Updates of thesis

main/Ch.1.tex

@@ -45,7 +45,7 @@ ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2
 \end{equation}
 
 \noindent
-with the following:
+where $c = 3 \times 10^8$ m/s is the speed of light, with the following:
 
 \begin{equation}
 \centering
@@ -101,11 +101,12 @@ The dynamical equations derivated by Einstein consider the energy-momentum tenso
 
 \begin{equation}
 \centering
-G_{ik} = R_{ik} - \frac{1}{2}g_{ik}R = \frac{8\pi G}{c^4}T_{ik}.
+G_{ik} = R_{ik} - \frac{1}{2}g_{ik}R = \frac{8\pi G}{c^4}T_{ik}
 \label{EE}
 \end{equation}
 \\
 \noindent
+with $G = 6,67 \time 10^{-11}$ Nm$^2$/Kg$^2$.
 The Einstein's equations expressed in the form of eq. \ref{EE} are valid in the weak field (or Newtonian) approximation:
 \begin{enumerate}
 \item The motion of particles is non-relativistic.
@@ -178,12 +179,12 @@ Fig. \ref{spec} summarizes the possible objects that can be gravitational waves
 \end{figure}
 
 \noindent
-The best modelled sources are binary systems, typically Neutron stars (NS), White Dwarfs (WD) and Black Holes (BH), orbiting each other. Fig. \ref{binary} shows the main phases of the evolution of the systems, emitting gravitational waves at different frequencies, depending on the phase.
+The best modelled sources are binary systems, typically Neutron Stars (NS), White Dwarfs and Black Holes (BH), orbiting each other. Fig. \ref{binary} shows the main phases of the evolution of the systems, emitting gravitational waves at different frequencies, depending on the phase.
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=1]{images/bin.png}
-\caption[Phases of gravitational waves emission by a binary system]{The three phases of a BH-BH binary system emitting gravitational waves (amplitude vs time). \textbf{Inspiral phase}: the orbits shrink, velocity increases and frequency of the waves emitted increases as $f_{gw} = 2f_{orbital}$. \textbf{Merging phase}: the objects merge and the signal is maximum. \textbf{Ring-down phase}: a new BH is formed and the signal emitted decreases in frequency as a damped sinusoid.}
+\caption[Phases of gravitational waves emission by a binary system]{The three phases of a BH-BH binary system emitting gravitational waves (amplitude vs time) \cite{first}. \textbf{Inspiral phase}: the orbits shrink, velocity increases and frequency of the waves emitted increases as $f_{gw} = 2f_{orbital}$. \textbf{Merging phase}: the objects merge and the signal is maximum. \textbf{Ring-down phase}: a new BH is formed and the signal emitted decreases in frequency as a damped sinusoid.}
 \label{binary}
 \end{figure}
 
@@ -268,7 +269,7 @@ which gives a phase shift:
 The higher is F, the higher is the effective length of the cavity and higher is the measureble phase shift.\\
 
 \noindent
-The first detection of gravitational waves happened on the 14th September 2015 and confirmed the Theory General Relativity, opening a new window on the Universe: among others, black holes have been observed thanks to their emission of gravitational waves, confirming the existence of these object, still mostly unknown \cite{first}. The detector responsible of the new discovery is based in the USA and it is one of the terrestrial interferometers currently in use for gravitational waves detection.
+The first detection of gravitational waves happened on the 14th September 2015 and confirmed the Theory General Relativity, opening a new window on the Universe: the signal from a merger of two black holes have been observed thanks to the emission of gravitational waves, confirming the existence of these objects, still mostly unknown \cite{first}. The detector responsible of the new discovery is based in the USA and it is one of the terrestrial interferometers currently in use for gravitational waves detection.
 
 %\section{LIGO}
 %The ambition of this work is to give a contribution to the improvement of one of the interferometric detectors in use at present time, based in the USA: the Advanced Laser Interferometric Gravitational-wave Observatory (aLIGO).\\

main/main.tex

 \documentclass[a4paper,12pt,openright,titlepage]{scrbook}
 \usepackage[a4paper,top=3cm,bottom=3cm]{geometry}
+\usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc} 
+\usepackage{palatino}
 \usepackage[english]{babel} 
 \usepackage{graphicx}
 \usepackage[font=small,hang]{caption}
@@ -34,9 +36,44 @@ A brief summary of the project goes here, with main results.
 An introduction to frame the work and structure of the thesis go here.
 
 \chapter{Notations}
-Useful notations, constants and formulas go here.
+Useful notations, constants and formulas go here.\\
+Speed of light:\\
+$c = 3 \times 10^8$ m/s\\
+Gravitational constant:\\
+$G = 6,67 \time 10^{-11}$ Nm$^2$/Kg$^2$\\
+Gravitational wave amplitude:\\
+$h \sim 10^{-21} $ $1/\sqrt{Hz}$\\
+Solar mass:\\
+$M_{\odot} = 10^{33}$ g
 
 \chapter{Acronyms}
+aLIGO = Advanced Laser Interferometric Gravitational-wave Observatory\\
+BS = Beam Splitter\\
+BSC = Basic Symmetric Chamber\\
+BH = Black Hole\\
+CARM = Common Arm length\\
+CP = Compensation Plate\\
+CPS = Capacitive Position Sensors\\
+DARM = Differential Arm Length\\
+ETM = End Test Mass\\
+FIR = Finite Impulse Response\\
+HAM = Horizontal Access Module\\
+HEPI = Hydraulic External Pre-Isolator\\
+HP = High Pass filter\\
+ISI = Internal Seismic Isolation\\
+ITM = Input Test Mass\\
+LHO = LIGO Hanford Observaotry\\
+LLO = LIGO Livingston Observatory\\
+LP = Low Pass filter\\
+LSC = Length Sensing and Control\\
+MICH = Michelson length\\
+NS = Neutron Star\\
+PD = PhotoDiode\\
+PR = Power Recycling\\
+PRCL = Power Recycling Cavity Length\\
+SC = Sensor Correction\\
+SR = Signal Recycling\\
+SRCL = Signal Recycling Cavity Length\\
 
 \mainmatter
 
@@ -44,8 +81,25 @@ Useful notations, constants and formulas go here.
 
 \include{Ch.2}
 
+\include{Ch.3}
+
+\include{Ch.4}
+
+%\include{Ch.5}
+%
+%\include{Ch.6}
+%
+%\include{Ch.7}
+
+\appendix
+\include{A}
+\include{B}
+
 \backmatter
 
+\listoffigures
+\listoftables
+
 \begin{thebibliography}{}
 
 \bibitem{wei} S. Weinberg \textit{Gravitation and Cosmology: principles and applications of the General Theory of Relativity}, John Wiley \& Sons, Inc., 1972
@@ -61,14 +115,13 @@ Useful notations, constants and formulas go here.
 \bibitem{abb} B. P. Abbott et al, \textit{GW150914: The Advanced LIGO Detectors in the Era of First Discoveries}, Phys. Rev. Lett. 116, 131102, 2016
 
 \bibitem{mar} D. Martynov et al., \textit{The Sensitivity of the Advanced LIGO Detectors at the
-Beginning of Gravitational Wave Astronomy}, ...
+Beginning of Gravitational Wave Astronomy}
 
 \bibitem{mat} F. Matichard et al, \textit{Seismic isolation of Advanced LIGO: Review of strategy, instrumentation and performance}, Class. Quantum Grav. 32 185003, 2015
 
-\end{thebibliography}
+\bibitem{lsc} K. Izumi, D. Sigg, \textit{Advanced LIGO: length sensing and control in a dual recycled interferometric gravitational wave antenna}, 2017 Class. Quantum Grav. 34 015001
 
-\listoffigures
-\listoftables
+\end{thebibliography}
 
 \chapter{Acknowledgements}