@article{mollik_kennedy_ul shougat_li_fitzgerald_echols_kirk_silverberg_perkins_2022, title={Discrete element method simulator for joint dynamics: a case study using a red-tailed hawk's hallux digit}, volume={6}, ISSN={["1573-272X"]}, DOI={10.1007/s11044-022-09828-x}, journal={MULTIBODY SYSTEM DYNAMICS}, author={Mollik, Tushar and Kennedy, Scott and Ul Shougat, Md Raf E. and Li, Xiaofu and Fitzgerald, Timothy and Echols, Scott and Kirk, Nick and Silverberg, Larry and Perkins, Edmon}, year={2022}, month={Jun} }
 @article{mollik_geng_ul shougat_fitzgerald_perkins_2022, title={Genetic algorithm shape optimization to manipulate the nonlinear response of a clamped-clamped beam}, volume={8}, ISSN={["2405-8440"]}, DOI={10.1016/j.heliyon.2022.e11833}, abstractNote={Dynamical systems, which are described by differential equations, can have an enhanced response because of their nonlinearity. As one example, the Duffing oscillator can exhibit multiple stable vibratory states for some external forcing frequencies. Although discrete systems that are described by ordinary differential equations have helped to build fundamental groundwork, further efforts are needed in order to tailor nonlinearity into distributed parameter, continuous systems, which are described by partial differential equations. To modify the nonlinear response of continuous systems, topology optimization can be used to change the shape of the mechanical system. While topology optimization is well-developed for linear systems, less work has been pursued to optimize the nonlinear vibratory response of continuous systems. In this paper, a genetic algorithm implementation of shape optimization for continuous systems is described. The method is very general, with flexible objective functions and very few assumptions; it is applicable to any continuous system. As a case study, a clamped-clamped beam is optimized to have a more nonlinear or less nonlinear vibratory response. This genetic algorithm implementation of shape optimization could provide a tool to improve the performance of many continuous structures, including MEMS sensors, actuators, and macroscale civil structures.}, number={11}, journal={HELIYON}, author={Mollik, Tushar and Geng, Ying and Ul Shougat, Md Raf E. and Fitzgerald, Timothy and Perkins, Edmon}, year={2022}, month={Nov} }
 @article{li_kallepalli_mollik_ul shougat_kennedy_frabitore_perkins_2022, title={The pendulum adaptive frequency oscillator}, volume={179}, ISSN={["1096-1216"]}, DOI={10.1016/j.ymssp.2022.109361}, abstractNote={Adaptive oscillators are a type of nonlinear oscillator that are capable of learning and storing information in plastic states. Here, a typical mechanical pendulum is modified to have an adjustable rod length to create a pendulum adaptive frequency oscillator. Since the resonance frequency of the pendulum is a function of the rod length, this allows the pendulum to learn and encode frequency information from an external source. An experimental pendulum adaptive frequency oscillator is designed and constructed, and its performance is compared to numerical simulations. This nonlinear pendulum was approximated as a Duffing oscillator through the method of multiple scales to determine the physical constants of the experiment by using a curve fit. Utilizing the pendulum adaptive frequency oscillator’s dynamics, this system is able to learn a resonance condition and store this information in the rod length. This causes the system to seek resonance, even with considerable nonlinearity. As pendulums can be used to harvest energy, this type of adaptation could be used to further exploit vibratory energy sources.}, journal={Mechanical Systems and Signal Processing}, author={Li, XiaoFu and Kallepalli, Pawan and Mollik, Tushar and Ul Shougat, Md Raf E and Kennedy, Scott and Frabitore, Sean and Perkins, Edmon}, year={2022}, month={Nov}, pages={109361} }
 @article{ul shougat_li_mollik_perkins_2021, title={A Hopf physical reservoir computer}, volume={11}, ISSN={["2045-2322"]}, DOI={10.1038/s41598-021-98982-x}, abstractNote={AbstractPhysical reservoir computing utilizes a physical system as a computational resource. This nontraditional computing technique can be computationally powerful, without the need of costly training. Here, a Hopf oscillator is implemented as a reservoir computer by using a node-based architecture; however, this implementation does not use delayed feedback lines. This reservoir computer is still powerful, but it is considerably simpler and cheaper to implement as a physical Hopf oscillator. A non-periodic stochastic masking procedure is applied for this reservoir computer following the time multiplexing method. Due to the presence of noise, the Euler–Maruyama method is used to simulate the resulting stochastic differential equations that represent this reservoir computer. An analog electrical circuit is built to implement this Hopf oscillator reservoir computer experimentally. The information processing capability was tested numerically and experimentally by performing logical tasks, emulation tasks, and time series prediction tasks. This reservoir computer has several attractive features, including a simple design that is easy to implement, noise robustness, and a high computational ability for many different benchmark tasks. Since limit cycle oscillators model many physical systems, this architecture could be relatively easily applied in many contexts.}, number={1}, journal={SCIENTIFIC REPORTS}, author={Ul Shougat, Md Raf E. and Li, XiaoFu and Mollik, Tushar and Perkins, Edmon}, year={2021}, month={Sep} }
 @article{ul shougat_li_mollik_perkins_2021, title={An Information Theoretic Study of a Duffing Oscillator Array Reservoir Computer}, volume={16}, ISSN={["1555-1415"]}, DOI={10.1115/1.4051270}, abstractNote={Abstract
               Typically, nonlinearity is considered to be problematic and sometimes can lead to dire consequences. However, the nonlinearity in a Duffing oscillator array can enhance its ability to be used as a reservoir computer. Machine learning and artificial neural networks, inspired by the biological computing framework, have shown their immense potential, especially in the real-time temporal data processing. Here, the efficacy of a Duffing oscillator array is explored as a reservoir computer by using information theory. To do this, a reservoir computer model is studied numerically, which exploits the dynamics of the array. In this system, the complex dynamics stem from the Duffing term in each of the identical oscillators. The effects of various system parameters of the array on the information processing ability are discussed from the perspective of information theory. By varying these parameters, the information metric was found to be topologically mixed. Additionally, the importance of asynchrony in the oscillator array is also discussed in terms of the information metric. Since such nonlinear oscillators are used to model many different physical systems, this research provides insight into how physical nonlinear oscillatory systems can be used for dynamic computation, without significantly modifying or controlling the underlying dynamical system. To the authors' knowledge, this is the first use of Shannon's information rate for quantifying a reservoir computer of this kind, as well as the first comparison between synchronization phenomena and the computing ability of a reservoir.}, number={8}, journal={Journal of Computational and Nonlinear Dynamics}, author={Ul Shougat, Md. Raf E. and Li, XiaoFu and Mollik, Tushar and Perkins, Edmon}, year={2021}, month={Aug}, pages={081004} }
 @article{li_shougat_mollik_beal_dean_perkins_2021, title={Stochastic effects on a Hopf adaptive frequency oscillator}, volume={129}, ISSN={["1089-7550"]}, DOI={10.1063/5.0050819}, abstractNote={This paper explores the stochastic dynamics of a Hopf adaptive frequency oscillator when driven by noise. Adaptive oscillators are nonlinear oscillators that store information via plastic states. As noise is ubiquitous in physical systems, it is important to gain an understanding of the stochastic effects on adaptive oscillators. Previously, it has been shown that a simplified analysis of the Fokker–Planck equation results in affecting the plastic frequency state of these oscillators. However, when the full Fokker–Planck equation is considered, new behaviors are observed due to changes in oscillation amplitudes in addition to frequencies. The plastic frequency state of these oscillators may benefit from enhanced learning due to small amplitudes of noise, converge to incorrect values for medium amplitudes of noise, and even collapse to zero in the limit of large amplitudes of noise. Interestingly, not all averaged states collapse equally, which leads a two dimensional limit cycle to collapse into single dimensional oscillations when considering the averaged dynamics. These behaviors are compared analytically through the Fokker–Planck equation, numerically using the Euler–Maruyama simulations, and finally validated experimentally using an analog, electronic circuit. These results show that noise can enhance, mislead, or even reduce the dimensionality of the averaged adaptive Hopf oscillator.}, number={22}, journal={JOURNAL OF APPLIED PHYSICS}, author={Li, XiaoFu and Shougat, Md. Raf E. Ul and Mollik, Tushar and Beal, Aubrey N. and Dean, Robert N. and Perkins, Edmon}, year={2021}, month={Jun} }