Nonlinear Processes Research Articles

Optimal quantum metrology of two-photon absorption

Abstract Two-photon absorption (TPA) is a nonlinear optical process with wide-ranging applications from spectroscopy to super-resolution imaging. Despite this, the precise measurement and characterisation of TPA parameters are challenging due to their inherently weak nature. We study the potential of single-mode quantum light to enhance TPA parameter estimation through the quantum Fisher information (QFI). Discrete variable (DV) quantum states (defined to be a finite superposition of Fock states) are optimised to maximise the QFI for given absorption, revealing a quantum advantage compared to both the coherent state (classical) benchmark and the single-mode squeezed vacuum state. For fixed average energy ̄n ∈ 2N, the Fock state is shown to be optimal for large TPA parameters, while a superposition of vacuum and a particular Fock state is optimal for small absorption for all ̄n. This differs from single-photon absorption where the Fock state is always optimal. Notably, photon counting is demonstrated to offer optimal or nearly optimal performance compared to the QFI bound for all levels of TPA parameters for the optimised quantum probes, and their quantum advantage is shown to be robust to single-photon loss. Our findings provide insight into known limiting behaviours of Gaussian probes and their different Fisher information (FI) scalings under photon counting (∝ ̄n2 for squeezed vacuum states versus ̄n3 for coherent states). The squeezed state outperforms coherent states for small TPA parameters but underperforms in the intermediate regime, becoming comparable in the large absorption limit. This can be explained through fundamental differences between behaviours of even and odd number Fock states: the former’s QFI diverges in both large and small absorption limits, while the latter diverges only in the small absorption limit, dominating at intermediate scales.

Simulating Fuel Assembly Bowing: A Neutron-Diffusion Method Based on Arbitrary Quadrilateral Node and Conformal Mapping Technique

Fuel assembly bowing, widely observed in a pressurized water reactor (PWR), often results in an asymmetrical power distribution. This paper proposes a neutron-diffusion method that integrates the arbitrary quadrilateral node with the conformal mapping technique to characterize the impact of fuel assembly bowing on power distribution. The proposed method involves a nonlinear iteration process to solve the neutron-diffusion equation. The global coarse-mesh finite difference equation is established on the arbitrary quadrilateral nodes, which are redivided in response to fuel assembly bowing. The local two-node nodal expansion method equation is established on the rectangular nodes, which are mapped from the original arbitrary quadrilateral nodes using the conformal mapping technique. The proposed method has improved our self-developed core code, named SPARK, for PWRs. To verify this novel method, two distinct types of fuel assembly bowing are modeled based on the mini core. The reference results for these models were obtained using the Monte Carlo code NECP-MCX. The numerical results suggest a robust agreement between the biases of keff and power distributions and their corresponding reference results.

Nonlinear generation of vector beams by using a compact nonlinear fork grating

Vectorial beams have attracted great interest due to their broad applications in optical micromanipulation, optical imaging, optical micromachining, and optical communication. Nonlinear frequency conversion is an effective technique to expand the frequency range of the vectorial beams. However, the scheme of existing methods to generate vector beams of the second harmonic (SH) lacks compactness in the experiment. Here, we introduce a new way to realize the generation of vector beams of SH by using a nonlinear fork grating to solve such a problem. We examine the properties of generated SH vector beams by using Stokes parameters, which agree well with theoretical predictions. Then we demonstrate that linearly polarized vector beams with arbitrary topological charge can be achieved by adjusting the optical axis direction of the half-wave plate (HWP). Finally, we measure the nonlinear conversion efficiency of such a method. The proposed method provides a new way to generate vector beams of SH by using a microstructure of nonlinear crystal, which may also be applied in other nonlinear processes and promote all-optical waveband applications of such vector beams.

What are the dominant drivers and optimal thresholds for a healthy ecosystem in the Yellow River Basin, China? from a perspective of nonlinear nexus

Identifying the dominant factors influencing ecosystem health and their optimal thresholds is essential for the management and restoration of ecosystems. Most of the works, however, have less detected the importance level of individual factors, especially their changes over time and scale, and rarely determined their threshold effects on ecosystem health (EH), which seriously hinders the formulation of targeted policies for sustainable ecosystem management. To address these research gaps, we present an innovative visualization approach to reveal importance changes in natural and anthropogenic variables and their nonlinear coupling process with EH in the China’s Yellow River Basin (YRB) in the last two decades. Results show that (i) Although the EH in the YRB has improved slightly in the past 20 years, it is still not optimistic and shows distinct spatial heterogeneity. (ii) The impact of human activities on the ecosystem health of the YRB has increased and increasingly plays a decisive role, while that of the natural aspect has decreased recently. Specifically, environmental factors (slope, NDVI, and annual temperature) are the dominant factors affecting the upstream EH. Midstream EH is significantly affected by the synergistic effect of natural and anthropogenic factors, but the importance of the proportion of built-up land is intensified (ranked from 8th to 4th). Anthropogenic factors exert the greatest influence on downstream EH variation, especially for population density whose importance order rising from 7th to 2nd. (iii) By illustrating the nonlinear response curves of EH at multi-scale, the tipping point caused ecosystem deterioration in the YRB is explored and the optimal thresholds of leading factors oriented towards the most effective ecosystem conservation goal are obtained. These results help precisely identify the current health status of YRB's ecosystem, as well as providing a valuable reference for moderate restoration standards and sustainable ecosystem management.

Bayesian estimation of nonlinear Hawkes processes

Bayesian estimation of nonlinear Hawkes processes

Adaptive soft sensor modeling of chemical processes based on an improved just‐in‐time learning and random mapping partial least squares

AbstractThe just‐in‐time learning‐based partial least squares (JIT‐PLS) has been extensively applied to adaptive soft sensor modeling of complex nonlinear processes. However, it still has the problems of unreasonable relevant samples selection and unsatisfactory local modeling. Aiming at these problems, this paper proposes an improved just‐in‐time learning‐based random mapping partial least squares (IJIT‐RMPLS), including an improved relevant samples selection strategy and a random mapping PLS (RMPLS) model. On the one hand, considering the different correlation degrees between input variables and output variable, this method applies mutual information to evaluate the importance of each input variable and designs a variable‐weighted Euclidean distance to select relevant samples for local modeling. On the other hand, in order to prompt the prediction precision of local soft sensor models, this method combines the idea of nonlinear random mapping in extreme learning machines with PLS and builds a RMPLS with multiple activation functions. Applications on a numerical example and a real chemical process show that the proposed IJIT‐RMPLS has smaller prediction error compared with traditional JIT‐PLS.

Optical Parametric Amplification in Crossed Fabry‐Perot Cavities

AbstractOptical parametric amplification (OPA) is a promising method of producing extremely intense light. A new OPA scheme with comprehensively high performance is urgently required for future development. In this study, an amplification scheme known as crossed‐Fabry‐Perot‐cavity OPA (XOPA) is proposed. It is based on the principle of periodic idler elimination, which prevents energy back‐conversion among the three coupling waves, resulting in a monotonically increasing overall conversion efficiency. Using a signal at 808 nm and a pump at 532 nm, a chirped pulse XOPA is experimentally demonstrated with a conversion efficiency of 56.28% and a gain bandwidth of 120 nm. The measured pulse duration after compression is 19.2 fs, which is comparable to the Fourier‐transform‐limited 16.8 fs. Further investigations revealed several advantages. Stable pulse shaping in spatial, temporal, and frequency domains is realized by a spatiotemporally modulated pump. Pulse contrast adjustability on the front edge of the signal is verified in the XOPA of different Fabry‐Perot cavity lengths. These results indicate astringency and precise regulation of output in nonlinear processes. Considering numerous crystals suitable for noncollinear configurations from the near‐infrared to mid‐infrared regions, XOPA has a universal potential application in laser systems with extreme intensity, few‐cycle duration, and internal confinement fusion drivers.

Time varying risk aversion and its connectedness: evidence from cryptocurrencies

AbstractChanging patterns of risk aversion may follow a non-linear counter-cyclical process. However, the evidence so far has not considered developing cryptocurrency markets. Given some unique features of cryptocurrencies, it is interesting to distinguish how these assets differ from traditional products. This paper investigates the time effects of periodicity on risk aversion for a selection of major cryptocurrencies compared to major financial assets. Significant periodic time-varying patterns are identified when analysing risk aversion. Further, bilateral and bidirectional Granger causalities are identified within cryptocurrencies, as well as between cryptocurrencies and traditional financial assets. Bitcoin is identified as a leading information transmitter of the spillover of risk aversion upon other cryptocurrencies, while estimated risk aversion of traditional financial markets plays a dominant role in the spillover processes upon the cryptocurrency cluster. The latter finding presents further evidence of developing cryptocurrency market maturity. The COVID-19 pandemic is found to have significantly influenced the connectedness of risk aversion among cryptocurrency and traditional financial markets.

The influence of fractionality and unconstrained parameters on mathematical and graphical analysis of the time fractional phi-four model

In the framework of several nonlinear physical phenomena arising from water wave mechanics, this work recovers some new precise solutions to the time-fractional phi-four equation. For this, the phi-four equation's space and time fractional transformation is converted into an ordinary differential equation (ODE). The improved modified extended tanh function (imETF) approach is then employed by the ODE as a powerful method based on the conformable derivative. Thus, lump solutions, periodic solutions, solitary and multiple soliton solutions, dark-bright soliton solutions, and Jacobi elliptic doubly periodic type solutions are studied. The imETF appro solitons applications in many scientific and engineering fields develops mathematical methodologies, helps research solitons, and advances our knowledge of nonlinear processes. The differences between the results of this investigation and those obtained earlier using alternative methods are analyzed. In terms of fractionality, unconstrained parameters, and applied method sense, all generated wave solutions are found to be new. Physical explanations and a visual representation of the effects of unconstrained parameters and fractionality on the derived solutions are provided. We find that the wave portents change as the number of unconstrained parameters and fractionality increases. In conclusion, we dynamically show that the proper transformation and the applicable imETF method are more effective in analyzing water wave dynamics and might be employed in subsequent studies to shed light on various physical phenomena.

Opto-mechatronic dynamic characteristics in iron oxide-based nanofluid using spatial and frequency domain analysis

Iron oxide nanoparticles (IONPs) exhibit low toxicity and high chemical stability, attractive for developing of nanofluids (NFs) for advanced medical applications. This research focuses on the study of the optical, mechanical, and electrical dynamics of iron oxide–ethanol NFs. A novel sensitive methodology for analyzing the influence of nanoparticles (NPs) over the optical and electrical processes exhibited by IONFs is reported. The IONPs were synthesized by a microemulsion route and were characterized by transmission electron microscopy, scanning electron microscopy, and X-ray diffraction. The NPs exhibit a mean diameter of 30 nm and they were identified as Fe2O3. UV–Vis spectroscopy allows us determining the volume fraction of the fluid as a function of time. The assistance of a Michelson interferometer integrated with an image processing methodology was employed to explore the dynamics of the nanostructures. The percentage of NPs involved in linear and nonlinear dynamic fluid processes was estimated by taking a double-stage (spatial and frequency domains) Fast Fourier Transform in the interferometric pattern. A DC voltage source was used to study the electrical conductivity of the NF as it was being sedimented. The opto-mechatronic parameters were correlated, considering the volume fraction as the main variable to determine the optical and electrical characteristics. For the Fe2O3 NF, it is identified that the linear effects of sedimentation present a stronger impact on the optical properties, while the nonlinear interactions have more influence on the electrical conductivity. The main findings of this research have potential applications in rheological instrumentation to analyze complex effects using transient opto-mechatronic components.

Intra-oscillator high harmonic source reaching 100-eV photon energy

Resonant enhancement inside an optical cavity has been a wide-spread approach to increase efficiency of nonlinear optical conversion processes while reducing the demands on the driving laser power. This concept has been particularly important for high harmonic generation XUV sources, where passive femtosecond enhancement cavities allowed significant increase in repetition rates required for applications in photoelectron spectroscopy, XUV frequency comb spectroscopy, including the recent endeavor of thorium nuclear clock development. In addition to passive cavities, it has been shown that comparable driving conditions can be achieved inside mode-locked thin-disk laser oscillators, offering a simplified single-stage alternative. This approach is less sensitive to losses thanks to the presence of gain inside the cavity and should thus allow higher conversion efficiencies through tolerating higher intensity in the gas target. Here, we show that the intra-oscillator approach can indeed surpass the much more mature technology of passive enhancement cavities in terms of XUV flux, even reaching comparable values to single-pass sources based on chirped-pulse fiber amplifier lasers. Our system operates at 17 MHz repetition rate generating photon energies between 60 eV and 100 eV. Importantly, this covers the highly attractive wavelength for the silicon industry of 13.5 nm at which our source delivers 60 nW of outcoupled average power per harmonic order.

Deseasonalized trend of ground-level ozone and its precursors in an industrial city Kaohsiung, Taiwan

Mitigating ground-level ozone (GLO) remains challenging due to its highly nonlinear formation process. Thus, understanding GLO pollution trends is crucial for developing effective control strategies, especially Kaohsiung industrial city, Taiwan. Based on the long-term monitoring data set of 2011–2022, temporal analysis reveals that monthly mean GLO peaks in autumn (40.66 ± 5.10 ppb), carbon monoxide (CO) and major precursors such as nitrogen oxides (NOx), nonmethane hydrocarbons (NMHC) reach their highest levels in winter. The distinct seasonal variation of air pollutants in Kaohsiung is primarily influenced by the unique blocking effect of the mountainous area under the northeasterly wind, as the city is situated downwind, causing high GLO levels during autumn due to the accumulation of stagnant air hindering the dispersion of pollutants. Over the 12 years (2011–2022), the deseasonalized trend analysis was conducted with p < 0.001, revealing a stabilization trend of GLO (+0.04 ppb/yr) from a previous sharp increase. The observed improvement is credited to a drastic decrease in total oxidants (Ox) at −0.63 ppb/yr due to significantly reducing their precursors. Furthermore, the effectiveness of precursor reduction is also supported by GLO daily maximum profile changes. While high GLO events (>120 ppb) decrease, days within midrange (60–80 ppb) rise from 24.4% to 33.3%. A notable difference emerges when comparing daytime and nighttime GLO. While daytime GLO decreased at −0.22 ppb/yr, nighttime GLO increased at +0.34 ppb/yr. Weakened nocturnal titration effects accounted for the nighttime increase. The distinct spatial variations in GLO trends on a citywide scale underscore that areas with complicated industrial activities may not benefit from a continuing reduction of precursors compared to less-polluted areas. The findings of this study hold significant implications for improving GLO control strategies in heavily industrialized city and provide valuable information to the general public about the current state of GLO pollution.

The Influence of Nonlinear High-Intensity Dynamic Processes on the Standing Wave Precession of a Non-Ideal Hemispherical Resonator

The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange’s second kind equation. Then, the dynamic model is equivalently transformed into a simple harmonic vibration model of a point mass in two-dimensional space, which is analyzed using a method of averaging that separates the slow variables from the fast variables. The results reveal that taking the nonlinear terms about the square of the angular velocity and the angular acceleration in the dynamic equation into account can weaken the influence of the 4th harmonic component of a mass defect on standing wave drift, and the extent of this weakening effect varies with the dimensions of the mass defects, which is very important for steering the development of the high-precision hemispherical resonator gyroscope.

Rational Sine-Gordon expansion method to analyze the dynamical behavior of the time-fractional phi-four and (2 + 1) dimensional CBS equations

This study uses the rational Sine-Gordon expansion (RSGE) method to investigate the dynamical behavior of traveling wave solutions of the water wave phenomena for the time-fractional phi-four equation and the (2 + 1) dimensional Calogero-Bogoyavlanskil schilf (CBS) equation based on the conformable derivative. The technique uses the sine-Gordon equation as an auxiliary equation to generalize the well-known sine-Gordon expansion. It adopts a more broad strategy, a rational function rather than a polynomial one, of the solutions of the auxiliary equation, in contrast to the traditional sine-Gordon expansion technique. Several explanations for hyperbolic functions may be produced using the previously stated approach. The approach mentioned above is employed to provide diverse solutions of the time-fractional phi-four equation and the (2 + 1) dimensional CBS equations involving hyperbolic functions, such as soliton, single soliton, multiple-soliton, kink, cusp, lump-kink, kink double-soliton, and others. The RSGE approach enhances our comprehension of nonlinear processes, offers precise solutions to nonlinear equations, facilitates the investigation of solitons, propels the development of mathematical tools, and is applicable in many scientific and technical fields. The solutions are graphically shown in three-dimensional (3D) surface and contour plots using MATLAB software. All screens display the absolute wave configurations in the resolutions of the equation with the proper parameters. Furthermore, it can be deduced that the physical properties of the found solutions and their characteristics may help us comprehend how shallow water waves move in nonlinear dynamics.

"Connecting the Dots” for Recruiting Secondary Science Teachers in Urban Schools: An Exploration of Career Choice for Undergraduate Science Majors

AbstractDespite critical shortages of secondary science teachers in urban schools, relatively little research has focused on the recruitment of undergraduate science majors to teach in urban contexts. This study utilized a retrospective narrative inquiry methodology to explore the career pathways of 14 undergraduate science majors into secondary science teaching. The primary data source was interviews that were conducted at the beginning of an urban teacher education program. Interviews were analyzed through the framework of social cognitive career theory (SCCT) to identify the characteristics, beliefs, and experiences that featured prominently in their narrativizations of their career pathway into urban science education. Findings highlight a non-linear process of career choice characterized by three themes: rejecting traditional science careers, reevaluating their interests and skills for teaching, and prioritizing socially oriented career goals. Implications for enhancing the recruitment of undergraduate science majors into urban science teaching include transforming undergraduate science majors to value teaching careers and taking a more community-based approach to science teacher recruitment.

Analysis of remaining useful life of slope based on nonlinear wiener process

A remaining useful life (RUL) prediction model based on the nonlinear Wiener process is proposed to better tackle the life evaluation problem in the slope degradation process. Taking the displacement of the slope as its performance degradation index, and the nonlinear Wiener process is used to establish the RUL prediction model of the slope. For this model, the least squares method (LSM) is used to estimate the drift coefficients, the maximum likelihood estimation method (MLEM) is used to estimate the diffusion parameters, and then the probability density function (PDF) of the RUL of the slope is deduced and the RUL is predicted. The proposed model is verified by slope engineering examples. The results demonstrated that the RUL of the degradation model based on the nonlinear Wiener process has a greater prediction accuracy than the linear Wiener process. Because the various nonlinear functions have varying slope adaptations, and it can predict the RUL of a slope more accurately, which can provide more reliable preventive maintenance decisions.

Optimization-based multi-source transfer learning for modeling of nonlinear processes

This work develops an optimization-based multi-source transfer learning scheme for modeling of nonlinear chemical processes. Specifically, a transfer learning neural network model for a target process with limited data is developed using the pre-trained model obtained with multiple source processes. Since the performance of transfer learning models depends on the quality of the pre-trained models, we propose a novel Bayesian optimization problem to optimize the selection of multi-source data for the pre-trained models by first deriving a generalization error bound for multi-source domain adaptation using Y-discrepancy distance. Subsequently, the optimization problem is formulated using the theoretical error bound to select the optimal set of multiple sources, which can provide a good initial guess of the weight parameters for transfer learning model. Finally, a simulation study of a chemical reactor process in Aspen Plus Dynamics is conducted to illustrate the effectiveness of the optimization-based multi-source transfer learning scheme.

An integrated approach combining randomized kernel PCA, Gaussian mixture modeling and ICA for fault detection in non-linear processes

Principal component analysis (PCA) and independent component analysis (ICA), as well as their kernel extensions, have been widely applied in the past for industrial fault detection with Gaussian or non-Gaussian process data with linear or non-linear characteristics. Kernel-based techniques lead to computational complexity due to the high dimensionality of the dataset in the feature space. In this work, a randomization approach is used to obtain a low-rank approximation of the high-dimensional kernel matrix. A hybrid machine learning technique is proposed that integrates randomized kernel PCA (RKPCA) with ICA and Gaussian mixture modeling (GMM). The proposed approach, ICA-RKPCA-GMM, addresses the Gaussian and non-Gaussian characteristics of non-linear process data. Another hybrid algorithm combining three basic techniques of ICA, PCA and GMM is also developed (ICA-PCA-GMM). The fault detection performances of the proposed techniques (ICA-RKPCA-GMM and ICA-PCA-GMM) are compared with PCA, ICA, KPCA and combined ICA-PCA techniques by applying the techniques to two benchmark systems. Monitoring performances were evaluated by determining the false alarm rate and fault detection rate for different types of process and sensor faults. The simulation results show that the proposed ICA-RKPCA-GMM approach yields better results than individual ICA, PCA and KPCA techniques, the combined ICA-PCA and the proposed ICA-PCA-GMM technique.

Explicit machine learning-based model predictive control of nonlinear processes via multi-parametric programming

Machine learning-based model predictive control (ML-MPC) has been developed to control nonlinear processes with unknown first-principles models. While ML models can capture nonlinear dynamics of complex systems, the complexity of ML models leads to increased computation time for real-time implementation of ML-MPC. To address this issue, in this work, we propose an explicit ML-MPC framework for nonlinear processes using multi-parametric programming. Specifically, a self-adaptive approximation algorithm is first developed to obtain a piecewise linear affine function that approximates the behaviors of ML models. Then, multi-parametric quadratic programming (mpQP) problems are formulated to generate the solution map for states in discretized state–space. Furthermore, to accelerate the implementation of explicit ML-MPC, a neighbor-first search algorithm is developed. Finally, an example of a chemical reactor is used to demonstrate the effectiveness of the explicit ML-MPC.

Numerical Research on Water Tightness of a New Type of Water Stopping Device at the Shield Machine Receiving Shaft

To meet the water stopping requirement of the shield machine receiving shaft, preliminary calculations are carried out on the structural design of a new type of water stopping device. The device is arranged on the inner arc surface of the embedded parts of the inner lining hole ring of the shield machine receiving shaft. By inflating the inflatable bag, the restriction of the limit bending steel plate is overcome, the flap is made to rotate to contact the shield machine shell to fill the gap between the shield machine and the hole ring, and waterproof materials are injected into the grouting pipe to stop leakage and water. For verifying the water stopping effect of the above structures and preparing for the later indoor model test, the numerical research work is mainly carried out on the standard section model. The nonlinear deformation process of the inflatable bag expansion and the contact with the embedded parts of the hole ring, the flap, and other components are analyzed, and the selection and bearing capacities of rubber materials are confirmed, so as to provide reference and guidance for the indoor model test. Combining the calculation results of different working conditions and the results of the indoor model pre-test, it is concluded that the stresses of each component do not exceed the corresponding allowable values, which indicates that the current design of the water stopping device is reasonable and feasible, and can be applied to test research.