Several rigorous turbulent models have been developed in the past years and it can be seen that more research is needed to reach a better understanding of their generality and precision by verifying their applications for distinct hydraulic phenomena; under certain assumptions. This survey evaluates the performance of Standard k-ε, Realizable k-ε, RNG k-ε, k-ω and RSM models in predicting flow ...

(1.1) ∂tb(x, u) + div(F̄ (t, x, u)− k∇u) = f(t, x, u, s), s(t, x) = ∫ t 0 K(t, z)ψ(u(z, x))dz in Ω × (0, T ], T < ∞, Ω ⊂ R is a bounded domain, ∂Ω ∈ C, see [26]. If Ω is convex, then ∂Ω is assumed to be Lipschitz continuous. We consider a Dirichlet boundary condition (1.2) u(t, x) = 0 on I × ∂Ω, I = (0, T ], together with the initial condition (1.3) u(0, x) = u0(x) x ∈ Ω. We assume 0 < ε ≤ ∂sb(x...

A rather simple natural outer derivation of the graded Lie algebra of all vector valued differential forms with the Frölicher-Nijenhuis bracket turns out to be a differential and gives rise to a cohomology of the manifold, which is functorial under local diffeomorphisms. This cohomology is determined as the direct product of the de Rham cohomology space and the graded Lie algebra of ”traceless”...

and Applied Analysis 3 Definition 2.1. A function u x, t is called a weak solution of 2.1 if and only if i u ∈ L2 0, T ;H1 0 Ω , with u′ ∈ L2 0, T ;H−1 Ω , ii u| −τ,0 u0 ∈ L2 Ω , iii ∫T 0 〈ut, φ〉 Du,Dφ dt ∫T 0 f u t , u t − τ , φ dt, for each φ ∈ L2 0, T ;H1 0 Ω . Here 〈, 〉 and , denote the pair of H−1 Ω and H1 0 Ω , the inner product in L2 Ω , respectively. Next we will give two very important...

Primarily guided with the idea to express zero-time transitions by means of temporal propositional language, we have developed a temporal logic where the time flow is isomorphic to ordinal ω 2 (concatenation of ω copies of ω). If we think of ω 2 as lexicographically ordered ω×ω, then any particular zero-time transition can be represented by states whose indices are all elements of some {n} × ω....

Bloch and Esnault defined additive higher Chow groups with modulus (m + 1) on the level of zero cycles over a field k, denoted by TH(k, n;m), n, m ≥ 1. They prove TH(k, n; 1) ∼= Ω k/Z . In this paper we generalize their result and obtain an isomorphism TH(k, n;m) ∼= WmΩ n−1 k , where W−Ω·k is the generalized de Rham-Witt complex of Hesselholt-Madsen, generalizing the p-typical de Rham-Witt comp...

We examine the notion of structures and functions in the Ershov difference hierarchy, and of equivalence structures in particular. A equivalence structure A = (A,E) has universe A = ω and an equivalence relation E. The equivalence class [a] of a ∈ A is {b ∈ A : aEb} and the character K of A is {〈k, n〉 ∈ (ω − {0}) : A has at least n classes of size k}. It is known that for any character K, there...

where Ω ⊂ R2 is the image domain (a bounded open two-dimensional domain), g ∈ L∞(Ω) is the original image, that has to be segmented, K is a closed set of Hausdorff one-dimensional measure H1(K) and u ∈ C1(Ω \K). The set K is supposed to represent the edges of the segmented image u that is regular out of K and can be discontinuous across K (see Appendix A.2 for details). The actual minimization ...

In the petrochemical industry, multiphase flow, including oil–water two-phase stratified laminar is more common and can be easily obtained through mathematical analysis. However, there limited analytical model for simulation of flow under turbulent flow. This paper introduces a two-dimensional (2D) numerical method to investigate pressure gradient, field, interface height pipeline cross-section...

Problem 6.25 Consider a wide sense stationary random sequence X[n] input to a linear filter with impulse response h[n] = 1/2, n = {0, 1} 0, otherwise. (1) Write the PSD of the output sequence S Y Y (ω) in terms of the PSD of the input sequence S XX (ω). (a) Show that the PSD is real-valued, even if X[n] is a complex-valued random sequence. (b) Show that if X[n] is real-valued, then S XX (ω) = S...