Nonlinear Phenomena Research Articles

Electro-optically Modulated Nonlinear Metasurfaces.

Electrically reconfigurable nonlinear metasurfaces provide dynamic control over nonlinear phenomena such as second-harmonic generation (SHG), unlocking novel applications in signal processing, light switching, and sensing. Previous methods, like electric-field-induced SHG in plasmonic metasurfaces and Stark-tuned nonlinearities in quantum well metasurfaces, face limitations due to weak SHG responses from metals and mid-infrared constraints of quantum wells, respectively. Addressing the need for efficient SHG control in the visible and near-infrared ranges, we present a novel approach using the electro-optic (EO) effect to modulate SHG. By leveraging the exceptional EO and SHG properties of lithium niobate (LN), we integrate the EO effect with SHG within a metasurface framework for the first time. Our LN metasurface achieves an 11.3% modulation depth in SHG amplitude under a ±50 V alternating voltage. These results open new avenues for reconfigurable photonic applications. including tunable nonlinear light sources, quantum optics, and nonlinear information processing.

Exact Solutions of Nonlinear Fractional Cahn-Allen Equation Aries in Different Nonlinear Physical Phenomenon using Unified Technique

Exact Solutions of Nonlinear Fractional Cahn-Allen Equation Aries in Different Nonlinear Physical Phenomenon using Unified Technique

Characterization of Three-Mode Combination Internal Resonances in Electrostatically Actuated Flexible–Flexible Microbeams

Abstract Nonlinear intermodal coupling based on internal resonances in MEMS resonators has advanced significantly over the past two decades for various real-world applications. In this study, we demonstrate the existence of various three-mode combination internal resonances between the first five flexural modes of electrostatically actuated flexible–flexible beams and dynamic modal interaction between three modes via internal resonance. We first calculate the natural frequencies of the beam as a function of the stiffnesses of the transverse and rotational springs of the flexible supports, utilizing both analytical formulation and finite element analysis (FEA). Following this, we identify six combination internal resonances among the first five modes and use applied DC voltage to validate the exactness of one commensurable internal resonance condition (ω2=ω5−ω4). Subsequently, we studied a detailed forced vibration analysis corresponding to this resonance condition by solving the five-mode coupled governing equations through numerical time integration and the method of multiple scales. The results compellingly exhibit three-mode intermodal coupling among the second, fourth, and fifth modes as a function of excitation amplitude and frequency. Alongside this, intriguing nonlinear phenomena such as threshold behavior, saturation phenomena, and autoparametric instability are observed. Finally, this paper provides a systematic methodology for investigating three-mode combination internal resonances and related nonlinear dynamics, offering significant insights that could be used in observing phonon or mechanical lasing phenomena in MEMS resonators.

Unveiling non-monochromatic modes and nonlinearity in Piet Hein quantum semiconductor waveguides

We investigate the propagation characteristics of transverse electric (TE) and transverse magnetic (TM) modes in a semiconductor quantum plasma-filled coaxial waveguide with a Piet Hein cross-section. The unique geometry of the Piet Hein cross-section offers intriguing possibilities for tailoring modal properties and exploiting novel nonlinear phenomena. Using analytical and numerical methods, we unveil the non-monochromatic behaviour of TE and TM modes, characterized by distinct peaks and troughs in their field components. The Ez\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{z}$$\\end{document} component of the TM mode exhibits a suppressed field within the central core and higher concentration in the cladding region, potentially minimizing energy loss within the waveguide. The Eρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\rho }$$\\end{document} component exhibits pronounced oscillations near the waveguide boundaries, suggesting constructive and destructive interference patterns. The Eξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\xi }$$\\end{document} component displays a non-monotonic behaviour with multiple pits and bumps, highlighting the interplay between the TE mode, the Piet Hein geometry, and the semiconductor quantum plasma properties. The Bρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{\\rho }$$\\end{document} component of the TM mode exhibits a non-monochromatic behaviour with multiple maxima and minima, attributed to the complex interactions between propagating waves with different phase shifts. The Bξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{\\xi }$$\\end{document} component exhibits a non-uniform distribution with distinct pits and bumps, with a resurgence towards the waveguide edges potentially due to higher-order mode contributions and local field enhancement effects. Our findings pave the way for the development of novel photonic devices with enhanced functionalities based on Piet Hein semiconductor quantum plasma waveguides.

Nonlinear edge transport in a quantum Hall system.

Nonlinear transport phenomena in condensed matter reflect the geometric nature, quantum coherence, and many-body correlation of electronic states. Electric currents in solids are classified into (i) ohmic current, (ii) supercurrent, and (iii) geometric or topological current. While the nonlinear current-voltage (I-V) characteristics of the former two categories have been extensive research topics recently, those of the last category remains unexplored. Among them, the quantum Hall current is a representative example. Realized in two-dimensional electronic systems under a strong magnetic field, the topological protection quantizes the Hall conductance in the unit of e2/h (e, elementary charge; and h, Planck constant), of which the edge transport picture gives a good account. Here, we theoretically study the nonlinear I-VH characteristic of the edge transport up to third order in VH. We find that nonlinearity arises in the Hall response from electron-electron interaction between the counterpropagating edge channels with the nonlinear energy dispersions. We also discuss possible experimental observations.

Fractional-order hybridly polarized vector beams: generation, focusing, propagation, and spatial self-phase modulation

As a class of integer-order vector beams, hybridly polarized vector beams (HPVBs) are widely used in focus shaping, femtosecond laser filamentation, linear and nonlinear polarization evolution, etc. Recently, fractional-order vector beams have gained widespread interest due to their more control parameters, rich photophysical properties, and novel nonlinear optical phenomena. In this work, we report the experimental generation, focusing and propagation characteristics, and spatial self-phase modulation (SSPM) phenomenon of fractional-order HPVBs. It is shown that during the focusing and propagation processes, the intensity pattern of fractional-order HPVBs develops from a near-Gaussian structure in the incident plane to an asymmetric structure in both the focal field and the far field. Meanwhile, their distributions of state of polarization (SoP) also evolve, although it remains a hybrid polarization distribution overall. When the focused fractional-order HPVBs pass through the nonlinear optical sample, the far-field self-diffraction intensity pattern displays an irregular concentric multi-ring structure with a hybrid polarization distribution. It is found that the nonlinear medium not only modulates the far-field intensity pattern of fractional-order HPVBs but also controls their SoP distribution. This symmetric breaking HPVB has potential application prospects in optical micro-manipulation, light-matter interaction, optical spin-orbit conversion, etc.

Study on nonlinear coupled dynamic response of the integrated polar ocean nuclear energy platform

An integrated polar ocean nuclear energy platform is capable of providing adequate electrical and thermal energy essential for polar oceanic development activities. Precisely forecasting the platform's motion response within the marine environment is pivotal for the assurance of its safety. A scenario where the natural frequencies of heave, roll, and pitch of such an integrated polar ocean nuclear energy platform align closely to a 2:1:1 ratio, and when the wave frequency nearly matches the aggregate of the platform's natural heave and pitch frequencies, could induce a phenomenon known as sum-type nonlinear internal resonance. This phenomenon can significantly amplify the swing (roll or pitch) motion of the platform, posing a grave risk to both personnel and equipment onboard. Investigating these nonlinear internal resonance phenomena within the nuclear energy platform is critical for informing both the design and practical deployment of these platforms. Following the validation of the numerical simulation against experimental results, a detailed analysis of sum-type nonlinear internal resonance phenomena in the integrated polar ocean nuclear energy platform under regular wave conditions was performed using a combination of numerical simulations and nonlinear dynamics theory. It was observed that upon exceeding a certain wave height threshold, the platform enters a state of sum-type nonlinear internal resonance, engendering highly complex motion patterns. Notably, irrespective of initial conditions, this resonance triggers the roll motion of the platform, facilitating the external dissipation of energy in a half-sub-harmonic vibration manner. Increasing damping can effectively suppress the occurrence of nonlinear internal resonance phenomena in the platform. In designing the integrated polar ocean nuclear energy platform, it's crucial to avoid having the natural frequency ratios of heave, pitch, and roll align as 2:1:1. If unavoidable, adding side plates to increase damping can mitigate the effects of sum-type nonlinear internal resonance.

Microscopic view on the polarization-resolved S-SHG intensity of the vapor/liquid interface of pure water.

Second harmonic generation (SHG) is a nonlinear optical phenomenon where two photons at the frequency ω combine to form a single photon at the second-harmonic frequency 2ω. Since that second-order process is very weak in bulk isotropic media, optical SHG responses of interfaces provide a powerful and versatile technique to probe the molecular structure and dynamics of liquid interfaces. Both local dipole contributions and non-local quadrupole contributions can be interesting to investigate different properties of the interface, such as the molecular orientation or the charge density. However, a major difficulty is to comprehend the link between the S-SHG intensity and molecular details. This article reports a numerical approach to model the polarization-resolved SHG intensities of a model vapor/liquid interface of pure water. The influence of the interfacial local environment on the hyperpolarizability is taken into account using quantum mechanical/molecular mechanics calculations. The numerical predictions are in very good agreement with experiments. We detail the hypotheses made during the modeling steps and discuss the impact of various factors on the modeled SHG intensities, including the description of the exciting field in the interfacial layer, the effect of neighboring molecules on the second-harmonic polarization, and the presence of an additional static electric field at the interface.

Nonlinear Thermoplasmonics in Graphene Nanostructures.

The linear electronic dispersion relation of graphene endows the atomically thin carbon layer with a large intrinsic optical nonlinearity, with regard to both parametric and photothermal processes. While plasmons in graphene nanostructures can further enhance nonlinear optical phenomena, boosting resonances to the technologically relevant mid- and near-infrared (IR) spectral regimes necessitates patterning on ∼10 nm length scales, for which quantum finite-size effects play a crucial role. Here we show that thermoplasmons in narrow graphene nanoribbons can be activated at mid- and near-IR frequencies with moderate absorbed energy density, and furthermore can drive substantial third-harmonic generation and optical Kerr nonlinearities. Our findings suggest that photothermal excitation by ultrashort optical pulses offers a promising approach to enable nonlinear plasmonic phenomena in nanostructured graphene that avoids potentially invasive electrical gating schemes and excessive charge carrier doping levels.

GTP-24-1666 - Temperature Margin Calculation During Finite Element Creep Simulations (GT2024-121776)

Abstract Creep deformation in turbomachinery applications is a highly non-linear phenomenon where +/- 15°C may halve or double the average rupture life. Even in well-controlled laboratory conditions, this stochastic nature means that identical tests may differ by a factor of two. Analysts using implicit finite element user creep subroutines may not appreciate the uncertainty of their solution, or the design changes required to account for uncertainty in either the boundary conditions or the solution itself. Designing to a maximum strain limit does not consider the sudden acceleration of tertiary creep rates. Applying a time factor may extend the simulation time by multiple factors. This paper presents a methodology where two estimations of creep damage are made in parallel to the creep simulation at actual operating temperatures. These two estimations consider the predicted change in stress relaxation, at higher or lower temperatures, to estimate the temperature change required to reach the onset of creep, at any given node in the model, and at any given time in the analysis. This margin calculation is expanded to consider the uncertainty in creep prediction. A time-based scatter factor is incorporated into the temperature margin calculation to provide a minimum temperature margin that includes model uncertainty. The analyst can also consider the uncertainty of the temperature prediction and boundary conditions to produce a robust creep prediction in a real-world simulation. The methodology is validated through the FEA of example cases and applied to a creep-limited 2nd stage turbine blade.

Non-linear dynamics and control of COVID-19 in india revisited : evidence of synergistic, antagonistic and threshold effects

Various researchers have investigated the COVID-19 pandemic dynamics since 2020 focusing on various aspects of the epidemics. However, the non-linear dynamics of this epidemic is still not well understood. India having the largest population in the world with wide cultural, genomics, and immunity diversity is being considered a suitable case for present investigation to generate the crucial information of non-linear phenomena during the first two waves of the epidemics. An SIRD model is suggested, integrating varying transmission, recovery, and mortality rates over time to explore the nonlinear behavior of the epidemic in India. The time-dependent transmission, recovery, and mortality are calculated using the finite difference method with the aid of actual data released by the Indian government, for the periods before and during the lockdown phases. The novel results generated from the model show evidence of synergistic, antagonistic, and threshold effects and the role of various measures in controlling these epidemic trends.

New periodic solutions and solitary wave solutions for the time-fractional differential equations

In this paper, we obtain many different types of exact solutions to the time-fractional Klein–Gordon equation and the time-fractional generalized Hirota-Satsuma coupled KdV system by using the modified rational function approach. Some new solutions such as the kink-periodic solution, the anti-kink-periodic solution and the concave-convex-periodic solution are constructed. Furthermore, the kink and the singular kink waves, the bell shaped soliton and the singular soliton solutions of the two equations also are found. Some numerical simulations are presented, these works can effectively reflect the propagation phenomena of time-fractional nonlinear systems, and also enable us to understand time-fractional nonlinear physical phenomena more clearly.

Graph theoretic methods for assessing the effects of a background shear current on internal solitary waves

Internal solitary waves are a widely observed phenomenon in natural waters. Mathematically, they are fundamentally a nonlinear phenomenon that differs from the paradigm of turbulence, in that energy does not move across scales. Internal solitary waves may be computed from the Dubreil–Jacotin Long equation, which is a scalar partial differential equation that is equivalent to the stratified Euler equations. When a background shear current is present the algebraic complexity of the problem increases substantially. We present an alternative point of view for characterizing the situation with a shear current using Lagrangian (particle-like) models analysed with graph theoretic methods. We find that this yields a novel, data-centric framework for analysis that could prove useful well beyond the study of internal solitary waves.

Energy conversion performance in looped and stirling traveling-wave and standing-wave thermoacoustic engines

This present study conducts a comprehensive comparison of looped traveling-wave thermoacoustic engines (TWTAEs) and Stirling TWTAEs using two- and three-dimensional (2D and 3D) time-domain models. These models, validated through comparisons with existing experimental results, confirm the accuracy of our developed full-scale numerical TWTAE models. By evaluating the acoustic characteristics and comparing them with conventional standing-wave thermoacoustic engines, this work highlights the superior performance of the Stirling TWTAE. It achieves the highest heat-driven acoustic power and thermoacoustic energy conversion efficiency. This superior performance is attributed to its operation at a lower oscillation frequency (115 Hz) and an optimized phase between acoustic velocity and pressure oscillations (40 degrees). Additionally, our study explores rich nonlinear phenomena within the flow fields of the Stirling TWTAE. Notably, varying the temperature gradients between 410 K and 485 K introduces a bistable zone with distinct pressure amplitudes. Moreover, mass streaming under varying temperature gradients, and mode transitions due to external flow perturbations are observed inside the engine. These findings not only quantitatively confirm the high efficiency potential of the Stirling TWTAE but also demonstrate the effectiveness of CFD in the development of full-scale numerical models for predicting and optimizing the heat-driven acoustic characteristics and nonlinear phenomena of traveling-wave thermoacoustic systems.

Auto-Bäcklund transformation and exact solutions for a new integrable (2+1)-dimensional shallow water wave equation

Shallow water waves (SWWs) are often used to describe water flow and wave movement in shallow water areas. The article introduces a novel (2 + 1)-dimensional SWW equation. We prove that the equation is integrable and obtain an auto-Bäcklund transformation by truncating Painlevé expansion. Using the bilinear form of the equation, a new auto-Bäcklund transformation and some exact solutions are obtained. Besides, a convergent power series solution is derived using Lie symmetry method. These exact solutions can enrich mathematical modeling and help us understand nonlinear wave phenomena. Finally, conserved vectors are derived.

Thermodynamics-Informed Neural Networks for the Design of Solar Collectors: An Application on Water Heating in the Highland Areas of the Andes

This study addresses the challenge of optimizing flat-plate solar collector design, traditionally reliant on trial-and-error and simplified engineering design methods. We propose using physics-informed neural networks (PINNs) to predict optimal design conditions in a range of data that not only characterized the highlands of Ecuador but also similar geographical locations. The model integrates three interconnected neural networks to predict global collector efficiency by considering atmospheric, geometric, and physical variables, including overall loss coefficient, efficiency factors, outlet fluid temperature, and useful heat gain. The PINNs model surpasses traditional simplified thermodynamic equations employed in engineering design by effectively integrating thermodynamic principles with data-driven insights, offering more accurate modeling of nonlinear phenomena. This approach enhances the precision of solar collector performance predictions, making it particularly valuable for optimizing designs in Ecuador’s highlands and similar regions with unique climatic conditions. The ANN predicted a collector overall loss coefficient of 5.199 W/(m2·K), closely matching the thermodynamic model’s 5.189 W/(m2·K), with similar accuracy in collector useful energy gain (722.85 W) and global collector efficiency (33.68%). Although the PINNs model showed minor discrepancies in certain parameters, it outperformed traditional methods in capturing the complex, nonlinear behavior of the data set, especially in predicting outlet fluid temperature (55.05 °C vs. 67.22 °C).

Chaos analysis and traveling wave solutions for fractional (3+1)-dimensional Wazwaz Kaur Boussinesq equation with beta derivative

Wazwaz Kaur Boussinesq (WKB) equation can effectively simulate the behavior of water waves in shallow water, including the nonlinear effect and dispersion phenomenon of waves, which is of great significance for understanding the dynamic process of ocean, river and other water bodies. To enrich the wave equation theory, the (3+1)-dimensional integer order derivative of WKB equation is changed to the fractional one with beta derivative. The current work deals with the fractional (3+1)-dimensional WKB equation for discussing its chaotic behavior and establishing some new analytic solutions. The chaotic properties of the equation are verified by the trend of evolution along with time, Lyapunov exponents and initial sensitivity analysis. And then complete discrimination system for polynomial method is applied to derive some trigonometric, hyperbolic, Jacobi elliptic and other solutions. The graphical demonstrations are provided for part of these solutions. From these visualized graphs, the solitary, periodic and quasi-periodic wave are shown and the effect of fractional derivatives on the equation can be seen intuitively.

The effect of Lévy index coefficient on modulational instability and rogue wave excitation in nonlocal media with cubic–quintic nonlinearities

This paper explores the modulational instability (MI) of a plane wave and its behavior in the nonlinear Schrödinger equation (NLSE) with a fractional diffraction term quantified by its Lévy index coefficient and nonlocal cubic–quintic nonlinearities. First, we analyze the stability of the plane wave solution and examine how nonlocal nonlinearities and the Lévy index coefficient affect the MI gain. We observe that the stability in the fractional NLSE exhibits new features that differ from those in the standard NLSE. Specifically, when dealing with competing cubic and quintic nonlinearities, the interaction between nonlocality and the Lévy index coefficient α can eliminate MI for low values of α, unlike the classical NLSE with α=2, where we find the plane wave to be unstable. Besides the linear stability analysis, numerical simulations are performed to understand further the plane wave dynamics from its nonlinear stage in this model. The results reveal the generation of periodic chains of localized peaks. Guided by analytical predictions and using the plane wave solution subject to Gaussian perturbation, we numerically investigate the possibility of exciting rogue waves in the parameter spaces where MI exists. We find that the different combinations of signs of the cubic and quintic nonlinearities (focusing and defocusing) and the fractional diffraction term significantly impact the formation of rogue waves. These results may pave the way for the theoretical and experimental study of nonlinear phenomena in physical models with fractional derivatives and nonlocal nonlinearities.

Graph neural network-based multiscale thermal modeling for heterogeneous materials with complex structures

This study presents a novel GNN-based model for multiscale thermal characterization of heterogeneous materials with complex microstructures. It incorporates relationships between composition, structure, and thermal transport across multiple scales, leveraging the structure of GNNs. Results demonstrate enhanced performance of the GNN-based model compared with existing methods. Specifically, the GNN model improved thermal conductivity prediction with a mean absolute error of 0.18 W/mK (15 % improvement over the Bayesian neural network-based model) and provided a 30x speedup in computation time. The model successfully connected atomic-scale interactions to macroscale properties, achieving less than 5 % error in predicting effective thermal conductivity from one scale to another. Furthermore, it demonstrated the ability to capture nonlinear thermal transport phenomena with 92 % accuracy. The model also improved the prediction of the transient thermal responses by 20 %, accurately capturing the time-varying behaviour of materials. This work also proved the model’s ability to handle new material systems with transfer learning, achieving 88 % accuracy. Finally, Bayesian neural networks integrated into the model provided uncertainty quantification, with 95 % of experimental measurements falling within the predicted bounds. This work demonstrated the ability of the framework to handle complex microstructures, nonlinear phenomena, and transient responses while maintaining a computationally efficient model that can enable real-time applications in design and optimization needed in modern materials innovation. It represents a powerful tool for data-driven multiscale mechanics that could accelerate materials research and development for the aerospace, electronics cooling, and additive manufacturing industries.

Integrated Jacobi elliptic function solutions to the [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation by utilizing new solutions of the elliptic equation of order six

In this research, the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation ((3+1)-GKPE) that expresses various nonlinear phenomena was studied. An extended Jacobi elliptic function expansion method (JEFEM) was developed by considering new solutions for the Jacobi elliptic equation of order six. Then the extended method was used to (3+1)-GKPE, where new exact Jacobi elliptic function solutions were obtained. This equation is of particular interest as it required a special transformation in order to apply the JEFEM. Moreover, some of the solutions are shown graphically.