Multipole expansions depend on the coordinate system, so that coefficients of multipole moments can be set equal to zero by an appropriate choice of coordinates. Therefore, it is meaningless to say that a physical system has a nonvanishing quadrupole moment, say, without specifying which coordinate system is used. (Except if this moment is the lowest non-vanishing one.) This result is demonstra...

We review Maxwell’s multipole vectors, and elucidate some of their mathematical properties, with emphasis on the application of this tool to the cosmic microwave background (CMB). In particular, for a completely random function on the sphere (corresponding to the statistically isotropic Gaussian model of the CMB), we derive the full probability density function of the multipole vectors. This fu...

The clinical need for the design of small-diameter vascular substitutes with high patency rates has never been so urgent as nowadays. Mechano-compatibility is widely known as one of the main key parameter for the design and the development of highly-patent vascular substitutes independently of their nature, i.e., arterial prostheses, arterial grafts or tissue-engineered blood-vessel. In this wo...