CTP Summer Internship Programme – BUE
11 - 29 July 2021


The CTP Summer Internship Programme provides the opportunity for highly motivated undergraduate students to attend short courses in quantum field theory, black hole physics and cosmology. The programme enables the students to become familiar with active research areas in theoretical physics. The inaugural session this year included three main topics, with lectures given by the indicated CTP members:

  • Inflation and Cosmological Perturbations by Alexey Golovnev.
  • Physical Cosmology by Amr El-Zant.
  • Black Hole Mechanics and Thermodynamics by Adel Awad.

  • Under these general titles, there were also two or three sub-projects for each topic. Each of the following projects involved two or three students:

  • Dark Matter N-Body simulation by Mahmoud Hashim
  • Observational constraints of CPL Dark Energy Model by Mahmoud Hashim
  • Chaos in N-body Trajectories by Amr El-Zant and Mahmoud Hashim
  • Use GrTensor package (Schwarzschild, Kerr BHs and FLRW model) by Waleed El Hanafy
  • Search for Dark Matter Assoictaed with Z Prime Boson at the LHC by Sherif Elgammal
  • Using Garfield for the Calculation of Transport Parameters by Yasser Assran

  • Presentations involving additional topics for projects were delivered by CTP visitors

  • A short lecture on “Machine Learning in Biophysics, High Energy Physics and Astrophysics” by Mohamed Amin (University of Groningen) on Tuesday 27th July.
  • A QED project using Anaconda framework by Ahmed Hammad (University of Basel) during the second week of the programme.

  • Logistic details

    There were 18 lectures in all: six for each course and ranging between an hour to hour and a half. They took place from 11 to 17 July and 25 to 29 July, and were attended by 25 students; mostly junior students going into final year, from Zewail City, as well as Alexandria, Cairo and Port Said universities. The lectures were followed by lunch and then afternoon training sessions involving the projects. The programme was largely funded by the CTP budget. We thank the BUE for its support, and for the usage of the buses for transporting students, as well as discounted student housing for others.

    Outline of Lecture Courses

    I - Inflation and Cosmological Perturbations (Alexey Golovnev)

  • Introduction to quantum field theory
  • Further details, basic ideas of renormalisation
  • Various vacua, Bogoliubov transformation
  • Inflation
  • Cosmological perturbations from inflation
  • Review of some alternative models

  • II - Physical Cosmology and Galaxies (Amr El-Zant) [1, 2]

    • Background evolution
      • The FRW universe: Evidence and dynamical equations
      • Evolution of (and under) its components (matter radiation and dark energy)
      • Distance measures and cosmological parameters estimation
    • Thermal History
      • The hot big bang: Evidence and estimates from CMB
      • Decoupling from thermal equilibrium; examples including the abundance of dark matter in the standard WIMP scenario
      • Cosmological production of light elements
    • The formation of structure and the origin and evolution of galaxies <\li>
      • CMB fluctuations: cosmological parameter estimation and the initial conditions for structure formation under gravity
      • Large scale structure of the galaxy distribution, and its advent in the standard scenario
      • Properties of the galaxy population, pending problems and upcoming surveys

    III - Black Hole Mechanics and Thermodynamics (Adel Awad)

    • Introduction to general relativity (1.5 or 2 lec.)
    • Schwarzschild solution
    • More General BH and BH thermodynamics
    • Hawking radiation
    • Consequences of Hawking Radiation:
      • Information loss Paradox
      • Complementarity principle
      • Firewall proposal

    Description of Projects

    Dark Matter N-Body simulation [Supervisor: Mahmoud Hashim]

    In this project we do an N-Body cosmological simulation of Cold Dark Matter (CDM) using GADGET code. The project consists of creating the initial conditions, setting up parameters and running the simulation, then analyzing the simulation outputted snapshots. The aim of the simulation is to compare matter power spectrum with the theoretical predictions.

    Observational constraints of CPL Dark Energy Model [Supervisor: Mahmoud Hashim]

    In this project we do MCMC likelihood analysis to fit Chevallier-Polarski-Linder (CPL) Dark Energy (DE) model with cosmological background data such as Supernovae type Ia (SNIa) and Baryon Acoustic Oscillations (BAO) data. We use Boltzmann code CLASS and python package emcee to fit the data. The aim of this analysis is to check the variability of CPL DE model and give constraints of the model parameters.

    Chaos in N-body Trajectories [Supervisors: Amr El-Zant and Mahmoud Hashim]

    Self-gravitating N-body systems are ubiquitous in astrophysics, as a first approximation to everything from small star clusters to superclusters of galaxies. Except for the most compact objects, and the largest scales approaching the cosmological horizon, the Newtonian approximation is adequate. Nevertheless, Newton himself famously noted that, beyond N= 2 bodies, the N-body problem gave him a headache. From a modern point of view the pain partly comes from the fact that systems are not ‘integrable’, in the sense o being solvable in terms of symmetry principles (leading to enough conserved quantities as degrees of freedom). The ‘chaotic’ nature of the problem makes it difficult to tackle, and tricky to understand the meaning of it numerical simulation, due to the associated information loss. In this project (s) we investigate the divergence of various dynamical quantities (in 6-N phase space and in energy and angular momentum space) of neighbouring N-body trajectories when significant softening is present. Goals are to study effects of variation of:

  • Particle numbers and find optimal softening that minimizes divergence.
  • Numerical (ir)reversibility of (exactly reversible) trajectories.
  • In-out of (dynamical) equilibrium initial conditions (optional).

  • GR Tensor [Supervisor: Waleed El Hanafy]

    General Relativity is the most successful theory describing gravity so far. The theory encodes the gravitational field as a curvature of spacetime. It has many applications in astrophysics and cosmology. Indeed, these applications intersect with general area of differential geometry, which needs some basic knowledge of tensor calculus. Fortunately, the GRTensor II package provides an easy tool to calculate tensor components on curved spacetimes, specified in terms of a given metric. The package contains a library of standard definitions designed for use in the field of general relativity. GRTensor II is not a standalone package, but requires an algebraic engine (originally developed to run with different versions of Maple). A limited version has been designed to run with Mathematica. GRTensor II and related software and documentation are distributed free of charge, please visit the URL http://grtensor.phy.queensu.ca/ and download the Maple version of GRTensor II. For more details about the package installation see the documentation link in the aforementioned URL.

    Three group projects will be offered during the programme, each consisting of two to three members:

  • Project I: Schwarzschild metric, which describes the geometry of a spherically symmetric spacetime configuration. The general relativistic solution of an empty space is suitable for solar system applications.
  • Project II: Kerr metric, which describes the geometry of an axially symmetric spacetime configuration. The general relativistic solution of an empty space is suitable for rotating black hole applications.
  • Project III: Friedmann–Lemaître–Robertson–Walker (FLRW) metric, which describes the geometry of a homogeneous and isotropic spacetime configuration. The general relativistic solution is suitable for cosmological applications.

  • Search for Dark Matter Assoictaed with Z Prime Boson at the LHC [Supervisor: Sherif Elgammal]

    One of the unsolved problems in particle physics is the existence of dark matter (DM), which is a new type of non-luminous and non-baryonic matter. Astrophysical observations suggest that DM contributes to about 27% of the mass of the universe. In parallel to the evidences from astrophysical observations, search for DM at the Large Hadron Collider is on-going. The signature of DM at the LHC will be in a form of missing energy, since it is very weakly interacting with ordinary matter. On the other hand the standard model of particle physics is successful in the unification between the electromagnetic force and the weak nuclear force in a single force described by the electroweak theory that predicted W+, W- and Z bosons which has been already discovered. But The SM fails to unify the four fundamental universal fields (The electromagnetic, weak, strong and gravity fields) which lead to the need of unification beyond the SM. In grand unification theories, it is possible to unify the electroweak force and the strong force in a single interaction predicting new sort of heavy bosons (MGU less MSM) such as Z (Z prime). The life time of Z is very short such that it decays rapidly to either di-lepton or di-neutrinos or a pair of quark – antiquark. One of the interesting models based on the grand unification is known as Mono-Z model, which propose the production of dark matter particles in addition to Z' boson. This process can be produced at the LHC via quark - antiquark Annihilation process in proton-proton collision at 13 TeV. These processes come in three different possible scenarios indicated by the following Feynman diagrams. Where 𝜒1 and 𝜒2 stands for possible dark particles candidates. Diagram no.(1) for dark higgs model where no.(2) for light vector and no.(3) for Light Z’ with Inelastic EFT coupling.

    Tasks (to be divided among groups) include

  • Performing MC simulation for Mono-Z' model signal at several mass points of Z' for the di-leptons decay channel
  • Performing MC simulation for the expected background
  • Analyzing the data collected by CMS detector in 2016, 2017 and 2018 in order to search for the Dark Matter particles and Z'

  • Using Garfield for the Calculation of Transport Parameters [Supervisor: Yasser Assran]

    Garfield is a computer program for the detailed simulation of two and three-dimensional drift chambers. It has an interface to the Magboltz program for the computation of electron transport properties in arbitrary gas mixtures. Garfield also has an interface with the Heed program to simulate the ionization of gas molecules by particles traversing the chamber. Transport of particles, including diffusion, avalanches, and current induction is treated in three dimensions irrespective of the technique used to compute the fields. In this work, we use Garfield to calculate the transport parameters like drift velocity, longitudinal diffusion, transverse diffusion Townsend coefficient attachment coefficient, and Lorentz angle.

    QED project [Supervisor: Ahmed Hammad ]

    While we are going to cover several python modules in the first part, so it is useful to install these modules earlier. For this purpose we are going to use the Anaconda frame work. You can download it https://docs.conda.io/en/latest/miniconda.html. Once you install the Anaconda, open a terminal window and type the following:

  • conda create --name BUE_QED
  • conda activate BUE_QED
  • conda install sympy ## python module for symbolic and analytic calculations
  • conda install -c conda-forge matplotlib ##python module for data visualization
  • conda install -c conda-forge notebook ##Jupyter notebook for python code debugging

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