Nonlinear Mode Research Articles

A class of stable nonlinear non-Hermitian skin modes

Abstract The non-Hermitian skin effect (NHSE) is a well-known phenomenon in open topological systems that causes a large number of eigenstates to become localized at the boundary. Although many aspects of its theory have been investigated in linear systems, this phenomenon remains novel in nonlinear models. In the first step of this paper, we look at the conditions for the presence of quasi-skin modes in a semi-infinite, one-dimensional, nonlinear, nonreciprocal lattice. In the following phase, we explore the survival time of the quasi-skin mode in a finite nonlinear lattice with open edges. We study the dependency of the survival time on the system's parameters and demonstrate how the nonreciprocity of the system affects the survival time. This study introduces a method for achieving a stable localized state in a nonlinear finite lattice.

Lead‐Sulfide‐Based Hybrid Inorganic‐Organic Superlattice Particles for Prominent Nonlinear Optical Absorption

AbstractSimultaneously optimizing nonlinear absorption coefficient and modulation depth is a considerable challenge for nonlinear optical materials. Here we present an effective solution through constructing PbS2‐based inorganic‐organic superlattice. PbS2/Cn superlattice particles are synthesized, where n (4, 6, and 8) denotes the number of carbon atoms in the organic component. First‐principles simulations indicate the formation of covalent bonds and van der Waals interaction between PbS2 unit and interlayer organic molecules. All samples exhibit strong nonlinear absorption under femtosecond laser excitation with a wavelength range between 515 nm and 900 nm, and the nonlinear absorption coefficient increases with interlayer distance. The optimized sample, PbS2/C8, demonstrates outstanding nonlinear absorption and substantial modulation depth under 800 nm (the third‐order nonlinear absorption coefficient βeff, 10449 ± 609 cm GW−1; modulation depth, 39.1%) and 900 nm (the fifth‐order nonlinear absorption coefficient γeff, 6465 ± 68 cm3 GW−2; modulation depth, 88.1%), which exhibits saturable absorption under 515 nm (βeff, ‐4932 ± 818 cm GW−1; modulation depth, 48.1%). It exhibits a small optical limiting threshold of 1.23 mJ cm−2. These performances surpass those of typical single‐/few‐layer metal chalcogenides. Structural and spectral analyses elucidate that the remarkable optical nonlinearity can be attributed to quantum confinement in the inorganic layer and the dielectric enhancement of the superlattice.

Method for Constructing a Compact Component Mode Synthesis Model for Analyzing Nonlinear Normal Modes of Structures with Localized Nonlinearities

Abstract Nonlinear dynamics analysis is a crucial topic in mechanical and aerospace engineering. The analysis of nonlinear normal modes (NNMs) provides an effective mathematical tool for interpreting complex nonlinear vibration phenomena. Unlike the invariant normal modes of linear systems, NNMs often exhibit frequency-energy dependence and cannot be computed using the traditional eigen-decomposition method. Calculating NNMs relies on numerical methods that involve expensive iterative computations, especially for systems with numerous degrees-of-freedom. To relieve computational costs, this paper proposes a mode selection method for the component mode synthesis (CMS) technique to enable compact reduced-order modeling of structures with localized nonlinearities. The reduced-order model is then combined with a numerical continuation scheme to establish a low-cost NNM analysis framework. This framework can efficiently predict the NNMs of high-dimensional finite element models. The proposed framework is demonstrated on an I-shaped cantilever beam with localized nonlinear stiffness. The results show that the proposed approach can identify the key modes in the CMS modeling procedure. The NNMs of the nonlinear I-shaped beam structure can then be analyzed with a significant reduction in computational costs.

Backward test particle simulation of nonlinear cyclotron wave-particle interactions in the radiation belts

Wave-particle interaction plays a crucial role in the dynamics of the Earth’s radiation belts. Cyclotron resonance between coherent whistler mode electromagnetic waves and energetic electrons of the radiation belts is often called a coherent instability. Coherent instability leads to wave amplification/generation and particle acceleration/scattering. The effect of wave on particle’s distribution function is a key component of the instability. In general, whistler wave amplitude can grow over threshold of quasi-linear (linear) diffusion theory which analytically tracks the time-evolution of a particle distribution. Thus, a numerical approach is required to model the nonlinear wave induced perturbations on particle distribution function. A backward test particle model is used to determine the energetic electrons phase space dynamics as a result of coherent whistler wave instability. The results show the formation of a phase space features with much higher resolution than is available with forward scattering models. In the nonlinear regime the formation of electron phase space holes upstream of a monochromatic wave is observed. The results validate the nonlinear phase trapping mechanism that drives nonlinear whistler mode growth. The key differences in phase-space perturbations between the linear and nonlinear scenarios are also illustrated. For the linearized equations or for low (below threshold) wave amplitudes in the nonlinear case, there is no formation of a phase-space hole and both models show features that can be characterized as linear striations or ripples in phase-space.

A nonlinear manifold model order reduction approach for thermo‐mechanically coupled plasticity

AbstractThis study employs a nonlinear manifold mode order reduction (MOR) approach to address the high computational cost inherent in multi‐physical nonlinear models, which are discretized by the finite element method (FEM), with a particular focus on thermo‐mechanically coupled plasticity under finite strain conditions. Utilizing nodal snapshots obtained from a full‐order simulation, a projection matrix is constructed through singular value decomposition (SVD), facilitating the construction of a reduced system within a lower‐dimensional space. This reduction process entails the multiplication of the discretized residual vector and stiffness matrix by a linear projection matrix, complemented by the incorporation of a nonlinear projection component to ensure accurate reconstruction within the nonlinear part. Subsequently, a comprehensive three‐dimensional benchmark test is conducted to assess the accuracy and efficacy of the reduced‐order model.

Two twinning operators when imposing nonlinear modulation in short‐time Fourier transform

Two types of short‐time Fourier transforms involving respectively nonlinear modulation and nonlinear translation are designed in this note. Some important properties such as twin in time‐frequency domain and orthogonality relations are investigated. Moreover, Lieb type inequalities and uncertainty principle are established.

Nonlinear acoustic modulation utilizing designed acoustic bubble array.

Acoustic modulation has attracted significant investigative interest for their outstanding promising application scenes. Furthermore, acoustic bubble array has shown anticipated foreground in signal processing and acoustic manipulation. Here, we demonstrate a nonlinear acoustic modulation method via designed acoustic bubble array. Numerical calculations have been conducted to analyze several influential parameters and the corresponding effects on the vibrational behaviors of the acoustic bubbles. Appropriate corrections have been added on the numerical model to elucidate the physical scene. Experimental validation has confirmed the practicability and validity of the designation. Potential applications in biological tissue imaging and unidirectional sound transmission can be expected with further research.

224-fs soliton pulses generation at 1μm from ytterbium-doped fiber laser with CoTe2 nanosheets as an ultrafast modulator

Transition metal ditellurides (TMDTs) have numerous attractive properties, making them suitable for a wide range of applications. In this study, cobalt ditelluride (CoTe2) nanosheets, a promising TMDT for photonic applications, were prepared using an ultrasound-enhanced liquid phase exfoliation (LPE) method. A novel saturable absorber (SA) employing CoTe2 nanosheets was then fabricated by optically depositing them on microfiber. The nonlinear optical modulation properties of the CoTe2 SA were investigated. A high-performance 1 μm ultrafast fiber laser was demonstrated by incorporating newly developed CoTe2 nanosheets-based SA in a ring cavity ytterbium-doped fiber laser (YDFL). The dynamical behaviour of the proposed passively mode-locked YDFL in response to variations in pump optical power was investigated. The findings reveal that the device achieved a modulation depth of 2.5 %, and saturation light intensity of 30.6 MW/cm2. Moreover, a stable and robust mode-locked soliton optical pulse sequence with a fundamental repetition frequency of 3.089 MHz, and a pulse duration of 224 fs was generated at 1032 nm. The proposed YDFL, being all-fiber, compact, and cost-effective, is set to find extensive applications in various domains, including optical fiber communication, sensing, and biomedical imaging.

Singular and dark-singular straddled solitons in magneto-optic waveguides with generalized anti-cubic form of self-phase modulation

AbstractThis paper recovers optical soliton solutions in magneto-optic waveguides that maintain the generalized version of anti-cubic form of nonlinear self-phase modulation structure. The csch method as well as the tanh–coth approach recovers the singular and dark-singular straddled optical solitons in such forms of magneto-optic waveguide. The existence criteria of such solitons are also presented.

Modulation instability of whistler wave with electron loss cone distribution in magnetized plasma

Abstract The modulation instability of whistler mode waves caused by thermal electron anisotropy is studied. Based on MHD equations, the nonlinear schrödinger equation (NLSE) that describes the nonlinear modulation of whistler waves is derived by Using the Krylov-Bogoliubov-Mitropolsky (KBM) method. The condition for wave modulation instability is obtained from the loss cone distribution function of thermal electron anisotropy, revealing that the nonlinear growth of the waves tends towards electron perpendicular temperature anisotropy. By setting up continuous background waves and introducing small ion low frequency perturbations, we find that the change in the amplitude of the modulated wave is related with wave number. This finding has been validated through simulations that align with our analytical results. Additionally, we also calculate the maximum amplitude of the wave with loss cone angle and times, which revealed that the electron vertical temperature anisotropy will lead to the modulation instability of the whistler wave. This further confirms the occurrence of the modulation instability of the whistler wave in laboratory plasmas and strengthens their credibility.

Nonlinear optical research on 2D NbSe2 nanosheets and their ultrafast photonics applications

Two-dimensional (2D) NbSe2 is a new material with a variety of excellent properties. In this article, 2D NbSe2 nanosheets are prepared using liquid phase exfoliation (LPE) and spin coating methods. At the same time, the properties of NbSe2 were calculated by using density functional theory (DFT), exploring the changes in the electronic band structure of NbSe2 with the number of layers, and studying the optical properties of NbSe2. The nonlinear optical properties caused by the Pauli blocking effect and the absorption spectra are studied through typical nonlinear testing techniques and an ultraviolet–visible-near-infrared (UV–VIS-IR) spectrophotometer. In addition, 2 µm solid-state pulse lasers have important applications in a variety of fields. For the first time, 2D NbSe2 nanosheets are prepared as saturable absorbers (SA) and applied them to solid-state lasers as nonlinear optical modulation devices, successfully achieving the generation of ultra-short pulse lasers with a pulse duration of 445.4 ps in 2 µm band. Our research results prove that 2D NbSe2 nanosheets is a promising nanomaterial, can be prepared into nonlinear optical modulation devices with excellent performance, and show great application potential as ultrafast photonic devices. It is beneficial to the miniaturization of solid-state pulse lasers in subsequent applications.

Stationary scattering for the nonlinear Schrödinger equation with point-like obstacles: exact solutions

AbstractWe solve the Nonlinear Schrödinger Equation (NLSE) in 1D in presence of one, two and several Dirac delta potentials. With the help of an equivalent central force problem we obtain the analytical solutions in terms of a biparametric family containing the Jacobi functions. Elliptic Jacobi functions are already reported in the literature but they have not been used in the context of a scattering problem under causal boundary conditions. In the simplest examples of one or two Dirac deltas we analyze how the nonlinear term of the equation affects the modulus and phase profiles of the wave function. We also study the transmission curves under the nonlinear modification of the tunneling behavior for the first time. For a Fabri-Perot configuration made of two deltas, we obtain the effect of nonlinear coupling in the positions of the local maxima (resonances). We lay the foundations for nonlinear Anderson localization of 1D BECs in a speckle field. Upon redefinition of parameters these novel results describe the dynamics of a stationary Higgs field in 1D. Finally, we discuss the conditions for soliton formation under the influence of a Dirac comb potential, giving rise to fully correlated locations and intensities of the defects.

Robust Targeted Energy Transfer with Asymmetric Nonlinear Energy Sinks Under Random Excitations

This study introduces an Asymmetric Nonlinear Energy Sink (ANES) to enhance robust Targeted Energy Transfer (TET) in vibration control. Traditional cubic Nonlinear Energy Sinks (NES) often struggle with varying excitation levels in random vibrations. The ANES integrates a cubic NES, extra inertia, and asymmetric stiffness components like a tension-only rope, two linear springs, and a viscous damper. The rope adds asymmetric stiffness by only applying tension force. This setup effectively absorbs vibrational energy across different levels of excitation, facilitating energy transfer from low-damped to high-damped modes. Numerical simulations demonstrate the ANES’s superior performance compared to traditional NES, supported by modal energy redistribution, Nonlinear Normal Modes (NNM) analysis, and Frequency-Energy Plots (FEP). These findings suggest that this type of ANES is a promising advancement for practical NES applications in vibration control.

Conduction immunity modeling approach for nonlinear IB module based on multi-harmonic distortion theory in analog-digital integrated circuit (MADIC)

Conduction immunity modeling approach for nonlinear IB module based on multi-harmonic distortion theory in analog-digital integrated circuit (MADIC)

A Bioengineered Cathepsin B-sensitive Gas Vesicle Nanosystem That Responds With Increased Gray-level Intensity of Ultrasound Biomicroscopic Images

ObjectivesThis work aimed to promote the interaction of a modified Gas Vesicle (GV) with Cathepsin B (CTSB) protease and analyzed their backscattered signal by Ultrasound (US). MethodsWe modified the sequence of the gene coding for GvpC to contain a CTSB cleavage and expressed the protein in an Escherichia coli recombinant system. The protein was purified and added to GVs preparations in which the original GvpC was removed (ΔGV), constituting the modified GV (GV*). Western Blot (WB) test was used to compare GVs with GvpC and engineer GvpC at starting (T0) and after 24 hours (T24) reacting with CTSB. A 21 MHz US B-mode and nonlinear contrast-mode (5% total power) imaged US phantoms having samples of GVwt, ΔGV (stripped GV), GV*, and CTSB+GV*. Also, a 21MHz US B-mode imaged US phantoms having a tumor cell line extracellular fraction (TCEF) and the TCEF+GV* sample. A 100% total US power was applied to collapse the GV structure. ResultsIn WB we detected a decrease in engineered GvpC levels 24 h after the incubation of GV* with CTSB, compared to the concentration at T0, suggesting that CTSB cleaved the engineered GvpC. Regions-of-interest over image of phantom cross-sections were determined and the B-mode image mean gray level intensity resulted in a significant (p<0.05) increase comparing CTSB+GV* with PBS (control), GVwt, ΔGV and GV*. Non-linear mode image gray level intensity from CTSB+GV* increased by 11.79, 7.86 and 14.75 dB from samples containing GVwt, ΔGV and GV*, respectively. GV preparations incubated with TCEF and the TCEF+GV* sample showed an increase of 81% in signal compared to TCEF+GVwt. ConclusionsThe increased ultrasound backscattered signal intensity suggests GVs as a potential biosensor for protease activity, possibly aiding the detection of protease-rich tissue regions.

Boundary excitation of nonlinearly modulated bending strain waves in a metamaterial

A non-linear modulation of bending waves in a metamaterial mass-in-mass lattice model is studied. Various kinds of non-linear wave modulation are obtained using a harmonic boundary excitation. It is shown, that these waves can be described by an asymptotic simplification of the equations of motion resulting in a non-linear modulation equation for the displacements. Exact periodic traveling wave solutions to the equation demonstrate a dependence on the sign of the equation coefficients or the elastic parameters of the original model. Dispersion relation for the carrier part of the solution is obtained as a function of wave number versus frequency, it is found how its solutions relate to the acoustic and optic branches and the band gap. This form of the dispersion relation is further used for a description of numerical results on the wave modulation by a harmonic boundary excitation.

Nonlinear normal modes and response to random inputs of systems with bilinear stiffness

This work seeks to provide a comprehensive review of the effects that stiffness bilinearity can have on the nonlinear modes of a system, its response in a random vibration environment, and the connection between the two. Stiffness bilinearity here refers to a continuous piecewise linear force vs displacement function that is composed of two linear regions. This work focuses on a bilinear stiffness function that is regularized so there is a smooth transition at the point where the two linear regions meet. A single-degree-of-freedom system (SDOF) and a two-degree-of-freedom (2DOF) system are explored and several interesting behaviors are shown. The SDOF bilinear spring model is characterized by four parameters: the low amplitude frequency, the ratio of the linear stiffnesses on either side of the transition, the displacement at which the transition occurs, and the rate or sharpness of the transition. The effect of each parameter on the shape of the NNM is described. In a 2DOF system, these parameters have similar effects, but modal coupling is found to play a significant role. When a bilinear system is subjected to random excitation, many harmonics appear in the response for both the SDOF and 2DOF cases. The root-mean-square (RMS) response of the bilinear system can be larger or smaller than the corresponding linear case depending on the values of the parameters and the type of forcing (broadband, bandlimited, in the shape of a vibration mode, etc.). However, many cases were observed in which the RMS response of the bilinear system was almost the same as that of a linear system, and hence the response could be predicted well using linear analysis. It is hoped that the results presented herein can assist engineers in helping to determine when linear analysis would be adequate to predict the failure of a system, when a rigorous nonlinear analysis is required, and what phenomena are likely to be observed in the latter case.

A Novel Wiener‐Type Dynamic Neural Network Method for Large Signal Modeling of Power Amplifiers

ABSTRACTA novel Wiener‐type dynamic neural network (Wiener‐type DNN) method for large signal modeling of power amplifiers (PAs) is proposed in this paper. In this method, the proposed model structure for the PA contains two Wiener‐type DNNs to describe the input impedance and the amplification efficiency, respectively. The Wiener‐type DNN includes a simplified linear dynamic equation module and a nonlinear static equation module. For the simplification process of the linear dynamic equation, it is proposed to process fundamental frequency components of the large signal harmonic data of the PA by vector fitting. The neural network is used to implement the static equation in the Wiener‐type DNN. The formulas for training the proposed Wiener‐type DNN model of the PA using large signal data are derived. The training algorithm of the PA model is proposed to improve the training efficiency. A Motorola MOSFET PA example and a Freescale lateral double‐diffused MOSFET PA example are present to validate the proposed Wiener‐type DNN method. For the Motorola MOSFET PA, a dynamic neural network (DNN) model and a time‐delay deep neural network (TDDNN) are established for comparison. For the Freescale PA, the DNN model is used for comparison experiment. The comparison figures show that the Wiener‐type DNN model has better convergence properties than the DNN model in the nonlinear region of the PA. The established accurate PA model is conducive to the design of subsequent communication circuits.

Efficient Decoupling of a Nonlinear Qubit Mode from Its Environment

To control and measure the state of a quantum system, it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect, photon-induced dephasing from measurement backaction, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multimode element—an artificial molecule—with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential nonlinear modes, one of which is flux insensitive and used as the protected qubit mode. The second mode is flux tunable and serves via a cross-Kerr-type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit, which we refer to as P-mon, with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed. Published by the American Physical Society 2024

Analysis of a brake squeal functional model using a linear parameter varying perspective

Brake squeal is a limit cycle vibration induced by mode coupling instability that depends on operating conditions such as applied pressure, temperature, and disc velocity. This work proposes a simplified functional model of brake squeal that reproduces the main characteristics observed in a full-scale industrial test campaign: vibration growth, limit cycle saturation, vibration decay and parametric dependence. The proposed functional model differs from the well-known Hoffmann model by the introduction of a nonlinear contact law and a quasi-static pressure loading. First, using a harmonic balance perspective, non-linear forces are shown to lead to a pressure and amplitude dependent contact stiffness. This Linear Parameter Varying perspective allows complex mode computations in the pressure/amplitude domain which are then correlated with a series of transient responses of the nonlinear modes for three different pressure profiles. The chosen profiles represent usual experiments: drag where a constant pressure is applied, pressure ramps and pressure oscillations mimicking the effect of wheel spin on the contact surfaces.