Researches
Researches
Embedded Files
I am currently focused on doing research on Partial Differential Equations and its applications to Acoustics and Electromagnetic Waves. My other research interests include Graph Theory, Algebra (Group and Ring Theory), Numerical Analysis and Mathematics Education.
Research Profile Pages
Research Profile Pages
Our Current Research Group at UH
Our Current Research Group at UH
From left to right: Cristian Calota, Dr. Daniel Onofrei (our advisor), Arash Goligerdian, myself and Lander Besabe
Recent Works
Recent Works
New Paper Published
New Paper Published
Adaptive Beamforming with a Double-Cross Array of Dipoles on a Drone
Adaptive Beamforming with a Double-Cross Array of Dipoles on a Drone
Bibliographic Information:
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, and Pratik Deb. Adaptive Beamforming with a Double-Cross Array of Dipoles on a Drone. IEEE Xplore: 2024 IEEE Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS), Waco, TX, 2024, DOI: https://doi.org/10.1109/WMCS62019.2024.10619021.
My PhD Dissertation Defense
My PhD Dissertation Defense
Active Control of Exterior Wavefields and Applications*
Active Control of Exterior Wavefields and Applications*
Broadly speaking, this dissertation is centered on developing a mathematical understanding of wave phenomena in acoustics and electromagnetism towards the design of numerically stable methods for their active control. More specifically, it is focused on the study of constructive schemes for the active manipulation of fields satisfying the scalar or vector Helmholtz equation, or Maxwell's equations. This includes the theoretical analysis of these equations supported by numerical simulations in various geometrical settings.
We studied the control of Helmholtz fields in three environments, namely, in free space, in a homogeneous ocean and in a two-layered ocean with constant depth. In the first two, we developed a strategy for a near field control with a simultaneous multi-directional far field control. On the other hand, we worked on the control of electromagnetic waves only in a homogeneous environment, but included several dynamic applications and passive control strategies. In each of these areas, we included a detailed theoretical analysis and a multitude of numerical experiments.
*Presented April 08, 2020, 3PM CDT via MS Teams
Recent Recorded Paper Presentations
Recent Recorded Paper Presentations
Maths in Action: Controlling Sound and EM Waves*
Maths in Action: Controlling Sound and EM Waves*
I bet that at one point in your life you have asked, “Will I ever need the maths I am learning at school?”. Or when deciding what course to take in college, you have asked, “What would be my job prospects if I get a degree in mathematics?”. These were my questions too, back in my younger days. In this talk, I will share some answers I found to these questions, along with some insights about pursuing a career in STEM, or mathematics in particular. I will highlight my research work which aims to design strategies to control sound and electromagnetic waves. This will show that math can lead to cool stuff, such as designing smart audio systems, making a submarine invisible to SONAR or hiding an airplane from radar, and using drones to optimize long distance communications. Pretty amazing, huh? So join us and let’s see Maths in action!
*Delivered during as part of the FilSciHub Webinar Series last 23 October 2021
Controlling Acoustics Fields*
Controlling Acoustics Fields*
Do you know that there is rich and profound mathematics behind cool sound technologies such as active noise cancellation headphones and stealth automated underwater vehicles? In this talk, we will explore how math can be used to develop strategies to control sound waves. We will discuss the theoretical and numerical framework we developed to prove and illustrate the manipulation of acoustic waves in a free-space environment. This involves modeling the propagation of sound in this medium and designing a stable numerical scheme to produce cool simulations. The machinery we developed, which involves the Tikhonov regularization routine coupled with the Morozov discrepancy principle, can also be applied to other inverse problems, such as in electromagnetism and imaging. Rudimentary functional and numerical analysis background is a plus but is not a prerequisite. So, feel free to join us with a curious mind and a cup of coffee.
*Delivered during the IMSP Webinar Series last 10 May 2021
Beam Focusing by Scattering from an Array of Scatterers on a Drone*
Beam Focusing by Scattering from an Array of Scatterers on a Drone*
Beamforming by scattering from an array of scatterers carried by a drone is explored. By positioning the vertical heights of the scatterers on the drone, beam focusing can be achieved in a desired direction. Various horizontal layouts of the scatterers on the drone can be used, with a “double-cross” layout used here for the case of 9 scatterers. The formation of a null in the pattern in a desired direction is also possible using optimization of the scatterer positions.
*Presented during the 2021 National Radio Science Meeting
Publications
Publications
Journal Articles
Journal Articles
Chaoxian Qi, Shubin Zeng, Neil Jerome A. Egarguin, Daniel Onofrei & Jiefu Chen (2023) Active Control of Electromagnetic Fields in Layered Media. Journal of Electromagnetic Waves and Applications, DOI: 10.1080/09205071.2023.2270602
Chaoxian Qi, Shubin Zeng, Neil Jerome A. Egarguin, Daniel Onofrei & Jiefu Chen (2023) Active Control of Electromagnetic Fields in Layered Media. Journal of Electromagnetic Waves and Applications, DOI: 10.1080/09205071.2023.2270602
Abstract: This article presents a numerical strategy for actively manipulating electromagnetic (EM) fields in layered media. In particular, we develop a scheme to characterize an EM source that will generate some predetermined field patterns in prescribed disjoint exterior regions in layered media. The proposed question of specifying such an EM source is not an inverse source problem (ISP) since the existence of a solution is not guaranteed. Moreover, our problem allows for the possibility of prescribing different EM fields in mutually disjoint exterior regions. This question involves a linear inverse problem that requires solving a severely ill-posed optimization problem (i.e. suffering from possible non-existence or non-uniqueness of a solution). The forward operator is defined by expressing the EM fields as a function of the current at the source using the layered media Green’s function (LMGF), accounting for the physical parameters of the layered media. This results to integral equations that are then discretized using the method of moments (MoM), yielding an ill-posed system of linear equations. Unlike in ISPs, stability with respect to data is not an issue here since no data is measured. Rather, stability with respect to input current approximation is important. To get such stable solutions, we applied two regularization methods, namely, the truncated singular value decomposition (TSVD) method and the Tikhonov regularization method with the Morozov Discrepancy Principle. We performed several numerical simulations to support the theoretical framework and analyzes, and to demonstrate the accuracy and feasibility of the proposed numerical algorithms.
Chaoxian Qi , Neil Jerome A. Egarguin, Shubin Zeng, Daniel Onofrei and Jiefu Chen. Sensitivity analysis for active electromagnetic field manipulation in free space. Applied Mathematics in Science and Engineering, Vol. 30 No. 1, pp 660-686, DOI: https://doi.org/10.1080/27690911.2022.2118270 (open access article)
Chaoxian Qi , Neil Jerome A. Egarguin, Shubin Zeng, Daniel Onofrei and Jiefu Chen. Sensitivity analysis for active electromagnetic field manipulation in free space. Applied Mathematics in Science and Engineering, Vol. 30 No. 1, pp 660-686, DOI: https://doi.org/10.1080/27690911.2022.2118270 (open access article)
Abstract: This paper presents a detailed sensitivity analysis of the active manipulation scheme for electromagnetic (EM) fields in free space. The active EM fields control strategy is designed to construct surface current sources (electric and/or magnetic) that can manipulate the EM fields in prescribed exterior regions. The active EM field control is formulated as an inverse source problem. We follow the numerical strategies in our previous works, which employ the Debye potential representation and integral equation representation in the forward modelling. We consider two regularization approaches to the inverse problem to approximate a current source, namely the truncated singular value decomposition (TSVD) and the Tikhonov regularization with the Morozov discrepancy principle. Moreover, we discuss the sensitivity of the active scheme (concerning power budget, control accuracy, and quality factor) as a function of the frequency, the distance between the control region and the source, the mutual distance between the control regions, and the size of the control region. The numerical simulations demonstrate some challenges and limitations of the active EM field control scheme.
Neil Jerome A. Egarguin, Larry Guan, and Daniel Onofrei. Defect Characterization in a 1D Spring Mass System Using the Laplace and Z‑Transforms . J. Vib. Eng. Technol. (2022). DOI: https://doi.org/10.1007/s42417-022-00433-y (copy here)
Neil Jerome A. Egarguin, Larry Guan, and Daniel Onofrei. Defect Characterization in a 1D Spring Mass System Using the Laplace and Z‑Transforms . J. Vib. Eng. Technol. (2022). DOI: https://doi.org/10.1007/s42417-022-00433-y (copy here)
Abstract: Purpose. We present a scheme to characterize the defects within a one-dimensional spring–mass system comprised of an arbitrary number of bodies with otherwise uniform masses connected in series by springs using only a discrete set of vibrational data of the first body. Methods. The system of ordinary differential equations modeling spring–mass systems was analyzed using the Laplace transform with the unknown mass and location of the defects as parameters. We propose a two-phase strategy to determine these unknown parameters using a set of discrete measurements of the longitudinal displacements of the first mass after the system is excited by a Dirac impulse on the first mass. The Z-transform of the discrete time-measurements is used to obtain an approximation for the Laplace-domain solution curve of the vibration of the first body. First, we show how the poles of this simulated data can be used to determine the masses of the defects. Then the location of these defects were calculated using an optimization routine. Results. We also show several simulations with two defects highlighting the instances when the scheme is highly accurate as well as its limitations. In these cases, the algorithm was able to predict the mass and locations accurately. Conclusions. In this paper, we were able to design a stable numerical scheme that can characterize the defects, i.e., estimate their masses and locations, using only a discrete set of vibrational data of the first mass.
Abstract: Purpose. We present a scheme to characterize the defects within a one-dimensional spring–mass system comprised of an arbitrary number of bodies with otherwise uniform masses connected in series by springs using only a discrete set of vibrational data of the first body. Methods. The system of ordinary differential equations modeling spring–mass systems was analyzed using the Laplace transform with the unknown mass and location of the defects as parameters. We propose a two-phase strategy to determine these unknown parameters using a set of discrete measurements of the longitudinal displacements of the first mass after the system is excited by a Dirac impulse on the first mass. The Z-transform of the discrete time-measurements is used to obtain an approximation for the Laplace-domain solution curve of the vibration of the first body. First, we show how the poles of this simulated data can be used to determine the masses of the defects. Then the location of these defects were calculated using an optimization routine. Results. We also show several simulations with two defects highlighting the instances when the scheme is highly accurate as well as its limitations. In these cases, the algorithm was able to predict the mass and locations accurately. Conclusions. In this paper, we were able to design a stable numerical scheme that can characterize the defects, i.e., estimate their masses and locations, using only a discrete set of vibrational data of the first mass.
Chaoxian Qi , Neil Jerome A. Egarguin, Daniel Onofrei and Jiefu Chen. Feasibility analysis for active near/far field acoustic pattern synthesis in free space and shallow water environments. Acta Acustica Vol. 5, 2021. DOI: https://doi.org/10.1051/aacus/2021030 (open access article)
Chaoxian Qi , Neil Jerome A. Egarguin, Daniel Onofrei and Jiefu Chen. Feasibility analysis for active near/far field acoustic pattern synthesis in free space and shallow water environments. Acta Acustica Vol. 5, 2021. DOI: https://doi.org/10.1051/aacus/2021030 (open access article)
Abstract: In this paper, a detailed sensitivity and feasibility analysis of the active manipulation scheme for scalar Helmholtz fields proposed in our previous works, in both free space and constant-depth homogeneous ocean environments, is presented. We apply the method of moments (MoM) together with Tikhonov regularization with the Morozov discrepancy principle to investigate the effects of varying the problem parameters to the accuracy and feasibility of the proposed active field control strategy. We discuss the feasibility of the active scheme (with respect to power budget, control accuracy and process error) as a function of the frequency, the distance between the control region and the source, the mutual distance between the control regions, and the size of the control region. Process error is considered as well to investigate the possibility of an accurate active control in the presence of manufacturing or feeding noise. The numerical simulations show the accuracy of the active field control scheme and indicate some challenges and limitations for its physical implementation.
Neil Jerome A. Egarguin, Daniel Onofrei, Chaoxian Qi and Jiefu Chen. Active manipulation of Helmholtz scalar fields in an ocean of two homogeneous layers of constant depth. Inverse Problems in Science and Engineering. 2021, DOI: https://doi.org/10.1080/17415977.2021.1918688. (free e-prints available here*)
Neil Jerome A. Egarguin, Daniel Onofrei, Chaoxian Qi and Jiefu Chen. Active manipulation of Helmholtz scalar fields in an ocean of two homogeneous layers of constant depth. Inverse Problems in Science and Engineering. 2021, DOI: https://doi.org/10.1080/17415977.2021.1918688. (free e-prints available here*)
Abstract: In this article, we propose a strategy for the active manipulation of scalar Helmholtz fields in bounded near-field regions of an active source while maintaining desired radiation patterns in prescribed far-field directions. This control problem is considered in two environments: free space and homogeneous ocean of constant depth, respectively. In both media, we proved the existence of and characterized the surface input, modeled as Neumann data (normal velocity) or Dirichlet data (surface pressure) such that the radiated field satisfies the control constraints. We also provide a numerical strategy to construct this predicted surface input by using a method of moments-approach with a Morozov discrepancy principle-based Tikhonov regularization. Several numerical simulations are presented to demonstrate the proposed scheme in scenarios relevant to practical applications.
*Number of free e-prints is limited. If the link stops working, just send me an email for a copy.
Neil Jerome A. Egarguin, Daniel Onofrei, Chaoxian Qi and Jiefu Chen. Active Manipulation of Helmholtz Scalar Fields: Near-field Synthesis with Directional Far-field Control. Inverse Problems Vol. 36. 2020, DOI: https://doi.org/10.1088/1361-6420/aba106. (preprint availabe here)
Neil Jerome A. Egarguin, Daniel Onofrei, Chaoxian Qi and Jiefu Chen. Active Manipulation of Helmholtz Scalar Fields: Near-field Synthesis with Directional Far-field Control. Inverse Problems Vol. 36. 2020, DOI: https://doi.org/10.1088/1361-6420/aba106. (preprint availabe here)
Abstract: In this article, we propose a strategy for the active manipulation of scalar Helmholtz fields in bounded near-field regions of an active source while maintaining desired radiation patterns in prescribed far-field directions. This control problem is considered in two environments: free space and homogeneous ocean of constant depth, respectively. In both media, we proved the existence of and characterized the surface input, modeled as Neumann data (normal velocity) or Dirichlet data (surface pressure) such that the radiated field satisfies the control constraints. We also provide a numerical strategy to construct this predicted surface input by using a method of moments-approach with a Morozov discrepancy principle-based Tikhonov regularization. Several numerical simulations are presented to demonstrate the proposed scheme in scenarios relevant to practical applications.
Neil Jerome A. Egarguin, Shubin Zeng, Daniel Onofrei and Jiefu Chen. Active control of Helmholtz fields in 3D using an array of sources. Wave Motion Vol. 94, 2020. DOI: https://doi.org/10.1016/j.wavemoti.2020.102523 . (preprint availabe here)
Neil Jerome A. Egarguin, Shubin Zeng, Daniel Onofrei and Jiefu Chen. Active control of Helmholtz fields in 3D using an array of sources. Wave Motion Vol. 94, 2020. DOI: https://doi.org/10.1016/j.wavemoti.2020.102523 . (preprint availabe here)
Abstract: In this paper, we present a strategy for the active manipulation of Helmholtz fields using an array (swarm) of coupling sources with prescribed fixed positions. More specifically, we consider the problem of using an array of active surface sources to approximate prescribed fields in several given exterior regions of space including possibly the far field region. In this regard, we extend the results presented in our previous works for the case of a single source to allow for multiple active sources considering the first-order mutual coupling between them. We prove the existence of boundary inputs on the sources (pressure or normal velocity), so that the desired control effect is obtained. We also devise a stable numerical scheme to compute these boundary inputs by using local basis functions defined on the source boundaries in a method of moments approach together with a Morozov discrepancy principle-based Tikhonov regularization. Several numerical simulations were presented to demonstrate the accuracy of the proposed scheme.
Daniel Onofrei, Eric Platt and Neil Jerome A. Egarguin. Active Manipulation of Exterior Electromagnetic Fields by using Surface Sources. Quarterly of Applied Mathematics Vol. 78 No. 4, pp 641-670, 2020. DOI: https://doi.org/10.1090/qam/1567. (preprint available here)
Daniel Onofrei, Eric Platt and Neil Jerome A. Egarguin. Active Manipulation of Exterior Electromagnetic Fields by using Surface Sources. Quarterly of Applied Mathematics Vol. 78 No. 4, pp 641-670, 2020. DOI: https://doi.org/10.1090/qam/1567. (preprint available here)
Abstract: In this paper, we establish a scheme for the active manipulation of electromagnetic fields in prescribed exterior regions using a surface source. We prove the existence of the necessary surface current (electric or magnetic) on a single source to approximate prescribed electromagnetic fields on given regions of space (bounded or possibly the far field). We provide two constructive schemes for the computation of the required surface currents: our first strategy makes use of the Debye representation results for the electromagnetic field and builds up on previous control results for scalar fields discussed in [J. Integral Equations Appl. 26 (2014), pp. 553–579]; the second strategy we propose makes use of integral electromagnetic representation results and follows theoretically from the first. We provide theoretical validation for both computational schemes and present supporting numerical simulations for the first strategy in several applied scenarios.
Neil Jerome A. Egarguin, Taoufik Meklachi, Daniel Onofrei and Noam D. Harari-Arnold. Vibration Suppression and Defect Detection Schemes in 1D Spring- Mass Systems. Journal of Vibration Engineering and Technologies, Vol. 8 No. 4, pp 489-503, 2020. Published online May 07, 2019, DOI: https://doi.org/10.1007/s42417-019-00104-5. (preprint available here)
Neil Jerome A. Egarguin, Taoufik Meklachi, Daniel Onofrei and Noam D. Harari-Arnold. Vibration Suppression and Defect Detection Schemes in 1D Spring- Mass Systems. Journal of Vibration Engineering and Technologies, Vol. 8 No. 4, pp 489-503, 2020. Published online May 07, 2019, DOI: https://doi.org/10.1007/s42417-019-00104-5. (preprint available here)
Abstract: Purpose: In this paper, we present strategies for active vibration suppression and defect detection in a one-dimensional network of an arbitrary number of coupled spring–mass units connected in series. The choice of a spring–mass system is not arbitrary, as the latter is found in many applications throughout a wide range of fields, for instance in defense detection/ shielding studies, biomedical engineering, structures engineering, computer graphics and acoustics among others. Methods: The system of differential equations that model the spring–mass systems was analyzed and solved using the Laplace transform and other analytic tools. The data used in the numerical simulations were obtained by solving the associated forward problems analytically or numerically. Some of the simulations required numerical integration and minimization routines. Results: A scheme for active vibration suppression is given via explicit formulas for the required control forces. The detect defection strategy is given in terms of an explicit formula whenever only the location or mass of a lone defect is unknown and in terms of a minimization procedure whenever more than one information about the defect(s) are unknown. Several numerical simulations were done to validate these results. Conclusion: As we show in the paper, the success of the vibration suppression scheme we developed depends on the speed and accuracy of the intervening active controls. Meanwhile, the defect detection algorithm only requires measurements in a sufficiently large time interval of the longitudinal vibrations in the first mass.
Neil Jerome A. Egarguin, Daniel Onofrei and Eric Platt. Sensitivity Analysis for the Active Manipulation of Helmholtz Fields in 3D. Inverse Problems in Science and Engineering Vol. 28 No. 3, pp 314-339, 2020. Published online 2018. DOI: https://doi.org/10.1080/17415977.2018.1555248 (preprint available at this arxiv link )
Neil Jerome A. Egarguin, Daniel Onofrei and Eric Platt. Sensitivity Analysis for the Active Manipulation of Helmholtz Fields in 3D. Inverse Problems in Science and Engineering Vol. 28 No. 3, pp 314-339, 2020. Published online 2018. DOI: https://doi.org/10.1080/17415977.2018.1555248 (preprint available at this arxiv link )
Abstract: In this paper, we continue to study the feasibility of active manipulation of Helmholtz fields and by using an improved and more robust numerical strategy we present a detailed sensitivity analysis for the active methods proposed in our previous works [Onofrei D. Active manipulation of fields modelled by the Helmholtz equation. J Integral Equ. Appl. 2014;26(4):553–579; Onofrei D, Platt E. On the synthesis of acoustic sources with controllable near fields. Wave Motion. 2018;77:12–27]. In this regard, we study the behaviour of physically relevant parameters (i.e. source power, control accuracy, stability) with respect to variations in the type of control regions (bounded or unbounded), relative position of the control regions, distances between the control regions and the source, frequency range and fields to be approximated. We produce strong numerical evidence indicating the accuracy of our scheme and at the same time develop a better understanding of several important challenges for its physical implementation.
Neil Jerome A. Egarguin and Rolando G. Panopio. Signatures of the Disjoint Union and Box Product of some Proper Autographs. The UPLB Journal XIII pp 37-44, January- December 2015
Neil Jerome A. Egarguin and Rolando G. Panopio. Signatures of the Disjoint Union and Box Product of some Proper Autographs. The UPLB Journal XIII pp 37-44, January- December 2015
Abstract: A proper autograph is a graph whose vertices can be labeled by a set S of positive integers, called a signature, in such a way that vertices are adjacent if and only if the absolute difference of their labels is in S. The disjoint union and box product of some proper autographs are taken and signatures are derived.
Articles in Refereed Conference Proceedings
Articles in Refereed Conference Proceedings
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, and Pratik Deb. Adaptive Beamforming with a Double-Cross Array of Dipoles on a Drone. IEEE Xplore: 2024 IEEE Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS), Waco, TX, 2024, DOI: https://doi.org/10.1109/WMCS62019.2024.10619021.
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, and Pratik Deb. Adaptive Beamforming with a Double-Cross Array of Dipoles on a Drone. IEEE Xplore: 2024 IEEE Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS), Waco, TX, 2024, DOI: https://doi.org/10.1109/WMCS62019.2024.10619021.
Abstract: Adaptive and reconfigurable beamforming from an array of vertical half-wavelength dipole elements on a drone is considered. The array consists of nine dipole radiators that are located on a “double-cross” layout consisting of a central element that is surrounded by eight adjacent neighboring dipoles. The double-cross layout dimensions are optimized beforehand. The amplitudes and phases of the nine dipole radiators are then used as degrees of freedom and are optimized to give specified farfield patterns. The desired patterns may have one or more main beams, together with one or more nulls and low sidelobes. A fast relaxation method is proposed to optimize the associated nonlinear (and non-convex) cost functional and obtain the complex dipole currents (magnitudes and phases). A simple iterative approach that does not require an optimizer is also proposed. Dynamic null steering is also examined, in which the current of the central array element is adjusted dynamically tosteer a null on the fly.
Chaoxian Qi, Chenpei Huang, Neil Jerome A. Egarguin, Daniel Onofrei, Miao Pan and Jiefu Chen. Enhanced Underwater Acoustic Communication via Active Field Control. ACM Proceedings: The 15th International Conference on Underwater Networks & Systems, Shenzhen, Guangdong, China 2021. DOI: DOI: https://doi.org/10.1145/3491315.3491367
Chaoxian Qi, Chenpei Huang, Neil Jerome A. Egarguin, Daniel Onofrei, Miao Pan and Jiefu Chen. Enhanced Underwater Acoustic Communication via Active Field Control. ACM Proceedings: The 15th International Conference on Underwater Networks & Systems, Shenzhen, Guangdong, China 2021. DOI: DOI: https://doi.org/10.1145/3491315.3491367
Abstract: In this paper, an active source control scheme for manipulation of the acoustic field in ocean environment is presented. This active field control is formulated as an inverse source problem, where the target is to maximize the radiated power in several far directions while keeping a low radiated power in one or more other far field regions. Hence, the controlled source enables acoustic beamforming, i.e., enhancing the acoustic wave-based underwater wireless communication. Numerical simulations are performed to demonstrate the good performance of the proposed method.
Chaoxian Qi, Jiefu Chen, Neil Jerome A. Egarguin and Daniel Onofrei. Feasibility Analysis for Active Manipulation of Electromagnetic Fields in Free Space. IEEE Xplore: 2021 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (APS/URSI), 2021. DOI: https://doi.org/10.1109/APS/URSI47566.2021.9704484
Chaoxian Qi, Jiefu Chen, Neil Jerome A. Egarguin and Daniel Onofrei. Feasibility Analysis for Active Manipulation of Electromagnetic Fields in Free Space. IEEE Xplore: 2021 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (APS/URSI), 2021. DOI: https://doi.org/10.1109/APS/URSI47566.2021.9704484
Abstract: In this work, a feasibility analysis of the active manipulation for electromagnetic (EM) fields is presented. The strategy of the EM fields control is to construct surface current sources that are able to control the EM fields in some near and far regions. We discuss the feasibility of the active scheme (with respect to power budget, control accuracy, and quality factor Q) as a function of the frequency and the distance between the control region and the source. The numerical simulations discuss the performance of the active field control scheme and illustrate some challenges and limitations.
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, Julien Leclerc and Aaron Becker. Beam Focusing by using Scattering From Drones. IEEE Xplore: 2021 IEEE 19th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM), Winnipeg, MB, Canada, 2021, DOI: 10.1109/ANTEM51107.2021.9518835
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, Julien Leclerc and Aaron Becker. Beam Focusing by using Scattering From Drones. IEEE Xplore: 2021 IEEE 19th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM), Winnipeg, MB, Canada, 2021, DOI: 10.1109/ANTEM51107.2021.9518835
Abstract: Beam focusing is commonly done by using phased arrays. However, the size of a phased array typically increases as the frequency is lowered, making beamforming at lower frequencies more difficult to achieve. For example, at 30 MHz, the wavelength is about 10 meters, making the needed element separation in the range of 5–10 meters. Such a large array would be difficult to easily make in a mobile or airborne form. One possible solution is to use drones as the radiating elements, since it is easy to position them almost arbitrarily in space. Such a drone-based array could be useful in certain applications. For example, communications between a transmitter and a remote receiver might be blocked, so that there is no direct line of sight between the transmitter and the receiver. This might happen, for example, if the transmitter is located inside of a forest or mountainous region. In this case the drone swarm could be used as a relay between the transmitter and receiver, flying at a sufficient altitude to overcome the blockage. (The transceiver that is located inside the forest or mountainous region is being thought of as the transmitter for convenience.)
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, Julien Leclerc and Aaron Becker. Beam Focusing by Scattering from an Array of Scatterers on a Drone. IEEE Xplore: 2021 United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM), Boulder, CO, USA, 2021, pp. 140-141, DOI: 10.23919/USNC-URSINRSM51531.2021.9336436
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, Julien Leclerc and Aaron Becker. Beam Focusing by Scattering from an Array of Scatterers on a Drone. IEEE Xplore: 2021 United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM), Boulder, CO, USA, 2021, pp. 140-141, DOI: 10.23919/USNC-URSINRSM51531.2021.9336436
Abstract: Beamforming by scattering from an array of scatterers carried by a drone is explored. By positioning the vertical heights of the scatterers on the drone, beam focusing can be achieved in a desired direction. Various horizontal layouts of the scatterers on the drone can be used, with a “double-cross” layout used here for the case of 9 scatterers. The formation of a null in the pattern in a desired direction is also possible using optimization of the scatterer positions.
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, Julien Leclerc and Aaron Becker. Adaptive Beamforming Using Scattering from a Drone Swarm. IEEE Xplore: 2020 IEEE Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS), 2020. DOI: https://doi.org/10.1109/WMCS49442.2020.9172335
Neil Jerome A. Egarguin, David R. Jackson, Daniel Onofrei, Julien Leclerc and Aaron Becker. Adaptive Beamforming Using Scattering from a Drone Swarm. IEEE Xplore: 2020 IEEE Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS), 2020. DOI: https://doi.org/10.1109/WMCS49442.2020.9172335
Abstract: There may be situations where a direct line of sight between a transmitter and a receiver is blocked. In such a situation it may be possible to transmit a signal upward from a transmitter to a swarm of drones, each of which carries a scattering object. By positioning each drone properly, the scattered signal from the drones can add coherently in a given direction, forming a beam in that direction. The altitude of each drone is used as a degree of freedom in order to change the phase of the signal scattered by the drone. For a given set of horizontal drone positions, the drone altitudes can be determined to produce a main beam in a given direction. The drone positions can also be optimized to focus a beam in a given direction while producing pattern nulls in other prescribed directions with very small sidelobes.
Shubin Zeng, Neil Jerome A. Egarguin, Daniel Onofrei and Jiefu Chen. Active Control of Electromagnetic Waves in Layered Media Using a Current Source. IEEE Xplore : 2020 IEEE Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS), 2020. DOI: https://doi.org/10.1109/WMCS49442.2020.9172412
Shubin Zeng, Neil Jerome A. Egarguin, Daniel Onofrei and Jiefu Chen. Active Control of Electromagnetic Waves in Layered Media Using a Current Source. IEEE Xplore : 2020 IEEE Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS), 2020. DOI: https://doi.org/10.1109/WMCS49442.2020.9172412
Abstract: In this work, we propose a strategy for the construction of current sources that can control the electromagnetic (EM) fields in some near and far control egions embedded in multilayered media. By formulating the field with the current source using the integral equation and layered media Green’s function (LMGF), the forward operator is defined. The Galerkin method is then applied to get the linear algebraic equations for such an inverse source problem, resulting in a discrete inverse problem. A regularization algorithm, such as truncated singular value decomposition (TSVD) is used to construct a stable approximate current source solution. Several relevant numerical examples are given to demonstrate the feasibility of the developed algorithms for the active control of the fields in layered media.
Neil Jerome A. Egarguin and Rolando G. Panopio. G(A, B)- labeling of Cacti over Groups. AIP Proceedings: Vol. No. 1739 Art. No. 020006: The 2nd International Conference on Mathematical Sciences and Statistics, 2016. DOI: https://doi.org/10.1063/1.4952486
Neil Jerome A. Egarguin and Rolando G. Panopio. G(A, B)- labeling of Cacti over Groups. AIP Proceedings: Vol. No. 1739 Art. No. 020006: The 2nd International Conference on Mathematical Sciences and Statistics, 2016. DOI: https://doi.org/10.1063/1.4952486
Abstract: Let G be a group with nonempty subsets A and B. The graph G(A, B) is the simple graph obtained by deleting all loops from the graph whose vertex set is A and where vertices x and y are adjacent if and only if there is a b ∈ B such that xb = y or yb = x. In this paper, we present realizations of some cacti as G(A, B)’s.
Neil Jerome A. Egarguin and Rolando G. Panopio. G(A, B)- labeling of Forest and Trees. AIP Proceedings Vol. No. 1707 Art. No. 020005: The 7th South East Asian Mathematical Society (SEAMS)- Universitas Gadjah Mada (UGM) International Conference on Mathematics and its Applications, 2016. DOI: https://doi.org/10.1063/1.4940806
Neil Jerome A. Egarguin and Rolando G. Panopio. G(A, B)- labeling of Forest and Trees. AIP Proceedings Vol. No. 1707 Art. No. 020005: The 7th South East Asian Mathematical Society (SEAMS)- Universitas Gadjah Mada (UGM) International Conference on Mathematics and its Applications, 2016. DOI: https://doi.org/10.1063/1.4940806
Abstract: Let G be a group or a ring with non-empty subsets A and B. The graph G(A,B) is the simple graph obtained by deleting all loops from the graph with vertex set A and where vertices x and y are adjacent if and only if there is a b ∈ B such that xb = y or yb = x. It can also be defined using a group G acting on a set X by replacing A by a subset of X and vertices x and y are adjacent if and only if there is a b ∈ B ⊆ G such that (b, x) → y or (b, y) → x. In this paper, we shall present several structural properties of G(A, B)’s leading to establishing ways of realizing forests and trees as labeled graphs over groups and rings.
Paper Presentations
Paper Presentations
Oral Presentations
*name of presenter in bold italicsOral Presentations
Egarguin, Neil Jerome A., Soaring Signals: Creating Beam Patterns using EM Mounted on Drones. The 2024 Mathematical Society of the Philippines CALABARZON Annual Convention and General Assembly, Cavite State University, 04- 05 July 2024
Balicot, Imiesan Jace C., and Egarguin, Neil Jerome. A. Cloaking Defects in a 1D Spring Mass System. The 2024 Mathematical Society of the Philippines CALABARZON Annual Convention and General Assembly, Cavite State University, 04- 05 July 2024
Egarguin, Neil Jerome A. Active Control of Sound in Environments with Enclosures and Reflecting Obstacles. Mathematical Society of the Philippines CALABARZON Annual Convention, Batangas State University- The National Engineering University, July 18, 2023
Egarguin, Neil Jerome A., The Mathematics of the Manipulation of Sound: from theory to numerics and approximation. The 2022 Mathematical Society of the Philippines CALABARZON Annual Convention and General Assembly, Online, 16 July 2022
Sadsad, Den Mark, and Egarguin, Neil Jerome. A. An Analysis of the Numerical Solutions to Laplace’s Equation in 2D. The 2022 Mathematical Society of the Philippines CALABARZON Annual Convention and General Assembly, Online, July 16, 2022
Egarguin, Neil Jerome A., Onofrei, Daniel, and Platt, Eric. Controlling EM Waves using Debeye Potentials. Mathematical Society of the Philippines Annual Convention, Online (c/o UPLB and DLSU), May 21, 2022
Qi, Chaoxian, Chen, Jiefu, Egarguin, Neil Jerome. A., and Onofrei, Daniel. Feasibility Analysis for Active Manipulation of Electromagnetic Fields in Free Space. 2021 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Marina Bay Sands, Singapore, Dec. 04-10, 2021
Qi, Chaoxian, Huang, Chenpei, Egarguin, Neil J. A., Onofrei, Daniel, Pan, Miao, Chen, Jiefu. Enhanced Underwater Acoustic Communication via Active Field Control. ACM International Conference on Underwater Network and Systems (WUWNet 2021), Shenzhen, China, November 23-26, 2021
Egarguin, Neil Jerome A., Jackson, David R., Onofrei, Daniel, Leclerc Julien and Becker, Aaron. Beam Focusing by using Scattering from Drones. 2021 IEEE 19th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM), Winnipeg, MB, Canada, 2021
Egarguin, Neil Jerome A., Jackson, David R., Onofrei, Daniel, Leclerc Julien and Becker, Aaron. Beam Focusing by Scattering from an Array of Scatterers on a Drone. National Radio Science Meeting, Jan. 04-09, 2021, Online (c/o University of Colorado Boulder)
Guan, Larry, Egarguin, Neil Jerome A., and Onofrei, Daniel. Analysis of Mass Defects in 1D Spring-Mass Systems. 4th Annual Texas- Louisiana Undergraduate Mathematics Conference. October 31 to November 1, 2020, Online
Spencer, Damon, Onofrei, Daniel and Egarguin, Neil Jerome A. On passive Backscatter Cloaking in One Dimensional Oscillation Phenomena. 4th Annual Texas- Louisiana Undergraduate Mathematics Conference. October 31 to November 1, 2020, Online
Egarguin, Neil Jerome A., Jackson, David R., Onofrei, Daniel, Leclerc Julien and Becker, Aaron. Adaptive Beamforming using Scattering from a Drone Swarm. IEEE 2020 Texas Symposium on Wireless and Microwave Circuits and Systems, May 26-28, 2020, Online
Zeng, Shubin, Egarguin, Neil Jerome A., Onofrei, Daniel and Chen, Jiefu. Active Control of Electromagnetic Waves in Layered Media using a Current Source. IEEE 2020 Texas Symposium on Wireless and Microwave Circuits and Systems, May 26-28, 2020, Online
Egarguin, Neil Jerome A., Onofrei, Daniel, Qi, Chaoxian and Chen, Jiefu. Active Manipulation of Acoustic Fields in Homogeneous Constant Depth Ocean Environments. Texas Differential Equations (DE) Conference. March 7-8, 2020, University of Texas at Austin, Austin, Texas, USA
Onofrei, Daniel, Egarguin, Neil Jerome A., and Platt, Eric. Active surface sources for the exterior manipulation of acoustic fields. 178th Meeting of the Acoustical Society of America. December 2- 6, 2019, San Diego, California, USA. Abstract published at The Journal of the Acoustical Society of America 146(4), page 2876. DOI: 10.1121/1.5136980
Guan, Larry, Egarguin, Neil Jerome A., and Onofrei, Daniel. Defect Analysis of 1D Spring-Mass Systems via Laplace Transform and Asymptotics. 3rd Annual Texas- Louisiana Undergraduate Mathematics Conference. October 19-20, 2019, Texas A&M University, College Station, Texas, USA
Fegan, Lance, Egarguin, Neil Jerome A., and Onofrei, Daniel. Two Approaches for Optimal Synthesis of a Thin Wire Antenna. 3rd Annual Texas- Louisiana Undergraduate Mathematics Conference. October 19-20, 2019, Texas A&M University, College Station, Texas, USA
Egarguin, Neil Jerome A. Control of Wave Phenomena. 2019 Annual Performace Review. April 08, 2019. University of Houston, Houston, Texas, USA
Egarguin, Neil Jerome A., and Onofrei, Daniel. Active control of Helmholtz fields using an array of almost non-radiating sources. Texas Differential Equations (DE) Conference. March 30-31, 2019, Texas A&M University Corpus Christi, Corpus Christi, Texas, USA
Woelfel, Charlene M., Egarguin, Neil Jerome A., and Onofrei, Daniel. Scattering cancellation using dipolar arrays. SIAM Texas- Louisiana Undergraduate Mathematics Conference. October 5-7, 2018, Louisiana State University, Baton Rouge, Louisiana, USA
Egarguin, Neil Jerome A., and Onofrei, Daniel. Locating defects in a vibrating string using eigenfunction expansion and the method of moments. Texas Differential Equations (DE) Conference. March 24-25, 2018, University of Texas San Antonio, San Antonio, Texas, USA
Harari-Arnold, Noam D., Egarguin, Neil Jerome A., and Onofrei, Daniel. Locating defects in spring-mass systems through Laplace domain and function limit analysis. Texas- Louisiana Undergraduate Mathematics Conference. November 11-12, 2017, University of Houston, Houston, Texas, USA
Alcala, Jeric S., Egarguin Neil Jerome A., and Lampos, JMT. Adjacency matrices of replacement products of families of graphs and related codes. The 2016 Mathematical Society of the Philippines CALABARZON Annual Convention. July 21, 2016, De La Salle University-Dasmariñas, Cavite.
Egarguin, Neil Jerome A., and Panopio RG. G(A, B)-labeling of Cacti over Groups. The 2nd International Conference on Mathematical Sciences and Statistics (organized by the Universiti Putra Malaysia). January 26-28, 2016, Kuala Lumpur, Malaysia
Egarguin, Neil Jerome A., and Panopio RG. G(A, B)-labeling of -cages. Symposium on Graph Theory and Applications. January 13-15, 2016, Ateneo de Manila University, Quezon City
Egarguin, Neil Jerome A., and Panopio RG. G(A, B)-labeling of graphs using products of groups and rings. The 8th CAS Student Faculty Research Conference. November 16, 2015, UPLB, College, Laguna.
Egarguin, Neil Jerome A., and Panopio RG. G(A, B)-labeling of forest and trees. The 7th South East Asian Mathematical Society (SEAMS)- Universitas Gadjah Mada (UGM) International Conference on Mathematics and its Applications. August 18-21, 2015, UGM campus, Yogyakarta, Indonesia
Alcala, Jeric S., Egarguin Neil Jerome A., and Lampos, JMT. Expander graphs from replacement product of some regular graphs. The 2015 Mathematical Society of the Philippines CALABARZON Annual Convention. July 18, 2015, UPLB, College, Laguna.
Egarguin, Neil Jerome A., and Panopio RG. Constructions of graphs over group and rings. The 2015 Mathematical Society of the Philippines Annual Convention. May 18-19, 2015, Laoag City, Ilocos Norte.
Egarguin, Neil Jerome A., and Panopio RG. Autographs: operations and signatures. The 2011 Mathematical Society of the Philippines CALABARZON Chapter Annual Convention. May 4, 2011, De La Salle Lipa, Lipa City, Batangas.
A drone carrying an array of scatterers, used as a relay when there is no direct line-of-sight between two transceivers as discussed in the talk "Beam Focusing by Scattering from an Array of Scatterers on a Drone".
Diagram of a possible application of the talk "Active Manipulation of Acoustic Fields in Homogeneous Constant Depth Ocean Environments" in enhancing secure underwater communications
Geometric description of the problem from the talk "Active control of Helmholtz fields using an array of almost non-radiating sources."
Snapshots from my first presentation off my PhD research: Locating defects in a vibrating string using eigenfunction expansion and the method of moments.
Cover slide of the first Presentation off my Master's Thesis
Poster Papers
(*name of presenter in bold italics)Poster Papers
Guan, Larry, Egarguin, Neil Jerome A., and Onofrei, Daniel. Analysis of Mass Defects in 1D Spring-Mass Systems. 4th Annual Texas- Louisiana Undergraduate Mathematics Conference. October 31 to November 1, 2020, Online
ABSTRACT
The spring-mass system is an invaluable model with unmatched versatility for studying wave-like physical phenomena or material deformation. We consider linear spring-mass systems and the use of experimental data to locate and characterize defects ("error" masses) somewhere along its length. By taking the Laplace transform of the first body’s trajectory, the system eigenvalues are recoverable if damping is negligibly weak. Encoded within the trace/determinant eigenvalue relations are the masses of the defects; a minimization procedure with the recovered masses can then reveal their locations. For up to two present defects, this scheme is reasonably successful.} % Body
Spencer, Damon, Onofrei, Daniel and Egarguin, Neil Jerome A. On passive Backscatter Cloaking in One Dimensional Oscillation Phenomena. 4th Annual Texas- Louisiana Undergraduate Mathematics Conference. October 31 to November 1, 2020, Online
ABSTRACT
Backscattered cloaking attempts to mask vibrations in the direction of measurement. This research focuses on one dimensional backscattered cloaking. This problem can be described in terms of spring mass mechanics, circuits, acoustics, and atomic lattice vibrations. In this poster, we discuss methods for cloaking both a ten mass system toy problem and a large one hundred mass system. We utilize Plancherel’s theorem to allow optimization of both systems in the Fourier domain. We then proceed to optimize the ten mass system using a Fourier transform polynomial and the hundred mass system using Tikhonov regularization. Simulation results are provided, and results show a large improvement in the residual value from optimizing both the ten and one hundred mass systems. The results also show that the residual value decreases significantly in dissipative media, and an explanation for why this is true is provided. Overall, we find that cloaking can be done well at a large scale using Tikhonov regularization.
Click here to download the poster
Poster presented by Alexandra Vaughn at the 3rd Annual Texas- Louisiana Undergraduate Mathematics Conference last Oct. 19-20, 2019 at the Texas A&M University (College Station, Texas, USA )
Vaughn, Alexandra, Egarguin, Neil Jerome A., and Onofrei, Daniel. The Butterfly Effect on Traffic. 3rd Annual Texas- Louisiana Undergraduate Mathematics Conference. October 19-20, 2019, Texas A&M University, College Station, Texas, USA
ABSTRACT
Sometimes traffic seemingly appears out of thin air. There are no traffic lights, exits, entrances or accidents but somehow all the cars are at a standstill and everyone is left wondering “what happened?” We have set out to investigate this phenomena starting with a fairly simply model. All cars are traveling at the same speed in one lane with no other possible interceptions (traffic light, exits, entrances, etc.) when suddenly one car makes the decision to decelerate below the common speed for a few seconds. Perhaps they got distracted by the scenery or let their mind wander somewhere else. Regardless, we analyze how this seemingly insignificant event could cause a bottleneck of traffic down the line.
Download the poster here.
Guan, Larry, Egarguin, Neil Jerome A., and Onofrei, Daniel. Defect Analysis of 1D Spring-Mass Systems via Laplace Transform and Asymptotics. 3rd Annual Texas- Louisiana Undergraduate Mathematics Conference. October 19-20, 2019, Texas A&M University, College Station, Texas, USA
ABSTRACT
Spring-mass systems have seen utility for decades in modeling multiple physical phenomena like elastic deformation and wave propagation. Our focus is on linear spring-mass systems and the use of experimental data to analytically locate and characterize defects ("error" masses) along the chain. Asymptotics within the Laplace domain enabled us to numerically trial each block for defect status using the vibrational data of only the first block in the chain while simultaneously counting the number of defects. However, despite the theoretical soundness, this process works only for data without measurement/numerical noise and any defects beyond the first are undetectable.
Download the poster here.
Poster presented by Larry Fegan at the 3rd Annual Texas- Louisiana Undergraduate Mathematics Conference last Oct. 19-20, 2019 at the Texas A&M University (College Station, Texas, USA )
Poster presented by Lance Fegan at the 3rd Annual Texas- Louisiana Undergraduate Mathematics Conference last Oct. 19-20, 2019 at the Texas A&M University (College Station, Texas, USA )
Fegan, Lance, Egarguin, Neil Jerome A., and Onofrei, Daniel. Two Approaches for Optimal Synthesis of a Thin Wire Antenna. 3rd Annual Texas- Louisiana Undergraduate Mathematics Conference. October 19-20, 2019, Texas A&M University, College Station, Texas, USA
ABSTRACT
In this study, we explore a strategy for determining the current distribution of a thin-wire antenna based on a given radiation pattern. By this we mean seeking for a current distribution on the antenna so that the generated radiation pattern closely approximates a prescribed far field pattern. The integral equation that models the relationship between the current distribution and the generated radiation pattern was analyzed using the method of moments. The unknown current distribution was approximated with a truncated series leading to a system of linear equations. This linear system is then solved using Tikhonov regularization.This study directly compares the results obtained from two series representations, namely the Taylor and Fourier series. Our results show that the accuracy of this strategy is primarily dependent upon the approximating series used. The results from this study has potential applications in radar and radar defense technologies. Further research on this problem may lead to the development of more effective techniques in terms of accuracy and stability
Download the poster here.
Woelfel, Charlene M., Egarguin, Neil Jerome A., and Onofrei, Daniel. Scattering cancellation using dipolar arrays. SIAM Texas- Louisiana Undergraduate Mathematics Conference. October 5-7, 2018, Louisiana State University, Baton Rouge, Louisiana, USA and at the UH Undergraduate Research Day. October 18, 2018, University of Houston, Houston, Texas, USA
ABSTRACTThis study explores a strategy for cancelling the scattered far field of a dipole interrogating a perfectly conducting plane. The interrogating dipole acts as a monostatic radar (i.e., an interrogator collocated with a receiver) and for the scattering cancellation effect we are using a distribution of infinitesimal dipoles located above the target. We assume that the interrogating dipole is located at (0,0,𝑞). The goal is to determine the current feed required for the defending dipoles to cancel the scattered far field on a patch around the interrogating dipole while having a near zero effect on the field elsewhere. We mention that the additional effect of very small fields outside a small patch around the interrogating dipole could lead to other important applications such as field focusing, for example.
We present some numerical simulations of this strategy applied to the scattering cancellation of the interrogator’s magnetic far field. We begin with the specific case of a vertical interrogating dipole, in which the cancellation was done using vertical dipoles and their appropriate line currents. We then consider the general case of an arbitrarily-oriented interrogating dipole. Here, cancellation was achieved using dipoles oriented in the three fundamental directions, 𝐢,j and 𝐤, with appropriate currents.
Download the poster here.
Poster presented by Charlene Woelfel at the SIAM Texas- Louisiana Undergraduate Mathematics Conference last October 5-7, 2018, Louisiana State University, (Baton Rouge, Louisiana, USA) and at the UH Undergraduate Research Day last October 18, 2018, University of Houston (Houston, Texas, USA )
Poster presented by Noam Harari at the Texas- Louisiana Undergraduate Mathematics Conference last November 11-12, 2017 at the University of Houston (Houston, Texas, USA )
Harari-Arnold, Noam D., Egarguin, Neil Jerome A., and Onofrei, Daniel. Locating defects in spring-mass systems through Laplace domain and function limit analysis. Texas- Louisiana Undergraduate Mathematics Conference. November 11-12, 2017, University of Houston, Houston, Texas, USA
ABSTRACTChains of springs and masses can be used to model many real world phenomena, such as deformable objects, acoustic vibrations, soft tissue deformation, automobile suspension systems, and more. As such, it is a matter of interest to analyze the behavior of non-uniform spring-mass systems, as well as to examine how experimental data can be used to find the location of defects in a chain. We start by converting a spring-mass system in matrix form into the Laplace domain in a way that allows the length of the system to remain unspecified. This allows us to find an empirical solution for any chain length. We then expand the solution to account for an “error” mass: one location in the chain that has a higher or lower mass than the rest of the objects. We then use the resulting empirical solution of a non-uniform spring-mass system to devise a method for obtaining the location of the defect by analyzing the behavior of the first mass, and devise a proof based on function limit analysis to confirm the method's validity. We then confirm that this method works when starting from a standard time-domain description of the first mass’ movement. As a final step, we explore minimization methods as a solution to dealing with systems with two or more unknowns.
Download the poster here.
Egarguin, Neil Jerome A. and Panopio RG. Graph operations and their induced autographs. The Second CAS Student-Faculty Research Conference. December 14, 2009, UPLB, College, Laguna.
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