Nonlinear Numerical Simulations Research Articles

Corrigendum to “The impacts of the individual activity and attractiveness correlation on spreading dynamics in time-varying networks” [Communications in Nonlinear Science and Numerical Simulation, Volume 122, July 2023, 107233]

Corrigendum to “The impacts of the individual activity and attractiveness correlation on spreading dynamics in time-varying networks” [Communications in Nonlinear Science and Numerical Simulation, Volume 122, July 2023, 107233]

Splitting of triply quantized vortices in Bose-Einstein condensates of finite temperature

Abstract Utilizing the dissipative Gross-Pitaevskii equation, we investigated the splitting dynamics of triply quantized vortices at finite temperature. Through linear perturbation analysis, \textcolor{red}{we determined the excitation modes of these vortices across various dissipation parameters. We identified three unstable modes with $p=2, 3, $ and $4$ fold rotational symmetries, } revealing a significant dynamic transition of the most unstable mode. That is, as the dissipation parameter increases, the most unstable mode transitions from $p=2$ mode to $p=3$ mode. Throughout the entire range of dissipation parameters, the $p=4$ unstable mode is never the dominant mode. Subsequently, we performed nonlinear numerical simulations of the vortex splitting process. Under random perturbations, we confirmed the dynamical transition, and under specific perturbations, we confirmed the instability of the $p=4$ mode. Our findings on the finite temperature dependence of the splitting dynamics of triply quantized vortices are expected to be verifiable in experiments.

Breaking onset and breaking strength of focused wave packets: Linear prediction model and nonlinear numerical simulations

The possibility of predicting the occurrence of wave breaking and the intensity of the breaking events using linear wave models is investigated. For this purpose, a new linear breaking onset criterion is proposed, based on the definition of a linear-equivalent wave, which has the same energy and impulse as the associated nonlinear wave. The strength of breaking is characterized by the Γ parameter introduced by Derakhtiet al. (2018) and we derive an empirical law to estimate the breaking strength from the linear-equivalent wave model. The predictive ability of this criterion is assessed through comparisons with results of fully nonlinear potential flow simulations, for focused wave packets of various characteristics. For the considered configurations, the proposed approach is able to predict the onset and strength of breaking with good accuracy.

Experimental and numerical investigation on hyperelastic sealing disc contact behavior in pipeline, a comparison between fluid-driven and pull-through approaches

Pipelines are widely recognized as the safest and most efficient means of fluid transportation. Pipeline pigging, a secure and reliable technique, is employed for both cleaning and sealing pipelines to optimize efficiency. Since pigging operation requires differential pressure (ΔP) to facilitate pig movement, this pressure must correspond to the pipeline's operational conditions. Consequently, studying the required ΔP for sealing discs, which serve as primary sealing elements of pigs, is crucial. The primary focus of this study is to examine the difference between pulling the pig using a cable and propelling it with fluid. Furthermore, the main novelty of this research is to experimentally investigate a single sealing disc and conduct fluid-driven tests on it. To study more precisely, three sealing discs with various thicknesses and the same hardness have been launched into a 6-inch spool test, containing five pipes with different wall thicknesses, resulting in multiple oversize ratios (%OSz). In the experimental study, both fluid-driven and pull-through tests were conducted. The range of discrepancy between two methods varies from 15% to 26% for different oversize ratios which is considerable. Additionally, A 2-D axisymmetric nonlinear numerical simulation was conducted in a finite element software ABAQUS in order to study the behavior of sealing discs. Using a pressure-dependent friction coefficient with the proper hyperelastic model was key to achieving simulations that have good agreements with experimental results, with discrepancy of less than 10 percent in all extracted pressures.

Tracking Evidence of Seismic Damage by Nonlinear Numerical Simulations for Dating in Archaeological Contexts

Tracking Evidence of Seismic Damage by Nonlinear Numerical Simulations for Dating in Archaeological Contexts

Design and Simulation Analysis of Bridge Anti-collision Structure based on Nonlinear Numerical Simulation

In order to solve the dynamic nonlinear problem of bridge loads and responses during ship collisions, a design method for bridge anti-collision structures based on nonlinear numerical simulation was proposed. The author describes in detail the entire process of collision force evolution, energy conversion, and plastic deformation of the anti-collision energy dissipator, and conducts a comprehensive simulation of it. The experimental results show that when a ship with a mass of 1000 tons collides forward at speeds of 1, 3, and 5 meters per second, the collision depth is 0.23, 1.46, and 3.95 meters, respectively, less than the maximum allowable collision depth of 4.3 meters, and the collision energy dissipator is still in the protective working state for the bridge pier. When a ship with a mass of 3000 tons collides with the collision avoidance energy dissipator at a speed of 3 or 5 meters per second, the collision depth exceeds the maximum allowable collision depth, and the collision avoidance energy dissipator fails, the ship will directly collide with the wharf. The plastic deformation of the anti-collision energy dissipator provided has important reference value for design.

Hydrodynamic modulation instability triggered by a two-wave system.

The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in the form of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive media, such as hydrodynamics, optics, plasma, mechanical systems, electric transmission lines, and Bose-Einstein condensates, while its impact on applied sciences is steadily growing. It is well-known that the classical MI dynamics can be triggered when a pair of small-amplitude sidebands are excited within a particular frequency range around the main peak frequency. That is, a three-wave system, consisting of the carrier wave together with a pair of unstable sidebands, is usually adopted to initiate the wave focusing process in a numerical or laboratory experiment. Breather solutions of the nonlinear Schrödinger equation (NLSE) revealed that MI can generate much more complex localized structures, beyond the three-wave system initialization approach or by means of a continuous spectrum. In this work, we report an experimental study for deep-water surface gravity waves asserting that a MI process can be triggered by a single unstable sideband only, and thus, initialized from a two-wave process when including the contribution of the peak frequency. The experimental data are validated against fully nonlinear hydrodynamic numerical wave tank simulations and show very good agreement. The long-term evolution of such unstable wave trains shows a distinct shift in the recurrent Fermi-Pasta-Ulam-Tsingou focusing cycles, which are captured by the NLSE and fully nonlinear hydrodynamic simulations with some distinctions.

Enhancing the overturning resistance capacity of high aspect ratio structure through hybrid base isolation and inter-storey isolation

The high-aspect ratio of structures is usually limited to a small range for base isolation (BI), due to the necessity of ensuring resistance to overturning. This limitation restricts the application of friction pendulum bearings (FPBs) in structures with large high-aspect ratios. This article aims to explore the application of hybrid base isolation and inter-storey isolation (BIISI) in structures with large high-aspect ratio. The theoretical basis of the BIISI was first analyzed in terms of overturning resistance. Subsequently, nonlinear dynamic numerical simulations were conducted on a building with a high aspect ratio to simulate its response subjected to typical pulse-type and non-pulse-type earthquakes. The overturning resistance of the structure and seismic dynamic responses were evaluated. A series of parametric studies were also conducted to investigate the effects of FPB properties, peak ground acceleration (PGA), the friction coefficient ratio and the radius of FPBs between inter-storey isolation storey and base isolation storey on the overturning resistance performance of isolated structures. It is demonstrated that superstructure is meticulously partitioned into two independent sliding structural elements through the BIISI, and it can significantly improve the overturning resistance of buildings with a large high-aspect ratio. PGA and FPB properties show significant differences, but the friction coefficient ratio and the radius of FPBs between the inter-storey isolation storey and base isolation storey show limited influences on the overturning resistance of the structure.

Modelling of non-linear elastic constitutive relationship and numerical simulation of rocks based on the Preisach–Mayergoyz space model

SUMMARY The existence of pores, cracks and cleavage in rocks results in significant non-linear elastic phenomena. One important non-linear elastic characteristic is the deviation of the stress–strain curve from the linear path predicted by Hooke's law. To provide a more accurate description of the non-linear elastic characteristics of rocks and to characterize the propagation of non-linear elastic waves, we introduce the Preisach–Mayergoyz space model. This model effectively captures the non-linear mesoscopic elasticity of rocks, allowing us to observe the stress–strain and modulus–stress relationships under different stress protocols. Additionally, we analyse the discrete memory characteristics of rocks subjected to cyclic loading. Based on the Preisach–Mayergoyz space model, we develop a new non-linear elastic constitutive relationship in the form of an exponential function. The new constitutive relationship is validated through copropagating acousto-elastic testing, and the experimental result is highly consistent with the data predicted by the theoretical non-linear elastic constitutive relationship. By combining the new non-linear elastic constitutive relationship with the strain–displacement formula and the differential equation of motion, we derive the non-linear elastic wave equation. We numerically solve the non-linear elastic wave equation with the finite difference method and observe two important deformations during the propagation of non-linear elastic waves: amplitude attenuation and dispersion. We also observe wave front discontinuities and uneven energy distribution in the 2D wavefield snapshot, which are different from those of linear elastic waves. We qualitatively explain these special manifestations of non-linear elastic wave propagation.

Study on Nonlinear Parameter Inversion and Numerical Simulation in Condensate Reservoirs

The B6 metamorphic buried hill condensate gas reservoir exhibits a highly compact matrix, leading to a rapid decline in bottom-hole pressure during initial production. The minimal difference between formation and saturation pressures results in severe retrograde condensation, with multiphase flow further increasing resistance. Conventional numerical simulations often overestimate reservoir energy supply due to their failure to account for this additional resistance, leading to inaccuracies in bottom-hole pressure predictions and gas–oil ratio during history matching. To address these challenges, this study conducted research on nonlinear numerical simulation for buried hill condensate gas reservoirs and established a method for calculating a multiphase pressure sweep range based on the well testing theory. By correcting and fitting the pressure propagation boundaries with numerical simulation, the nonlinear flow parameters applicable to the B6 gas field were inversed. This study revealed that conventional Darcy flow is inadequate for predicting pressure propagation boundaries and that it is possible to reasonably characterize the pressure sweep range through nonlinear flow. This approach resulted in an improvement in the accuracy of historical matching for bottom-hole pressure and gas–oil ratio, which improve the historical fitting accuracy to 85%, providing valuable insights for the development of similar reservoirs.

Optimization of latching control for duck wave energy converter based on deep reinforcement learning

In the field of wave energy extraction, employing active control strategies amplifies the Wave Energy Converter's (WEC) response to wave motion. In this regard, a numerical simulation study was conducted on the interaction between Duck WEC and waves under discrete latching control, proposing an optimized latching duration strategy based on Deep Reinforcement Learning (DRL). The study utilized an improved Edinburgh Duck model to establish a numerical wave flume (NWF), verifying the motion of waves and the device. A DRL and Computational Fluid Dynamics (CFD) coupled framework was developed to implement the latching control strategy. In the limited trichromatic wave testing conditions provided in this paper, the latching control time is optimized using a DRL agent, and its capture efficiency is compared with two non-predictive latching control strategies. The DRL agent control showed a 13.4% improvement relative to reference threshold control, with less than 6.3% differences compared to optimal threshold latching results. Improvement of approximately 5.6% was observed compared to optimal constant latching control. For the first time in nonlinear fluid dynamics numerical simulation, this study demonstrates the efficacy of model-free reinforcement learning with discrete latching actions, establishing an environment-driven control strategy, and having the potential to become a general strategy for WEC latching control.

Unravelling the operation of organic artificial neurons for neuromorphic bioelectronics

Organic artificial neurons operating in liquid environments are crucial components in neuromorphic bioelectronics. However, the current understanding of these neurons is limited, hindering their rational design and development for realistic neuronal emulation in biological settings. Here we combine experiments, numerical non-linear simulations, and analytical tools to unravel the operation of organic artificial neurons. This comprehensive approach elucidates a broad spectrum of biorealistic behaviors, including firing properties, excitability, wetware operation, and biohybrid integration. The non-linear simulations are grounded in a physics-based framework, accounting for ion type and ion concentration in the electrolytic medium, organic mixed ionic-electronic parameters, and biomembrane features. The derived analytical expressions link the neurons spiking features with material and physical parameters, bridging closer the domains of artificial neurons and neuroscience. This work provides streamlined and transferable guidelines for the design, development, engineering, and optimization of organic artificial neurons, advancing next generation neuronal networks, neuromorphic electronics, and bioelectronics.

Robust-augmentation nonlinear dynamic inversion control of over-actuated coaxial high-speed helicopter in transition mode

As the elevator and rudder can be used actively for control, in addition to the rotors, Coaxial High-speed Helicopters (CHHs) have the problems of control redundancy and changing control authority in the transition mode. This paper presents a robust-augmentation transitioning flight control design for a CHH under the adverse conditions of parametric uncertainties and external disturbances. First, based on control characteristic analysis, an Adaptive Filtered Nonlinear Dynamic Inversion (AFNDI) controller is proposed for the angular rate to handle the effect of unknown unstructured uncertainties and external turbulence. Theoretical analysis proves that the presented angular rate controller can guarantee steady-state and transient performance. Furthermore, the attitude angle and velocity controllers are also added. Then, an Incremental-based Nonlinear Prioritizing Control Allocation (INPCA) method is designed to take into account control surface transition and changing control authority, which efficiently distributes the required moments between coaxial rotors and aero-surfaces, and avoids the control reversal problem of the yaw channel. In the proposed control architecture, the low-pass filter is introduced to alleviate the adverse influence of time delay and measurement noise. Finally, the effectiveness of the proposed controller is demonstrated through nonlinear numerical simulations, and is compared with existing methods. Simulation results show that the proposed control law can improve both capabilities of disturbance rejection and fast response, and works satisfactorily for the CHH transitioning control characteristic.

Enhanced gas-lift system operation using LPV nonlinear model predictive control

In this work, we propose a novel Linear Parameter Varying (LPV) Model Predictive Control (MPC) scheme for oil production maximisation in wells operated with gas-lift systems. The control of a gas-lift system poses several engineering challenges, including the nonlinear nature of its behaviour and different kinds of process constraints. Recent studies indicate that MPC strategies stand out as promising solutions to address many of these issues — with results already published for gas-lift applications. However, when nonlinear models are used, the corresponding nonlinear MPC (NMPC) algorithms entail substantial computational costs, potentially complicating the feasibility of (real-time) embedded implementation. Furthermore, certain complexities in standard gas-lift system representations hinder the use of typical NMPC solvers (e.g. CasADi), thus making approximation-based schemes unavoidable. Accordingly, we propose an LPV formulation to describe the gas-lift system that ensures closed-loop stability and recursive feasibility when implemented as a model for MPC. In this regard, we synthesise an LPV MPC scheme and compare it to an NMPC through CasADi. Several realistic nonlinear numerical simulations are presented and our results indicate that the proposed LPV MPC scheme, in addition to being three times faster (in average), achieved an increase in the total amount of produced oil when compared to an NMPC via CasADi. Then, aiming to maximise oil production rate, we introduce a modified version of the LPV MPC approach, resulting in an increase in the total amount of produced oil of approximately 3% in the studied scenario, when compared to the unmodified LPV MPC scheme.

A study of nonlinear fractional-order biochemical reaction model and numerical simulations

This article depicts an approximate solution of systems of nonlinear fractional biochemical reactions for the Michaelis–Menten enzyme kinetic model arising from the enzymatic reaction process. This present work is concerned with fundamental enzyme kinetics, utilised to assess the efficacy of powerful mathematical approaches such as the homotopy perturbation method (HPM), homotopy analysis method (HAM), and homotopy analysis transform method (HATM) to get the approximate solutions of the biochemical reaction model with time-fractional derivatives. The Caputo-type fractional derivatives are explored. The proposed method is implemented to formulate a fractional differential biochemical reaction model to obtain approximate results subject to various settings of the fractional parameters with statistical validation at different stages. The comparison results reveal the complexity of the enzyme process and obtain approximate solutions to the nonlinear fractional differential biochemical reaction model.

Generation of diurnal internal solitary waves (ISW-D) in the Sulu Sea: From geostationary orbit satellites and numerical simulations

Our recent study reported the existence of internal solitary waves with the diurnal tidal cycle (ISW-D) in the Sulu Sea, however, the three-dimensional characteristics and generation mechanism of ISW-D are still unclear (Huang et al., 2023). In this work, the spatial–temporal characteristics, generation mechanism and propagating process of ISW-D in the Sulu Sea are first preliminary investigated based on high-temporal-resolution Geostationary Orbiting Satellite (GOS) images and high-spatial-resolution two-dimensional numerical model (MITgcm). GOS images from 2018-2022 are retrieved and a total of 13 pairs of ISW-D packets are found. ISW-D occur at spring tide during May–August, with an average interpacket distance of 198 km and a phase speed of 2.30 m/s. To further knowledge of the generation mechanism and propagation process of ISW-D, the non-linear and non-hydrostatic numerical simulations are conducted. The comparison of ISW-D parameters with GOS images proves the validity of numerical simulations. The results of numerical simulations and theoretical parameters indicate that ISW-D are generated at the sill near Pearl Bank by internal tide release mechanism. Moreover, three sensitivity experiments are designed to investigate the effects of tidal force and seawater stratification on the generation and propagation of ISW-D. The results reveal that the ISW-D is generated by diurnal tides with stronger intensity than semidiurnal tides. Seawater stratification does not influence the generation of ISW-D but modulates the propagation process. Phase speeds from GOS images and theoretical model show a positive correlation between the phase speeds of ISW-D and the intensity of seawater stratification.

Theoretical and numerical study on the bond behavior between reinforcing steel and concrete

The bond-slip interaction between reinforcing steel and concrete plays a crucial role in transferring stress and the synergistic mechanical behavior of reinforced concrete members. Based on the interface tensile mechanism of reinforcing steel and concrete, a novel simple bond-slip model was developed to consider the tensile fracture behavior of the interface in different stress stages. According to the influencing factors including concrete strength, cover thickness, reinforcing steel rib spacing, stirrup arrangements, reinforcing steel diameter and anchorage length, characteristic points are established. The results show that the calculated results of this model agree well with the experimental results under monotonic loading. Finally, the different stages of slip behavior are simulated with the elastic, plastic and damage behavior of the connector elements according to a three-dimensional modeling method. Comparisons that were performed between the nonlinear numerical simulations and theoretical results have clearly shown that the connector element can predict the interface behavior of reinforcing steel and concrete.

A set of calculation tools supporting the design, modelling and application of plywood-based seismic retrofitting interventions on timber floors in existing buildings

The application of timber-based strengthening solutions to existing wooden and masonry structures, combines several benefits, such as reversibility, compatibility, lightness, sustainability, affordability, and effectiveness. With reference to existing timber floors, an efficient method to enhance their seismic response is the fastening of an overlay of plywood panels to the existing sheathing, an intervention that greatly improves in-plane strength, stiffness, and energy dissipation. In order to promote the use of this retrofitting solution in practice, this work presents a set of calculation tools supporting the design and advanced numerical modelling of timber diaphragms strengthened with plywood panels. The suite of tools allows to first estimate the full nonlinear, cyclic in-plane response of the strengthened diaphragms starting from the geometrical and material properties of the existing sheathing and the plywood overlay, as well as the mechanical characteristics of the fasteners. As second step, such estimated in-plane response can be transformed into a constitutive law for performing nonlinear numerical simulations, by means of a user-supplied subroutine developed for finite element software DIANA FEA. The presented calculation examples and the performed validation against reference studies from literature, show that the developed tools can provide an accurate estimate of the in-plane response of the diaphragms, and enable an efficient numerical simulation of their seismic behaviour. The implemented tools can be used to both obtain preliminary indication for plywood-based seismic retrofitting design, and to calibrate the interventions on existing diaphragms based on the specific characteristics and needs of a building, relying on the adaptability and versatility of this strengthening method.

Trade Off between Hydrodynamic and Thermodynamic Forces at the Liquid-Liquid Interface.

Viscous fingering (VF) instability has been investigated in the case of a partially miscible binary system by nonlinear numerical simulations. Partially miscible fluid systems offer the possibility of phase separation coupled with VF instability. The thermodynamics of such systems are governed by the Margules parameter (interaction parameter) as well as the fluid concentrations. Kinetics of the decomposition is also influenced by dynamical parameters such as the viscosity of the fluid, which incidentally also affects the hydrodynamic forces. Here, we explore the effects of concentration and Margules parameter in order to ascertain the trade-offs incurred between hydrodynamic and thermodynamic effects at the interface as well as the thermodynamics of the bulk. Based on the Gibb's free energy versus concentration curve, we select concentrations (i) outside spinodal and binodal regions, (ii) within binodal but outside the spinodal, and (iii) within the spinodal curve. We solve the modified Cahn-Hilliard-Hele-Shaw equation employing the COMSOL Multiphysics software. Applying high-resolution numerical simulations, we show a strong dependence of the thermodynamic forces on the concentration of the mixtures. Rapid phase separation and hence a faster rate of droplet formation have been found when the concentration lies inside the spinodal region. Further, we have investigated the correlation between the fractal dimension and dynamics of the system. The spatiotemporal studies presented in this work clearly illustrate the competition between hydrodynamic and thermodynamic forces and provide insights on the kinetics of decomposition and growth of interfacial instabilities.

Self-propulsion of a droplet induced by combined diffusiophoresis and Marangoni effects.

Chemically active droplets display complex self-propulsion behavior in homogeneous surfactant solutions, often influenced by the interplay between diffusiophoresis and Marangoni effects. Previous studies have primarily considered these effects separately or assumed axisymmetric motion. To understand the full hydrodynamics, we investigate the motion of a two-dimensional active droplet under their combined influences using weakly nonlinear analysis and numerical simulations. The impact of two key factors, the Péclet number ( ) and the mobility ratio between diffusiophoretic and Marangoni effects ( ), on droplet motion is explored. We establish a phase diagram in the space, categorizing the boundaries between four types of droplet states: stationary, steady motion, periodic/quasi-periodic motion, and chaotic motion. We find that the mobility ratio does not affect the critical for the onset of self-propulsion, but it significantly influences the stability of high-wavenumber modes as well as the droplet's velocity and trajectory. Scaling analysis reveals that in the high regime, the Marangoni and diffusiophoresis effects lead to distinct velocity scaling laws: and , respectively. When these effects are combined, the velocity scaling depends on the sign of the mobility ratio. In cases with a positive mobility ratio, the Marangoni effect dominates the scaling, whereas the negative diffusiophoretic effect leads to an increased thickness of the concentration boundary layer and a flattened scaling of the dropletvelocity.