Nonlinear Interaction Research Articles

Heteroclinic dynamics in network dynamical systems with higher-order interactions

Abstract Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.

Application of Stacked Ensemble Techniques for Classifying Recurrent Head and Neck Squamous Cell Carcinoma Prognosis

A feature selection technique should, in theory, be able to reliably extract pertinent features, identify non-linear feature interactions, scale linearly with the number of features and dimensions, and permit the integration of known sparsity structure. Identifying a machine learning algorithm that performs best given varied distributions may be quite challenging because not all machine learning algorithms are equally created, even though many of them suit very well for a given task. The heterogeneous ensemble feature selection (HETR-EFS) technique learns to combine the feature subsets provided by base feature selectors in an ensemble. Similarly, the stacked ensemble (SE) technique learns how to best combine base classifier models to form a strong model. As a prognostic model for classifying Head and Neck Squamous Cell Carcinoma {HNSCC} recurrence patterns, this study sought to identify the combination of SE classification model and EFS technique that fit optimally when the same ML classifiers for EFS and SE learning are used. Four SE classification models; in which first one used two base classifiers: gradient boosting machine (GBM) and distributed random forest (DRF); second one used three base classifiers: GBM, DRF, and deep neural network (DNN); third one used four base classifiers: GBM, DRF, DNN, and generalized linear model (GLM); and fourth one used five base classifiers: GBM, DRF, DNN, GLM, and Naïve bayes (NB), were developed based on various EFS techniques, using GBM meta-classifier in each case. The results showed that implementing SE technique consisting of five base classifiers on heterogeneous ensemble feature (HETR-EF) subset achieved better performance than achieved on other EF subsets and implementing this SE technique on HETR-EFs achieved better performance compared to other SE techniques implemented on HETR-EFs and other feature subsets used. Thus, learning SE technique having five base classifiers on HETR-EFs is clinically appropriate as a prognostic model for classifying and predicting HNSCC patients’ recurrence data.

Machine learning methods for the modelling and optimisation of biogas production from anaerobic digestion: a review.

Biogas plant operators often face huge challenges in the monitoring, controlling and optimisation of the anaerobic digestion (AD) process, as it is very sensitive to surrounding changes, which often leads to process failure and adversely affects biogas production. Conventional implemented methods and mechanistic models are impractical and find it difficult to model the nonlinear and intricate interactions of the AD process. Thus, the development of machine learning (ML) algorithms has attracted considerable interest in the areas of process optimization, real-time monitoring, perturbation detection and parameter prediction. This paper provides a comprehensive and up-to-date overview of different machine learning algorithms, including artificial neural network (ANN), fuzzy logic (FL), adaptive network-based fuzzy inference system (ANFIS), support vector machine (SVM), genetic algorithm (GA) and particle swarm optimization (PSO) in terms of working mechanism, structure, advantages and disadvantages, as well as their prediction performances in modelling the biogas production. A few recent case studies of their applications and limitations are also critically reviewed and compared, providing useful information and recommendation in the selection and application of different ML algorithms. This review shows that the prediction efficiency of different ML algorithms is greatly impacted by variations in the reactor configurations, operating conditions, influent characteristics, selection of input parameters and network architectures. It is recommended to incorporate mixed liquor volatile suspended solids (MLVSS) concentration of the anaerobic digester (ranging from 16,500 to 46,700mg/L) as one of the input parameters to improve the prediction efficiency of ML modelling. This review also shows that the combination of different ML algorithms (i.e. hybrid GA-ANN model) could yield better accuracy with higher R2 (0.9986) than conventional algorithms and could improve the optimization model of AD. Besides, future works could be focused on the incorporation of an integrated digital twin system coupled with ML techniques into the existing Supervisory Control and Data Acquisition (SCADA) system of any biogas plant to detect any operational abnormalities and prevent digester upsets.

Numerical investigation of effective nonlinear coefficient model for coupled third harmonic generation

In this paper, the optimal solution of effective nonlinear coefficient of quasi-phase-matching (QPM) crystals for coupled third harmonic generation (CTHG) was numerically investigated. The effective nonlinear coefficient of CTHG was converted to an Ising model for optimizing domain distributions of aperiodically poled lithium niobate (APPLN) crystals with lengths as 0.5 mm and 1 mm, and fundamental wavelengths ranging from 1000 nm to 6000 nm. A method for reconstructing crystal domain poling weight curve of coupled nonlinear processes was also proposed, which demonstrated the optimal conversion ratio between two coupled nonlinear processes at each place along the crystal. In addition, by applying the semidefinite programming, the upper bound on the effective nonlinear coefficients deff for different fundamental wavelengths were calculated. The research can be extended to any coupled dual χ(2) process and will help us to understand better the dynamics of coupled nonlinear interactions based on QPM crystals.

Measurement of nonlinear three-wave interaction using shear-vertical-wave point-focusing electromagnetic acoustic transducers

Abstract We developed a method of nonlinear three-wave interaction using shear-vertical-wave point-focusing electromagnetic acoustic transducers (SV-wave PF-EMATs). EMATs can excite and detect ultrasonic waves without couplants through interaction between electromagnetic fields and solid mechanics and are generally unsuitable for the nonlinear ultrasound measurement due to their low signal conversion efficiency. However, our originally developed PF-EMAT can focus SV waves at a focal point in phase, achieving a large local displacement. Here, two PF-EMATs with different driving frequencies are placed facing each other so as to match their focal points, where the focused SV waves intersect to induce the third waves with the frequencies of the sum and difference of the incident frequencies through the nonlinear three-wave interaction. We demonstrate that the local nonlinearity can be measured by this method with EMATs and demonstrate its applicability to evaluation of fatigue damage in a fatigue crack initiation phase with aluminum alloy specimens.

Land-Use Change Prediction in Dam Catchment Using Logistic Regression-CA, ANN-CA and Random Forest Regression and Implications for Sustainable Land–Water Nexus

For sustainable water resource management within dam catchments, accurate knowledge of land-use and land-cover change (LULCC) and the relationships with dam water variability is necessary. To improve LULCC prediction, this study proposes the use of a random forest regression (RFR) model, in comparison with logistic regression–cellular automata (LR-CA) and artificial neural network–cellular automata (ANN-CA), for the prediction of LULCC (2019–2030) in the Gaborone dam catchment (Botswana). RFR is proposed as it is able to capture the existing and potential interactions between the LULC intensity and their nonlinear interactions with the change-driving factors. For LULCC forecasting, the driving factors comprised physiographic variables (elevation, slope and aspect) and proximity-neighborhood factors (distances to water bodies, roads and urban areas). In simulating the historical LULC (1986–2019) at 5-year time steps, RFR outperformed ANN-CA and LR-CA models with respective percentage accuracies of 84.9%, 62.1% and 60.7%. Using the RFR model, the predicted LULCCs were determined as vegetation (−8.9%), bare soil (+8.9%), built-up (+2.49%) and cropland (−2.8%), with water bodies exhibiting insignificant change. The correlation between land use (built-up areas) and water depicted an increasing population against decreasing dam water capacity. The study approach has the potential for deriving the catchment land–water nexus, which can aid in the formulation of sustainable catchment monitoring and development strategies.

Aerodynamic and Aeroacoustic Effects of Different Transition Mechanisms on an Airfoil

The paper delves into the detailed sound generation and propagation mechanisms associated with tripping-induced flow perturbations and trailing-edge scattering using wall-resolved large-eddy simulations. Two distinct boundary-layer tripping techniques, namely a geometrically resolved stair strip and an artificially modeled trip using suction and blowing, are investigated. To facilitate comparison, the natural boundary-layer transition is also simulated as a baseline scenario. The analysis takes into account a Reynolds number of 4×105, a Mach number of 0.058, and a nonzero angle of attack of 6.25° over a NACA 0012 airfoil configuration. The mechanisms for sound generation and propagation related to trailing-edge noise remain consistent across the three transition scenarios. However, boundary-layer tripping notably leads to intricate, scenario-specific noise generation: there is an interaction between the laminar separation bubble and tripping for the stair strip case, whereas laminar boundary-layer instability is evident for the suction and blowing scenario. Aerodynamic flowfields involving acoustic noise sources, their propagating natures near the wall, and far-field acoustics are cross-examined in detail. The comprehensive analysis of observed phenomena provides valuable insights for understanding nonlinear flow and acoustic interactions relevant to airfoil noise and designing new types of trips under adverse pressure gradient flows.

Cascaded Second Harmonic Generation for Deep‐UV Radiations with a 2D Nonlinear Photonic Quartz Crystal

AbstractHarmonic generation can broaden the laser wavelength in a great scope and is rich in physics, but the efficient cascaded second harmonic generation especially those directly deep into deep‐ultraviolet (DUV) with one single crystal seems to be impossible, due to the extremely strict phase‐matching conditions and relative narrow bandgap of present nonlinear optical crystals. Here, this work designs a nonlinear photonic quartz crystal where the phase difference of interacted light waves is manipulated in two dimensions and realizes an unprecedented cascaded phase‐matched 2nd–5th harmonic generation simultaneously with the photon energy up to 6 eV, representing the shortest wavelength by cascaded second harmonic generation in the solid‐state nonlinear medium. The generated light is located in the visible‐DUV region with a total conversion efficiency of 2.7%. The present nonlinear photonic quartz scheme not only provides a multi‐wavelength solid‐state laser source applied in modern devices but also develops a new route for studying the light‐matter nonlinear interaction in the DUV region.

Probing nonlinear excitation conditions: photoluminescence and nonlinear absorption studies in laser-irradiated dielectrics

Understanding the fundamentals of laser-matter interactions is crucial for developing and optimizing ultrafast laser processing strategies. In optically transparent solids, the key event by which energy is deposited in the material is through the generation of an electron–hole plasma via nonlinear excitation mechanisms. As the energy stored in the plasma relaxes, local distortions of the lattice may occur, such as point defects. These defects give rise to new discrete energy states located in the bandgap. In this study, we investigate how the presence of these energy states influences the transmission of ultrashort near-infrared laser pulses in fused silica. Experimental results of laser pulse transmission and photoluminescence from defects are correlated with optical microscopy of the irradiated spots, allowing us to identify different nonlinear interaction regimes. Numerical simulations indicate that photo-induced defects influence the nonlinear losses of ultrashort laser pulses and explain why a non-destructive damage regime with detectable excitation is only observed for a narrow intensity range in multipulse experiments.

Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics

Divisive Normalization and the Wilson–Cowan equations are well-known influential models of nonlinear neural interaction (Carandini and Heeger in Nat Rev Neurosci 13(1):51, 2012; Wilson and Cowan in Kybernetik 13(2):55, 1973). However, they have been always treated as different approaches and have not been analytically related yet. In this work, we show that Divisive Normalization can be derived from the Wilson–Cowan dynamics. Specifically, assuming that Divisive Normalization is the steady state of the Wilson–Cowan differential equations, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson–Cowan kernel but also depends on the signal. A standard stability analysis of a Wilson–Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability suggests the appropriateness of our steady state assumption. The proposed theory provides a mechanistic foundation for the suggestions that have been done on the need of signal-dependent Divisive Normalization in Coen-Cagli et al. (PLoS Comput Biol 8(3):e1002405, 2012). Moreover, this theory explains the modifications that had to be introduced ad hoc in Gaussian kernels of Divisive Normalization in Martinez-Garcia et al. (Front Neurosci 13:8, 2019) to reproduce contrast responses in V1 cortex. Finally, the derived relation implies that the Wilson–Cowan dynamics also reproduce visual masking and subjective image distortion, which up to now had been explained mainly via Divisive Normalization.

Ground states of a distinct spin–orbit-coupled spin-1 Bose–Einstein Condensate in a toroidal trap

This study delves into the influence of a new type of spin–orbit coupling (SOC) on spin-1 Bose–Einstein condensates (BECs) in quasi-two-dimensional annular regions. The unconventional characteristics of the annular potential trap coupled with innovative artificial gauge field bring about a diverse array of phase diagrams for the ground state behavior of the BECs. In the antiferromagnetic state, we observe a distinct petal-like phase structure with components exhibiting novel density and phase distributions. In the ferromagnetic state, the spin-1 BECs exhibit rich asymmetric states which showcase a new type of vortex-molecule structure with multiple winding numbers in the huge hole. Many other novel breaking structures have also been discovered by modulating the strength of the nonlinear interaction. We contribute the different ground states of distinct spin–orbit couplings to the different symmetries.

Giant electric field-induced second harmonic generation in polar skyrmions

Electric field-induced second harmonic generation allows electrically controlling nonlinear light-matter interactions crucial for emerging integrated photonics applications. Despite its wide presence in materials, the figures-of-merit of electric field-induced second harmonic generation are yet to be elevated to enable novel device functionalities. Here, we show that the polar skyrmions, a topological phase spontaneously formed in PbTiO3/SrTiO3 ferroelectric superlattices, exhibit a high comprehensive electric field-induced second harmonic generation performance. The second-order nonlinear susceptibility and modulation depth, measured under non-resonant 800 nm excitation, reach ~54.2 pm V−1 and ~664% V−1, respectively, and high response bandwidth (higher than 10 MHz), wide operating temperature range (up to ~400 K) and good fatigue resistance (>1010 cycles) are also demonstrated. Through combined in-situ experiments and phase-field simulations, we establish the microscopic links between the exotic polarization configuration and field-induced transition paths of the skyrmions and their electric field-induced second harmonic generation response. Our study not only presents a highly competitive thin-film material ready for constructing on-chip devices, but opens up new avenues of utilizing topological polar structures in the fields of photonics and optoelectronics.

Isotope effects on transport characteristics of edge and core plasmas heated by neutral beam injection (NBI) in an inward shifted configuration at the Large Helical Device

Isotope effects have been investigated in Neutral Beam Injection (NBI) heated plasmas on the Large Helical Device with similar operational parameters between Hydrogen (H) and Deuterium (D) plasmas. Experimental results show that the global energy confinement has no significant dependence on the isotope mass under similar discharge conditions with nearly the same heating power, line-averaged density ( nˉe ) and magnetic field. For both electron and ion energy transport, the transport coefficients, which are obtained based on local power balance analysis, have analogous profiles between H and D dominant plasmas. For neoclassical χe and χi values, they are almost equal between H and D dominant plasmas in low nˉe discharges, whereas in high nˉe cases they are lower in H plasmas than those in D ones. At low nˉe , the electron and ion thermal transport in both H and D plasmas are dominated by neoclassical transport at a certain zone ( ρ≈0.6−0.85 ), while the anomalous transport process has primary effects in the remaining area, and the density fluctuations exhibit ion temperature gradient mode nature. With increase of nˉe , the anomalous transport becomes prevailing and the density fluctuations propagate along electron diamagnetic drift direction. Bispectral analysis reveals that the H plasma has stronger nonlinear coupling in edge density fluctuations in both low and high density discharges, which is probably due to that the D plasma has stronger damping rate for the nonlinear interaction of turbulence. For a comparative study, the present results have been compared with those observed in the ECRH discharges (Tanaka et al 2019 Nucl. Fusion 59 126040). The reasons for the similarities and dissimilarities between these two different heating manners are not clear yet. To unravel the underlying physics, essential inputs from theories and simulations are required.

Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media

Ultrafast diffusion disperses faster than super-diffusion, and this has been proven by several theoretical and experimental investigations. The mean square displacement of ultrafast diffusion grows exponentially, which provides a significant challenge for modeling. Due to the inhomogeneity, nonlinear interactions, and high porosity of cement materials, the motion of particles on their surfaces satisfies the conditions for ultrafast diffusion. The investigation of the diffusion behavior in cementitious materials is crucial for predicting the mechanical properties of cement. In this study, we first attempted to investigate the dynamic of ultrafast diffusion in cementitious materials underlying the Riemann–Liouville nonlocal structural derivative. We constructed a Riemann–Liouville nonlocal structural derivative ultrafast diffusion model with an exponential function and then extended the modeling strategy using the Mittag–Leffler function. The mean square displacement is analogous to the integral of the corresponding structural derivative, providing a reference standard for the selection of structural functions in practical applications. Based on experimental data on cement mortar, the accuracy of the Riemann–Liouville nonlocal structural derivative ultrafast diffusion model was verified. Compared to the power law diffusion and the exponential law diffusion, the mean square displacement with respect to the Mittag–Leffler law is closely tied to the actual data. The modeling approach based on the Riemann–Liouville nonlocal structural derivative provides an efficient tool for depicting ultrafast diffusion in porous media.

Numerical simulation of bichromatic wave propagation based on the paddle- and modified mass source wave-maker methods

A second-order numerical wave-maker is realized by combining the paddle wave-maker theory proposed by Schäffer for physical experiments with the Fluent software. The numerical results from the paddle wave-maker method are compared with the results from the modified mass source wave-maker method, the theoretical solutions, and the physical experimental data. The numerical model based on the paddle wave-maker method is verified, and the applicable scopes of the two wave-maker methods are discussed. The paddle wave-maker method is not suitable for bichromatic wave combinations that include shallow-water waves. However, within their common applicable range, the numerical results from the paddle wave-maker method are better than those from the modified mass source wave-maker method, at least for the grid divisions adopted in this study. The effects of the incident wave parameters on the nonlinear wave-wave interaction are also analyzed.

Generating synthetic population for simulating the spatiotemporal dynamics of epidemics.

Agent-based models have gained traction in exploring the intricate processes governing the spread of infectious diseases, particularly due to their proficiency in capturing nonlinear interaction dynamics. The fidelity of agent-based models in replicating real-world epidemic scenarios hinges on the accurate portrayal of both population-wide and individual-level interactions. In situations where comprehensive population data are lacking, synthetic populations serve as a vital input to agent-based models, approximating real-world demographic structures. While some current population synthesizers consider the structural relationships among agents from the same household, there remains room for refinement in this domain, which could potentially introduce biases in subsequent disease transmission simulations. In response, this study unveils a novel methodology for generating synthetic populations tailored for infectious disease transmission simulations. By integrating insights from microsample-derived household structures, we employ a heuristic combinatorial optimizer to recalibrate these structures, subsequently yielding synthetic populations that faithfully represent agent structural relationships. Implementing this technique, we successfully generated a spatially-explicit synthetic population encompassing over 17 million agents for Shenzhen, China. The findings affirm the method's efficacy in delineating the inherent statistical structural relationship patterns, aligning well with demographic benchmarks at both city and subzone tiers. Moreover, when assessed against a stochastic agent-based Susceptible-Exposed-Infectious-Recovered model, our results pinpointed that variations in population synthesizers can notably alter epidemic projections, influencing both the peak incidence rate and its onset.

Weakly nonlinear analysis of thermoacoustic oscillations in can-annular combustors

Can-annular combustors feature clusters of thermoacoustic eigenvalues, which originate from the weak acoustic coupling between $N$ identical cans at the downstream end. When instabilities occur, one needs to consider the nonlinear interaction between all $N$ modes in the unstable cluster in order to predict the steady-state behaviour. A nonlinear reduced-order model for the analysis of this phenomenon is developed, based on the balance equations for acoustic mass, momentum and energy. Its linearisation yields explicit expressions for the $N$ complex-valued eigenfrequencies that form a cluster. To treat the nonlinear equations semianalytically, a Galerkin projection is performed, resulting in a nonlinear system of $N$ coupled oscillators. Each oscillator represents the dynamics of a global mode that oscillates in the whole can-annular combustor. The analytical expressions of the equations reveal how the geometrical and thermofluid parameters affect the thermoacoustic response of the system. To gain further insights, the method of averaging is applied to obtain equations for the slow-time dynamics of the amplitude and phase of each mode. The averaged system, whose solutions compare very well with those of the full oscillator equations, is shown to be able to predict complex transient dynamics. A variety of dynamical states are identified in the steady-state oscillatory regime, including push–push (in-phase) and spinning oscillations. Notably, the averaged equations are able to predict the existence of synchronised states. These states occur when the frequencies of two (or more) unstable modes with nominally different frequencies lock onto a common frequency as a result of nonlinear interactions.

Active oscillatory associative memory

Traditionally, physical models of associative memory assume conditions of equilibrium. Here, we consider a prototypical oscillator model of associative memory and study how active noise sources that drive the system out of equilibrium, as well as nonlinearities in the interactions between the oscillators, affect the associative memory properties of the system. Our simulations show that pattern retrieval under active noise is more robust to the number of learned patterns and noise intensity than under passive noise. To understand this phenomenon, we analytically derive an effective energy correction due to the temporal correlations of active noise in the limit of short correlation decay time. We find that active noise deepens the energy wells corresponding to the patterns by strengthening the oscillator couplings, where the more nonlinear interactions are preferentially enhanced. Using replica theory, we demonstrate qualitative agreement between this effective picture and the retrieval simulations. Our work suggests that the nonlinearity in the oscillator couplings can improve memory under nonequilibrium conditions.

Sum-frequency triad interactions among surface waves propagating through an ice sheet

We study nonlinear resonant wave–wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. The theoretical predictions are supported by a high-order spectral (HOS) method capable of simulating nonlinear interactions in both open water and the ice sheet. Using the HOS method, the amplitude evolution predictions are extended to multiple (coupled) triad interactions and a single ice sheet of finite length. We relate the amplitude evolution to mechanisms with strong frequency dependence – ice bending strain, related to ice breakup, as well as wave reflection and transmission. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearised theory. For an ice sheet of finite length, we show that nonlinear wave reflection and transmission coefficients depend on a parameter in terms of wave steepness and ice length, and can have values significantly different than those from linear theory. In particular, we show that nonlinear sum-frequency interactions can appreciably decrease the total wave energy transmitted past the ice sheet. This work has implications for understanding the occurrence of ice breakup, wave attenuation due to scattering in the marginal ice zone and the resulting ice floe size distribution.

Enhancing Heart Disease Prediction using Advanced Feature Engineering and Ensemble Learning Techniques

This study introduces a holistic model for predicting heart disease ,integrating advanced algorithms with a focus on feature engineering. The dataset encompasses a diverse range of patient parameters, including demographics, lifestyle factors, and medical history. Feature engineering involves a meticulous process of selecting, transforming, and augmenting relevant features to enhance the model's ability to discern patterns and relationships within the data. This stage is essential for increasing the predicted accuracy of the model and gleaning insightful information from intricate datasets. The logistic regression algorithm is employed to establish a baseline predictive model, providing insights into the individual contribution of each feature. Subsequently, a neural network is implemented to capture intricate non-linear dependencies and interactions within the data, further refining the predictive capabilities. Results indicate that the incorporation of feature engineering significantly improves the model's performance compared to traditional approaches. Early experiments demonstrate promising accuracy rates in heart disease prediction, showcasing the potential for early detection and proactive healthcare interventions. This method not only enhances predictive modeling for heart disease but also emphasizes the significance of feature engineering in maximizing the full capabilities of machine learning algorithms for medical applications.