Nonlinear Membrane Research Articles

Deformation and enclosed volume change of axisymmetric non-linear dielectric elastomer membrane pump: a theoretical study

Abstract This work investigates the change in the enclosed volume of an axisymmetric non-linear hyper-elastic membrane pump subjected to dielectric actuation. The equilibrium equations in cylindrical coordinates, coupled with non-linear constitutive relations, are solved numerically to obtain the deformed membrane geometry under pressure loading (using Variational Calculus). The effect of dielectric actuation is then incorporated by considering the change in material properties and deformation induced by the applied electric field. The deformed geometry under dielectric actuation is determined, and the change in enclosed volume is calculated by comparing the deformed states with and without the applied electric field. The proposed approach enables quantifying the volumetric change in non-linear hyper-elastic membrane pumps due to dielectric actuation for potential applications in soft robotics, adaptive optics, and microfluidics. By non-dimensionalizing variables, key dimensionless parameters governing the problem are identified for broader applicability. Furthermore, this methodology can estimate volume changes for different electric actuations when a specific material is chosen with experimentally derived parameter trends, facilitating material selection or synthesis to meet targeted volumetric requirements.

Referring Image Segmentation with Multi-Modal Feature Interaction and Alignment Based on Convolutional Nonlinear Spiking Neural Membrane Systems.

Referring image segmentation aims to accurately align image pixels and text features for object segmentation based on natural language descriptions. This paper proposes NSNPRIS (convolutional nonlinear spiking neural P systems for referring image segmentation), a novel model based on convolutional nonlinear spiking neural P systems. NSNPRIS features NSNPFusion and Language Gate modules to enhance feature interaction during encoding, along with an NSNPDecoder for feature alignment and decoding. Experimental results on RefCOCO, RefCOCO[Formula: see text], and G-Ref datasets demonstrate that NSNPRIS performs better than mainstream methods. Our contributions include advances in the alignment of pixel and textual features and the improvement of segmentation accuracy.

Synthetic control of actin polymerization and symmetry breaking in active protocells.

Nonlinear biomolecular interactions on membranes drive membrane remodeling crucial for biological processes including chemotaxis, cytokinesis, and endocytosis. The complexity of biomolecular interactions, their redundancy, and the importance of spatiotemporal context in membrane organization impede understanding of the physical principles governing membrane mechanics. Developing a minimal in vitro system that mimics molecular signaling and membrane remodeling while maintaining physiological fidelity poses a major challenge. Inspired by chemotaxis, we reconstructed chemically regulated actin polymerization inside vesicles, guiding membrane self-organization. An external, undirected chemical input induced directed actin polymerization and membrane deformation uncorrelated with upstream biochemical cues, suggesting symmetry breaking. A biophysical model incorporating actin dynamics and membrane mechanics proposes that uneven actin distributions cause nonlinear membrane deformations, consistent with experimental findings. This protocellular system illuminates the interplay between actin dynamics and membrane shape during symmetry breaking, offering insights into chemotaxis and other cell biological processes.

Realization of nonreciprocal acoustic energy transfer using an asymmetric strong nonlinear vibroacoustic system

AbstractIn this paper, an asymmetric vibroacoustic system that can passively realize nonreciprocal transmission of acoustic energy is reported. This experimental system consists of a waveguide, a strongly nonlinear membrane, and three acoustic cavities with different sizes. The theoretical modeling of the system is verified by experiments, and parametric analysis is also carried out. These intensive studies reveal the nonreciprocal transmission of acoustic energy in this prototype system. Under forward excitation, internal resonance between the two nonlinear normal modes of the vibroacoustic system occurs, and acoustic energy is irreversibly transferred from the waveguide to the nonlinear membrane. However, under backward excitation, there is no internal resonance in the system. Energy spectra and wavelet analysis are used to highlight the mechanism of nonreciprocal transfer of acoustic energy. Consequently, nearly unidirectional (preferential) transmission of acoustic energy transfer is shown by this system. The nonreciprocal acoustic energy transfer method illustrated in this paper provides a new way to design the odd acoustic element.

Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems

Complex mechanical systems often exhibit strongly nonlinear behavior due to the presence of nonlinearities in the energy dissipation mechanisms, material constitutive relationships, or geometric/connectivity mechanics. Numerical modeling of these systems leads to nonlinear full-order models that possess an underlying Lagrangian structure. This work proposes a Lagrangian operator inference method enhanced with structure-preserving machine learning to learn nonlinear reduced-order models (ROMs) of nonlinear mechanical systems. This two-step approach first learns the best-fit linear Lagrangian ROM via Lagrangian operator inference and then presents a structure-preserving machine learning method to learn nonlinearities in the reduced space. The proposed approach can learn a structure-preserving nonlinear ROM purely from data, unlike the existing operator inference approaches that require knowledge about the mathematical form of nonlinear terms. From a machine learning perspective, it accelerates the training of the structure-preserving neural network by providing an informed prior (i.e., the linear Lagrangian ROM structure), and it reduces the computational cost of the network training by operating on the reduced space. The method is first demonstrated on two simulated examples: a conservative nonlinear rod model and a two-dimensional nonlinear membrane with nonlinear internal damping. Finally, the method is demonstrated on an experimental dataset consisting of digital image correlation measurements taken from a lap-joint beam structure from which a predictive model is learned that captures amplitude-dependent frequency and damping characteristics accurately. The numerical results demonstrate that the proposed approach yields generalizable nonlinear ROMs that exhibit bounded energy error, capture the nonlinear characteristics reliably, and provide accurate long-time predictions outside the training data regime.

A novel time-domain approach for identifying nonlinear structural dynamical system with explicit model based on observer/Kalman filter identification method

In this paper, a novel time-domain method for identifying nonlinear structural dynamical system with explicit model is proposed. By exploiting the observer/Kalman filter identification (OKID) and nonlinear feedback interpretation, the nonlinear parameters of the system are estimated accurately. The effectiveness of the proposed nonlinear OKID (NOKID) method is demonstrated through three numerical examples, namely a five degree-of-freedom system with one nonlinear spring, a three degree-of-freedom system with three nonlinear springs and a nonlinear rectangular membrane structure with all edges clamped. Comparing with the time-domain nonlinear subspace identification (TNSI) method, the proposed NOKID method can identify the nonlinear parameters without system order determination, and the identification results obtained by the proposed method are real numbers and have no dependency on frequency.

Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature

We consider the rigorously derived thin shell membrane \Gamma -limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regularity of both the midsurface deformation m\colon \omega\subset \mathbb{R}^{2}\to \mathbb{R}^{3} and the orthogonal microrotation tensor field R\colon \omega\subset \mathbb{R}^{2}\to \operatorname{SO}(3) . The only further structural assumption is that the curvature energy depends solely on the uni-constant isotropic Dirichlet-type energy term |\mathrm{D}R|^{2} . We use Rivière’s regularity techniques of harmonic-map-type systems for our system which couples harmonic maps to \operatorname{SO}(3) with a linear equation for m . The additional coupling term in the harmonic map equation is of critical integrability and can only be handled because of its special structure.

Blow up and lifespan of solutions for elastic membrane equation with delay

The primary objective of this research is to examine a nonlinear elastic membrane equation incorporating delay and source terms within a bounded domain. We obtain sufficient conditions on the initial data and the involved functionals for which the energy of solutions with non positive initial energy as well as positive initial energy blow up in a finite-time. In addition, this research work provides estimates for the lifespan of these solutions.

Fluid-structure interaction behaviors of tension membrane roofs by fully-coupled numerical simulation

This study aims to investigate fluid-structure interaction (FSI) behaviors of an enclosed-type tension membrane flat roof. The roof with rectangular shape is chosen as the object because of its relatively idealized geometry for FSI analysis, which is a simplified shape compared to typical membrane roofs. Fully-coupled numerical simulations are performed to obtain the wind induced vibration, aerodynamic forces and surrounding flow field of the tension membrane roof structure, where large-eddy simulation (LES) is used for solving of the flow field, non-linear membrane elements are adopted for the structure field and partitioned algorithm is applied for the coupling between the flow and membrane vibration. The numerical simulations are validated by the aero-elastic experimental results. The characteristics of the wind-induced displacements and aerodynamic forces of the tension membrane roof are investigated in both time and frequency domains. The energy transfer characteristics between wind and the vibrating roof are investigated based on the phase analysis between the generalized forces and displacements of the membrane roof. The underlying mechanism of the modal-jump phenomena that the vibration mode of the membrane jumps from the first mode to the second mode with increasing wind velocity, as well as the instability mechanism of the tension membrane roof, are revealed by flow visualizations and unsteady aerodynamic forces identifications. It is found that the aero-elastic instability of the flat membrane roof is a kind of vortex-induced vibration (VIV), where the modal-jump phenomena and unstable vibration of the membrane roof occur with the occurrence of negative aerodynamic damping, induced by the interaction between the vortex transporting and the roof motion.

The partial null conditions and global smooth solutions of the nonlinear wave equations on [formula omitted] with d = 2,3

In this paper, we investigate the fully nonlinear wave equations on the product space R3×T with quadratic nonlinearities and on R2×T with cubic nonlinearities, respectively. It is shown that for the small initial data satisfying some space-decay rates at infinity, these nonlinear equations admit global smooth solutions when the corresponding partial null conditions hold and while have almost global smooth solutions when the partial null conditions are violated. Our proof relies on the Fourier mode decomposition of the solutions with respect to the periodic direction, the efficient combinations of time-decay estimates for the solutions to the linear wave equations and the linear Klein-Gordon equations, and the global weighted energy estimates. In addition, an interesting auxiliary energy is introduced. As a byproduct, our results can be applied to the 4D irrotational compressible Euler equations of polytropic gases or Chaplygin gases on R3×T, the 3D relativistic membrane equation and the 3D nonlinear membrane equation on R2×T.

Design of a Fuzzy Adaptive Voltage Controller for a Nonlinear Polymer Electrolyte Membrane Fuel Cell with an Unknown Dynamical System

This paper presents a fuzzy adaptive controller (FAC) for improving the efficiency and stability of fuel cells, assuming that the nonlinear dynamic model of the system is unknown. In polymer electrolyte membrane fuel cells, the output voltage should be controlled within a given interval. In contrast to prior studies that focused on designing controllers for known dynamical models of PEM fuel cells, the suggested approach addresses the real-world case of a PEM fuel cell with unknown dynamics. An intelligent technique is identified in the suggested strategy to approximate the state-space model of fuel cells to manage unknown functions. On an unknown model of fuel cells, traditional adaptive and fuzzy adaptive controllers are both implemented and compared. The main advantages of the proposed methodology are (1) stability of the closed-loop system using Lyapunov, (2) robustness against external disturbances, (3) application of the FAC to a PEM fuel cell, (4) convergence of the tracking error to 0, and (5) overcoming both unknown dynamics and uncertainty in the system. The most important and valuable advantages of the proposed system are its robustness, tracking error convergence, and Lyapunov stability. This manuscript aims to illustrate the responsiveness and fluency of the proposed procedure using a mathematical formulation of a multi-quadrotor system. As a result, the FAC is more efficient than the traditional one. To validate the controller performance, both the adaptive and fuzzy adaptive controllers are applied to a numerical model of a fuel cell and then compared.

Chemical osmosis-induced deformation of mudstone: Nonlinear semipermeable membrane behavior and dimensionless analysis

Mudstones can act as semipermeable membranes that induce osmotic flow and pressure changes which, in turn, cause deformation of mudstones. A numerical model was developed for describing these coupled processes by considering the nonlinear concentration-dependent semipermeable membrane properties and was applied to laboratory-scale experimental results to describe the deformation behavior. The strain behaviors obtained from the laboratory experiments were compared with the type curves obtained from the numerical simulations with constant and nonlinear concentration-dependent reflection coefficients. Both type curves efficiently explained the deformation of the sample in the early stage of the experiment, whereas incremental extension in the latter stage was only explained by the type curves with nonlinear concentration-dependent reflection coefficient. Nonlinear semipermeable membrane behavior should be considered to fully understand the long-term coupled processes observed in mudstones in the presence of a concentration gradient.

Effects of nonlinear membrane capacitance in the Hodgkin-Huxley model of action potential on the spike train patterns of a single neuron

The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane potential in various types of cells. But the role of the nonlinear membrane capacitance in neurons has not been studied in detail. Herein, by considering the membrane capacitance to be a nonlinear parameter, we have explored the behavior of the cell membrane in three different types of neurons, i.e., squid giant neuron, rodent hippocampal interneuron, and rodent cortical neuron. The Hodgkin-Huxley equation of action potential was modified accordingly and simulated computationally. Our simulated results suggest that the action potential amplitude of a neuron almost remains the same for some duration when the voltage dependence parameter of the nonlinear capacitance increases up to a certain range, the initiation of the next action potential is delayed and the reduction in spike frequencies occurs in comparison to constant membrane capacitance. This indicates the importance of nonlinearity in membrane capacitance. Simultaneously the inter-spike interval (ISI) changes with the nonlinear membrane capacitance parameter. The gating dynamics show changes mainly in the activation current while the membrane capacitance is considered to be nonlinear. The above-mentioned computational results are primarily predictive pending experimental verification.

Megahertz Sampling of Prestin (SLC26a5) Voltage-Sensor Charge Movements in Outer Hair Cell Membranes Reveals Ultrasonic Activity that May Support Electromotility and Cochlear Amplification.

Charged moieties in the outer hair cell (OHC) membrane motor protein, prestin, are driven by transmembrane voltage to power OHC electromotility (eM) and cochlear amplification (CA), an enhancement of mammalian hearing. Consequently, the speed of prestin's conformational switching constrains its dynamic influence on micromechanics of the cell and the organ of Corti. Corresponding voltage-sensor charge movements in prestin, classically assessed as a voltage-dependent, nonlinear membrane capacitance (NLC), have been used to gauge its frequency response, but have been validly measured only out to 30 kHz. Thus, controversy exists concerning the effectiveness of eM in supporting CA at ultrasonic frequencies where some mammals can hear. Using megahertz sampling of guinea pig (either sex) prestin charge movements, we extend interrogations of NLC into the ultrasonic range (up to 120 kHz) and find an order of magnitude larger response at 80 kHz than previously predicted, indicating that an influence of eM at ultrasonic frequencies is likely, in line with recent in vivo results (Levic et al., 2022). Given wider bandwidth interrogations, we also validate kinetic model predictions of prestin by directly observing its characteristic cut-off frequency under voltage-clamp as the intersection frequency (Fis), near 19 kHz, of the real and imaginary components of complex NLC (cNLC). The frequency response of prestin displacement current noise determined from either the Nyquist relation or stationary measures aligns with this cut-off. We conclude that voltage stimulation accurately assesses the spectral limits of prestin activity, and that voltage-dependent conformational switching is physiologically significant in the ultrasonic range.SIGNIFICANCE STATEMENT The motor protein prestin powers outer hair cell (OHC) electromotility (eM) and cochlear amplification (CA), an enhancement of high-frequency mammalian hearing. The ability of prestin to work at very high frequencies depends on its membrane voltage-driven conformation switching. Using megahertz sampling, we extend measures of prestin charge movement into the ultrasonic range and find response magnitude at 80 kHz an order of magnitude larger than previously estimated, despite confirmation of previous low pass characteristic frequency cut-offs. The frequency response of prestin noise garnered by the admittance-based Nyquist relation or stationary noise measures confirms this characteristic cut-off frequency. Our data indicate that voltage perturbation provides accurate assessment of prestin performance indicating that it can support cochlear amplification into a higher frequency range than previously thought.

Integrated models for prediction and global factors sensitivity analysis of ultrafiltration (UF) membrane fouling: statistics and machine learning approach

In this work, machine learning was employed to quantitatively describe nonlinear ultrafiltration membrane fouling behaviors, from existing data process modeling, process analysis and predictive modeling of unknown data prediction and feature analysis. Instead of using the secondary data calculation that the traditional model required, direct observation data is used for modeling and analysis. This simplifies the prediction process and lowers the cost of the prediction. Besides, the problem that the long-term serial data and the short-term rapid change process were difficult to quantify has been resolved. Two distinct prediction models were established: one is semi-automatic prediction of future data with existing data based on statistics (for long-term study and prediction), and the other is fully autonomous prediction based on tree model (for short-term). 2520 12-dimentional laboratory measurements were collected enabling precise modeling prediction (less than 4 % error) for 50 % of the future timeline through supervised learning of process modeling. Results revealed that the UF membrane had a strong “rejection” impact when it came into contact with a polluted environment, which caused an inconsistent self-pollution coefficient and rapid fouling at initially. For process analysis, a global variable-based weighting factor sensitivity analysis and a statistically significant likelihood estimation were conducted using random put-back samples to accurately predict membrane fouling in an uncertain environment (MSE = 0.2 to 0.26). A high-dimensional variable-specific real-time weighting analysis was derived for inform lifespan extension of the UF membrane at environmental relevant conditions. Overall, this study illustrates the feasibility and interpretability of machine learning-based data-driven approaches in quantitatively describing and understanding nonlinear complex dynamics in membrane fouling.

Ageing-induced shrinkage of intervessel pit membranes in xylem of Clematis vitalba modifies its mechanical properties as revealed by atomic force microscopy.

Bordered pit membranes of angiosperm xylem are anisotropic, mesoporous media between neighbouring conduits, with a key role in long distance water transport. Yet, their mechanical properties are poorly understood. Here, we aim to quantify the stiffness of intervessel pit membranes over various growing seasons. By applying an AFM-based indentation technique "Quantitative Imaging" we measured the effective elastic modulus (E effective) of intervessel pit membranes of Clematis vitalba in dependence of size, age, and hydration state. The indentation-deformation behaviour was analysed with a non-linear membrane model, and paired with magnetic resonance imaging to visualise sap-filled and embolised vessels, while geometrical data of bordered pits were obtained using electron microscopy. E effective was transformed to the geometrically independent apparent elastic modulus E apparent and to aspiration pressure P b. The material stiffness (E apparent) of fresh pit membranes was with 57 MPa considerably lower than previously suggested. The estimated pressure for pit membrane aspiration was 2.20+28 MPa. Pit membranes from older growth rings were shrunken, had a higher material stiffness and a lower aspiration pressure than current year ones, suggesting an irreversible, mechanical ageing process. This study provides an experimental-stiffness analysis of hydrated intervessel pit membranes in their native state. The estimated aspiration pressure suggests that membranes are not deflected under normal field conditions. Although absolute values should be interpreted carefully, our data suggest that pit membrane shrinkage implies increasing material stiffness, and highlight the dynamic changes of pit membrane mechanics and their complex, functional behaviour for fluid transport.

Analytic modeling of neural tissue: II. Nonlinear membrane dynamics.

Computational modeling of neuroactivity plays a central role in our effort to understand brain dynamics in the advancements of neural engineering such as deep brain stimulation, neuroprosthetics, and magnetic resonance electrical impedance tomography. However, analytic solutions do not capture the fundamental nonlinear behavior of an action potential. What is needed is a method that is not constrained to only linearized models of neural tissue. Therefore, the objective of this study is to establish a robust, straightforward process for modeling neurodynamic phenomena, which preserves their nonlinear features. To address this, we turn to decomposition methods from homotopy analysis, which have emerged in recent decades as powerful tools for solving nonlinear differential equations. We solve the nonlinear ordinary differential equations of three landmark models of neural conduction-Ermentrout-Kopell, FitzHugh-Nagumo, and Hindmarsh-Rose models-using George Adomian's decomposition method. For each variable, we construct a power series solution equivalent to a generalized Taylor series expanded about a function. The first term of the decomposition series comes from the models' initial conditions. All subsequent terms are recursively determined from the first. We show rapid convergence, achieving a maximal error of with only eight terms. We extend the region of convergence with one-step analytic continuation so that our complete solutions are decomposition splines. We show that this process can yield solutions for single- and multi-variable models and can characterize a single action potential or complex bursting patterns. Finally, we show that the accuracy of this decomposition approach favorably compares to an established polynomial method, B-spline collocation. The strength of this method, besides its stability and ease of computation, is that, unlike perturbation, we make no changes to the models' equations; thus, our solutions are to the problems at hand, not simplified versions. This work validates decomposition as a viable technique for advanced neural engineering studies.

Fractional PIλDµ controller design for non-linear PEM fuel cell for pressure control based on a genetic algorithm

ABSTRACT A fractional-order dynamic model could more accurately model many real scenarios than an integer-order model and provide a more accurate description of numerous genuine dynamical processes. A seventh-order nonlinear proton exchange membrane fuel cell (PEMFC) model is linearised in this research, taking into account correct initial conditions and equilibrium points.We consider the fluctuating load current as a disturbance parameter to affect the system. The goal is to find a control law for the MIMO system using a fractional PID controller based on a genetic algorithm. The controller is a critical part of the fuel cell which controls its functioning and efficiency. The goal is accomplished by designing a fractional controller to adjust the natural response of the fuel cell reactor and maintain the desired Power output in the face of uncertainties and disturbances. The validation results demonstrate that the fractional PIλDµ(FOPID) control method has a smaller overshoot and higher stability than the PID control method. Moreover, it is also observed that the operation efficiency of the PEMFC has risen by 2% with a response timing of less than 0.1 s using the developed fractional PIλDµ(FOPID) control technique.

Application of a Variant of Mountain Pass Theorem in Modeling Real Phenomena

Mountain Pass Theorem (MPT) is an important result in variational methods with multiple applications in partial differential equations involved in mathematical physics. Starting from a variant of MPT, a new result concerning the existence of the solution for certain mathematical physics problems involving p-Laplacian and p-pseudo-Laplacian has been obtained. Based on the main theorem, the existence, possibly the uniqueness, and characterization of solutions for models such as nonlinear elastic membrane, glacier sliding, and pseudo torsion problem have been obtained. The novelty of the work consists of the formulation of the central result under weaker conditions requested by the chosen variant of MPT, the proof of this statement, and its application in solving above mentioned problems. While the expressions of such Dirichlet and/or von Neumann problems were already completed, this proposed solving method suggests some specific numerical methods to construct the appropriate solution. A general goal of this paper is the extension of the applicative pallet of this way to construct the solutions encountered in modeling real processes developed within new emerging technologies.

Influence of Boundary Impedance of 3D Cavity on Targeted Energy Transfer between a Damped Acoustic Mode and a Nonlinear Membrane Absorber

In order to apply the nonlinear energy sink (NES) to reduce the low-frequency noise inside a 3D acoustic cavity with an impedance boundary, a two degrees-of-freedom (DOF) dynamic model of the coupled system of one damped acoustic mode of a regular 3D acoustic cavity and a nonlinear membrane absorber as the NES is established. The damping coefficient of the acoustic mode is obtained based on the finite element analysis method and the relationship of the boundary impedance and the absorption coefficient of the cavity. Based on the set-up of the system, the damping coefficient of the acoustic mode is determined. The frequency responses and the targeted energy transfer (TET) phenomenon of the coupled system are analyzed, and the theoretical and numerical results of the frequency responses of the system are in good agreement with the experimental ones. The effects of the wall impedance of the cavity on the optimal TET are discussed. With the increase in the impedance ratio of the wall, the amplitude of the acoustic displacement plateau decreases, and the frequency bandwidth of the plateau and the two thresholds of the optimal TET interval of the excitation increase. It provides a comprehensive theoretical model and experimental basis for the application of NES in the actual complex structure and provides a reliable design method and control strategy for controlling vehicle interior low-frequency broadband noise.