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1. Strong nonreciprocity in a bistable pendulum with contactless coupling to a monostable pendulum

   https://doi.org/10.1007/s11071-025-10992-w  

   Rouleau, Michael; Booker, Zachary; Shi, Chengzhi; Meaud, Julien (February 2025, Nonlinear Dynamics)

   Abstract This article studies the nonreciprocity of a system that consists of a bistable element coupled to a monostable element through a contactless magnetic interaction. To illustrate the concept, the bistable element is physically realized using a pendulum that interacts with a stationary magnet and the monostable element is a classical pendulum. A numerical model is implemented to simulate the nonlinear dynamics of the system. Both simulations and experiments show that the system exhibits a strong amplitude-dependent nonreciprocity in response to initial excitations. At small input amplitudes, the system has an intrawell response with minimal transmission of energy whether the excitation is exerted on the side of the bistable pendulum or on the other side. However, at high input amplitude, a strong nonreciprocal behavior is observed: excitation of the bistable pendulum causes an interwell response which considerably reduces the distance between the two pendulums and allows energy to be efficiently transmitted through the contactless magnetic interaction; excitation of the monostable pendulum does not cause any interwell response and results in limited energy transmission. The combination of bistability and contactless nonlinear interactions allows the system to exhibit very strong amplitude-dependent nonreciprocity, which may be useful in a wide range of applications. 

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2. Constrained Nonlinear and Mixed Effects Integral Differential Equation Models for Dynamic Cell Polarity Signaling

   https://doi.org/10.3389/fpls.2022.847671  

   Xiao, Zhen; Brunel, Nicolas; Tian, Chenwei; Guo, Jingzhe; Yang, Zhenbiao; Cui, Xinping (May 2022, Frontiers in Plant Science)

   Polar cell growth is a process that couples the establishment of cell polarity with growth and is extremely important in the growth, development, and reproduction of eukaryotic organisms, such as pollen tube growth during plant fertilization and neuronal axon growth in animals. Pollen tube growth requires dynamic but polarized distribution and activation of a signaling protein named ROP1 to the plasma membrane via three processes: positive feedback and negative feedback regulation of ROP1 activation and its lateral diffusion along the plasma membrane. In this paper, we introduce a mechanistic integro-differential equation (IDE) along with constrained semiparametric regression to quantitatively describe the interplay among these three processes that lead to the polar distribution of active ROP1 at a steady state. Moreover, we introduce a population variability by a constrained nonlinear mixed model. Our analysis of ROP1 activity distributions from multiple pollen tubes revealed that the equilibrium between the positive and negative feedbacks for pollen tubes with similar shapes are remarkably stable, permitting us to infer an inherent quantitative relationship between the positive and negative feedback loops that defines the tip growth of pollen tubes and the polarity of tip growth. 

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3. Modeling neuron growth using isogeometric collocation based phase field method

   https://doi.org/10.1038/s41598-022-12073-z  

   Qian, Kuanren; Pawar, Aishwarya; Liao, Ashlee; Anitescu, Cosmin; Webster-Wood, Victoria; Feinberg, Adam W.; Rabczuk, Timon; Zhang, Yongjie Jessica (May 2022, Scientific Reports)

   Abstract We present a new computational framework of neuron growth based on the phase field method and develop an open-source software package called “NeuronGrowth_IGAcollocation”. Neurons consist of a cell body, dendrites, and axons. Axons and dendrites are long processes extending from the cell body and enabling information transfer to and from other neurons. There is high variation in neuron morphology based on their location and function, thus increasing the complexity in mathematical modeling of neuron growth. In this paper, we propose a novel phase field model with isogeometric collocation to simulate different stages of neuron growth by considering the effect of tubulin. The stages modeled include lamellipodia formation, initial neurite outgrowth, axon differentiation, and dendrite formation considering the effect of intracellular transport of tubulin on neurite outgrowth. Through comparison with experimental observations, we can demonstrate qualitatively and quantitatively similar reproduction of neuron morphologies at different stages of growth and allow extension towards the formation of neurite networks. 

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4. Dynamic Analysis of Chlorophyll a Fluorescence in Response to Time-Variant Excitations during Strong Actinic Illumination and Application in Probing Plant Water Loss

   https://doi.org/10.34133/plantphenomics.0151  

   Chen, Junqing; Guo, Ya; Tan, Jinglu (January 2024, Plant Phenomics)

   Magnitude measurement of chlorophyllafluorescence (ChlF) involves challenges, and dynamic responses to variable excitations may offer an alternative. In this research, ChlF was measured during strong actinic light by using a pseudo-random binary sequence as a time-variant multiple-frequency illumination excitation. The responses were observed in the time domain but were primarily analyzed in the frequency domain in terms of amplitude gain variations. The excitation amplitude was varied, and moisture loss was used to induce changes in the plant samples for further analysis. The results show that when nonphotochemical quenching (NPQ) activities start, the amplitude of ChlF responses vary, making the ChlF responses to illumination excitations nonlinear and nonstationary. NPQ influences the ChlF responses in low frequencies, most notably below 0.03 rad/s. The low-frequency gain is linearly correlated with NPQ and can thus be used as a reference to compensate for the variations in ChlF measurements. The high-frequency amplitude gain showed a stronger correlation with moisture loss after correction with the low-frequency gain. This work demonstrates the usefulness of dynamic characteristics in broadening the applications of ChlF measurements in plant analysis and offers a way to mitigate variabilities in ChlF measurements during strong actinic illumination. 

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5. Deep Learning of Material Transport in Complex Neurite Networks

   Li, A; Farimani, A.B.; Zhang, Y.J. (January 2021, Scientific reports)

   Neurons exhibit complex geometry in their branched networks of neurites which is essential to the function of individual neuron but also brings challenges to transport a wide variety of essential materials throughout their neurite networks for their survival and function. While numerical methods like isogeometric analysis (IGA) have been used for modeling the material transport process via solving partial differential equations (PDEs), they require long computation time and huge computation resources to ensure accurate geometry representation and solution, thus limit their biomedical application. Here we present a graph neural network (GNN)-based deep learning model to learn the IGA-based material transport simulation and provide fast material concentration prediction within neurite networks of any topology. Given input boundary conditions and geometry configurations, the well-trained model can predict the dynamical concentration change during the transport process with an average error less than 10% and 120∼330 times faster compared to IGA simulations. The effectiveness of the proposed model is demonstrated within several complex neurite networks. 

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