From f49e9b3bcac3121dde290573b52b273dd661010c Mon Sep 17 00:00:00 2001
From: JanHab <jan.habscheid@rwth-aachen.de>
Date: Wed, 26 Mar 2025 16:13:18 +0100
Subject: [PATCH] report innit 3

---
 .DS_Store                                | Bin 6148 -> 6148 bytes
 Project3/LyX/Abbreviations.lyx           | 311 +++++++++
 Project3/LyX/Abstract.lyx                | 104 +++
 Project3/LyX/Appendix.lyx                | 108 ++++
 Project3/LyX/Bibliography.bib            |  64 ++
 Project3/LyX/DiscussionAndConclusion.lyx | 110 ++++
 Project3/LyX/Implementation.lyx          | 103 +++
 Project3/LyX/Introduction.lyx            | 217 +++++++
 Project3/LyX/ListOfVariables.lyx         | 767 +++++++++++++++++++++++
 Project3/LyX/Project3Habscheid.lyx       | 418 ++++++++++++
 Project3/LyX/Results.lyx                 | 110 ++++
 Project3/LyX/TheoryAndMethods.lyx        | 121 ++++
 12 files changed, 2433 insertions(+)
 create mode 100644 Project3/LyX/Abbreviations.lyx
 create mode 100644 Project3/LyX/Abstract.lyx
 create mode 100644 Project3/LyX/Appendix.lyx
 create mode 100644 Project3/LyX/Bibliography.bib
 create mode 100644 Project3/LyX/DiscussionAndConclusion.lyx
 create mode 100644 Project3/LyX/Implementation.lyx
 create mode 100644 Project3/LyX/Introduction.lyx
 create mode 100644 Project3/LyX/ListOfVariables.lyx
 create mode 100644 Project3/LyX/Project3Habscheid.lyx
 create mode 100644 Project3/LyX/Results.lyx
 create mode 100644 Project3/LyX/TheoryAndMethods.lyx

diff --git a/.DS_Store b/.DS_Store
index 69cd2a7b162016d5fe4558d23892b1d94461135c..2725a680427d7609912bfc2358fcb62f7d571cc9 100644
GIT binary patch
delta 16
XcmZoMXffE}$~HNGRdjO{+bTf-F69L;

delta 18
ZcmZoMXffE}%ErhrIgnLka}?VuK>#zl1uy^r

diff --git a/Project3/LyX/Abbreviations.lyx b/Project3/LyX/Abbreviations.lyx
new file mode 100644
index 0000000..15e2a3e
--- /dev/null
+++ b/Project3/LyX/Abbreviations.lyx
@@ -0,0 +1,311 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\use_default_options true
+\maintain_unincluded_children no
+\language ngerman
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment class
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008080
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Section*
+List of Abbreviations
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Abbreviation
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Definition
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+PDE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Partial Differential Equation
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+MOC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Method of Characteristics
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+FEM
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Finite Element Method
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+AD
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Artificial Diffusion
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+SU
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Streamline-Upwind
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+SUPG
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Streamline-Upwind Petrov-Galerkin
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+GLS
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Generalized Least-Squares
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Pe 
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\lang american
+Péclet number
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Courant number
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/Abstract.lyx b/Project3/LyX/Abstract.lyx
new file mode 100644
index 0000000..d2f5309
--- /dev/null
+++ b/Project3/LyX/Abstract.lyx
@@ -0,0 +1,104 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\use_default_options true
+\maintain_unincluded_children no
+\language american
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment center
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 2.5cm
+\topmargin 2.5cm
+\rightmargin 2.5cm
+\bottommargin 2.5cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Abstract
+###
+\end_layout
+
+\begin_layout Keywords
+###
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/Appendix.lyx b/Project3/LyX/Appendix.lyx
new file mode 100644
index 0000000..6cc3470
--- /dev/null
+++ b/Project3/LyX/Appendix.lyx
@@ -0,0 +1,108 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\use_default_options true
+\maintain_unincluded_children no
+\language english
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment class
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008080
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\start_of_appendix
+Inserting the Dimensionless Parameter
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Appendix_AInserting-the-Dimensionless"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/Bibliography.bib b/Project3/LyX/Bibliography.bib
new file mode 100644
index 0000000..2b77587
--- /dev/null
+++ b/Project3/LyX/Bibliography.bib
@@ -0,0 +1,64 @@
+@unpublished{SteinerEvje-Lecture,
+    author = {Steinar Evje},
+    note   = {},
+    title  = {Lecture notes: Data-Driven Modeling of Conservation Laws},
+    year   = {2025}
+}
+
+@unpublished{LectureNotes,
+    author = {Siddhartha Mishra, Ulrik Skre Fjordholm and R´emi Abgrall},
+    note   = {},
+    title  = {Lecture notes: Numerical methods for conservation laws
+and related equations},
+    year   = {2025}
+}
+
+@unpublished{Intro_ConsLaw_2021,
+    author = {Steinar Evje},
+    note   = {},
+    title  = {Basic theory for nonlinear conservation laws + exercises},
+    year   = {2021}
+}
+
+
+@article{KUZNETSOV20085695,
+title = {Modeling traffic jams in intracellular transport in axons},
+journal = {International Journal of Heat and Mass Transfer},
+volume = {51},
+number = {23},
+pages = {5695-5699},
+year = {2008},
+note = {Biomedical-Related Special Issue},
+issn = {0017-9310},
+doi = {https://doi.org/10.1016/j.ijheatmasstransfer.2008.04.022},
+url = {https://www.sciencedirect.com/science/article/pii/S0017931008002731},
+author = {A.V. Kuznetsov and K. Hooman},
+keywords = {Molecular motors, Motor-assisted transport, Neurons, Axons and dendrites, Intracellular organelles, Traffic jams},
+abstract = {Irregularities in intracellular traffic in axons caused by mutations of molecular motors may lead to “traffic jams”, which often result in swelling of axons causing various neurodegenerative diseases. The purpose of this paper is to suggest a model of the formation of traffic jams in axons during molecular-motor-assisted transport of intracellular organelles utilizing transport equations developed in Smith and Simmons [D.A. Smith, R.M. Simmons, Models of motor-assisted transport of intracellular particles, Biophys. J. 80 (2001) 45–68], which describe the motion of intracellular particles under the combined action of diffusion and motor-driven transport. According to this model, large intracellular organelles are transported in the cytoplasm by a combined action of diffusion and motor-driven transport. In an axon, organelles are transported away from the neuron’s body toward the axon’s terminal by kinesin-family molecular motors running on tracks composed by microtubules; old and used components are carried back toward neuron’s body by dynein-family molecular motors. Binding/detachment kinetic processes between the organelles and microtubules are specified by first rate reaction constants; these lead to coupling between the three organelle concentrations.}
+}
+
+Péclet number. (2024, May 6). In Wikipedia. https://en.wikipedia.org/wiki/P%C3%A9clet_number
+@misc{Peclet_Wikipedia,
+    author       = {{Péclet number}},
+    month        = {May},
+    day          = {6},
+    url          = {https://en.wikipedia.org/wiki/P%C3%A9clet_number},
+    year         = {2024},
+    howpublished = {In \textit{Wikipedia}},
+}
+
+@unpublished{HabscheidProject1,
+    author = {Jan Habscheid},
+    note = {},
+    title = {Project 1: Data-Driven Modeling of Conservation Laws},
+    url = {https://git.rwth-aachen.de/JanHab/ddm},
+    year = {2024}
+}
+
+@software{Repository,
+    author = {Habscheid, Jan},
+    month = {March},
+    title = {Reproducibility Repository for Data-Driven Modeling of Conservation Laws},
+    URL = {https://git.rwth-aachen.de/JanHab/ddm},
+    year = {2025},
+}
diff --git a/Project3/LyX/DiscussionAndConclusion.lyx b/Project3/LyX/DiscussionAndConclusion.lyx
new file mode 100644
index 0000000..b511ccf
--- /dev/null
+++ b/Project3/LyX/DiscussionAndConclusion.lyx
@@ -0,0 +1,110 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\use_default_options true
+\maintain_unincluded_children no
+\language american
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment class
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\spellchecker_ignore american Fortran
+\spellchecker_ignore american parallelized
+\spellchecker_ignore american parallelizes
+\spellchecker_ignore american OpenMP
+\spellchecker_ignore american openMP
+\spellchecker_ignore american parallelization
+\spellchecker_ignore american parallelizing
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Section
+Discussion and Conclusion
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Discussion-and-Conclusion"
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/Implementation.lyx b/Project3/LyX/Implementation.lyx
new file mode 100644
index 0000000..f011135
--- /dev/null
+++ b/Project3/LyX/Implementation.lyx
@@ -0,0 +1,103 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\use_default_options true
+\maintain_unincluded_children no
+\language english
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment class
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008080
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Section
+Implementation
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Implementation"
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/Introduction.lyx b/Project3/LyX/Introduction.lyx
new file mode 100644
index 0000000..5d9fc57
--- /dev/null
+++ b/Project3/LyX/Introduction.lyx
@@ -0,0 +1,217 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\begin_preamble
+\usepackage{tikz}
+\usetikzlibrary{decorations.pathreplacing}
+\end_preamble
+\use_default_options true
+\begin_modules
+eqs-within-sections
+figs-within-sections
+\end_modules
+\maintain_unincluded_children no
+\language american
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment center
+\paperfontsize default
+\spacing single
+\use_hyperref true
+\pdf_title "Modeling Traffic Flow"
+\pdf_author "Jan Habscheid"
+\pdf_subject "Data-Driven Modeling of Conservation Laws"
+\pdf_keywords "Traffic Flow, Advection, Riemann Problem, Lax-Entropy"
+\pdf_bookmarks true
+\pdf_bookmarksnumbered false
+\pdf_bookmarksopen false
+\pdf_bookmarksopenlevel 1
+\pdf_breaklinks false
+\pdf_pdfborder false
+\pdf_colorlinks false
+\pdf_backref false
+\pdf_pdfusetitle true
+\papersize default
+\use_geometry true
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine natbib
+\cite_engine_type numerical
+\biblio_style plainurl
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\branch 18.11.2024
+\selected 0
+\filename_suffix 0
+\color background background
+\end_branch
+\branch 21.11.2024
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch 14112024
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch 07112024
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch 28112024
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Inputs
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Abstract
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Introduction
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Theory and Methods
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Implementation and Validation
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Results
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Discussion and Conclusion
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch References
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Abbreviations
+\selected 0
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Implementation
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch List of Variables
+\selected 0
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Appendix
+\selected 0
+\filename_suffix 0
+\color background background
+\end_branch
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 2cm
+\topmargin 1.5cm
+\rightmargin 2cm
+\bottommargin 1.5cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Section
+Introduction
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Introduction"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/ListOfVariables.lyx b/Project3/LyX/ListOfVariables.lyx
new file mode 100644
index 0000000..95c35cd
--- /dev/null
+++ b/Project3/LyX/ListOfVariables.lyx
@@ -0,0 +1,767 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\use_default_options true
+\maintain_unincluded_children no
+\language english
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment class
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008080
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Subsection*
+List of Variables
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:ListOfVariables"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All the variables,
+ listed in the following table,
+ are in their dimensionless form.
+\end_layout
+
+\begin_layout Standard
+\align center
+
+\lang american
+\begin_inset Tabular
+<lyxtabular version="3" rows="19" columns="3">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<row>
+<cell multicolumn="1" alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+DIMENSIONLESS VARIABLES
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Variable
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Default Value
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Property
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $L$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $20$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Axon length
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $D_{0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $0.4$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Diffusion coefficient
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $N_{0}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $0.1$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\lang american
+Concentration of free particles at left boundary
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $N_{L}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $0.01$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\lang american
+Concentration of free particles at right boundary
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $k_{-}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\lang american
+binding rate in negative direction
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\sigma_{0},\sigma_{L}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $0.1,0.1$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\lang american
+Degree of loading at left and right boundary
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $k_{p},k_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $0.5$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\lang american
+Detachment rate for particles in positive and negative direction
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Delta x$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Cell size
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $t_{\text{end}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+10
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Final time
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $N_{\text{time}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+200
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number of time steps
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Delta t$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $0.05$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Time step size
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multicolumn="1" alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multicolumn="1" alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multicolumn="1" alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+INDEXING
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Variable
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Meaning
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cdot^{j}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $j$
+\end_inset
+
+-th time step
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\cdot_{i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $i$
+\end_inset
+
+-th grid point
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/Project3Habscheid.lyx b/Project3/LyX/Project3Habscheid.lyx
new file mode 100644
index 0000000..7c83601
--- /dev/null
+++ b/Project3/LyX/Project3Habscheid.lyx
@@ -0,0 +1,418 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\begin_preamble
+\usepackage{tikz}
+\usetikzlibrary{decorations.pathreplacing}
+\end_preamble
+\use_default_options true
+\begin_modules
+eqs-within-sections
+figs-within-sections
+\end_modules
+\maintain_unincluded_children no
+\language american
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics pdftex
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment center
+\paperfontsize default
+\spacing single
+\use_hyperref true
+\pdf_title "Modeling Traffic Flow"
+\pdf_author "Jan Habscheid"
+\pdf_subject "Data-Driven Modeling of Conservation Laws"
+\pdf_keywords "Traffic Flow, Advection, Riemann Problem, Lax-Entropy"
+\pdf_bookmarks true
+\pdf_bookmarksnumbered false
+\pdf_bookmarksopen false
+\pdf_bookmarksopenlevel 1
+\pdf_breaklinks false
+\pdf_pdfborder false
+\pdf_colorlinks false
+\pdf_backref false
+\pdf_pdfusetitle true
+\papersize default
+\use_geometry true
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine natbib
+\cite_engine_type numerical
+\biblio_style plainurl
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\branch 18.11.2024
+\selected 0
+\filename_suffix 0
+\color background background
+\end_branch
+\branch 21.11.2024
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch 14112024
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch 07112024
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch 28112024
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Inputs
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Abstract
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Introduction
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Theory and Methods
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Implementation and Validation
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Results
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Discussion and Conclusion
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch References
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Abbreviations
+\selected 0
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Implementation
+\selected 1
+\filename_suffix 0
+\color background background
+\end_branch
+\branch List of Variables
+\selected 0
+\filename_suffix 0
+\color background background
+\end_branch
+\branch Appendix
+\selected 0
+\filename_suffix 0
+\color background background
+\end_branch
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 2cm
+\topmargin 1.5cm
+\rightmargin 2cm
+\bottommargin 1.5cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Title
+
+\lang english
+USING MONTE CARLO MARKOV CHAIN (MCMC) TO IDENTIFY UNKNOWN FLUX FUNCTION FROM OBSERVATION DATA
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+
+\lang english
+Date:
+ 05.04.2025,
+ 
+\begin_inset Newline newline
+\end_inset
+
+Referee:
+ Steinar Evje
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Author
+
+\lang english
+Jan Habscheid
+\begin_inset Foot
+status open
+
+\begin_layout Plain Layout
+
+\lang english
+Author:
+ Jan Habscheid,
+ 
+\begin_inset CommandInset href
+LatexCommand href
+name "J.Habscheid@stud.uis.no"
+target "J.Habscheid@stud.uis.no"
+type "mailto:"
+literal "false"
+
+\end_inset
+
+,
+ Student ID:
+ 287338
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Branch Inputs
+inverted 0
+status open
+
+\begin_layout Standard
+\begin_inset Branch Abstract
+inverted 0
+status open
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand input
+filename "Abstract.lyx"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Branch Introduction
+inverted 0
+status open
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand input
+filename "Introduction.lyx"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Branch Theory and Methods
+inverted 0
+status open
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand input
+filename "TheoryAndMethods.lyx"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Branch Implementation
+inverted 0
+status open
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand input
+filename "Implementation.lyx"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Branch Results
+inverted 0
+status open
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand input
+filename "Results.lyx"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Branch Discussion and Conclusion
+inverted 0
+status open
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand input
+filename "DiscussionAndConclusion.lyx"
+literal "false"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Branch References
+inverted 0
+status open
+
+\begin_layout Standard
+\begin_inset CommandInset bibtex
+LatexCommand bibtex
+btprint "btPrintCited"
+bibfiles "Bibliography"
+options "plainurl"
+encoding "default"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/Results.lyx b/Project3/LyX/Results.lyx
new file mode 100644
index 0000000..55ad163
--- /dev/null
+++ b/Project3/LyX/Results.lyx
@@ -0,0 +1,110 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\begin_preamble
+\usepackage{tikz}
+\end_preamble
+\use_default_options true
+\maintain_unincluded_children no
+\language american
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment center
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 2.5cm
+\topmargin 2.5cm
+\rightmargin 2.5cm
+\bottommargin 2.5cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Section
+Results
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Results"
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/Project3/LyX/TheoryAndMethods.lyx b/Project3/LyX/TheoryAndMethods.lyx
new file mode 100644
index 0000000..88cc351
--- /dev/null
+++ b/Project3/LyX/TheoryAndMethods.lyx
@@ -0,0 +1,121 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 620
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass IEEEtran-CompSoc
+\begin_preamble
+\usepackage{tikz}
+\usetikzlibrary{decorations.pathreplacing}
+\end_preamble
+\use_default_options true
+\maintain_unincluded_children no
+\language american
+\language_package default
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\float_placement class
+\float_alignment center
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_formatted_ref 0
+\use_minted 0
+\use_lineno 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\spellchecker_ignore american Sobolev
+\spellchecker_ignore american OpenMP
+\spellchecker_ignore american scalable
+\spellchecker_ignore american discretized
+\spellchecker_ignore american splitted
+\spellchecker_ignore american bilinear
+\leftmargin 2.5cm
+\topmargin 2.5cm
+\rightmargin 2.5cm
+\bottommargin 2.5cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tablestyle default
+\tracking_changes false
+\output_changes false
+\change_bars false
+\postpone_fragile_content true
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\docbook_table_output 0
+\docbook_mathml_prefix 1
+\end_header
+
+\begin_body
+
+\begin_layout Section
+Theory and Methods
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Theory-and-Methods"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\end_body
+\end_document
-- 
GitLab