Skip to content
Snippets Groups Projects
Commit c6efa028 authored by Jan Habscheid's avatar Jan Habscheid
Browse files

rm old LyX folder

parent 420f656e
No related branches found
No related tags found
1 merge request!1Project2 working
Hide whitespace changes
Inline Side-by-side
Showing
with 0 additions and 2451 deletions
Project2/LyX/Figures/TrafficFlow_InitialCondition.pdf
+ 0
− 0
View file @ c6efa028
No preview for this file type
Project2/LyX/Figures/TrafficFlow_Solution_A.pdf
+ 0
− 0
View file @ c6efa028
No preview for this file type
Project2/LyX/Figures/TrafficFlow_Solution_B.pdf
+ 0
− 0
View file @ c6efa028
No preview for this file type
Project2/LyX_old/Abbreviations.lyx deleted 100644 → 0
+ 0
− 311
View file @ 420f656e
#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
Project2/LyX_old/Abstract.lyx deleted 100644 → 0
+ 0
− 104
View file @ 420f656e
#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
ldjf
\end_layout
\begin_layout Keywords
lsjf
\end_layout
\end_body
\end_document
Project2/LyX_old/Abstract.tex deleted 100644 → 0
+ 0
− 9
View file @ 420f656e
\begin{abstract}
ldjf
\end{abstract}
\begin{IEEEkeywords}
lsjf
\end{IEEEkeywords}
Project2/LyX_old/Appendix.lyx deleted 100644 → 0
+ 0
− 108
View file @ 420f656e
#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
Project2/LyX_old/Appendix.tex deleted 100644 → 0
+ 0
− 9
View file @ 420f656e
\selectlanguage{english}%
\appendix
\section{Inserting the Dimensionless Parameter}\label{sec:Appendix_AInserting-the-Dimensionless}
\selectlanguage{american}%
\selectlanguage{american}
Project2/LyX_old/Bibliography.bib deleted 100644 → 0
+ 0
− 57
View file @ 420f656e
@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}
}
@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 = {February},
title = {Reproducibility Repository for Data-Driven Modeling of Conservation Laws},
URL = {https://git.rwth-aachen.de/JanHab/ddm},
year = {2025},
}
Project2/LyX_old/DiscussionAndConclusion.lyx deleted 100644 → 0
+ 0
− 114
View file @ 420f656e
#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
\begin_layout Standard
\end_layout
\end_body
\end_document
Project2/LyX_old/DiscussionAndConclusion.tex deleted 100644 → 0
+ 0
− 4
View file @ 420f656e
\section{Discussion and Conclusion}\label{sec:Discussion-and-Conclusion}
Project2/LyX_old/Figures/TrafficJam.jpg deleted 100644 → 0
+ 0
− 0
View file @ 420f656e
Project2/LyX_old/Figures/TrafficJam.jpg

2.61 MiB

Project2/LyX_old/Implementation.lyx deleted 100644 → 0
+ 0
− 100
View file @ 420f656e
#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
\end_layout
\begin_layout Standard
\end_layout
\end_body
\end_document
Project2/LyX_old/Implementation.tex deleted 100644 → 0
+ 0
− 7
View file @ 420f656e
\selectlanguage{english}%
\section{Implementation}
\selectlanguage{american}%
\selectlanguage{american}
Project2/LyX_old/ImplementationAndValidation.lyx deleted 100644 → 0
+ 0
− 122
View file @ 420f656e
#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
\spellchecker_ignore american xns
\spellchecker_ignore american parallelization
\spellchecker_ignore american openMP
\spellchecker_ignore american slurm
\spellchecker_ignore american discretization
\spellchecker_ignore american discretized
\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 Standard
\begin_inset Note Note
status open
\begin_layout Section
Implementation and Validation
\begin_inset CommandInset label
LatexCommand label
name "sec:Implementation-and-Validation"
\end_inset
\end_layout
\end_inset
\end_layout
\end_body
\end_document
Project2/LyX_old/Introduction.lyx deleted 100644 → 0
+ 0
− 543
View file @ 420f656e
#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 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
\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
Traffic jams occur in our everyday life.
Most people use the road,
either by car,
bus or bike,
every day to get to their job,
do grocery shopping,
to meet friends or to get to their hobbies.
Through this enormous use of the road,
traffic jams occur.
Traffic jams lead to a smaller speed of vehicles,
if too many vehicles are close to each other.
\end_layout
\begin_layout Standard
The arising engineering question is,
how to reduce these traffic jams?
With a reduction of traffic jams,
the traffic quality can increase,
with less time on the road.
However,
to reduce traffic jams it is essential to understand how these work.
\end_layout
\begin_layout Standard
For this,
it is necessary to study the underlying mathematical model of traffic jams,
which states a smaller vehicle speed at higher number densities.
\begin_inset Float figure
placement document
alignment document
wide false
sideways false
status open
\begin_layout Plain Layout
\begin_inset Graphics
filename Figures/TrafficJam.jpg
lyxscale 5
width 60text%
\end_inset
\begin_inset Caption Standard
\begin_layout Plain Layout
Image by Al Gг from Pixabay
\end_layout
\end_inset
\end_layout
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
Engineering Problem:
\end_layout
\begin_layout Itemize
Traffic jams occur in our everyday life
\end_layout
\begin_deeper
\begin_layout Itemize
Many people use the road on an every day basis
\end_layout
\begin_deeper
\begin_layout Itemize
Get to job,
grocery shopping,
meeting friends,
get to sports
\end_layout
\begin_layout Itemize
Car,
bus,
bike
\end_layout
\end_deeper
\begin_layout Itemize
We want to reduce these traffic jams,
but how?
\end_layout
\begin_layout Itemize
How do we need to construct good roads,
speed-limits to reduce traffic jam to a minimum?
\end_layout
\begin_deeper
\begin_layout Itemize
For these need to understand the underlying mathematical problem of a traffic jam
\end_layout
\begin_layout Itemize
smaller velocity at higher density
\end_layout
\end_deeper
\begin_layout Itemize
\begin_inset Float figure
placement document
alignment document
wide false
sideways false
status open
\begin_layout Plain Layout
\begin_inset Graphics
filename Figures/TrafficJam.jpg
lyxscale 5
width 60text%
\end_inset
\begin_inset Caption Standard
\begin_layout Plain Layout
Image by Al Gг from Pixabay
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\end_deeper
\end_inset
\end_layout
\begin_layout Subsection
The Mathematical Model
\end_layout
\begin_layout Standard
The underlying mathematical model of traffic jams relies on the general conservation of mass
\begin_inset Formula
\begin{equation}
u_{t}+\left(V(u)u\right)_{x}=0,\quad x\in[a,b]
\end{equation}
\end_inset
where
\begin_inset Formula $u$
\end_inset
is the number density of vehicles (
\begin_inset Formula $u\in[a,b]$
\end_inset
),
\begin_inset Formula $V(u)$
\end_inset
is the velocity of vehicles,
depending on the number density and
\begin_inset Formula $b-a$
\end_inset
is the length of the road.
Furthermore,
an inflow boundary condition
\begin_inset Formula
\begin{equation}
u\big|_{x=a}=u_{\text{in}}
\end{equation}
\end_inset
is assumed to hold true.
This inflow boundary condition models the number of arriving cars at the beginning of the road.
\end_layout
\begin_layout Standard
Finally,
the problem can be reformulated to the general,
scalar,
nonlinear conservation law
\begin_inset Formula
\begin{align}
u_{t}+f(u)_{x} & =0\quad\text{in}x\in\Omega\\
u\big|_{x=x_{\text{in}}} & =u_{\text{in}}
\end{align}
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
Mathematical model
\end_layout
\begin_layout Itemize
\begin_inset Formula $u_{t}+\left(V(u)u\right)_{x}=0,\quad x\in[a,b]$
\end_inset
\end_layout
\begin_deeper
\begin_layout Itemize
with
\begin_inset Formula $b-a$
\end_inset
length of road
\end_layout
\begin_layout Itemize
\begin_inset Formula $V(u)$
\end_inset
velocity of vehicles
\end_layout
\begin_layout Itemize
\begin_inset Formula $u=u(x,t)\in[0,1]$
\end_inset
number density of vehicles
\end_layout
\begin_layout Itemize
Inflow boundary condition:
\begin_inset Formula $u\bigg|_{x=a}=u_{\text{in}}$
\end_inset
\end_layout
\begin_layout Itemize
Get the general,
scalar nonlinear conservation law:
\begin_inset Formula $u_{t}+f(u)_{x}=0$
\end_inset
\end_layout
\end_deeper
\end_inset
\end_layout
\begin_layout Standard
The main assumption for this model is,
that the vehicle velocity depends on the number density
\begin_inset Formula
\begin{equation}
V(u)\propto(1-u)
\end{equation}
\end_inset
Increasing number densities lead to a decreased vehicle velocity and vice versa.
Finally,
the velocity is scaled to its maximum value
\begin_inset Formula $V_{\text{max}}$
\end_inset
and this maximum value is set to
\begin_inset Formula $1$
\end_inset
(
\begin_inset Formula $V_{\text{max}}=1$
\end_inset
),
resulting in
\begin_inset Formula
\begin{align}
V(u) & =V_{\text{max}}(1-u)\\
& =(1-u)\\
\Rightarrow u_{t}+\left(u(1-u)\right)_{x} & =0,\quad x\in[a,b]\\
\Leftrightarrow u_{t}+\left(f(u)\right)_{x} & =0\\
\text{for: }f(u) & =u(1-u)
\end{align}
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
Main assumption in the construction of model is mass balance
\begin_inset Formula $u_{t}+(V(u)u)_{x}=0$
\end_inset
with fluid velocity
\begin_inset Formula $V(u)=V_{\text{max}}(1-u)$
\end_inset
\end_layout
\begin_layout Itemize
What is the underlying assumption of
\begin_inset Formula $V(u)$
\end_inset
?
\end_layout
\begin_deeper
\begin_layout Itemize
The more cars (
\begin_inset Formula $u$
\end_inset
increases),
the lower the speed
\begin_inset Formula $V(u)$
\end_inset
decreases
\end_layout
\begin_layout Itemize
Use
\begin_inset Formula $V(u)=V_{\text{max}}(1-u)$
\end_inset
with
\begin_inset Formula $V_{\text{max}}$
\end_inset
as constant maximum velocity (
\begin_inset Formula $V_{\text{max}}=1$
\end_inset
),
arrive at
\end_layout
\begin_deeper
\begin_layout Itemize
\begin_inset Formula $u_{t}+\left(u(1-u)\right)_{x}=0,\quad x\in[a,b]$
\end_inset
\end_layout
\end_deeper
\end_deeper
\end_inset
\end_layout
\begin_layout Subsection
Arising Research Questions
\end_layout
\begin_layout Standard
From this mathematical model and the physical background some research questions arise.
\end_layout
\begin_layout Enumerate
How does the number density evolve over time?
What influence has the initial distribution on the transient behavior of the number densities?
\end_layout
\begin_layout Enumerate
What is the highest number density?
Is there a mathematical explanation for this highest number density?
\end_layout
\begin_layout Enumerate
What is the flux of the moving vehicles?
How does it change over time?
When is it high and when is it low?
\end_layout
\begin_layout Enumerate
Is it more efficient to have a high distance or short distance between the cars?
With a higher distance a higher speed is possible,
but less cars are on the road.
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
Relevant research questions
\end_layout
\begin_layout Itemize
How density evolves over time (from initial distribution)
\end_layout
\begin_deeper
\begin_layout Itemize
Whats the peak of densities?
And why?
\end_layout
\begin_layout Itemize
What's the flux of moving vehicles?
How does it change,
when is it high,
when low?
More efficient to get high distance between cars (less cars for higher speed) or short distance (more cars with less speed)?
\end_layout
\end_deeper
\end_inset
\end_layout
\end_body
\end_document
Project2/LyX_old/Introduction.tex deleted 100644 → 0
+ 0
− 81
View file @ 420f656e
\section{Introduction}\label{sec:Introduction}
Traffic jams occur in our everyday life. Most people use the road,
either by car, bus or bike, every day to get to their job, do grocery
shopping, to meet friends or to get to their hobbies. Through this
enormous use of the road, traffic jams occur. Traffic jams lead to
a smaller speed of vehicles, if too many vehicles are close to each
other.
The arising engineering question is, how to reduce these traffic jams?
With a reduction of traffic jams, the traffic quality can increase,
with less time on the road. However, to reduce traffic jams it is
essential to understand how these work.
For this, it is necessary to study the underlying mathematical model
of traffic jams, which states a smaller vehicle speed at higher number
densities.
\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{Figures/TrafficJam}\caption{Image by Al G\textcyrillic{г} from Pixabay}
\end{figure}
\subsection{The Mathematical Model}
The underlying mathematical model of traffic jams relies on the general
conservation of mass
\begin{equation}
u_{t}+\left(V(u)u\right)_{x}=0,\quad x\in[a,b]
\end{equation}
where $u$ is the number density of vehicles ($u\in[a,b]$), $V(u)$
is the velocity of vehicles, depending on the number density and $b-a$
is the length of the road. Furthermore, an inflow boundary condition
\begin{equation}
u\big|_{x=a}=u_{\text{in}}
\end{equation}
is assumed to hold true. This inflow boundary condition models the
number of arriving cars at the beginning of the road.
Finally, the problem can be reformulated to the general, scalar, nonlinear
conservation law
\begin{align}
u_{t}+f(u)_{x} & =0\quad\text{in}x\in\Omega\\
u\big|_{x=x_{\text{in}}} & =u_{\text{in}}
\end{align}
The main assumption for this model is, that the vehicle velocity depends
on the number density
\begin{equation}
V(u)\propto(1-u)
\end{equation}
Increasing number densities lead to a decreased vehicle velocity and
vice versa. Finally, the velocity is scaled to its maximum value $V_{\text{max}}$
and this maximum value is set to $1$ ($V_{\text{max}}=1$), resulting
in
\begin{align}
V(u) & =V_{\text{max}}(1-u)\\
& =(1-u)\\
\Rightarrow u_{t}+\left(u(1-u)\right)_{x} & =0,\quad x\in[a,b]\\
\Leftrightarrow u_{t}+\left(f(u)\right)_{x} & =0\\
\text{for: }f(u) & =u(1-u)
\end{align}
\subsection{Arising Research Questions}
From this mathematical model and the physical background some research
questions arise.
\begin{enumerate}
\item How does the number density evolve over time? What influence has the
initial distribution on the transient behavior of the number densities?
\item What is the highest number density? Is there a mathematical explanation
for this highest number density?
\item What is the flux of the moving vehicles? How does it change over time?
When is it high and when is it low?
\item Is it more efficient to have a high distance or short distance between
the cars? With a higher distance a higher speed is possible, but less
cars are on the road.
\end{enumerate}
Project2/LyX_old/ListOfVariables.lyx deleted 100644 → 0
+ 0
− 767
View file @ 420f656e
#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
Project2/LyX_old/Results.lyx deleted 100644 → 0
+ 0
− 111
View file @ 420f656e
#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 Section
Results
\begin_inset CommandInset label
LatexCommand label
name "sec:Results"
\end_inset
\end_layout
\begin_layout Standard
\end_layout
\end_body
\end_document
Project2/LyX_old/Results.tex deleted 100644 → 0
+ 0
− 4
View file @ 420f656e
\section{Results}\label{sec:Results}
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment