Tuning of Generalized K-Omega Turbulence Model by Using Adjoint Optimization and Machine Learning for Gas Turbine Combustor Applicationsdoi:10.1115/1.4064367turbulence modelingmachine learningneural networksgas turbine combustionswirling flowsTurbulence modeling plays a crucial role in swirl-stabilized gas turbine...
$${\Omega }_{A}(t)=\frac{1}{{t}^{2}}\int_{0}^{t}\int_{0}^{t}d{t}_{1}d{t}_{2}[\langle A({t}_{1})A({t}_{2})\rangle -\langle A({t}_{1})\rangle \langle A({t}_{2})\rangle ].$$ (12) The finite-time averaged observable A = v, \(\bar{v}...
Indeed, let \(y\in F(x)\cap \Omega \) be fixed. Then, \(f(x,y)<0\) and, choosing \(U_y=\Omega \) there exists \(U_x\) such that \(\inf _{y'\in U_y}f(x',y')\le f(x,y)/2<0\) for all \(x'\in U_x\cap X\), that is there is \(y'\in \Omega \)...
First, the state set can be written as: \(\Omega = \left\{ {V,\lnot V} \right\}\), which contains two complementary states, respectively belonging to state and not belonging to state, V(P) indicates that the object is in V, and \(\lnot V(N)\) indicates that the object is ...
In this paper, we introduce the concept of almost-complete-closed time scales (ACCTS) that allows independent variables of functions to possess almost-periodicity under translations. For this new type of time scale, a class of piecewise functions with double-almost-periodicity is proposed and studie...
{e^{j[{\theta_{a}}(\omega)+2n\omega ]}} = \cos [{\theta_{a}}(\omega)+2n\omega ]+j\sin [{\theta_{a}}(\omega)+2n\omega ]. $$ ((8)) correspondingly, the right-hand of equation 7 becomes: $$ \frac{{1 + \sum\limits_{k = 1}^{2n} {{a_{k}}{e^{jk\omega }...
$$\begin{array}{*{20}{l}} {\sigma ^{abb}\left( \omega \right) = - \frac{{\pi e^3}}{\hbar }{\int} {\frac{{d{{{\boldsymbol{k}}}{{\left( {2\pi } \right)^d}}} \mathop {\sum }\limits_{nm} f_{nm}R_{mn}^{a,b}\left( {{{\boldsymbol{k}}} \right)r_{nm...
,vˆm) is a feasible solution of model (8), and the value of objective function for this solution is: ∑r=1suˆryrj0−δ1uˆ0=∑r=1sũk∑r=1sũr(Yrj0)αL∑r=1sũryrj0yrj0−δ1ũ0=∑r=1sũr(Yrj0)αL−δ1ũ0=(Ej0)αL. Thus we have (Ej0...
Therefore the function u(x ,t), given by (1.6), is a generalized solution of problem PK in \Omega_{m}. □Proof of Theorem 1.3 Theorem 1.1 and Theorem 1.2 claim the existence and uniqueness of generalized solutions u(x ,t) of problem PK in \Omega_{m}, which has the form (1.6...
If an agent j∈Ni concludes its update while agent i is still computing its future strategy during iteration k, then the value of the strategy of j, which agent i is using, becomes outdated. We denote the vector of possibly outdated strategy used for the update during iteration k as ϖ...