Nonlinear Conduction Research Articles

Modeling the Inception and Stepped Propagation of Upward Positive Lightning Leaders

AbstractPositive lightning leaders are a ubiquitous, yet poorly understood, component of lightning flashes. Upward lightning started by positive leaders may be formed when nearby storm activity induces electrical charges in a tall structure, such as communications towers or wind turbines. Alternatively, upward lightning can be triggered with the rocket‐and‐wire technique. In this paper, we introduce a new self‐consistent model for this important discharge mode, one which solves Maxwell's equations under the quasi‐electrostatic approximation. The model also includes a realistic treatment of the nonlinear plasma conductivity within the leader channel. This new computational tool explains the origin of the positive leader speed, of 10s of km/s, as well as why it displays a steady behavior over time. The model also explains the temporal evolution of current to ground measured during the early stages of rocket‐triggered lightning, where the current exhibits a series of small‐amplitude pulses, which disappear over time. The article also outlines straightforward criteria for leader inception, which may have practical applications for lightning protection.

Nonlinear conductivity of aqueous electrolytes: Beyond the first Wien effect.

The conductivity of strong electrolytes increases under high electric fields, a nonlinear response known as the first Wien effect. Here, using molecular dynamics simulations, we show that this increase is almost suppressed in moderately concentrated aqueous electrolytes due to the alignment of the water molecules by the electric field. As a consequence of this alignment, the permittivity of water decreases and becomes anisotropic, an effect that can be measured in simulations and reproduced by a model of water molecules as dipoles. We incorporate the resulting anisotropic interactions between the ions into a stochastic density field theory and calculate ionic correlations as well as corrections to the Nernst-Einstein conductivity, which are in qualitative agreement with the numerical simulations.

Flexible TiO2-WO3−x hybrid memristor with enhanced linearity and synaptic plasticity for precise weight tuning in neuromorphic computing

Tungsten oxide (WO3)-based memristors show promising applications in neuromorphic computing. However, single-layer WO3 memristors suffer from issues such as weak memory performance and nonlinear conductance variations. In this work, a functional layer based on the hybrids of WO3−x and TiO2 is proposed for constructing flexible memristors featuring outstanding synaptic characteristics. Applying diverse electrical stimulations to the memristor enables a range of synaptic functions, elucidating its conduction mechanism through the conductive filament model. The incorporation of TiO2 not only enhances the memristor’s memory characteristics but makes its conductance more linear, symmetrical and uniform during the long-term changes. Furthermore, in view of the enhanced device performance by TiO2 doping, the potential of this device for simple behavioral simulation and processing of complex computing problems is explored. The “learning-forgetting-relearning” characteristics and device integrability are visually demonstrated. Applying the device to a convolutional neural network, the recognition accuracy of MNIST handwritten digits reaches 98.7%.

Self‐Powered Wearable Pressure Sensors for Detection and Separation of Signals for Various Human Movements

A detailed study on the dynamic response of mountable pressure sensors is presented, with a focus on foot pressure sensors integrated with carbon nanotube (CNT)‐coated cotton fibers. The research explores the sensor's sensitivity to pressure changes, repeatability, hysteresis, and durability through rigorous modeling and experimental validation. Computational simulations using Python and experimental data demonstrate the sensor's nonlinear conductance response to applied force, attributed to the varying contact area and number of contact points among the fibers. Long‐term outdoor exposure tests confirm the material's resilience, maintaining electrical conductivity and structural integrity. The study also demonstrates the sensor's ability to monitor human activities like walking, running, stair climbing, and jumping, as well as detecting muscle movements during swallowing, coughing, and speech, highlighting potential applications in health monitoring and artificial voice synthesis. The MRMR algorithm is used for feature selection to distinguish activities, demonstrating the sensor's potential for activity recognition. Additionally, a piezoelectric sensor on the pressure sensors estimates harvested electric power to power wearable devices. This work contributes to the advancement of self‐powered wearable pressure sensors to monitor real‐time human activity, with implications for healthcare, sports performance, and assistive technologies.

Linearly programmable two-dimensional halide perovskite memristor arrays for neuromorphic computing.

The exotic properties of three-dimensional halide perovskites, such as mixed ionic-electronic conductivity and feasible ion migration, have enabled them to challenge traditional memristive materials. However, the poor moisture stability and difficulty in controlling ion transport due to their polycrystalline nature have hindered their use as a neuromorphic hardware. Recently, two-dimensional (2D) halide perovskites have emerged as promising artificial synapses owing to their phase versatility, microstructural anisotropy in electrical and optoelectronic properties, and excellent moisture resistance. However, their asymmetrical and nonlinear conductance changes still limit the efficiency of training and accuracy of inference. Here we achieve highly linear and symmetrical conductance changes in Dion-Jacobson 2D perovskites. We further build a 7 × 7 crossbar array based on analogue perovskite synapses, achieving a high device yield, low variation with synaptic weight storing capability, multi-level analogue states with long retention, and moisture stability over 7 months. We explore the potential of such devices in large-scale image inference via simulations and show an accuracy within 0.08% of the theoretical limit. The excellent device performance is attributed to the elimination of gaps between inorganic layers, allowing the halide vacancies to migrate homogeneously regardless of grain boundaries. This was confirmed by first-principles calculations and experimental analysis.

Neural network-augmented differentiable finite element method for boundary value problems

Classical numerical methods such as finite element method (FEM) face limitations due to their low efficiency when addressing large-scale problems. As a novel paradigm, the physics-informed neural network (PINN) has demonstrated significant potential to solve partial differential equations. However, conventional PINNs utilize meshless control at discrete sampling points, which limits their ability to effectively handle complex boundaries. Moreover, catastrophic failure may occur in the deep energy method (DEM, a specific type of PINN). To handle these challenges, this study proposes a Neural Network-augmented Differentiable Finite Element Method (NNDFEM) by combining PINN and finite element approximation. In NNDFEM, the neural network backend solely predicts nodal variables. Derivatives and complex boundary conditions can be well handled by the finite element frontend. The governing equation over the domain, Dirichlet, and Neumann boundary conditions are directly enforced on the finite element frontend. Thus, losses of boundary conditions in PINN are rendered unnecessary. The overfitting problem in DEM is also significantly mitigated. Fully connected neural network (FCNN), modified FCNN, and graph-convolutional network are tested as backends. NNDFEM circumvents nodal force calculation and matrix assembly in FEM. Functional losses of linear elasticity, finite strain nonlinear elasticity, heat conduction, and flow in porous media are validated. A systematic exploration unveils the role of 3D finite element mesh. For large-scale problems, a multi-fidelity learning strategy is employed. Thus, the three-dimensional case with over three million degrees of freedom trains well in two minutes. Benefiting from the fast inference of the neural network backend, the forward pass is 8,550 times faster than FEM.

Nonlinear dielectric response and conductivity characteristics of epoxy resin in high voltage AC electric field

Abstract High-voltage dielectric and AC conduction behaviors of epoxy resin (EP) insulation are beneficial for the design and application of solid-state power electronic devices. This study investigates the nonlinear dielectric response and AC conduction characteristics of EP. The dielectric relaxation characteristics, including permittivity and AC conductivity of the EP samples, were investigated using high-voltage dielectric spectroscopy and the ionic polarization model. The results demonstrate a nonlinear increase in the relative permittivity and AC conductivity concerning the AC electric field. The increase in AC conduction under a high-frequency electric field is attributed to the reduction in the threshold field for charge injection caused by elevated temperatures. Considering the dielectric response and carrier hopping, it is evident that the nonlinear dielectric response of EP primarily originates from the ionic process under high electric fields. Ionic polarization, in conjunction with ion-hopping conduction, enhances the dielectric loss at high frequencies and electric fields, thereby facilitating the nonlinear conversion of AC conduction. The equivalent free volume is likely to increase in high-frequency fields. This phenomenon leads to an increase in AC conduction and even dielectric breakdown. This study offers a pivotal theoretical framework for the design and application of high-frequency insulation.

Thermodynamic Calculations of the Main Characteristics of the Combustion Process of Pyrotechnic Nitrate-Metallized Mixtures with Additives of Organic and Inorganic Substances under External Thermal Influences

The aim of the article is to determine the dependencies of the combustion product temperatures of four-component mixtures, the content of high-temperature condensate, and unoxidized metal on the excess oxidizer coefficient, the number of additives, and external pressure using thermodynamic calculations. Modern methods of physicochemical analysis (such as cinephotography and microcinephotography methods, X-ray analysis methods, non-contact and contact temperature measurement methods), nonlinear thermal conductivity and thermal stability methods, as well as mathematical and experimental-statistical modeling, were employed to investigate the influence of elevated heating temperatures (up to 800 K) and external pressures (up to 107 Pa) on the ignition and combustion processes of pyrotechnic products. Standard pyrotechnic equipment was used to test pyrotechnic product samples under specified conditions. Calculations based on models were conducted in real-time and dialog mode on computer devices that meet modern requirements for the use of specialized software. The results of thermodynamic calculations are presented for the dependencies of combustion product temperatures of multicomponent pyrotechnic mixtures based on powders of metal fuels (magnesium, aluminium), nitrate oxidizer (sodium nitrate), additives of organic and inorganic substances (paraffin, sodium fluoride), and the content of high-temperature condensate and unoxidized metal depending on the excess oxidizer coefficient α = 0.1…4.0, the amount of paraffin additive εp = 0…0.2, sodium fluoride additive εf = 0…0.06, and external pressure P = 105…107 Pa. Based on the obtained results of thermodynamic calculations, statistical models in the form of regression dependencies of the specified combustion characteristics on their technological parameters and external conditions have been developed. These models enable the determination of fire hazardous properties of mixtures in real-time dialog and PC-based scenarios, considering premature initiation of products based on them under external thermal actions.

Microscopic analysis of relaxation behavior in nonlinear optical conductivity of graphene

We produce a general formalism to study the interband dynamical optical conductivity in the nonlinear regime of graphene in the presence of a quantum bath comprising phonons and electrons. When a quantum solid of graphene is subjected to an intense electric field in the optical frequency range, the observation of a nonlinear response is facilitated by formulating a quantum master equation of the density operator associated with the Hamiltonian encapsulated in a spin-boson model of dissipative quantum statistical mechanics. Our results reveal the nonlinear steady-state regime’s population inversion and decoherence. The present method enables us to investigate further the nonlinear interband optical conductivity of pristine and gapped graphene characterized by a single dimensionless parameter at finite temperatures. Different bath spectra’ effects on phonons and electrons are examined in detail. The temperature dependence of conductivity reveals that changing temperature can enable us to make a transition from the linear to the nonlinear regime for fixed optical field parameters. Interestingly, a fascinating switching-like behavior is observed for the low-temperature optical conductivity of the gapped graphene while we vary the energy gap as well as the frequency of the externally applied field. Although our general formulation can address a variety of nonequilibrium responses of the two-band system, it also facilitates a connection with the phenomenological modeling of nonlinear optical conductivity.

In-plane electrical conductivity of PEDOT:PSS/Halloysite composite thin films

PEDOT:PSS has found numerous applications in the field of advanced materials, especially in the development of organic electronics. Embedding nanoparticles into the polymer matrix has emerged as an effective strategy to modify the properties of PEDOT:PSS and develop advanced functional composites. Over the past decade, Halloysite nanotubes (HNT) have garnered significant interest and utility as nanofillers and/or templates due to their unique physical-chemical properties, small size, relatively low cost, and large availability. Interestingly, pairing PEDOT:PSS with non-conductive HNT has been demonstrated to enhance the charge transport properties of the composite film. Our discoveries show how the HNT can act as scaffolding for PEDOT:PSS by improving the local ordering of PEDOT chains and enabling the formation of conductive pathways. Consequently, the mechanism responsible for the observed changes in conductivity and the correlation between PEDOT:PSS and insulating nanofillers (HNT) could be different to that previously proposed. Hence, in this work it was observed that PEDOT:PSS/HNT composite films exhibited a non-linear conductivity dependence as a function of the HNT loading. From thermogravimetric analysis, infrared and UV-Vis-NIR spectroscopies, as well as impedance spectroscopy, a more complex interaction between the polymer chains and the nanotubes is revealed. Our study includes the modification of the interaction between the PEDOT chains and the nanofillers by using the secondary doping effect and functionalization of the nanotubes, which confirms our findings. These results represent a significant progress toward a deeper understanding of the emergence of a conductive polymer network on the nanofiller surface, leading to improvements in the electrical conductivity in the composite material.

Застосування методу двобічних наближень до розв’язання першої крайової задачі для одновимірного рівняння теплопровідності з експоненціально нелінійним коефіцієнтом теплопровідності

The problem of heat conduction in nonlinear media reduces to solving boundary value problems for nonlinear heat conduction equations, where the coefficients of the equation or the function of the power of heat sources depend on temperature according to some law. Among the numerical methods for solving problems for nonlinear equations of mathematical physics, one can distinguish finite difference methods, finite element methods, variational and projection methods, as well as iterative methods. Among the latter group, the two-sided approximation method is particularly attractive due to its ability to provide a convenient estimate for the error of the approximate solution and to prove the existence of a solution to the original problem. The theory of linear partially ordered spaces was developed by L. V. Kantorovich in the second half of the 1930s. Further development of this theory is associated with the works of M. A. Krasnosel’skii, H. Amann, V. I. Opojtsev, N. S. Kurpel, B. A. Shuvar, A. I. Kolosov etc. The aim of this article is to develop a two-sided approximation method based on the use of Green's functions for solving the first boundary value problem for a one-dimensional nonlinear heat conduction equation and to investigate its performance when solving test problems. To achieve this goal, the unknown function was replaced, and the boundary value problem was reduced to a Hammerstein integral equation, which was considered as a nonlinear operator equation in a partially ordered Banach space. Conditions for the existence of a unique positive solution to the problem and conditions for two-sided convergence of successive approximations to it were obtained. The developed method was implemented in software and tested on solving test problems. The results of the computational experiment are illustrated with graphical and tabular information

Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems

This study introduces an innovative neural network framework named spectral integrated neural networks (SINNs) to address both forward and inverse dynamic problems in three-dimensional space. In the SINNs, the spectral integration technique is utilized for temporal discretization, followed by the application of a fully connected neural network to solve the resulting partial differential equations in the spatial domain. Furthermore, the polynomial basis functions are employed to expand the unknown function, with the goal of improving the performance of SINNs in tackling inverse problems. The performance of the developed framework is evaluated through several dynamic benchmark examples encompassing linear and nonlinear heat conduction problems, linear and nonlinear wave propagation problems, inverse problem of heat conduction, and long-time heat conduction problem. The numerical results demonstrate that the SINNs can effectively and accurately solve forward and inverse problems involving heat conduction and wave propagation. Additionally, the SINNs provide precise and stable solutions for dynamic problems with extended time durations. Compared to commonly used physics-informed neural networks, the SINNs exhibit superior performance with enhanced convergence speed, computational accuracy, and efficiency.

Evaporated Copper‐Based Perovskite Dynamic Memristors for Reservoir Computing Systems

AbstractDynamic memristors are considered as the optimal hardware devices for reservoir computing (RC) enabled by their nonlinear conductance variations. This significantly reduces the extensive training workload typically required by traditional neural networks. Lead halide perovskites, with their tunable band structure and active ion migration properties, have emerged as highly promising materials for developing dynamic memristors. However, large‐scale and consistently stable production remains a challenge for perovskite functional films, while lead elements' toxicity and environmental impact also partly restrict their practical device utilization. In this work, lead‐free copper‐based perovskite (i.e., CsCu2I3) films are prepared by thermal evaporation for constructing dynamic memristors. The effective conductivity modulation of CsCu2I3‐based memristor can be utilized in artificial neural networks, achieving a high handwritten digit recognition accuracy of 91.2%. In addition, the RC system is also constructed based on the dynamic behavior of the devices, by which a letter recognition accuracy of 98.2% with simple training is achieved. This technology provides a feasible pathway to construct copper‐based perovskite dynamic memristors for future neural network information processing.

Formation of Conjugated Polymer Monolayer Networks on Water Surface and Nonlinear Charge Transport

AbstractMaterial‐networked conduction paths provide nonlinear electronic properties, which are essential components of computing and physically mimic the brain. In this study, the formation of conjugated polymer monolayer networks and their nonlinear charge transport is demonstrated. Poly(3‐hexylthiophene) (P3HT) monolayer networks doped with 2,3,5,6‐tetrafluoro‐7,7,8,8‐tetracyanoquinodimethane (F4TCNQ) is fabricated using the co‐spread method with an amphiphilic liquid crystal molecule at the air–water interface. Atomic force microscopy and Ultraviolet–visible–near‐infrared absorption spectroscopy measurements reveal the network surface morphologies and doped electronic states. The correlation between the nonlinear electronic characteristics and network structures of the P3HT/F4TCNQ monolayer networks is further systematically investigated through current–voltage and voltage–time measurements for various doping levels, network densities, and numbers of transferred layers. The current–voltage characteristics of the P3HT/F4TCNQ monolayer network device with a simple two‐terminal structure exhibit nonlinear and ohmic conduction behavior, which depend strongly on the network density and geometric dimension (number of transferred layers). It is concluded that the nonlinear properties arise from the limited and unique network of 2D conduction passes. This study highlights the unique features of conducting polymer monolayer networks, paving the way for neuromorphic device applications including conjugated semiconducting polymer‐based material reservoirs with controllable nanostructures.

Solution of the plane thermoelasticity problems based on a new set of equations

The interaction of thermal and mechanical fields in modern technologies for the synthesis and processing of materials attracts more and more attention. This is due to the need to predict the behavior and properties of new materials and products depending on the conditions of their creation. In the present work, attention is focused on the comparison of the solutions to the thermoelasticity plane problems with and without accounting for the temperature dependence of the material properties. It is assumed that an external heat source traveling over the surface with a specific velocity and following a given trajectory is responsible for a significant temperature increase. It may correspond to a laser source, for example. The new way of problem formulation in stresses is used. The temperature dependence of the characteristics leads to nonlinear thermoelasticity equations when the equilibrium equations, the requirement of strain compatibility, and the Duhamel-Neuman relation for the plane stress state case are combined. To determine the temperature field, a nonlinear thermal conductivity equation is used. To solve the problem numerically, the use of an implicit finite-difference scheme and coordinate splitting for the thermal conductivity equation and the finite-difference method of successive over-relaxation with Chebyshev acceleration for the equations for stresses was made. As a result, the difference in the solution of linear and nonlinear problems is demonstrated for the considered cases. Using the example of a mixture of titanium and aluminum powders, numerical modeling demonstrated that some stress components can reach values up to 3.5 times higher than those obtained in the case of temperature-independent material properties when there is a 500-degree local temperature increase.

Modeling methods in overlapping electroporation treatments: Pulse number effects on tissue conductivity and ablation area

Irreversible electroporation (IRE) is a non-thermal tissue ablation technique that utilizes high-voltage pulses between electrode pairs to destroy tissue. Numerical models are essential for predicting treatment outcomes and aiding in treatment planning. This paper studies a nonlinear conductivity model (NC) and a multiparametric nonlinear conductivity model (MPNC) to investigate overlapping electroporation treatments using a three-needle electrode configuration. The NC model accounts for the effects of the electric field and temperature on tissue conductivity during multiple pulsed electric field applications. The MPNC model incorporates the influence of pulse number, alongside electric field and temperature, on tissue conductivity. Results indicate that in the MPNC model, tissue conductivity is significantly higher in regions where the electric field intensity is below the threshold for irreversible electroporation, with the maximum difference reaching 0.4S/m. In contrast, tissue conductivity is slightly lower in regions where the electric field intensity exceeds the IRE threshold. Additionally, the MPNC model predicts a smaller area of irreversible electroporation and a larger area of reversible electroporation, with these differences becoming more pronounced as the distance between electrode needles increases. These findings underscore the importance of considering pulse number effects in numerical models to enhance the accuracy of treatment planning for irreversible electroporation-based therapies.

Improving the optical properties of magnesium spinel chromites through Ni and Cu substitutions for optoelectronic applications.

In this study, we investigated the optoelectronic performance of magnesium spinel chromites with nickel (Ni) and copper (Cu) substitutions. Using the sol-gel method, we synthesized two spinel chromites: Mg0.6Ni0.4Cr2O4 (MNCO) and Mg0.6Cu0.4Cr2O4 (MCCO). We extensively characterized these samples to analyze their thermal, structural, elastic, and optical properties. Structural analysis reveals good agreement between the calculated and refined structural parameters, which supports the proposed cation distributions for the samples. By calculating stiffness constants from force constants, we derived elastic moduli such as bulk modulus, longitudinal modulus, and rigidity modulus. MCCO exhibited lower values for these moduli, as well as the Debye temperature, compared to MNCO. Both samples displayed a brittle mechanical nature according to the Pugh ratio, while the Poisson ratio remained constant at 0.25, indicating isotropic elasticity. UV-vis-NIR spectroscopy revealed that MNCO has higher band-gap (E g) and Urbach (E u) energies than MCCO. Further analysis of refractive index, penetration depth, extinction coefficients, nonlinear optical parameters, optical conductivity, and optical dielectric constants highlighted the promising optoelectronic applications of the synthesized materials. Our study found that the band-gap energy values of the as-synthesized samples were smaller than reported values for MgCr2O4 spinel chromites, indicating that Ni and Cu substitutions offer an opportunity to extend the sunlight absorption range of magnesium chromites.

The mechanism of tuning filler orientation degree in composites based on AC electric field assist: from microscopic dynamical model to macroscopic electrical properties

Using the AC electric field to induce the orientation of nonlinear conductive fillers in composites is an effective solution for alleviating electric field distortion in power modules. However, the mechanism by which the electric field affects the filler dynamic characteristics and the composites’ electrical properties remains unclear. In this paper, the correlation between the microscopic dynamic processes of fillers and the macroscopic current amplitude was analyzed. The results show that the current increases rapidly (0 ∼ 173 s) and then slowly (173 ∼ 869 s) at 600 V mm−1, influenced by the rotation and attraction processes of the fillers. This demonstrates that the orientation stops at about 869 s and the filler orientation state is a key factor in determining the dielectric properties. Secondly, the global orientation evaluation index D for the filler network was proposed, which can also derive the minimum time and energy loss required for preparation. Finally, the impact of different filler orientations on the composites’ conductivity was investigated. In the low electric field stress region, with the average carrier jump distance decreasing from 150.23 to 109.71 nm as the D increases from −0.93 to −0.05. On this basis, materials with nonlinear conductivity gradient distribution can be easily prepared. Before optimization, the electric field stress of the power module at the triple point was 35.79 kV. This composite can reduce the value to 15.42 kV, a decrease of 56.9%, while maintaining good electric field uniformity.

A hybrid shape functions based temporal finite element method to solve transient heat conduction problems

A novel temporal finite element method is presented to solve Fourier and non-Fourier heat conduction problems. Two kinds of temporal finite element models are developed using Gurtin variational principle and weighted residual technique, respectively. A kind of hybrid shape function with polynomial and trigonometric basis is stressed to give more flexible and appropriate description of temporal behavior of temperature. A recursive algorithm is developed by which the temperature solution at a specific time can be obtained only via a matrix power product with the initial condition, and a criterion of stability analysis is derived, which is can numerically be conducted when the constitution of shape function and time step size are prescribed. The proposed approach is available for Fourier and non-Fourier heat transfer problems, and can conveniently be combined with well-developed numerical algorithms for the boundary value problem, such as FE, SBFEM, etc. Various numerical examples, including those with the nonlinear thermal conductivity, radiative boundary condition, etc. are provided to illustrate the efficiency of proposed approaches, and impacts of the temporal FE model, constitution of shape functions, and step size, etc. are taken into account. Satisfactory results are achieved in comparison with the analytical and the ABAQUS based numerical solutions.

Chiral orbital texture in nonlinear electrical conduction

Chiral orbital texture in nonlinear electrical conduction