Bulletin of the American Physical Society
Annual Meeting of the Four Corners Section of the APS
Volume 59, Number 11
Friday–Saturday, October 17–18, 2014; Orem, Utah
Session I4: General Physics II |
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Chair: Jean-Francois van Huele, Brigham Young University Room: Science Building 073 |
Saturday, October 18, 2014 10:15AM - 10:39AM |
I4.00001: Emergent theories and predictive models in physics, biology, and beyond Invited Speaker: Mark Transtrum The success of science is due in large part to the hierarchical nature of physical theories. These effective theories model natural phenomena as if the physics at macroscopic length scales were almost independent of the underlying, shorter-length-scale details. Using information theory, the emergence of effective theories for long-scale observations can be traced to a systematic compression of the underlying parameter space when the observations are coarsened. This compression is quantified by the Fisher Information Matrix and is observed in other diverse areas of science for which effective theories have historically been difficult to find. Interpreting the underlying model as a manifold of predictions in data space, I show how effective models can be systematically derived from microscopic first principles for a variety of complex systems in physics, biology, and other fields. [Preview Abstract] |
Saturday, October 18, 2014 10:39AM - 10:51AM |
I4.00002: Quantifying and Classifying Nonlinearities in Mathematical Models Alexander Shumway, Mark Transtrum Mathematical models, such as those used within physics, can be interpreted simply as mappings from a ``parameter space'' to predictions in a ``data space.'' It's therefore natural to interpret a generic model as a manifold of possible predictions embedded in the space of data. Using the language of differential geometry, we can therefore understand and compare properties of models from a variety of disciplines in a single, unified language. Most interesting models are nonlinear, and understanding that nonlinearity is crucial for understanding the physical properties of the systems being modeled. Information about nonlinearity is contained in the three-index array of second derivatives of model predictions with respect to parameters. I discuss using a multilinear singular value decomposition to quantify different types of nonlinearity contained in this array and give examples from a variety of models. [Preview Abstract] |
Saturday, October 18, 2014 10:51AM - 11:03AM |
I4.00003: Visualization and Analysis of Landau Damping Simulations Emma Hoggan Landau damping is a fundamental behavior of plasma physics in which electrostatic waves propagating in collisionless plasma become damped as individual particles exchange energy with the wave. While we have a general understanding of this process, not all of the details are completely understood. In our research, we use MATLAB and other computer applications for visualization and analysis of data from electron plasma simulations created by Dr. Grant Hart. These visualization techniques include generating animations of how the particle midplane velocities evolve and investigating the change in kinetic energy stored by the particles over time. Through these efforts we hope to reveal new information and a more comprehensive understanding about the discrete particle motions involved in the Landau damping process. [Preview Abstract] |
Saturday, October 18, 2014 11:03AM - 11:15AM |
I4.00004: Quantum mechanics over a finite field John Gardiner In the usual formulation of quantum mechanics the state of a system is described as a vector over the complex numbers. Replacing the field of complex numbers with a field of positive characteristic results in a toy theory with novel properties, which we call finite field quantum mechanics (FFQ). A characterizing feature of usual quantum mechanics is quantum entanglement. We discuss the analogous concept of entanglement in FFQ and its status as a resource for information processing tasks. [Preview Abstract] |
Saturday, October 18, 2014 11:15AM - 11:27AM |
I4.00005: Understanding Chaos Vandy Durfey Chaos is characterized by sensitivity to initial conditions. Predicting the time evolution of a simple chaotic pendulum is practically impossible. The behavior (time evolution) of chaotic systems may seem random, but they often exhibit an underlying order. Using computer simulations, I demonstrate a simple ``chaos game'' that shows that order can arise from random processes and to illustrate a ``strange attractor.'' The example of a damped driven oscillator will also be discussed in relation to chaotic behavior. The notion of a strange attractor can be used to understand physical systems that also exhibit chaos. Cardiac arrhythmias have been said to exemplify chaos and understanding chaotic behavior can be helpful in gaining an understanding of this problem. [Preview Abstract] |
Saturday, October 18, 2014 11:27AM - 11:39AM |
I4.00006: Equivalence-principle Analog of the Gravitational Red Shift Mario Serna To the best of our knowledge, the equivalence-principle analog of the gravitational red shift in special relativity has never been measured. This red shift is the loss of synchronization associated with observes along a rigid beam being accelerated along a path preserving Born rigidity. We discuss some special conditions which simplify its experimental observation. Consider two initially synchronized clocks on the ends of a rigid rod that begins at rest and then accelerates along its length to a final velocity. Special relativity predicts that the two clocks initially synchronized will be shifted by an amount proportional to $\Delta \tau \approx L v/c^2$. Experimental accuracy is just beginning to make this effect observable. We estimate the tolerance of the effect to experimental realities. If validated this new effect may one day aid in understanding and enhancing future ultra precision navigation systems. [Preview Abstract] |
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