This paper describes the main features of the CARPET language and its practical use for programming three-dimensional models of the contamination of soils developed in the CABOTO project. CARPET is a high-level language based on the cellular automata model, which supports rapid prototyping of a large number of applications in science and engineering. A CARPET implementation has been used for pr...

Consider a family of bounded domains Ωt in the plane (or more generally any Euclidean space) that depend analytically on the parameter t, and consider the ordinary Neumann Laplacian ∆t on each of them. Then we can organize all the eigenfunctions into continuous families u (j) t with eigenvalues λ (j) t also varying continuously with t, although the relative sizes of the eigenvalues will change ...

Let X be a standard 2-dimensional Brownian motion. There exists a.s. t ∈ (0, 1) such that X([0, t)) ∩ X((t, 1]) = ∅. It follows that X([0, 1]) is not homeomorphic to the Sierpiński carpet a.s.

Carpet manufacturers have wear labels assigned to their products by human experts who evaluate carpet samples subjected to accelerated wear in a test device. There is considerable industrial and academic interest in going from human to automated evaluation, which should be less cumbersome and more objective. In this paper, we present image analysis research on videos of carpet surfaces scanned ...

The results are in. Recent studies conducted by an independent testing laboratory show that when it comes to acoustics, commercial cushion makes carpet even better. To specifiers and end-users, it will come as no surprise that properly specified carpet cushion reduces noise when used in a commercial installation. What will be of interest is the degree of improvement that has been quantified in ...

A collaborative research programme between University of Bolton and Bradford University is investigating the effect of surplus carpet fibres on the strength as well as other important geotechnical properties of cohesive soils. Initial work concentrates on the manner in which the fibres affect the quick undrained properties of the reinforced soil. Four different surplus carpet fibre types are be...

The purpose of quantization of a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonhomogeneous probability measure P on R which has support the Sierpiński carpet generated by a set of four contractive similarity mappings with equal similarity ratios has been considered . For this probability measure, the optimal sets of n-...

controlling the electromagnetic waves propagation using optical transformation is a topic that finds many applications in recent years. one of the most important applications of these transformations is hiding the objects from radar waves, i.e. cloaking. hiding under the carpet or carpet cloak is a special type of cloaking that hides the objects situated between a metal sheet and the ground. in...

Realization of a perfect invisibility cloak still challenges the current fabricating technologies. Most experiments, if not all, are hence focused on carpet cloaks because of their relatively low requirements to material properties. Nevertheless, present invisibility carpets are used to hide beneath objects. Here, we report a carpet-like device to directionally conceal objects and further to cr...

Grating cloaks are a variation of dielectric carpet (or ground-plane) cloaks. The latter were introduced by Li and Pendry. In contrast to the numerical work involved in the quasi-conformal carpet cloak, the refractive-index profile of a conformal grating cloak follows a closed and exact analytical form. We have previously mentioned that finite-size conformal grating cloaks may exhibit better cl...