Applications of an Extended Kalman Filter in nonlinear mechanics
Azeem Iqbal, 2019
Data processing is a challenging task in the realms of experimental physics. An experimental physicist is poised with statistical and probabilistic techniques that enable to cater to uncertainties and the unknown parameters. But in a teaching laboratory today there are transducers, highly susceptible to noise due to sensitivity. This is desirable in the context of exposing students to the realities of a real-world experiment and also creates a potential for them to learn about data cleaning and finding the embedded unknowns. In this regard, we propose the use of Kalman Filters to not only filter the system but also estimate its unknown parameters. In the 1960s, the Kalman filter was applied to the navigation system of the Apollo Project. It was a pivotal invention that enabled humans to reach the moon. This application propelled Kalman filtering into the dynamical linear and nonlinear research of that time. It was explored in signal processing, navigational radar systems, robotics, GPS systems and in recent years in image processing and machine learning. This research work concentrates on deploying Kalman Filter and its two variants in an experimental physics teaching laboratory. We explore the notions of filtering linear and non-linear mechanics problems, simulate the applications and then heuristically develop a sound understanding of the Kalman Filter and its facets in experimental physics.
Muzzammil Abbasi, 2019
Muons have a mean lifetime of 2:197 us. This project aimed to build an electronic setup to measure the mean lifetime. Three scintillators are stacked over each other and when a muon passes through a scintillator, it generates photons, these photons are sensed by photomultiplier tubes, which produce electric pulses accordingly. The pulses then go to a discriminator circuit which discriminates true signal from
the false signal, which might occur because of ringing in the signal propagation. A subsequent mono-stable multi-vibrator outputs a square pulse whose width can be adjusted by adjusting a variable. The pulses generated are in the range 100 ns to 2 us.
The output of the monostable multivibrator then goes to the FPGA which has a Virtual Delay buffer, Logic Unit, Data buffer and Data Link and a clock speed of 200 MHz. The virtual delay buffer is a FIFO buffer of size 2000 bits. The FPGA, programmed through Verilog, reads the incoming signal from GPIO pins as binary and sets the least insignificant bit of the buffer accordingly at each clock cycle, simultaneously the buffer also shifts left, thus working as a memory for previous readings. Every bit from the left of the buffer corresponds to a delay of 5 ns. By observing the delays between pulses coming from all three channels using an oscilloscope, a bit value from which signal is to be read is selected. Once all the signals are synced, they move to the logic unit. The data from a Data buffer is transferred to MATLAB on PC through UART serial communication. The data is processed with computer codes, yielding a measured mean lifetime of 2:133 us.
For a copy of the report, email Muzamil Abbasi.
Sultan Abdul Wadood, 2016
Injila Rasul, bachelor’s thesis (2017)
The mechanics and dynamics of a rotating object depend heavily on the physical conditions of its environment and its own physical dimensions. In this project, I seek to explore and understand how exactly these changes affect it’s motion, what are the parameters that influence it, what are the initial conditions for which it behaves the way it does? And as all scientific work aims to do how can I predict and control the motion?
Our investigation into the behavior of spinning bodies is built from the ground up, we start with the most simplistic version of the problem and add complexities step by step. At each step, we pause and vary the conditions imposed to see how they affect and influence the motion of the object and attempt to understand how these conditions work together and influence each other to produce the results we obtain.
Muhammad Waleed Khalid, bachelor’s thesis (2017)
Magnetooptics deals with the interaction between light and matter. When the matter is subjected to external magnetic field. The presence of external magnetic field varies optical anisotropy of the material. Different orientation of magnetic fields produces different magnetic effects. In the series of experiments performed at physics optics lab, magnetic circular and magnetic linear effects were observed in TGG crystal. Magnetic circular birefringence (MCB), Faraday effect, was observed at room temperature for 405 nm laser. Magnetic linear dichroism (MLD) and magnetic linear birefringence (MCB), stokesCottonMouton effect, was observed at cryogenic temperatures ranging from 8K- 150K in TGG crystal. These two effects were observed for 405 nm and 633 nm laser. ComStokespolarimetry using Fourier series coefficients was also done for observing magnetic linear effects,for 633 nm laser, in TGG crystal .
Ramish Ashraf, independent study (2017)
Coincidence counting modules (CCM) are a central part of experiments on quantum optics. However, the cost attached with a typical CCM renders them inaccessible for many undergraduate labs. A typical CCM would include Time-to-Amplitude Converters (TACS), a Nuclear-Instrumentation module (NIM) and a bin to house them. The costs add up to around 10000$. Our proposed design drastically lowers the cost by employing fast logical AND Gates. Moreover, by employing logical gates the effect of dead time can also be minimized.
Usman Javed, final year project (2015-2016)
In this project, we have developed an atomic force microscope (AFM) capable of resolving vertical features of the order of 20 nm over an area of 12 microns square. This is achieved by analyzing the reflection of a laser beam off a cantilever making contact with the surface of a sample placed on a motorized transition stage driven by piezoelectric based nano-positioning actuator. The reflected beam’s position is monitored by a closed loop proportional-integral control system that was specifically designed for this purpose. This AFM is a cost effective solution for a very sensitive instrument that has become essential in today’s research and development in Nanotechnology, Solid State Physics, Microbiology and many other fields of Science and Engineering.
Muhammad Umer, semester-long Masters project (2015).
We have studied the magneto-optical Kerr eect in textured magnetic proles by using a universal approach. We have employed the thin film approximation in the derivation of the analytical expression for the multilayer system. This approximation helps us to ignore the higher order term of layer thickness and magneto-optical coefficient. Dierent geometries have been studied and simulations have been performed by using MATLAB as a tool. During the simulation, we have not employed any approximation and simulate each system as exact. A graphical user interface has also been built using MATLAB which enable ones to simulate multilayer systems.
Syed Alamdar Hussain Shah, SBASSE Physics Major, LUMS (2014). Final year undergraduate project.
This project primarily aims at developing a vibrating sample magnetometer (VSM) for measuring the magnetization of any material sample. The project deals with basic physics and methodology of magnetometery. Different magnetometer schemes are reviewed and a special focus is paid to VSM. A detailed analysis on the mechanism required for vibrating a physical sample is being done. Different detection schemes with different geometries of Faraday coils are tested and aimed at the lab implementation and some experimental results.
Abdullah Khalid, SSE Physics Major, LUMS.
This is a report for an independent study project
Differential detection of Faraday Rotation, Generation and Detection of Elliptically Polarized Light
Hafiz Muhammad Ahmad Masood, B.Sc. University of the Punjab (2010). Contact me for a copy of the thesis.
Phase-sensitive Faraday rotation on terbium gallium garnet crystal and various diamagnetic liquids
Aysha Aftab, M.Phil Physics, University of the Punjab (2009). Contact me for a copy of the thesis.
Concomitant Gradients in Magnetic Resonance Imaging
Rafiullah, B.Sc. Honours Physics, University of the Punjab (2008). Contact me for a copy of the thesis.
Magnetic Resonance Imaging (MRI) is a beautiful application of the phenomenon of Nuclear Magnetic Resonance (NMR). MRI’s foremost identity lies in being a non-invasive diagnostic technique, but in fact, it has many other very important applications in biology, engineering and materials science. Classically, the field strength is regarded as one major measure of its quality because high field strength gives higher signal to noise ratios, better resolution and reduced scan times. So high field MRI has historically drawn a lot of attention.
However high field MRI has some disadvantages like reduced relaxation times and high susceptibility gradients. Furthermore high field MRI systems are bulky, immovable and very expensive. These reasons have motivated interest in the subject of low field MRI. The downside is that in the low field regime, we encounter the problem of undesired inhomogeneous fields (gradients) appearing along with the desired ones. The presence of these additional gradients, generally known as concomitant gradients, directly follows from the fundamental Maxwell equations. The concomitant gradients cause strong image distortions. This is one of the most crucial handicaps of low field MRI.
In this manuscript we discuss concomitant gradients and work out their quantitative contribution towards the resulting image distortion. An introduction to the basics of NMR is outlined in the first chapter. Extending the basics of NMR, a brief account of MRI is presented in chapter 2. We have introduced and demonstrated a new method of MRI simulations with significantly reduced processing times in chapter 3. In chapter 4, we address concomitant gradients. We have computed the contribution of concomitant gradients analytically and simulated results for various arrangements of the gradient fields.
Numerical Optimization of Pulse Sequences for NMR Quantum Information Processors
Saman Naseer, B.Sc. Honours Physics, University of the Punjab (2008). Contact me for a copy of the thesis.
The technique of nuclear magnetic resonance (NMR) makes use of various radio frequency pulses for the transference of the nuclear magnetization vector form one state to the other. In addition, one form of quantum information processing (QIP) utilizes NMR to implement unitary (and non-unitary) dynamics with the far-reaching goal of realizing computers that can surpass their classical counterparts. NMR based QIP, that is the focus of this dissertation, involves designing accurate unitary transformations of the spin state. The overlap of the theoretical and experimentally achieved values, called the fidelity, is an important parameter in the design of robust, accurate unitary transformations. Besides, the transformations need also be time optimal.
In this one year undergraduate research project we used gradient-based optimization methods for designing pulse sequences for NMR based QIP. These sequences implement unitary operations. The goal of the optimization was to achieve high fidelities. Specially, we used gradient ascent pulse engineering (GRAPE) as the optimization paradigm.
An introduction to the basics of NMR is given in Chapter 1. Chapter 2 covers basic gradient-based optimization techniques and line search methods, especially the methods that are relevant to the present work. The next two chapters cover the formulation and implementation of the GRAPE algorithm. We have used the GRAPE algorithm along with line search to engineer pulse sequences for state-to-state transfer as well as the more general problem of unitary transformation design. We study the role of algorithmic parameters in quantum fidelity maximization, the number of steps required to achieve maximal fidelity and the robustness of the algorithm with respect to the choice of initial controls. We determine that the algorithm also returns results that are known to be optimal from the analytical perspective. This work helps us in understanding better the modus operandi of the GRAPE algorithm itself. Last, the present work also includes the design of pulse sequences that are robust against pulse width errors.