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Demian Arancibia edited untitled.tex
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\section{Overview}
This document presents a parametric model to help design an Interferometric Array. It describes the design parameters in
section 2 \ref{variables} and the system performance objectives in
section 3, \ref{objectives}, and the relationship between them.
Section 4 provides the A python code used to generate data in the format required for visual analysis of array design options
performance. performance is presented in \ref{array-performance-data-generation---python-implementation}. The python code is consistent with parameters and objectives selection in sections 2 and 3, and the mathematical relationships between them.
\section{Variables}
This section aims to include all relevant design parameters that might influence the selected performance objectives in section 4.
\subsection{Antenna Aspects}
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\text{Correlator cost} = 2N^2 + 112N +1360
\end{equation}
\subsubsection{Cost of Re-configuration Systems Construction}
\section{Mathematical Formulation}
Thus if we are using vector $x = {\text{antenna diameter}, \text{antenna efficiency}, \}$, the antenna diameter, as the optimization variable the problem we would like to solve is:
\begin{equation*}
\begin{aligned}
& \underset{x}{\text{minimize}}
& & f(x) = {\frac{2k_B}{\eta_s \eta_a}}{\frac{T_{sys}}{\pi x^2 \sqrt{2 \Delta \nu \tau_{acc}}}}\\
& \text{subject to}
& & X_{ij} = M_{ij}, \; (i,j) \in \Omega, \\
&&& X \succeq 0.
\end{aligned}
\end{equation*}
\section{Array Performance Data Generation - Python Implementation}
\section{Visualization Tool Notes}
\section{Conversation notes}
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