Why Your Mean Is More Stable Than Your Standard Error Suggests
If you have ever taken dozens, hundreds or millions of measurements and marveled at how steady your average seems this short blog article may shed some light on the effects causing this. While naive statistics tell us the standard error should shrink with more samples, real-world measurements often don't behave so cleanly. We explore why your mean can appear surprisingly stable, even when standard deviation or error bars suggest high uncertainty, and what role correlated noise plays in this apparent contradiction. Taking a look at the limits of traditional assumptions like white noise and sample to sample independence, we take a peek how phenomena like drift and flicker noise distort common statistical tools - and when they lead you to under- or overestimate your actual uncertainty. We mention why Allan deviation is an essential tool for uncovering the true nature of your data and how blindly trusting standard error can mislead both your interpretation and reporting precision.
FDM Printed PLA in Cryogenic Environments
Can 3D-printed PLA handle extreme cryogenic conditions? In this article, I explore how FDM-printed PLA performs when exposed to liquid nitrogen at 77K (-196°C). I tested two different crucible designs, with (not so) surprising results—one even allowed safe handling with bare hands! Learn about the experimental setup, design insights, and what this might mean for using PLA in unconventional cryogenic applications.
Nuclear magnetic resonance and electron paramagnetic resonance: Basics
Nuclear Magnetic Resonance (NMR) and Electron Paramagnetic Resonance (EPR) are pivotal techniques used to explore molecular structures and dynamics through the magnetic properties of atomic nuclei and unpaired electrons. This article provides an introducory level examination of NMR, integrating both classical and quantum mechanical descriptions. Key topics include the Zeeman effect, Bloch equations, relaxation processes, and the quantum mechanical framework involving spin operators, eigenstates, and the density matrix formalism. The discussion delves into the effects of RF driving fields, Rabi oscillations, and the incorporation of relaxation processes using the Lindblad master equation. The article concludes by demonstrating how these quantum mechanical models align with the phenomenological Bloch equations, providing a comprehensive understanding of the dynamics of spin systems under resonance conditions. While the primary focus is on NMR, the article also offers insights into EPR, broadening the perspective on magnetic resonance techniques.
Electric dipole interaction of atoms with radiated electromagnetic waves
A short summary on the interaction of alkali atoms with electromagnetic radiation
A mini recipe to fit arbitrary models to data using lmfit in Python
In this blog post, we navigate through an unorthodox yet effective method of building models using the lmfit library, a wrapper around scipy's fitting routines. The article dives into a hands-on approach for fitting noisy data with a custom-defined Gaussian model, while suggesting that the conventional wisdom of lmfit isn't the only path to success. The tutorial initializes by installing lmfit and swiftly moves to crafting a function for the Gaussian model, which involves defining an objective function to decipher the best parameters for data fit. It guides the reader through generating synthetic noisy data, plotting it for visual aid, and conducting the fitting process. Through this procedure, a parameters are constructed and optimized to fit our model to the noisy data, followed by a presentation of the fitting report. Finally, the results are visualized, and the article concludes by discussing the advantages of this method, especially when dealing with complex or iterative models. The full code for the exercise is accessible in a GitHub GIST, allowing readers to directly engage with the material covered.
Detecting frequency, delay and phase relation as well as multiple targets using correlation functions
A short story about how one can use autocorrelation and cross-correlation functions on discretized samples of radio frequency data and also noise to detect the frequency of a single signal, the delay of a reflected signal, the phase relation between two signals and how one can track multiple reflective targets in applications like LIDAR, sonar or radar using correlations - and how to get them robust against external influence.
Heterodyne, Superheterodyne, Homodyne and Lock-In Amplifier
A mini introduction about the terms heterodyne, superheterodyne, homodyne and lock-in amplifier
Measuring the speed of light at Wiener Forschungsfest 2022
This article allows you to discover how we (a group from TU Vienna and University of Vienna) brought the fascinating world of physics to life at the Wiener Forschungsfest 2022! Using a visible range laser, a bicycle wheel, and modern photodiodes, we demonstrated how to measure the speed of light in an interactive and engaging setup designed mainly for children. This hands-on experiment highlighted the incredible speed of light while also conveying the fact that light is fast but not infinitly fast and allowed visitors to influence the accuracy of the measurement themselves. This article provides a short summary about the historical context, experimental setup, and the exciting outcomes of this educational outreach project.
OpAmp based voltage controllable current source
A simple temperature drift compensated voltage controlled current source up to 8A (10A peak) and 30V rail to rail based on OPA549 or other power operational amplifiers
Controlling the Korad KA3005P using Python
A short summary on how to control the Korad KA3005P power supply using Python as well as some simple samples on how to use my own control library
Logarithm and exponential function with OpAmps
A summary how to implement the logarithmic and exponential function using operational amplifiers - and how to use this to build simple mixers when combining with a simple summation amplifier
Building simple function generators using OpAmps (OpAmp based multivibrator)
Summary on how to use operational amplifiers to build simple function generators such as square wave function generators. This approach can be used to build simple laboratory function generators as well as low frequency oscillators used for various applications.
Mini summary on how to solve linear equations in Krylov subspaces
A write up of the methods used to iteratively solve arbitrary linear equations systems. This includes the definition of Krylov subspace solvers, the Lanczos and Arnoldi algorithm to build orthogonal subspaces, a summary of the steepest descent and projective methods and then as an real world realization of projective methods the conjugate gradient (CG) and generalized minimal residual (GMRES) method.
QR decomposition using Givens rotations
Mini recipe and hopefully descriptive summary on how to perform QR decomposition using Givens rotations which forms the basis of many linear algebra numeric applications such as least squares, GMRES, etc.
Gold plating on copper surfaces
A summary on a procedure on how to use a galvanic process to plate copper (and other metallic surfaces) with gold using a galvanic bath
Rendering static two dimensional electric fields caused by point charges using Python
A mini summary on how one can use Python and matplotlib to calculate and render two dimensional static electric fields generated by point charges in infinitly sized space based on Coulombs law and the superposition principle.
The capstan equation
A summary on how to derive the capstan equation describing the friction of a rope on a bollard, winch or a capstan
Building a simple 6 kV DC power supply
Short summary on how to build a small 6 kV power supply using an 2.1 kV microwave oven transformer, two of the accompanying capacitors and a bunch of diodes that is capable of delivering a little bit more than half a kilowatt of power
A simple OpAmp photodiode readout circuit
A short summary on the workings of photodiodes, how one can interface them to simple electronics and a simple amplifier circuit
Controlling Pfeiffer Turbopumps using RS485
Pfeiffer makes great turbopumps but sometimes you want to log information or control them from an existing control system. Out of this desire I played around with the RS485 protocol used by Pfeiffer and wrote some simple unofficial tools - that's what this blog entry is about
A vacuum oil well - using water to check for oily contamination in a vacuum chamber
This blog post describes a really simple method to get a hint if the interior of a vacuum chamber has been contaminated with some oil without the use of expensive chemical analysis.
Ethernet control of Gamma vacuum quad ion pump controller
Notes on the the protocol that's required to remotely control Gamma vacuum ion pumps / titan sublimation pumps via a quad pump controller and some views on the inner workings of my own library implementing the protocol
Composition of atmospheric air and mean thermal speed
Table containing the typical atmospheric air components as well as their mean thermal speed and mean molecular mass.
Matching impedance using NanoVNA v2, NanoVNASaver and SimSmith
A mini summary on how to perform impedance matching for antennas or other devices using the NanoVNA v2 together with the NanoVNASaver and SimSmith applications based on the impedance matching of an electron deflection system
Summary: Pierce type electron gun essentials and most basic geometry
A short summary about the basic conditions in a pierce type electron gun
Building a simple improvised electron gun from common of the shelf components
Mini blog article that summarizes the build of a simple 2 mA beam current electron gun from common of the shelf components gathered from the hardware store as well as some 3D printed components.
Basic behaviour of thermionic emission cathodes
A short summary about the operation and characteristics of thermionic emission cathodes, the current limiting factors and the most important failure modes
Cutting glass vacuum tubes using hot wire
Something easy and simple. How to cut glass tubes and other glass parts using electrically heated hot wire.
3D printed parts using PLA and standard FDM process in vacuum?
Just a short description of what I've tried (and didn't expect to work) about the usage of 3D printed parts made out of PLA in the typical desktop FDM 3D printing process, i.e. a method to build really low cost parts at home.
Maxwell equation summary
A short summary about the basic properties of Maxwell equations, the resulting electromagnetic wave equations and commonly used gauges (Lorenz, Coulomb).
Some Gaussian integrals in 1 dimension
Short summary of various commonly used Gaussian integrals (1 dimensional) most of the time not shown in school textbooks.
Z, ABCD, S and T parameters in two port networks
A short summary about the different meaning and interpretation of impedance, ABCD, scattering and transfer parameters in simple (linear) two port networks.
Capacitance measurement with AVR (simple, fast)
Mini article about the measurement of capacitance with AVRs with a minimum of external components (in it's most extreme form none external components exploiting the gate capacitance of the micro-controllers input)
Where does complex impedance come from?
This post describes a simple derivation of the complex inpedance formulas well known from electronics.
Fast ballpark calculation of maximum speed for maximum car througput (using simple high-school physics and math)
The fast and short answer to the question which speed would be (under optimal conditions) the speed to choose for maximum car throughput on a single lane. Contrary to the often believed fact it's shown that higher speed does not correlate with higher throughput by using simple high-school math.
WKB-Näherung
This is a short (German) summary of the WKB approximation applied to the time invariant Schrödinger equation, which is a method used for finding approximate solutions to linear differential equations with spatially varying coefficients.
Zusammenfassung Reaktorphysik
This is a (German) summary of basic nuclear reactor physics that has been written by me during learning for the exam of an university course.
