The commonly used linear k-ε turbulence model is shown to be incapable of accurate prediction of turbulent flows, where non-isotropy is dominant. Two examples of non-isotropic flows, which have a wide range of applications in marine waters, are saline water flow and the stratified flows due to temperature gradients. These relate to stratification and consequently, variation of density through...

The temperature dependent band edge energy of the novel tungsten bronze type calcium barium niobate (CBN) is measured over a temperature range from 80 K to 573 K. CBN has been under investigation for serveral years and is believed to be a promising material for future applications. Czochralski-grown, colorless single crystals from the congruently melting composition with a calcium content of 0....

Let k ∈ {1, . . . , n}. The k-numerical range of A ∈Mn is the set Wk(A) = {(trX∗AX)/k : X is n× k, X∗X = Ik}, and the k-numerical radius of A is the quantity wk(A) = max{|z| : z ∈ Wk(A)}. Suppose k > 1, k′ ∈ {1, . . . , n′} and n′ < C(n, k)min{k′, n′ − k′}. It is shown that there is a linear map φ : Mn → Mn′ satisfying Wk′(φ(A)) = Wk(A) for all A ∈ Mn if and only if n′/n = k′/k or n′/n = k′/(n−...