Yuanpeng @ Blogger

Simulation box for bulk (left) and nano (right) systems In Ref. [1], we discussed the theoretical principles for correcting the nano-size effect when modeling the pair distribution function (PDF). The fundamental idea is to bring back the uncorrelated pairings in between atoms belong to different nanoparticles, based on the assumption of random distribution of nanoparticles in system. Such uncorrelated pairings will then be added to the partial PDF's calculated explicitly from the structural model in simulation box, as presented in the right of the picture shown above. The kernel mathematical expression in Ref. [1] is reproduced as follows, \[G(r) = \sum_{i,j}c_ic_jf_if_j[\frac{\rho^{RMC}}{\rho}g_{ij}^{RMC}(r) + U(r) - 1]\] where the meaning of all symbols can be found in Ref. [1] and we won't reproduce them all here. Instead, we are going to focus on the term \(g_{ij}^{RMC}(r)\) which represents the partial PDF's calculated explicitly from the simulation box and \(U(r)\) w

Neutron scattering length table by NIST [1] When we do calculations relevant to neutron scattering, it is unavoidable that we will come across either coherent, incoherent or total scattering length of elements, which describes the strength of scattering neutrons by different elements, either coherently, incoherently or both. In this article, I will try to uncover the three different types of neutron scattering length, by going through the derivation in details. First, the differential cross section for neutron scattering by a certain structure is given as below -- here we do the derivation for a single-species system so we can derive the relevant scattering length conveniently. \[\frac{d\sigma}{d\Omega} = \sum_{i,j}b_ib_je^{-i\vec{Q}\cdot (\vec{R}_i - \vec{R}_j)}\] where \(i\), \(j\) refers to atoms located at different locations in the structure under beam. In practice, every single \(b_i\), \(b_j\) depends on the corresponding nuclear isotope, spin orientation relative to neutron, nu

Image reproduced from Ref. [5]. In this blog, I will put down my learning notes as reading through the article on topological electrons by A. P. Ramirez and B. Skinner [1]. Basically, I will follow the story flow in Ref. [1] and therefore, first, I will note down the main flow that one can follow to arrive at the notion of topological electrons. Then I will cover the implications of topology and its connection to quantum Hall effect and quantum spin Hall effect. Finally, Weyl semimetal will be covered. It should be pointed that I will not reproduce all the nice discussions presented in Ref. [1]. Rather instead, I will just try to note down those key points or questions that I came across during reading Ref. [1]. First, the topological structure of an geometric object is defined by the Gauss-Bonnet integral, \[\frac{1}{2\pi}\int_S K dA = n\] where \(K\) refers to the curvature at points on surface \(A\). The integral will give us a constant \(n\) which corresponds to the genus (number o

Ernst Ising (Left) and Wilhelm Lenz (Right) - Ising was Lenz's student and the Ising model was claimed (by Ising himself) to be originated by Lenz but named after Ising. Ising model was originally proposed for ferromagnetism and owing to its simplicity in describing the system interaction, it has been widely used in not only describing magnetic systems in theoretical physics area but also in other areas involving similar interaction mechanism. In fact, Ising model can potentially find its position in describing systems involving binary states whereby we have active influence upon each other between neighbors. Here in this blog, I will not try to reproduce those already available beautiful introduction to Ising model - see e.g., Ref. [1-4] and a whole bunch of others one can easily find on Internet. Instead, I will just write down the outline of the problem we are facing once we have the simple Ising model set up for describing the system energy. For example, we always hear people t

Having multiple kernels available for Jupyter service, we may need to manage them at some point, e.g., rename kernel names and remove kernels. First, to show all available kernels, run the following command, jupyter kernelspec list we will then see output like this, Available kernels:   python3    /opt/jupyterhub/lib64/python3.6/site-packages/ipykernel/resources   diffpy     /usr/local/share/jupyter/kernels/diffpy   py37       /usr/local/share/jupyter/kernels/py37   python     /usr/local/share/jupyter/kernels/python This is the full list of all available kernels on our machine and the directory specifies where the configuration file for each kernel is located. To change kernel name, we then need to go into the corresponding directory for a specific kernel and open the 'kernel.json' file to change the 'display_name' entry to whatever we want. To remove a kernel, we want to use the following command, jupyter kernelspec remove KERNEL_NAME For example, if we want to remove

When trying to set up our own Jupyterlab server where general users can visit and use, the link in Ref. [1] could be followed. Once we follow literally the step-1 specified in the link, the server should be running without problem and we can just start using our own online Jupyterlab service. However, since the Jupyterlab service we just set up is a system-wise available service and therefore when we want to add kernels to the Jupyterlab service, we cannot use those kernels belonging to a specific user. Instead, we should set up system-wise available environment which then can be used as system-wise available kernels. The step-2 in Ref. [1] provides us with a generic way to set up the system-wise available environment using conda . Definitely we can follow the instructions there to set up conda in such way that conda itself is also system-wise available. As an alternative, we can be a bit flexible - we can use general users' local conda environment to do this as well, as long as

Docstring is part of Python script which will keep record of documentation and description of the relevant section in the script. It won't make any effect upon the execution of the script but whenever needed, the docstring could be pulled out and displayed for users' reference. Based on that, we can go further to generate dedicated documentation pages/docs for general purpose. At this point, Sphinx is a commonly used package to transform the docstrings in Python script into either HTML, LaTeX or some other suitable formats. Here in this blog, I am going to write down some notes in using Sphinx for building documentation based on the docstring in Python scripts. The steps below could be used as sort of general guidance to set things up with Sphinx. 1. Installation The official link to Sphinx gives rather detailed instructions about the installation and here I am not going to reproduce those details - refer to Ref. [1]. 2. Initial setup Once Sphinx is installed, we may want to se

Talking about magnetic field, we have three relevant physical quantities - magnetic field \(\vec{H}\), magnetic induction field \(\vec{B}\) and magnetization field \(\vec{M}\). It is straightforward to understand \(\vec{M}\) - when applying magnetic field (here, by 'magnetic field', we mean something in general, but not specifically refer to \(\vec{H}\)), we use \(\vec{M}\) to characterize how much the matter in question is magnetized. However, concerning \(\vec{H}\) and \(\vec{B}\), it seems that both are describing some sort of 'strength' of magnetic field (again, we mean 'magnetic field' in general. The same applies below until we become specific about what we mean by 'magnetic field'). But why do we have two quantities here to describe the 'same' thing? The answer is - they are not the same thing, as described by \(\vec{H}\) and \(\vec{B}\), respectively. Fundamentally, this goes back to the foundation of the electromagnetic theory - specific

Illustration for Stern-Glach experiment [1] Angular moment means rotation - this applies to electron as well. For electrons, any movement is associated with current and therefore angular moment naturally is tightly linked to current as well. Furthermore, current means magnetic field, as originated by Orsted. Mathematically, starting from expressing the current with the angular moment of rotating electrons, followed by detailed mathematics based on Biot-Savart law (induction \(\vec{B}\) as the function of current), one can arrive at the expression of magnetic induction in terms of magnetic (dipole) moment \(\vec{m}_l\). In another word, it can be shown that the magnetic field generated by electron rotation current is equivalent to that generated by magnetic dipole, with the equivalent dipole moment defined as (see Ref. [2] for detailed derivation), \[\vec{m}_l = -\frac{1}{2}eR^2\vec{\omega}\] Given that the angular moment can be written as \(\vec{l} = m_eR^2\vec{\omega}\), we can obtain

One can follow Ref. [1] to build up site with Jekyll - it contains quite a few steps concerning the set-up of sites through GitHub pages. However, this is not necessary if one just wants to set up site locally and test. Therefore, after installing Ruby and Bundle, one can directly create a local folder and go into it. From there, one needs to follow the steps given below, Run bundle init  - this will create the Gemfile . According to Ref. [1], GitHub pages depends on certain version of packages (a link can be found there in Ref. [1] about details) and therefore one may need to install certain version of Jekyll with Bundle (though, again this may not be necessary if one only wants to do it locally). To install a certain version of Jekyll with Bundle, one need to put in the following line into Gemfile , gem 'jekyll', '3.9.0'  Then one needs to execute bundle install  to install the required version of Jekyll. At this stage if one continues, as instructed in Ref. [1], to e