The study of the isoperimetric problem in the presence of crystallographic symmetries is an interesting unsolved question in classical differential geometry: Given a space group G, we want to describe, among surfaces dividing Euclidean 3-space into two G-invariant regions with prescribed volume fractions, those which have the least area per unit cell of the group. We know that this periodic iso...

An unsupervised detection method for automatic flaw segmentation in patterned materials (textile, non-woven, paper) that has no need of any defect-free references or a training stage is presented in this paper. Printed materials having a pattern of colored squares, bands, etc. superimposed to the background texture can be advantageously analyzed using NIR illumination and a camera with enough s...

‎in this paper‎, ‎we investigate a damped korteweg-de‎ ‎vries equation with forcing on a periodic domain‎ ‎$mathbb{t}=mathbb{r}/(2pimathbb{z})$‎. ‎we can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic.

Composite materials are ideally suited to achieve multifunctionality since the best features of different materials can be combined to form a new material that has a broad spectrum of desired properties. Nature's ultimate multifunctional composites are biological materials. There are presently no simple examples that rigorously demonstrate the effect of competing property demands on composite m...

Catalyst selectivity is associated with well-defined homogeneous active sites. Transition metal complexes and organocatalysts are highly active and selective in the homogeneous phase, and their heterogenization by incorporating them into inorganic solid materials allows combining their excellent catalytic activity with improved separation, recovering and recycling properties. In this article, w...

A multiphysics micromechanics model is developed to predict the effective properties as well as the local fields of periodic smart materials responsive to fully coupled electric, magnetic, thermal and mechanical fields. This work is based on the framework of the variational asymptotic method for unit cell homogenization (VAMUCH), a recently developed micromechanics modeling scheme. To treat the...

In this study, we report a novel periodic material with negative Poisson's ratio (also called auxetic materials) fabricated by denting spherical dimples in an elastic flat sheet. While previously reported auxetic materials are either porous or comprise at least two phases, the material proposed here is non-porous and made of a homogeneous elastic sheet. Importantly, the auxetic behavior is indu...

1 Abstract This paper describes a topology optimization method for structures in electromagnetic materials. The material structures that exhibit special characteristics in terms of the repulsion of electromagnetic waves tend to be configured as periodical composite structures built of two or more materials. Generally termed “metamaterials”, these sometimes have especially unusual or even counte...

Several methods for the analysis of composite materials with periodic microstructure in which localized effects (such as concentrated loads, cracks and stationary/progressive damage) occur are resented. Owing to the loss of periodicity caused by these localized effects, it is no longer possible to identify and analyse a repeating unit cell that characterizes the periodic composite. For elastost...