Nonlinear Phenomena Research Articles

Experimental Observation of Raman Assisted and Kerr Optical Frequency Comb in a 4H-Silicon-Carbide on Insulator Microresonator

Kerr nonlinear microcavities have garnered significant interest owing to their rich dynamics of nonlinear optical phenomena and compatibility with on-chip photonic integration. Recently, silicon carbide has emerged as a compelling platform due to its unique optical properties. In this study, we demonstrate Raman-assisted and Kerr optical frequency generation in a 4H-silicon carbide-on-insulator microresonator. By pumping the transverse electric (TE00) mode within the device, we observe a stimulated Raman scattering (SRS) Stokes with the Raman shift at approximately 775 cm-1, achieved with an on-chip power of 350 mW. Furthermore, by red-tuning the TE00 pump wavelength, we have achieved the coexistence of Raman and Kerr frequency combs. Using another device on the same chip with light variation of the taper we can observe the Raman and Kerr frequency combs within a spectral bandwidth ranging from ∼ 1440 to 1960 nm. The inclusion of the Raman-assisted comb extends the comb’s coverage into longer wavelength regimes, making it highly desirable for spectroscopy applications.

Uncovering the stochastic dynamics of solitons of the Chaffee–Infante equation

In this paper, we apply stochastic differential equations with the Wiener process to investigate the soliton solutions of the Chaffee–Infante (CI) equation. The CI equation, a fundamental model in mathematical physics, explains concepts such as wave propagation and diffusion processes. Exact soliton solutions are obtained through the application of the modified extended tanh (MET) method. The obtained wave figures in 3D, 2D, and contour are highly localized and determine an individual frequency shift under the behavior of sharp peak, periodic wave, and singular soliton. The MET method shows to be a valuable analytical tool for obtaining soliton solutions, essential for understanding the dynamics of nonlinear wave phenomena. Numerical simulations enable us to explore soliton solutions in two and three dimensions, shedding light on their properties over time. Our results have wide applications in various domains, including stochastic processes and nonlinear dynamics, impacting advancements in physics, engineering, finance, biology, and beyond.

Hybrid spin-orbit exciton-magnon excitations in FePS3

FePS3 is a layered van der Waals (vdW) Ising antiferromagnet that has recently been studied in the context of true 2D magnetism and emerged as an ideal material platform for investigating strong spin-phonon coupling, and non-linear magneto-optical phenomena. In this work, we demonstrate an important unresolved role of spin-orbit coupling (SOC) in the ground state and excitations of this compound. Combining first-principles calculations with linear flavor wave theory (LFWT), we find strong mixing and spectral overlap of different spin-orbital single-ion states. Low-lying excitations form hybrid spin-orbit exciton/magnon modes. Complete parameterization of the low-energy model requires nearly half a million coupling constants. Despite this complexity, such a model can be inexpensively derived using local many-body-based approaches, which yield quantitative agreement with recent experiments. The results highlight the importance of SOC even in first-row transition metals and provide essential insight into the properties of 2D magnets with unquenched orbital moments.

Optical soliton solutions of the nonlinear complex Ginzburg-Landau equation with the generalized quadratic-cubic law nonlinearity having the chromatic dispersion

In this study, we consider the complex Ginzburg-Landau equation with the generalized quadratic-cubic law of self-phase modulation. This model finds applications in various fields, such as the study of superconductivity, nonlinear optical phenomena, pattern formation, and designing photonic devices and systems. This manuscript successfully employs the new Kudryashov method to derive analytical solutions for complex Ginzburg-Landau equations with the generalized quadratic-cubic law of self-phase modulation. The 3D, contour, and 2D graphical representations of the acquired solutions are represented. Therefore, W-shaped, bright, and dark soliton structures are derived. Through rigorous analysis and interpretation, valuable insights into the influence of the parameters of the presented model on the soliton behavior are achieved.

Electromagnetic effects on solitons propagation of the (3+1)-dimensional extended Zakharov-Kuznetsov dynamical model with applications

This paper investigates wave solutions and electromagnetic wave phenomena governed by the (3+1)-dimensional extended Zakharov-Kuznetsov equation (EZKE) utilizing the Sardar sub-equation method. With a focus on electromagnetic wave generation and propagation, we rigorously analyze fundamental properties, soliton solutions, and dynamic behaviors of the EZKE. Through this analytical technique, we unravel the complex interplay among various wave types, including solitary waves and electromagnetic structures, elucidating their formation mechanisms and interaction dynamics. Furthermore, we delve into the stability characteristics of the EZKE, enhancing our understanding of its mathematical and physical implications. Our findings not only contribute to theoretical insights into nonlinear wave phenomena in (3+1)-dimensional space but also hold practical significance in plasma physics, nonlinear optics, and electromagnetic wave propagation. This study advances the development of innovative wave manipulation and control techniques, with applications ranging from plasma confinement in fusion devices to the design of advanced photonic devices for telecommunications and sensing purposes.

Dynamics of pH Oscillators in Continuous Stirred Tanks in Series.

Complex reaction networks with positive and negative feedback can produce diverse nonlinear phenomena in open reactors, such as multistability and oscillations. pH oscillators driven by hydrogen or hydroxide autocatalytic processes show sustained oscillations in continuously stirred tank reactors (CSTR) but only a sharp pH switch in batch. Here, we present a numerical study on the dynamics of pH oscillators in a series of CSTRs. We show a critical residence time under which bistability and above which oscillations develop. The dynamics of the CSTR cascade show the cross-shaped phase diagram of nonlinear activatory inhibitory systems. In the domain of oscillations, one reactor starts to oscillate autonomously and induces forced complex oscillations in the following tanks with damped amplitudes. These results, with their practical implications, may contribute to understanding the recent experimental observations of nonlinear phenomena in the presence of a residence time ramp and inspire further research in this area.

Drilling performance analysis of a polycrystalline diamond compact bit via finite element and experimental investigations

The significance of improving the drilling productivity and reducing the cost and non-productive time of drilling process, substantially relies on the efficiency of drilling performance. This paper provides a comprehensive understanding of drilling process, aiming to predict drilling performance and investigate drilling parameters using a validated finite element (FE) model. Experimental validation of the FE model was achieved through testing on a laboratory drilling rig, ensuring the accuracy and reliability of the numerical simulations. To accurately capture the nonlinear characteristics of bit-rock interaction, the Riedel–Hiermaier–Thoma model was adopted as a material model, and its parameters were identified through a series of carefully conducted experimental tests. The numerical results obtained from the FE rock failure model during the compressive and tensile tests demonstrated a robust correlation with the experimental data. The verified material model was then employed into another FE drilling model to simulate rock breaking in an actual drilling scenario. This analysis sheds light on the impact of drill-bit interaction with the rock formation, providing valuable insights into its behaviour during drilling operations. The FE drilling model was further utilised in a parametric study to predict the effects of critical drilling parameters, like loading rate and rotary speed, on the weight on the bit, torque on the bit, and rate of penetration. Both the FE drilling and experimental results provided a significant consistency when the drilling parameters were compared, and nonlinear dynamic phenomena, such as stick–slip and bit-bouncing, were observed. By investigating these effects, this study contributes to optimising drilling operations, enabling better control of premature vibrations and enhancing drilling efficiency.

Tunable Stochastic State Switching in 2D MoS2 Nanomechanical Resonators with Nonlinear Mode Coupling and Internal Resonance.

Coupled nanomechanical resonators have unveiled fascinating physical phenomena, including phonon-cavity coupling, coupled energy decay pathway, avoided crossing, and internal resonance. Despite these discoveries, the mechanisms and control techniques of nonlinear mode coupling phenomena with internal resonances require further exploration. Here, we report on the observation of stochastic switching between the two resonance states with coupled 1:1 internal resonance, for resonant two-dimensional (2D) molybdenum disulfide (MoS2) nanoelectromechanical systems (NEMS), which is directly driven to the critical coupling regime without parametric pumping. We further demonstrate that the probability of state switching is linearly tunable from ∼0% to ∼100% by varying the driving voltage. Furthermore, we gradually increase the white noise amplitude and show that the probability of obtaining the higher-energy state decreases, and the stochastic switching phenomenon eventually disappears. The results provide insights into the dynamics of coupled NEMS resonators and open up new possibilities for sensing and stochastic computing.

Isolated attosecond pulse generation in a semi-infinite gas cell driven by time-gated phase matching

Isolated attosecond pulse (IAP) generation usually involves the use of short-medium gas cells operated at high pressures. In contrast, long-medium schemes at low pressures are commonly perceived as inherently unsuitable for IAP generation due to the nonlinear phenomena that challenge favourable phase-matching conditions. Here we provide clear experimental evidence on the generation of isolated extreme-ultraviolet attosecond pulses in a semi-infinite gas cell, demonstrating the use of extended-medium geometries for effective production of IAPs. To gain a deeper understanding we develop a simulation method for high-order harmonic generation (HHG), which combines nonlinear propagation with macroscopic HHG solving the 3D time-dependent Schrödinger equation at the single-atom level. Our simulations reveal that the nonlinear spatio-temporal reshaping of the driving field, observed in the experiment as a bright plasma channel, acts as a self-regulating mechanism boosting the phase-matching conditions for the generation of IAPs.

High-frequency nonlinear vibration analysis through low-frequency stereo-camera systems

This paper describes a new methodology that expands the capabilities of low-frame, high-resolution stereo-camera systems in studying the dynamic behavior of components in the presence of nonlinear phenomena. A new downsampling technique called the Smoothed Harmonics Analysis (SHA) is proposed. This technique addresses the limitations due to the low-frame rate cameras for the study of high-frequency periodic steady-state nonlinear oscillations. SHA enables accurate reconstruction of downsampled signals, thus opening up numerous potential applications. The feasibility of this technique is demonstrated by analyzing the motion of a beam with nonlinear behavior. The nonlinearity is caused by intermittent contact while the beam is subjected to harmonic excitation.

Identification of critical drought thresholds affecting vegetation on the Mongolian Plateau

The increasing frequency of drought events due to global climate change has significant impacts on ecosystems, often resulting in reduced vegetation productivity. However, vegetation responses to drought often exhibit non-linear threshold phenomena, where vegetation growth sharply decreases once water stress reaches a certain level. Our study, conducted on the Mongolian Plateau, focuses on revealing the drought response thresholds and distribution patterns of different vegetation types. These thresholds mark critical turning points from high drought resistance to high vulnerability in vegetation response and serve as early warning indicators, crucial for accurately assessing how terrestrial ecosystems adapt to climate change. We utilized remote sensing observation datasets and inversion datasets spanning from 2001 to 2020, including six representative vegetation indices. The results indicate that: (1) Over 70 % of the Mongolian Plateau experiences low vegetation growth (<10th) predominantly influenced by drought, with low vegetation growth often occurring when water availability falls below the 30th percentile; (2) Areas with higher vegetation coverage and relatively moist climates have lower proportions of drought thresholds, implying that more complex ecosystems can better mitigate water stress, while background climatic conditions also regulate vegetation response to water availability; (3) According to multi-model climate predictions, the overall probability of drought risk on the Mongolian Plateau is projected to significantly increase during 2080–2100, especially in drought-prone regions. These findings provide important insights into better understanding the impacts of drought on ecosystems. Additionally, they emphasize the urgency of taking early measures to adapt to future drought risks.

Subharmonic response suppression of a quasi-zero stiffness system

Quasi-zero stiffness (QZS) isolators can effectively suppress low-frequency vibration due to high-static-low-dynamic stiffness (HSLDS) characteristics. The existence of nonlinearity induces intricate nonlinear phenomena in QZS isolators, particularly under conditions of small damping and large excitation. These nonlinear characteristics can seriously affect the vibration isolation performance, which has rarely been focused on in existing studies. This study examines a typical QZS isolator with nonlinear damping. The modified incremental harmonic balance (IHB) method is applied to directly analyze its dynamic characteristics and investigate the suppression of the subharmonic response. The dynamic analysis results indicate multiple subharmonic vibration intervals, including the 1/2, the 1/3, and the 1/9 subharmonic vibration. The basin of attraction at different excitation frequencies shows that subharmonic vibration is highly likely to occur. The effect of different damping on the transmissibility proves to be different. Simultaneously, rational parameter matching can guarantee the absence of subharmonic vibration while maintaining the primary resonance frequency and amplitude unchanged. The research results of this study provide theoretical support for the parameter selection of QZS isolators. In addition, the higher-order approximations of most isolators have the same form, so these results can guide other QZS isolators in suppressing subharmonic vibrations and improving their operating range.

Nonlinear flow phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface

In this paper, we present a comprehensive study of the fingering phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface. A theoretical analysis is firstly carried out and the governing equation describing the film thickness is established for the non-Newtonian fluid denoted by a power-law index n. Using the lubrication theory with dimensionless variables, the partial differential equation for the film thickness is derived, and both two-dimensional flow and three-dimensional flow are investigated. The traveling wave characteristic of the two-dimensional flow is displayed by using the finite difference scheme associated with a Newton iteration technique. The effect of changing the radius of the cylinder, precursor-layer thickness and power-law index is then considered through examining the variation of the capillary waves. Furthermore in three-dimensional complex flow, the fingering patterns for different parameters are simulated. The linear stability analysis based on the traveling wave solutions is given to elucidate the influence of different physical parameters, explaining the physical mechanism of nonlinear flow behaviors in two dimension and three dimension. Results from linear stability analysis show that the power-law index reinforces the fingering instability whether the fluid is shear-thinning or shear-thickening. Moreover, the numerical results illustrate that increasing the radii of the cylinder expands the unstable region. The flow profiles for different power-law coefficients are consistent with the result of the linear stability analysis, proving the unstable role of the power-law coefficient.

A hybrid yang transform adomian decomposition method for solving time-fractional nonlinear partial differential equation

Nonlinear time-fractional partial differential equations (NTFPDEs) play a great role in the mathematical modeling of real-world phenomena like traffic models, the design of earthquakes, fractional stochastic systems, diffusion processes, and control processing. Solving such problems is reasonably challenging, and the nonlinear part and fractional operator make them more problematic. Thus, developing suitable numerical methods is an active area of research. In this paper, we develop a new numerical method called Yang transform Adomian decomposition method (YTADM) by mixing the Yang transform and the Adomian decomposition method for solving NTFPDEs. The derivative of the problem is considered in sense of Caputo fractional order. The stability and convergence of the developed method are discussed in the Banach space sense. The effectiveness, validity, and practicability of the method are demonstrated by solving four examples of NTFPEs. The findings suggest that the proposed method gives a better solution than other compared numerical methods. Additionally, the proposed scheme achieves an accurate solution with a few numbers of iteration, and thus the method is suitable for handling a wide class of NTFPDEs arising in the application of nonlinear phenomena.

Experimental investigation on the mode transition characteristics of a phase-change thermofluidic oscillator with external loads

Phase-change thermofluidic oscillator has drawn significant attention thanks to its low operating temperature, which is beneficial for recovering low-grade heat. The vapor–liquid coupling oscillation in the thermofluidic oscillator leads to complex non-linear mode transition phenomenon that affects the steady operation. In this work, the mode transition characteristics of a thermofluidic oscillator with external loads (i.e., a needle valve and a load reservoir) are experimentally investigated through bifurcation analysis. A low-order van der Pol model is employed to examine the effect of acoustic resistance on mode transition. Experimental results demonstrate that modifying the valve opening and load volume under a constant temperature difference can trigger bifurcation, resulting in high-frequency limit cycle, low-frequency limit cycle and quasi-periodic modes. The non-linear features of each mode are revealed through phase space and Poincaré section, with Neimark-Sacker bifurcation, second bifurcation and inverse Neimark-Sacker bifurcation observed. Steady-state performance of oscillator is then characterized under different oscillation modes. The maximum pressure amplitudes measured are 11.54 kPa during the high-frequency oscillation and 1.35 kPa during the low-frequency oscillation, while the maximum displacement amplitudes obtained are 45.5 mm during the high-frequency oscillation and 91.4 mm during the low-frequency oscillation. The oscillation modes can be adjusted by external load to maximize output performance. This study offers comprehensive guidelines for constructing phase-change thermofluidic oscillators.

CIELAB Color Space as a Field for Tracking Color-Changing Chemical Reactions of Polymeric pH Indicators.

Two types of cross-linked polymeric dye films that exhibit reversible color changes in response to pH were prepared. Upon protonation, films with a nitrophenol dye moiety (NP) changed from yellow to colorless, whereas films with an azobenzene dye moiety (AB) changed from yellow to reddish-purple. The colored light transmitted through these films from a D65 white-light source was measured colorimetrically, and the transition of the chromaticity point in CIELAB upon protonation of the polymeric dyes was observed. At low dye concentrations ([NP] < 4.7 × 10-5 and [AB] < 2.7 × 10-5 mol L-1), linear loci of the chromaticity points were displayed for both polymeric dye films, indicating perceptual linearity. This linearity is caused by the avoidance of nonlinear perceptual phenomena such as the Abney effect and the Bezold-Brücke phenomenon. The perceptual linearity of space is a necessary condition for achieving stoichiometric linearity, which requires an additional linear relationship between the dye concentration and each component, a*, b*, and L*. A geometric equation that included the AB concentration and the protonation ratio of AB was used to successfully depict, on the basis of stoichiometric linearity, the protonation of the polymeric AB films three-dimensionally in the restricted area of CIELAB.

Exciton-Exciton Interactions in Van der Waals Heterobilayers

Exciton-exciton interactions are key to understanding nonlinear optical and transport phenomena in van der Waals heterobilayers, which emerged as versatile platforms to study correlated electronic states. We present a combined theory-experiment study of excitonic many-body effects based on first-principle band structures and Coulomb interaction matrix elements. Key to our approach is the explicit treatment of the fermionic substructure of excitons and dynamical screening effects for density-induced energy renormalization and dissipation. We demonstrate that dipolar blueshifts are almost perfectly compensated by many-body effects, mainly by screening-induced self-energy corrections. Moreover, we identify a crossover between attractive and repulsive behavior at elevated exciton densities. Theoretical findings are supported by experimental studies of spectrally narrow, mobile interlayer excitons in atomically reconstructed, h-BN-encapsulated MoSe2/WSe2 heterobilayers. Both theory and experiment show energy renormalization on a scale of a few meV even for high injection densities in the vicinity of the Mott transition. Our results revise the established picture of dipolar repulsion dominating exciton-exciton interactions in van der Waals heterostructures and open up opportunities for their external design. Published by the American Physical Society 2024

Non-linear dynamics and critical phenomena in the holographic landscape of Weyl semimetals

This study presents a detailed analysis of critical phenomena in a holographic Weyl semi-metal (WSM) using the D3/D7 brane configuration. The research explores the non-linear response of the longitudinal current J when subjected to an external electric field E at both zero and finite temperatures. At zero temperature, the study identifies a potential quantum phase transition in the J-E relationship, driven by background parameters the particle mass, and axial gauge potential. This transition is characterized by a unique reconnection phenomenon resulting from the interplay between WSM-like and conventional nonlinear conducting behaviors, indicating a quantum phase transition.Additionally, at non-zero temperatures with dissipation, the system demonstrates first- and second-order phase transitions as the electric field and axial gauge potential are varied. The longitudinal conductivity is used as an order parameter to identify the current-driven phase transition. Numerical analysis reveals critical exponents in this non-equilibrium phase transition that show similarities to mean-field values observed in metallic systems.

Painlevé analysis and Hirota direct method for analyzing three novel physical fluid extended KP, Boussinesq, and KP-Boussinesq equations: Multi-solitons/shocks and lumps

Due to the extensive and diverse connections of the Kadomtsev-Petviashvili (KP) equation with various physical phenomena, such as the propagation of waves in sea and ocean water and the propagation of nonlinear waves in plasmas when two-dimensional perturbations are considered, thus in this study and based on the original KP equation, we construct and investigate three extended models, which are called the extended KP (eKP) equation, the extended Boussinesq (eBO) equation, and the extended KP-Boussinesq (eKP-BO) equation. These equations are commonly observed in many physical contexts involving nonlinear and dissipative media. Our research begins with thoroughly verifying the complete integrability of the three extended models. Once this crucial step is accomplished, we will examine these three extended models using the simplified Hirota approach (SHA), leading us to derive multiple soliton/shock solutions. Furthermore, the Hirota bilinear form of each model will be employed to derive a set of lump solutions for these three extended models, utilizing different parameter values. We also analyze some derived solutions graphically by presenting some two- and three-dimensional graphics to understand the dynamic behavior of the waves described by these solutions. The obtained results are anticipated to benefit a broad spectrum of academics interested in studying fluid mechanics, water wave characterization, and other interdisciplinary domains. Additionally, these models are anticipated to be essential in describing and understanding the dynamics of several nonlinear phenomena that arise and propagate in different plasma systems when perturbations are considered in multidimensions.

A generalized Bogdanov-Takens system with arbitrary degree

The aim of this paper is to give the bifurcation diagram and all global phase portraits in the Poincaré disc of a generalized Bogdanov-Takens system with arbitrary degree. Moreover, the system has abundant nonlinear phenomena, such as double limit cycle bifurcation, Hopf bifurcation, homoclinic bifurcation, heteroclinic bifurcation, and so on. Notice that the nonlinear phenomena of the system are more abundant and more complex than the classic Bogdanov-Takens system.