## Find below a list and summary of the course projects I worked on during my undergraduate degree.

Mechanobiology of Endocytosis in Yeast Cells and the Physics of Vesicle Formation

A Biophysics course project supervised by Professor Shahid Khan. I was paired up with a Biologist for this, the report contains both our works. We presented posters at the end of the course too, you can see the poster at the right. You can find the project report here. Following is the abstract of the report.

the actual vesicle without introducing unrealistic assumptions.

So we introduce a continuous and 3 dimensional membrane model which is a

much better model and gives us more insights about the physics behind vesicle

formation. I start with deriving the spontaneous curvature model of Helfrich

and study in detail the most basic model by making assumptions along the way.

In the end I give an overview of how we can further introduce sophistication

and use our model to study other interesting cases.

**Abstract:**We started to model vesicle formation as a 2D necklace model of circular particles connected by springs (Figure 4), but soon realised that the model made many assumptions and because of no third dimension we lost many important aspects of vesicle formation. Moreover we could only model bending of a membrane from it and it was impossible to model the pinching and the formation ofthe actual vesicle without introducing unrealistic assumptions.

So we introduce a continuous and 3 dimensional membrane model which is a

much better model and gives us more insights about the physics behind vesicle

formation. I start with deriving the spontaneous curvature model of Helfrich

and study in detail the most basic model by making assumptions along the way.

In the end I give an overview of how we can further introduce sophistication

and use our model to study other interesting cases.

mechanobiology_of_endocytosis_and_the_physics_of_vesicle_formation.pdf | |

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## The Rotating Black Hole

An Astrophysics and General Relativity project supervised by Dr. Babar Qureshi. You can find a presentation for this project here and the project report here. Following is the abstract.

We would use light as a test to see how the tangential and radial velocities of particles vary. We would discuss negative energy and how the Penrose process can be used to extract energy from a rotating black hole. This project is basically one of the projects suggested on the MIT OCW website as part of their GR course. I followed the project F in the book,'Exploring Black Holes' by Wheeler and Taylor which is a really nice book on guides to projects in GR. It gives a basic overview and then makes you derive equations and answer many queries along the way. I have tried to answer most of the queries as part of this project.

**Abstract:**In this project we explore some of the properties of space time near a spinning black hole. Analogous properties describe spacetime near other stellar spinning objects like Earth and the Sun too. Near a spinning black hole you are swept along tangentially in the direction of rotation, we would discuss the various properties of spacetime by analysing the Kerr metric that describes the rotating black hole. We would use the test cases of extreme spin and static limit to get an intuitive feel of the physics going on in describing the phenomenon.We would use light as a test to see how the tangential and radial velocities of particles vary. We would discuss negative energy and how the Penrose process can be used to extract energy from a rotating black hole. This project is basically one of the projects suggested on the MIT OCW website as part of their GR course. I followed the project F in the book,'Exploring Black Holes' by Wheeler and Taylor which is a really nice book on guides to projects in GR. It gives a basic overview and then makes you derive equations and answer many queries along the way. I have tried to answer most of the queries as part of this project.

rotating_black_holes.pptx | |

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the_rotating_black_hole_syed_ali_raza.pdf | |

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## Simulating 2D and 3D Ising model using Monte Carlo and Metropolis method

A Computational physics course project, supervised by Dr. Fakhrul Inam. The simulations were done in FORTRAN. You can see the project report here. Following is the Abstract.

temperatures. We would compare this value of the critical value temperature with the theoretical values. I will discuss the algorithms and the techniques. I have used two methods here; both the metropolis and the brute force iteration method.

**Abstract:**We will try to simulate a 2D Ising model with variable lattice size and then extend it to a 3 dimensional lattice. We would calculate the average magnitude of the magnetization, and then also try to simulate how the magnetization changes with temperature. We will try to locate a critical temperature at which the lattice undergoes a phase change and becomes disorderd from ordered at hightemperatures. We would compare this value of the critical value temperature with the theoretical values. I will discuss the algorithms and the techniques. I have used two methods here; both the metropolis and the brute force iteration method.

compphys_project.pdf | |

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## Superconductors and the BCS theory

This was my project for the Statistical Mechanics course taught by Dr. Babar Qureshi. This included a project report (Link below) and a project presentation. Following is the Abstract of the report.

We first motivate the need for a theory by studying the Drude model for metals and see how it does not cater for the superconducting phase shift. We also look at the evidences of superconducting behavior like the Meissener effect and diamagnetism. We discuss the distinction between the types of superconducting material and than derive the London Equation. This equation was the first time that the theory of superconductivity was modelled, we look into the limitations and assumptions of this theory and how it leaves space for a more complete theory. We move on to the Ginzburg Landau model and see how superconductivity can be explained through thermodynamic parameters, this is a macroscopic model and BCS theory is a special case of it when we apply certain limits. We also solve a example and do some calculation for the GL model.

We look into macroscopic coherent states and motivate the microscopic theory for superconductivity, we then discuss the BCS theory which is the most complete microscopic theory of conductivity up till now. We highlight the main features of the theory and discuss cooper pairs and energy gaps for a superconducting material. And finally we look at a couple of applications and examples related to the subject.

**Abstract:**In this report we would discuss the evolution of the theories of superconductivity. We would discuss theories that explain superconducting phenomenon at both macroscopic and microscopic scales. Superconductors are materials that undergo a phase transition below a certain critical temperature in which the resistivity of the material suddenly drops to zero. This is a very interesting quantum mechanical phenomenon and offers great insights into the exciting and mind boggling quantum world.We first motivate the need for a theory by studying the Drude model for metals and see how it does not cater for the superconducting phase shift. We also look at the evidences of superconducting behavior like the Meissener effect and diamagnetism. We discuss the distinction between the types of superconducting material and than derive the London Equation. This equation was the first time that the theory of superconductivity was modelled, we look into the limitations and assumptions of this theory and how it leaves space for a more complete theory. We move on to the Ginzburg Landau model and see how superconductivity can be explained through thermodynamic parameters, this is a macroscopic model and BCS theory is a special case of it when we apply certain limits. We also solve a example and do some calculation for the GL model.

We look into macroscopic coherent states and motivate the microscopic theory for superconductivity, we then discuss the BCS theory which is the most complete microscopic theory of conductivity up till now. We highlight the main features of the theory and discuss cooper pairs and energy gaps for a superconducting material. And finally we look at a couple of applications and examples related to the subject.

superconductivity_and_the_bcs_theory.pdf | |

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## Hepatitis C Mathematical Model

This was a Mathematical Biology course project that was supervised by Dr. Adnan Khan and Dr. Mudassar Imran. In this project we solved a multiple compartment mathematical model in terms of various parameters and simulated the results using MATLAB. You can find the project report here.

In our model we would be considering two modes of transport which are statistically significant. One is the transmission through intravenous drug use and the other mode is through blood transfusions. We would have separate compartments for both of these transmission modes. So the susceptible compartment can go into either Acute 1 or Acute 2 compartment depending on the 1st mode of transmission. It depends on the infection rate of susceptible which in turn depends on the contact rate etc.

You can either recover from the acute condition or progress to the chronic infection compartment. From the chronic compartment you can be moved to Quarantine or you could recover. If you recover you can go back to the susceptible compartment. If you are Quarantined then some fraction moves back to susceptible and some goes to the acute infection compartment. There is a recruitment rate at which people keep getting added to the susceptible population.

All compartments have a natural death rate, however Acute, Chronic and Quarantine have also their own corresponding death rates in addition to the natural death rate. Also there are similar compartments Acute 2, Chronic 2, Quarantined 2 and Recovered 2 for the other mode of transmission too.

**Abstract:**Hepatitis C is an infectious disease that really harms the liver. It is caused by the hepatitis C virus. The infection leads to adverse affects like damage of the liver and ultimately to cirrhosis, which is generally apparent after many years. In some cases, those with cirrhosis will go on to develop liver failure, liver cancer or life-threatening esophageal and gastric varices and so Hep C can be very deadly.In our model we would be considering two modes of transport which are statistically significant. One is the transmission through intravenous drug use and the other mode is through blood transfusions. We would have separate compartments for both of these transmission modes. So the susceptible compartment can go into either Acute 1 or Acute 2 compartment depending on the 1st mode of transmission. It depends on the infection rate of susceptible which in turn depends on the contact rate etc.

You can either recover from the acute condition or progress to the chronic infection compartment. From the chronic compartment you can be moved to Quarantine or you could recover. If you recover you can go back to the susceptible compartment. If you are Quarantined then some fraction moves back to susceptible and some goes to the acute infection compartment. There is a recruitment rate at which people keep getting added to the susceptible population.

All compartments have a natural death rate, however Acute, Chronic and Quarantine have also their own corresponding death rates in addition to the natural death rate. Also there are similar compartments Acute 2, Chronic 2, Quarantined 2 and Recovered 2 for the other mode of transmission too.

hep_c_project_2.pdf | |

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## Making A Geiger Muller Counter

This was part of an electrical engineering electronics laboratory course project. We built an electronic system capable of counting and displaying the output of a Geiger Muller tube. Hence, the complete device i.e. the GM Tube and Counter was able to measure the radioactivity of various sources. Such a device is an integral part of a physics laboratory setup, and used in almost every experiment that deals with radioactivity in some form. It is also an important safety device, since radioactivity can present a health hazard.

geiger_muller_counter.pdf | |

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