What Can the LGA Universe Compute?
Andrew Haddock and Scott Wisdom Project website
The second law of thermodynamics dictates that an isolated system will evolve towards a state of maximum entropy. Simulation engines such as the lattice gas automata (LGA) allow for the study of systems moving towards equilibrium by simulating micro- and macro-scale dynamics. In the last few decades, many problems in fields such as image processing have been formulated as constrained maximum entropy optimization problems, suggesting that LGA methods could provide a new method for solving such problems. However, the proper methods for representing arbitrary data in the LGA and how the LGA can be used to solve constrained maximum entropy optimization problems is not clear. This project aims to answer these questions through a combination of passive and active simulation methods in the LGA. In the passive scenario, chambers are initialized with an amount of particles corresponding to some data value; we then want to see if by running the system to equilibrium we can infer that data value. In the active scenario, chambers are initialized with an amount of particles proportional to gray-scale pixel value, and we develop a method for constraining maximum entropy to reconstruct images from blurred measurements with missing data.
Computational Logic in an LGA Environment
Skyler Peterson Project website
A Lattice Gas Autumata Simulation is an excellent tool for analyzing fluid dynamics. In this study however, the LGA environment is used to attempt circuit logic using particles as inputs and collisions as computationally significant interactions. It is determined that any circuit can be constructed; either forward propagating or recursive. In addition, a library of elementary circuit gates are given including; AND, NOT, and OR.
Exploring macro scale fluidic logic systems in LGA
Aaron N. Parks Project website
It has been shown that logic functions can be implemented given knowledge and control of the micro-state of the lattice gas automata (LGA). However, the deterministic behavior of the LGA at the micro scale does not well represent the far more stochastic behavior of moving particles in the real physical world, and therefore it's possible that use of micro scale LGA logic is limited to the realm of academic curiosity. In this project, I propose to use the macro scale behavior of the LGA (which is known to be similar to that of real fluids) to implement approximate or exact logic systems with macro scale inputs and outputs. Two classes of macro logic systems were attempted: Impulse gates, in which the transient response of the density of particles at specified locations has a logical dependence on initial particle distribution, and flow gates, in which the gate inputs and outputs are defined in terms of particle flow rates through well-defined thresholds.
Thermoelectric Rectification for Energy Harvesting
Brody Mahoney Project website
Harvesting energy from AC signals typically requires rectification since many of the payloads require DC power. Schottky diodes are a good choice for rectification in these lower systems because of their inherent low forward voltage drop. However, using a diode for rectification sets a lower limit on the amplitude of the signal that can be harvested. One solution is to use a resistor to rectify the AC signal. Because of Joule heating as current flows through a resistor, the energy is dissipated as heat. Of course, the direction of heat transfer, given a heat sink, is not alternating. In this sense, a resistor can theoretically harvest energy without the drawback of a forward voltage drop. In this paper, I investigate thermal power transfer between resistors, as well as harvesting arbitrarily small signals. Furthermore, a simple harvesting system using a thermoelectric generator is simulated.
An Investigation of Defect Scattering in 2D Classical Lattices using Lattice Gas Automata
Durmus U. Karatay Project website
In this study, the effects of defects on the scattering of particles in 2D classical lattices are investigated using lattice gas automata. The ratio of defect sites to lattice sites and different types of defects are explored in a parametric fashion. The results conform with the expectations from classical mechanics, however, there is no previous study to compare the results.
Analysis of Feynman Bi-Stable Compass Needle
Bryce Kellogg Project website
In his lectures on computation, Richard Feynman discussed a concept for a two state device which he used to demonstrate the possibility of doing certain computations without expending any energy at all. He used this idea, and a physical example of two axis aligned compass needles, to discuss a copy operation that dissipated zero energy. In this project I used standard magnetic dipole equations to analyse Feynman's concept. While his initial argument was not very rigorous, I found that he was basically correct with the minor caveat that the resulting operation is an inverting copy instead of a normal copy as described.
Investigation of Reusable and Reversible Logic Gate with LGA
Tsung-Wei Huang Project website
First, we construct some logic gates in LGA model using the scheme of billiard-ball model. We find out that the limit of the LGA model may result in some undesired properties of these gates. Therefore, rather than number of particle to build some logic structures, we use time-encoding method. It is shown that this method can produce reusable and reversible logic gate, which does not cost energy in the thermodynamic point of view. Finally, we investigate the properties of the logic structures and gates, and proposed some ideas which may make the construction easier. Since the construction of a logic gate is not easy (NP problem), an efficient way to calculate the output of a logic structure is necessary for building a non-trivial logic gate.
LGA Visualization for micro scale logic gate design
Tyler Libby Project website
In order to better visualize the creation of LGA logic gates, this project aimed to create a supplemental tool which emulated the LGA rule sets in a CAD-like environment. The current LGA design framework is limited in its visualization of the design space, which makes it difficult to diagnose errors in gate design. The newly developed supplemental tool utilizes the Processing development language to create an easy to use assisted drawing environment. This tool accurately portrays the rules in the original LGA environment in both single-step and continuous run modes. Reversing and reflective walls are distinguished by differing shape, while particle direction is indicated by arrows. Sources and sinks are similarly distinguished. Finally, the tool is able to output a series of coordinates that can be directly copied into an existing LGA experiment file. This allows for the linking of multiple gates in the original LGA environment.
Increasing Performance of Ambient Backscatter-based Communication by Using Method of Moments and C/A Codes
Aliasghar Tarkhan Project website
A communication system that enables two battery-free devices to communicate using ambient RF as the only source of power has been proposed [1]. In this system, the transmitter modulate information and send it to the receiver by changing the amount of reflection. In the proposed method in [1], authors neglected the effect of noise and used average power at the receiver to extract the signal. In this report we intend to use some novel methods to decrease the bit error rate (BER) and hence increase the data rate of the ambient backscatter system. First, we propose method of moments to estimate and extract the transmitted data from the sender at the receiver with the existence of noise. We consider two cases: 1) no delay between the original TV in the line of sight of the receiver and the backscattered signal from the transmitter, and 2) there is a fractional delay between the original TV signal and its backscattered signal. For both of these cases we formulate the detection criteria. We also discuss how we can estimate the variance of TV signal and noise by using method of moments. Then, we introduce using C/A codes to repeat our data at the transmitter based on a predefined pattern which is known at the receiver. Finally, we propose a hybrid method based on the method of moments and pre-coding by using C/A codes to achieve higher performance. We find that using method of moments and specially using it with C/A codes (or coding in general) results in performance enhancement from a BER point of view. We examine our method through numerous simulations and validate our arguments.
Sensing in Lattice Gas Automata
Gregory L. Nelson Project website
Sensing is an essential part of physics and science and deeply connected to questions about energy and intelligence. I attempted to better understand what sensing is by exploring it in the LGA, a simplified system that still exhibits complex properties. While I did not succeed in building a robust sensor according to my design criteria (to serve as a component for an opportunistic entropy-reducing demon), I made progress by highlighting how different designs failed. I detail the most interesting of those experiments, describe a design space for heuristic search, and provide commentary and possible approaches for future work. The difficulties in creating a sensor also prompted investigation into other designs, leading to the creation of a frequency splitter that can generate synchronized clock signals for us in billiard ball circuits and might also serve as a flow sensor.
Theory and simulation of thermodynamic quantities in LGA model
Angli Liu Project website
Proposed to simulate fluid ows for years, lattice gas automata (LGA) has shed lights on studying a range of macroscopic aspects in thermodynamics due to the fact that in theory, their dynamics are based on the same model as fluid ows. Specifically, interests in LGA methods have led to formal expression of entropy as a thermodynamic quantity using the Boltzman distribution, yet no work has exhibited that in practise, how the theoretical model and actual entropy by definition in the LGA simulator can be compared. In this report, by implementing the formal expression and the actual entropy in a two-chamber scenario in the LGA framwork, we show that the theoretical model can precisely describe the actual entropy of the system. Furthermore, we show systematically how other macroscopic quantities can be simulated in the LGA model in order to study complex behaviors that could happen for a Billiard-ball computer we could build using the LGA model.
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