Axial and radial gradient-index titania flint glasses

A gradient field is a vector field derived from a scalar field. A scalar field assigns a single numerical value to every point in space, such as temperature, pressure, or electric potential. The gradient field describes how that value changes from point to point. It gives both the direction of the fastest increase and the rate of change in that direction.For a scalar field f(x, y), the gradient is written as\begin{equation*}\nabla f=\left\langle \jfrac{\partial f}{\partial x},\jfrac{\partial...

The Law of rational indices is a fundamental principle in the field of crystallography. According to this law, the intercepts of a crystal face along the crystallographic axes (the three-dimensional axes along which a crystal is measured) can be expressed as either equivalent to the unit intercepts (a, b, c) or simple whole number multiples of them. These multiples are typically denoted as na, n'b, and n''c, where n, n', and n'' are simple whole numbers.To illustrate, consider a crystal with...

Aggregates typically contain pores, which can be either permeable or impermeable. Considering the pores in the aggregates, the specific gravity of aggregates is defined in three different forms, namely, bulk or gross specific gravity, apparent specific gravity, and absolute specific gravity.
Bulk or gross specific gravity is calculated by taking the ratio of the mass of aggregates in the saturated surface-dry state to the total volume that includes both the solids and the voids within the...