Kürşat Yurt

A simple cheatsheet to tmux

2022-05-15T00:00:00+02:00

I have never remember such a damn beautiful but easy to forget tool like tmux. Everytime I need a search it on Google and than just forgot about everything. I thought a small cheatsheet would be useful for me, but also you.

CTRL-B is default prefix to execute commands.

<prefix>+Command	Explanation
c	Creates a new session
d	Detach from a session
[0-9]	Move between sessions
,	Rename a window
p	Previous window
n	Next window
w	Shows all windows
&	Kill current window
”	Split pane horizontally
%	Split pane vertically
Arrows	Move between panels
x	Kill current panel
Spacebar	Toogle between horizontal and vertical panels

Some small adjustments

If you like to use mouse like me or want to adjust panel height/width quickly following tmux config file would be helpful

set -g mouse on
bind -n C-k resize-pane -U 5
bind -n C-j resize-pane -D 5
bind -n C-h resize-pane -L 5
bind -n C-l resize-pane -R 5

After adding to tmux config only thing you need would be just sourcing the config file

tmux source-file ~/.tmux.conf

Have a nice day

How to Draw Your Graphs using Tikz and Pgfplots

2021-06-08T00:00:00+02:00

Which packages are reqiured ?

In followign example we will use tikz and pgfplots packages for plotting 2D graphs in a latex document.

\usepackage{tikz}
\usepackage{pgfplots}

This blog post only demonstrate basics and common things. Further more options please check pgfplots¹ and tikz manuals².

Plotting Equations

Let’s start with a quick example to see how easy it is to do. In the following snippet. This is provide an entry point to us.

First we begin with tikzpicture environment. For 2D plots we are use axis. Inside squared brackets we define axis properties like xlabel, label. Since we will be use mathematical expressions in this example we will define a domain lying from -10 to 10 in x axis and we will take 20 sampling point along this path.

\begin{tikzpicture}
 \begin{axis}
  [
  xlabel={$x$},
  ylabel={$y$},
  domain=-10:10,
  samples=20,
  ]
  \addplot {x^2};
 \end{axis}
\end{tikzpicture}

It will produce following graph.

A sample graph using pgfplots.

Adding more options

Let’s add a grid, change grid to a thinner and lighter version, move the thicks to outside of axes. Also let’s define ytick settings and xticks settings. We can defined how often we will have ticks.

grid=both,
major grid style={thin,color=black!10},
tick align=outside,
ytick={0,10,...,100},
xtick={-10,-7,...,10},

An improved graph.

We can also specify color of lines,marker and thickness. Here some examples.

\addplot [no markers, color=black] {x^2};
\addplot [mark = x,color=red,very thin] {x^2+5};
\addplot [mark = otimes,color=blue,thick] {x};
\addplot [mark = diamond,color=pink, very thick] {x+50};

More improved graph.

Oh, we are adding more equations but there is no legend. How can one know which is which equation right?

We can add legend entries at after adding a new plot there is 2 style is available

\addplot [no markers, color=black] {x^2};
\addplot [mark = x,color=red,very thin] {x^2+5};
\addplot [mark = otimes,color=blue,thick] {x};
\addplot [mark = diamond,color=pink, very thick] {x+50};
\addlegendentry{$x^2$};
\addlegendentry{$x^2+5$};
\addlegendentry{$x$};
\addlegendentry{$x+50$};

\addplot [no markers, color=black] {x^2};
\addlegendentry{$x^2$};
\addplot [mark = x,color=red,very thin] {x^2+5};
\addlegendentry{$x^2+5$};
\addplot [mark = otimes,color=blue,thick] {x};
\addlegendentry{$x$};
\addplot [mark = diamond,color=pink, very thick] {x+50};
\addlegendentry{$x+50$};

Default position for legend entry is north east, one can override that settings adding legend pos option to axis options. This is based on geographical locations. It can be placed on south west|south east|north west|north east|outer north east. By default legends are boxed, using legend style option {draw=none} we can remove outer box of a legend.

[
legend pos=outer north east,
legend style={draw=none},
]

A graph with legend.

Plotting CSV Files

Generally we deal with plotting some data obtained from another source. One can easily store those values in a CSV file like below

x,entry1,entry2,entry3
0,1,0,0
1,2.71828182845904,1,0.25
2,7.38905609893065,8,4
3,20.0855369231877,27,20.25
4,54.5981500331442,64,64
5,148.413159102577,125,156.25
6,403.428793492735,216,324

Here we have 4 columns they are seperated by comma and first line gives the header for the values.

Plotting such kind of data is a really easy task to do.

\addplot [plot options] table [table options] {./path/to/data.csv};

Plot options are similar to what we have done above. The new entry table basicly need 3 option. We need to speficy header of x values, y values, and the column seperator used in data file.

Here an example.

\addplot [no markers, color=black, very thick] table [x=x, y=entry1, col sep=comma] {./data.csv};
\addlegendentry{$e^x$};
\addplot [no markers, color=red, very thick] table [x=x, y=entry2, col sep=comma] {./data.csv};
\addlegendentry{$x^3$};
\addplot [no markers, color=blue, very thick] table [x=x, y=entry3, col sep=comma] {./data.csv};
\addlegendentry{$x^4/4$};

A graph created using CSV.

Introduction to Linux Command Line

2021-06-07T00:00:00+02:00

Whenever it comes to some serious stuff like using a cluster or open-source software like OpenFOAM people are faced with the famous Linux command line. It was scary at the first sight but later on, when you get used to him, he will be your best friend.

Here some basic commands that it as a good start point

When you open a terminal you might only see a blinking cursor

If you type pwd, this will give you your current working directory’s absolute path

Here my current terminal output

pwd
/home/kursayurt

Now I know that I am on my home directory. I want to know which files or directories inside this directory. Simply typing ls is gives you that ones

ls
 Blog
 Desktop
 Documents
 Downloads
 hello.cpp
 Pictures
 Project
 Public
 Templates
 TUM
 Videos
 yd

As you see here is a hello.cpp file and some other directories are around here

Let’s go to my Desktop directory using cd command

cd Desktop
pwd
/home/kursatyurt/Desktop

Now as you see I have changed the current directory to my Desktop

ls
Ch8Sub.pdf               worksheet2.pdf
cfdlab-lecture-notes.pdf
ws-navier-stokes.pdf

There is pdf files around. If I want to open one of them I can simply open them using xdg-open command which is open any type of file using default software defined by the system

xdg-open woorksheet2.pdf

To go back we can type

cd ..
pwd
/home/kursatyurt

This take us one directory back.

Now if I want to copy a file from my Desktop to Home directory, I can follow this thing.

cp ./Desktop/worksheet2.pdf .

Here cp command takes two arguments first one is the source and the second one is the destination

./ denotes from current directory by this way we can espace from writing absolute path. Also in the second argument . means here.

If we want to move a folder or file we use mv command which is similar to cp, one important thing about copy is you cannot copy a folder using cp command alone you need to give recursive flag -r

cp -r /source/directory /destination/directory

By this way one can copy a folder.

In order to create a new directory, we are using mkdir command

mkdir directoryname

This creates a new directory under our current directory as like any other linux command we can do operation other than our current directory giving absolute path

mkdir /absolute/path/to/directory

Now take a look at removing files/directories. An important thing about removing is that this operation is irreversible, no Trash Bin deleted files from command line goes.

Let’s first look into deleting files

rm FileName

Removing directories are requires a recursive operation

rm -r DirectoryName

One other important thing is of course when you are doing an operation or running a program you might want to cancel that process. For this purpose [Control]+c is used.

A simple ODE Solver Using Python

2021-06-07T00:00:00+02:00

In this blog post we will understand what is an ODE and how to solve it numerically using Python.

What is an ODE?

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions ¹ .

Why do we need numerical methods?

Numerical methods are techniques to approximate mathematical procedures. Here we are approximate an time integral. We use numerical methods when an analytical solution does not exist (e.g. Navier Stokes Equations), or an analytical method is intractable.

Fundamental Approach: Euler’s Method

Here we want to solve an ODE in the form of

\[\frac{dx}{dt} = f(x,t)\]

Using Taylor series expansion around \(x(t_0)\) we can write following equation

\[x(t_0+dt) = x(t_0) + dt \cdot x'(t_0) + O(dt^2)\]

This method is called (Explicit) Euler’s method.

Physical Problem

Let’s consider the falling of a parachute jumper. Governing equation for this problem is \(F=m*a\) . To model the drag force we choose simple model \(F_{drag}=\frac{1}{2}\rho A C_D V^2\), where \(C_D\) is drag coefficent, \(A\) is area of parachute and \(\rho\) is air density. The other forces acting on the jumper is gravitationa force which is given by \(F_G=g*m\), where \(g\) is gravitational acceleration and \(m\) is mass. Resulting governing equation is the this problem is:

\[m \cdot g - \frac{1}{2}\rho A C_D V^2 = m \cdot a\] \[a = g- \frac{\rho A C_D V^2}{2m}\]

In other words,

\[\frac{dV}{dt} = g- \frac{\rho A C_D V^2}{2m}\]

Let’s code it

First of all we need to import libraries to python. In this project we will use 2 libraries called numpy and matplotlib.

import numpy as np
import matplotlib as plt

After importing libraries we will define the ODE’s function

def dvdt(V,t):
    a = g- rho * A * cd * V**2 / 2 / m
    return a

Since this is a rather simple ODE we have an analytical solution, which we will be use to check accuracy of solution.

def analyticalsol(t):
    v = (21.0262 * np.exp(0.933124 * t) -21.0262) / (np.exp(0.933124 * t) + 1)
    return v

This gives us the derivation of function at the a known point.

Let’s initialize the variables

v_0 = 0       #m/s    initial velocity
t_0 = 0       #s      initial time
t_end = 10  #s      end time
m = 100     #kg     mass
A = 3.14    #m^2    area
cd = 1.15   #       drag coefficent
rho = 1.229 #kg/m^3 air density
g = 9.81    # m/s^2 gravitational acceleration
dt = 1      #s      timestep

result = []  #empty of numerical results
time = []    #empy list of numerical time series

Now lets write the main solution loop

v=v_0  #Initialize Velocity
t=t_0  #Initialize Time
while (t < t_end):
  time.append(t)            #Store Current Time
  result.append(v)          #Store Current Velocity
  acceleration = dvdt(v,t)  #Get Acceleration
  v += acceleration * dt    #Advance velocity
  t += dt                   #Advance time

a_time = numpy.linspace(t_0,t_end,num=50) #Sample 50 Point betwen t_0 and t_end
a_result = analyticalsol(a_time)                #Get the solution

#Plot Analytical Solution
plt.plot(a_time, a_result, label="Analytical Solution")
#Plot Numerical Solution
plt.plot(time, result, label="Numerical Solution")
plt.legend()  #Add Legend
plt.grid()    #Add Grid
plt.show()    #Show plot on the screen

You can download the python script that I used to produce result below from here.

Results

Comparision of Solution.

Here we can clearly see that as we decrease the timestep we get a more accurate solution. There is a limit we can decrease the timestep, while decreasing we error. Using too small or too big timesteps causes inaccurate results.

Dennis G. Zill . A First Course in Differential Equations with Modeling Applications. ↩

Hello World!

2021-06-06T00:00:00+02:00

Hey there welcome to my blog page. I am Kürşat. Currently, I am studying Computational Science and Engineering at Technical University of Munich.

In this blog I will share some interesting posts that are related to engineering, programming, some daily useful tools and so on.

I hope you will enjoy!

printf("Hello World!")

write *,  "Hello World!"

print("Hello World!")