Rachad Zaki

The periodic unfolding method in domains with holes

We give a comprehensive presentation of the periodic unfolding method for perforated domains, both when the unit hole is a compact subset of the open unit cell and when this is impossible to achieve. In order to apply the method to boundary-value problems with non homogeneous Neumann conditions on the boundaries of the holes, the properties of the boundary unfolding operator are also extensively studied. The paper concludes with applications to such problems and examples of reiterated unfolding.

Students' interest in STEM education

In this paper we study the interest of students in the United Arab Emirates (UAE) from grade 9 to 12 in Science, Technology, Engineering, and Mathematics (STEM). Surveys were distributed to students who chose STEM tracks and students who chose non-STEM tracks in public and private schools, as well as universities, across the country. The data collected revealed a number of reasons that make students like, or dislike, scientific majors. These reasons include the presence or absence of capable teachers and the choice of the teaching language. The results presented in the paper also focus on differences between public and private institutions, male and female students, as well as nationals and non-nationals. We also compare our findings to similar research done in the USA We show that several factors remain valid in both countries whereas others are specific to each of them.

Homogenization of a Stokes problem in a porous medium by the periodic unfolding method

We consider the Stokes problem in a domain with holes periodically distributed with a period e. The size of the holes is of the order of e, a small parameter going to zero. On the boundary of the holes we prescribe a Robin-type condition depending on a parameter γ. The aim is to give the asymptotic behavior of the velocity and of the pressure of the fluid as e goes to zero. The study for a problem of this type was done in Math. Meth. Appl. Sci. 19 (1996), 857-881, via classical homogenization methods. In this work we use the periodic unfolding method in perforated domains (see C. R. Acad. Sci. Paris, Serie 1 342 (2006), 469-474; Portugaliae Mathematica 63(4) (2006), 467-496; Asymptotic Analysis 53(4) (2007), 209-235; in: Multiple Scales in Problems in Biomath., Mech., Physics and Numeric, Gakuto Int. Series, Math. Sci. App., Vol. 31, Gakkokotosho, 2009, pp. 37-68, and SIAM J. Math. Anal. 44(2) (2012), 718-760), which allows us to consider a general geometric framework. We give the limit problems corresponding to different values of γ (Darcy, Brinkmann or Stokes type problems).