Self-Assembling Families of LC Ladder Circuits With Frequency-Controlled Growth
A family of LC ladder circuits is analyzed with an abstract model for growth in a diverse set of systems, with possible applications to biological organisms, self-assembly of nanostructures, models of topological insulators, and classical simulation of quantum circuits. In the LC circuit tile assemb...
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IEEE
2025-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/11105381/ |
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| author | Russell Deaton Max Garzon Rojoba Yasmin Andrew Garth |
| author_facet | Russell Deaton Max Garzon Rojoba Yasmin Andrew Garth |
| author_sort | Russell Deaton |
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| description | A family of LC ladder circuits is analyzed with an abstract model for growth in a diverse set of systems, with possible applications to biological organisms, self-assembly of nanostructures, models of topological insulators, and classical simulation of quantum circuits. In the LC circuit tile assembly model (lc-CTAM), tiles of inductors and capacitors attach to a growing assembly if the magnitude of the electric node potential at the tip is greater than a threshold. The frequency response, including poles and zeros, and time and space behavior of the node potentials are characterized as a function of length and the circuit parameters. When a resistance is present, growth is always bounded. As the resistance goes to zero, growth is bounded for low frequencies. At higher frequencies, growth can be both bounded or unbounded, depending on frequency and circuit parameters. In some instances, the distribution of node potentials as a function of length exhibits complex, aperiodic behavior. Both the lc-CTAM model and the methods used to analyze it, including Chebyshev polynomials, are a novel application of lumped circuit analysis. Through exact mathematical characterization, the lc-CTAM demonstrates how complex behavior can arise from simple systems, has the potential to inform investigations of biological growth, and may assist in the design of new materials and computational paradigms. |
| format | Article |
| id | doaj-art-4b4c8d3772aa48e8a3c86988538e7637 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-4b4c8d3772aa48e8a3c86988538e76372025-08-20T03:40:11ZengIEEEIEEE Access2169-35362025-01-011313606213607210.1109/ACCESS.2025.359462411105381Self-Assembling Families of LC Ladder Circuits With Frequency-Controlled GrowthRussell Deaton0https://orcid.org/0000-0001-6760-4421Max Garzon1https://orcid.org/0000-0001-9552-2255Rojoba Yasmin2https://orcid.org/0000-0002-3157-7297Andrew Garth3Department of Electrical and Computer Engineering, The University of Memphis, Memphis, TN, USADepartment of Computer Science, The University of Memphis, Memphis, TN, USAResch School of Engineering, University of Wisconsin–Green Bay, Green Bay, WI, USADepartment of Electrical and Computer Engineering, The University of Memphis, Memphis, TN, USAA family of LC ladder circuits is analyzed with an abstract model for growth in a diverse set of systems, with possible applications to biological organisms, self-assembly of nanostructures, models of topological insulators, and classical simulation of quantum circuits. In the LC circuit tile assembly model (lc-CTAM), tiles of inductors and capacitors attach to a growing assembly if the magnitude of the electric node potential at the tip is greater than a threshold. The frequency response, including poles and zeros, and time and space behavior of the node potentials are characterized as a function of length and the circuit parameters. When a resistance is present, growth is always bounded. As the resistance goes to zero, growth is bounded for low frequencies. At higher frequencies, growth can be both bounded or unbounded, depending on frequency and circuit parameters. In some instances, the distribution of node potentials as a function of length exhibits complex, aperiodic behavior. Both the lc-CTAM model and the methods used to analyze it, including Chebyshev polynomials, are a novel application of lumped circuit analysis. Through exact mathematical characterization, the lc-CTAM demonstrates how complex behavior can arise from simple systems, has the potential to inform investigations of biological growth, and may assist in the design of new materials and computational paradigms.https://ieeexplore.ieee.org/document/11105381/Topological insulatorsself-assemblynanotechnologyChebyshev polynomialsharmonic oscillatorladder circuits |
| spellingShingle | Russell Deaton Max Garzon Rojoba Yasmin Andrew Garth Self-Assembling Families of LC Ladder Circuits With Frequency-Controlled Growth IEEE Access Topological insulators self-assembly nanotechnology Chebyshev polynomials harmonic oscillator ladder circuits |
| title | Self-Assembling Families of LC Ladder Circuits With Frequency-Controlled Growth |
| title_full | Self-Assembling Families of LC Ladder Circuits With Frequency-Controlled Growth |
| title_fullStr | Self-Assembling Families of LC Ladder Circuits With Frequency-Controlled Growth |
| title_full_unstemmed | Self-Assembling Families of LC Ladder Circuits With Frequency-Controlled Growth |
| title_short | Self-Assembling Families of LC Ladder Circuits With Frequency-Controlled Growth |
| title_sort | self assembling families of lc ladder circuits with frequency controlled growth |
| topic | Topological insulators self-assembly nanotechnology Chebyshev polynomials harmonic oscillator ladder circuits |
| url | https://ieeexplore.ieee.org/document/11105381/ |
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