive failure modelling and strength predictions of textile composites, based on 3-D Mosaic model, is demonstrated on the case of noncrimp 3-D orthogonal woven fabric composites. A combined theoretical-experimental study, performed for one typical E-glass 3D orthogonal non-crimp weave composite, showed excellent agreement between theoretical and experimental results.

Stepan Vladimirovitch Lomov

Papers

Computational aspects of modelling of ballistic impact on woven structures

Mathematical simulation of the high-velocity impact on woven targets

Stochastic multi-scale modelling of composite materials based on experimental data

A combined theoretical and experimental study of progressive failure of non-crimp 3D orthogonal weave composite

A novel textile composites analysis tool