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Mohammed Abdelaziz and Sushant Mahat

Dillon Guynup

Computational Physics

I would like to explore a very important question at our college: will I make it back to campus if I am taking steps in random directions this weekend? Starting from the Town Houses, what is the probability of making it back to my room while quite inebriated? In 2 dimensions, this is nigh guaranteed but how many steps will it take? By manipulating the distance traveled, I can find a trend in the average number of steps the student takes and fit a trend line to it.

Not only can this be mapped in MATLAB, I can also insert extra variables into the program. For example, I can introduce non-random movement at random times. In the real world, this could be seen either as a moment of clarity in a drunken mind or a helpful friend pushing you in the right direction. I would like to derive the expression to calculate the number of steps to go back to campus computationally. This could be an example of random drift and could be used to see how drift affects the time it takes to go home. I can add a lot more to this project by utilizing even more variables. For example, what if the student slips? I could add another random chance of a non-random movement this way.

For my computational project I would like to investigate two particular topics in celestial mechanics: the precession of the perihelion of Mercury and Kirkwood gaps. Astronomy is a very precise science, but nevertheless deviations from the accepted laws exist, and sometimes the exact results are poorly known; in these situations computational answers are the most useful and feasible. One such deviation from the accepted laws (here, Kepler’s laws) is the precession, or the rotation of the orientation axes of its orbit, of the planet Mercury- that is, the point at which Mercury is closest to the Sun rotates moves, most likely due to the gravitational effect from the other planets. This precession can be calculated using computational methods. A similar situation arises with the asteroids that orbit in our solar system- something, most likely the gravity of other planets, is causing a deviation from known laws, only here, the asteroids are conspicuously absent from certain orbital radii. The gaps, mostly caused by Jupiter, are referred to as Kirkwood gaps and are found at particular orbital resonances with Jupiter (i.e. 2/1, 3/1, 5/2 resonances). The same process occurs with the rings around a planet such as Saturn- for some orbital radii there is no such ring. The occurrence of such gaps, in orbital location and at resonance point, can be found via computational methods.

Computational Physics Project Proposal

Greg Cristina

Teddy Stanescu

Chapter of interest: Ch 11 – Vibrations, Waves, and the Physics of Musical Instruments. For this project, We want to explore different aspects of vibrations and waves as they occur in musical instruments. In general, we would like to explore everything in this chapter. This can involve modeling string displacement and decay through plucked and struck strings as well as analyzing the frequencies produced. We can also compare this data calculated in MatLab to a real life setting, recording a string being plucked or struck, then using measurements to model the same scenario in MatLab, then compared calculated vs. actual results. Also we would like to explore the overtones of the sounds generated and see if it correlates to the frequencies found using a Fourier Transformation on the recorded frequencies. If we have enough time, we would also like to repeat these experimental steps with a drum, exploring the way waves travel on a circular plane with locked or heavily damped edges (the rim of the drum). The drum can be struck in the center of the drumhead or the center and the rim at the same time, producing two different sounds and wave patterns.

Dillon Guynup

I would like to explore a very important question at our college: will I make it back to campus if I am taking steps in random directions this weekend? Starting from the Town Houses, what is the probability of making it back to my room while quite inebriated? In 2 dimensions, this is nigh guaranteed but how many steps will it take? By manipulating the distance traveled, I can find a trend in the average number of steps the student takes and fit a trend line to it. This should allow me to derive the expression for random movement.

Not only can this be mapped in MATLAB, I can also insert extra variables into the program. For example, I can introduce non-random movement at random times. In the real world, this could be seen either as a moment of clarity in a drunken mind or a helpful friend pushing you in the right direction. I would like to derive the expression to calculate the number of steps to go back to campus computationally. This could be an example of random drift and could be used to see how drift affects the time it takes to go home. I can add a lot more to this project by utilizing even more variables. For example, what if the student slips? I could add another random chance of a non-random movement this way. That’s about it, folks.

I am currently working on a senior thesis in Physics. As part of this project, I intend to harvest nerve spike train signals using either an EMG apparatus or a fine-needle electrode direct to the nerves in interest. These signals tend to be obscured heavily by noise, and as such are difficult to use experimentally. For this project, I intend to use a Fourier Transform or other computational methods to separate out EMG signals from background noise, and extract the relevant parameters from those nerve signals (duty cycle frequency, peak cycle stress) that can be used to help control a robotic agent elsewhere in my project.

Brian Deer

Tewa Kpulun

For our computational project Brian and I will be focusing our efforts on Neural Networks and the Brain. We will be using the Ising model and the Monte Carlo method to model a network of neurons and investigate pattern recognition. With this, we will be able to learn more about content addressable memory, an important component of human memory. Each neuron can be in either two states, spin up or spin down where spin up corresponds to a neuron being active and spin down corresponds to a neuron being inactive. With this comparison, we are able to apply the Ising model to understand the behavior of pattern recognition within the brain.

We will be looking at a very simplified version of the human brain, which we will refer to as the neural network. Our main topics will be how many patterns can the neural network store, the amount of input information that is needed for a successful retrieval of a stored pattern, how long those retrievals would take for various levels of input information, and if the size of the neural network affects it’s overall performance.

An acoustical plane wave, much like a light source, displays diffraction patterns based on the object it encounters (slits, shapes, objects, etc.). A sphere is one such object of particular interest, as the diffraction pattern produced by a sphere can be used to deconstruct sound signals on the surface of the sphere (a signal which would otherwise be nonsense because of the diffraction). Spheres have been increasingly used in recent years as the basic geometry of microphone arrays, and they offer many advantages over, for example, linear microphone arrays. The project will therefore focus on modelling and visually displaying diffraction of an acoustic wave due to a sphere, and will (hopefully) delve into spherical harmonic decomposition of the sound field on the sphere.

The advantage of using a computer to find a numerical solution rather than an analytical solution is quite clear when considering the relationship between Jupiter, the Sun, and the Earth. Rather, it is impossible to achieve an analytical solution for most celestial mechanics problems involving 3 or more bodies, thus numerical approaches are the only alternative.

Our project begins with modeling the Sun/Earth/Jupiter system with the Sun fixed at the origin. The three bodies are related via the inverse square law, and the positions of Jupiter and the Earth are calculated using their respective equations of motion (the sum of the forces from the other two bodies). Once a working model of the planetary orbits is established, it is worth investigating the effects of Jupiter on the Earth’s orbit when Jupiter’s mass is increased. We know that the current orbit is stable, but at what point does it become unstable?

If the mass of Jupiter is increased by roughly a thousand fold, it actually becomes comparable to the Sun’s mass. In this case, the model can be expanded to approximate a true 3-body system, with the origin at the center of mass of the system instead of fixed at the sun. The advantage of this model is that it allows us to observe how all three planets are effected by this change in mass. How large an effect, and at what point the orbits becomes unstable, remain open to investigation.

The Monte Carlo method has extended into many different aspects of the world, including, but not limited to physics and finance. The Ising model models ferromagnetism using the concept that an electron can either be spin up or spin down. A practical way to solve the Ising model is to use the Monte Carlo method, which calculates probabilities for a discrete number of iterations. Elias Kim and I want to investigate how the Ising model and the Monte Carlo method aid economists in making decisions on portfolios and risk analysis. The Ising model, which uses complex interactions between electrons and energy, can be translated to the complex parameters associated with stock volatility. To begin we will use MatLab to model the simple Ising model in chapter 8 of Computational Physics, by Nicholas J. Giordano and Hisao Nakanishi. Ultimately, we hope to compare our results in MatLab to studies that have already been published.