Nonlinear Propagation Model Research Articles

Weak and classical solutions to an asymptotic model for atmospheric flows

In this paper we study a recently derived mathematical model for nonlinear propagation of waves in the atmosphere, for which we establish the local well-posedness in the setting of classical solutions. This is achieved by formulating the model as a quasilinear parabolic evolution problem in an appropriate functional analytic framework and by using abstract theory for such problems. Moreover, for L2-initial data, we construct global weak solutions by employing a two-step approximation strategy based on a Galerkin scheme, where an equivalent formulation of the problem in terms of a new variable is used. Compared to the original model, the latter has the advantage that the L2-norm is a Liapunov functional.

Remote Sensing Small Explosives With an Ionospheric Radar

AbstractEarth's ionosphere has long been targeted as a medium for remote sensing of explosive terrestrial events such as earthquakes, volcanic eruptions, and nuclear/conventional weapon detonations. Until now, the only confirmed ionospheric detections have been of very large events that were easily detectable through other traditional global sensor systems (e.g., seismic). We present the first clear, confirmed detections of relatively low yield 1‐ton TNT‐equivalent chemical explosions using pulsed Doppler radar observations of isodensity layers in the ionospheric E region. The shape and spectra of the detected waveforms closely match predictions from the acoustic ray tracing and weakly nonlinear waveform propagation models. The explosions were roughly three orders of magnitude lower yield than any previous confirmed ionospheric detection and represent the first conclusive evidence that explosions of this size can have clear impacts on the ionosphere. This technique could improve the remote detection of both anthropogenic and natural explosive events.

Turbulence effects on shaped booms: Finite impulse response filter development

Numerical simulations of propagation through turbulent atmospheres can quantify effects on ground waveforms, but such simulations are computationally expensive. To enable quick turnaround analyses as required by NASA’s Quesst Mission, updating the N-wave filtering approach developed by researchers at The Pennsylvania State University to include shaped booms is proposed as an alternative method for estimating turbulence effects on acoustic metrics more quickly. Beginning with a nearfield pressure cylinder modeled after the on-design X-59 configuration, a database of propagation results at 45 turbulence conditions was compiled using nonlinear turbulence propagation modeling code (KZKFourier) and used as input to a process for generating finite impulse response (FIR) filters. Ground waveforms distorted by turbulence were selected to represent mean and mean±standard deviation levels for six metrics, and corresponding FIR filters were generated through a matrix deconvolution process. In order to evaluate how well the FIR filters perform, additional KZKFourier verification cases were devised with different input conditions, and results used as a benchmark. Convolution of shaped boom waveforms modeled using nonturbulent propagation simulations with the new FIR filters showed better agreement on average with KZKFourier statistical results than the N-wave-based FIR filters.

Tools for numerical modelling of nonlinear propagation in hollow capillary fibres and their application

The development of new coherent and ultrashort light sources is of great relevance for exploring fundamental processes and different applications in science. The most successful technique for generating ultrashort laser pulses, in terms of energy and pulse duration, is using hollow capillary fibre (HCF) compressors. The different strategies to further increase the pulse energy and to achieve shorter pulses at non-conventional wavelengths, lead to continuous improvement of this technique. In this work, we present the theoretical framework of the nonlinear propagation in HCFs through the propagation equation and the spatio-temporal effects that appear in the nonlinear dynamics. To numerically study the nonlinear propagation of the pulse in the HCF, we present different numerical models considering only the spatial effects, (1 + 1)D model, the full spatio-temporal dynamics and ionization, (2 + 1)D model, or the case with lack of cylindrical symmetry, (3 + 1)D model. To show the performance of some of these models in a particular case, we study the generation of ultrashort and energetic dispersive waves (DWs) inside the HCF. We show that the emission of a DW at a fixed wavelength for different pump wavelengths is possible by parameter scaling.

Modeling of a lattice model for nonlinear wave propagation in phononic crystals

We construct a nonlinear lattice model to investigate the dynamics of nonlinear behavior in phononic crystals (PnCs). Two types of mass points and springs are introduced in the model to reproduce the difference in material properties between the scatterers and background in PnCs. The nonlinearity is introduced to the model by changing the mass of each mass point depending on the displacement gradient at the mass point. We numerically confirm that both the 1D and 2D models have the bandgap in the linear dispersion relation. Moreover, in both model, switching behavior of wave propagation is found.

A Malware Propagation Model Considering Conformity Psychology in Social Networks

At present, malware is still a major security threat to computer networks. However, only a fraction of users with some security consciousness take security measures to protect computers on their own initiative, and others who know the current situation through social networks usually follow suit. This phenomenon is referred to as conformity psychology. It is obvious that more users will take countermeasures to prevent computers from being infected if the malware spreads to a certain extent. This paper proposes a deterministic nonlinear SEIQR propagation model to investigate the impact of conformity psychology on malware propagation. Both the local and global stabilities of malware-free equilibrium are proven while the existence and local stability of endemic equilibrium is proven by using the central manifold theory. Additionally, some numerical examples and simulation experiments based on two network datasets are performed to verify the theoretical analysis results. Finally, the sensitivity analysis of system parameters is carried out.

Global existence in a two-dimensional nonlinear diffusion model for urban crime propagation

In this paper, we will investigate the urban crime system with the nonlinear diffusion ∂tu=∇⋅um−1∇u−χ∇⋅uv∇v−uv+B1(x,t),x∈Ω,t>0,∂tv=Δv+uv−v+B2(x,t),x∈Ω,t>0under no-flux initial–boundary conditions in a bounded convex domain Ω⊂R2 with smooth boundary. Our first result asserts that when m>32, χ∈(0,∞) and when 1<m≤32, χ∈0,32, the nonlinear diffusion system possesses locally bounded solutions for arbitrary initial data and sufficiently regular source terms B1 and B2. Our second result further reveals that the solutions can be demonstrated to be globally bounded if the source terms satisfy mild additional conditions. In particular, this improves the related result for m>32 (Rodríguez and Winkler, 2020) to the case of arbitrary m>1 under the additional assumption on χ.

Dynamic Spatial Propagation Network for Depth Completion

Image-guided depth completion aims to generate dense depth maps with sparse depth measurements and corresponding RGB images. Currently, spatial propagation networks (SPNs) are the most popular affinity-based methods in depth completion, but they still suffer from the representation limitation of the fixed affinity and the over smoothing during iterations. Our solution is to estimate independent affinity matrices in each SPN iteration, but it is over-parameterized and heavy calculation.This paper introduces an efficient model that learns the affinity among neighboring pixels with an attention-based, dynamic approach. Specifically, the Dynamic Spatial Propagation Network (DySPN) we proposed makes use of a non-linear propagation model (NLPM). It decouples the neighborhood into parts regarding to different distances and recursively generates independent attention maps to refine these parts into adaptive affinity matrices. Furthermore, we adopt a diffusion suppression (DS) operation so that the model converges at an early stage to prevent over-smoothing of dense depth. Finally, in order to decrease the computational cost required, we also introduce three variations that reduce the amount of neighbors and attentions needed while still retaining similar accuracy. In practice, our method requires less iteration to match the performance of other SPNs and yields better results overall. DySPN outperforms other state-of-the-art (SoTA) methods on KITTI Depth Completion (DC) evaluation by the time of submission and is able to yield SoTA performance in NYU Depth v2 dataset as well.

Detailed analysis for chirped pulses to cubic-quintic nonlinear non-paraxial pulse propagation model

This paper's main focus is on chirped pulses (CP) for a cubic-quintic nonlinear non-paraxial pulse propagation (CQ-NNP-PP) model. Chirped solitons are a relatively new single wave phenomena. The exact CPs generate from the derivative nonlinear Schrödinger equations (NLSE). Chirp is a signal with a changing frequency over time. CPs are used in spread spectrum communications as well as some sonar and radar devices. The propagation of CPs in fibre optics is getting popular due to a wide range of applications in amplification and pulse compression. In an NLSE, the dispersion management (DM) term can influence the velocity of chirp-free nonautonomous soliton but has no effect on its shape. When there is no gain, the classical optical soliton can be expressed with a variable dispersion term and nonlinearity. DM can impact the shape and motion of non autonomous solitons for CPs. We obtain hyperbolic and periodic solutions, as well as a class of solitary wave (SW) solutions such as bright, dark, singular and bell soliton solutions. The governing model will be analyzed with the aid of Jacobian elliptic functions (JEF). We also show accomplished results in 3D and 2D structures.

Fracture of single crystal silicon caused by nonlinear evolution of surface acoustic waves

High-amplitude surface acoustic waves (SAWs) undergo nonlinear sharpening during propagation due to the elastic nonlinearity of the material, which leads to material fracture. The degree of nonlinear evolution and material strength are usually characterized by two parameters: the second-order nonlinearity parameter and the critical fracture stress. To study the influence of processing defects, residual stress and temperature on these two parameters, we carry out molecular dynamics modeling of nonlinear propagation of SAWs on non-ideal surfaces. The Stillinger and Weber (SW) and the Lee-modified second nearest-neighbor modified embedded-atom-method (2NN MEAM) potentials are used to study the SAW nonlinear evolution and surface crack nucleation in silicon 1111¯1¯2 geometry, respectively. The results show that processing defects have the greatest influence on the SAW evolution and material strength. For a defined level of defects, the size of initial SAW wavelength directly affects the degree of attenuation of harmonic waves and stress concentration, and then determines the measured nonlinear parameter and critical stress. Temperature can affect the magnitude of the two characterization parameters through thermal dissipation and thermal fluctuations. In the presence of residual stresses only, the relative degree of variation of these two parameters is weak. This study may provide a valuable reference for the establishment of nonlinear SAW atomic-level theory and material characterization experiments.

A flexible fully nonlinear potential flow model for wave propagation over the complex topography of the Norwegian coast

Coastal wave propagation and transformation are complicated due to the significant variations of water depth and irregular coastlines, which are typically present at the Norwegian fjords. A potential flow model provides phase-resolved solutions with low demands on computational resources. Many potential flow models are developed for offshore waves and lack of numerical treatments of coastal conditions. In the presented work, several modifications are introduced to a fully nonlinear potential flow model with a σ-grid for the purpose of coastal wave modelling: Shallow water breaking criteria are included in addition to deepwater breaking algorithms to approximate breaking waves over a complete range of water depth. A new coastline algorithm is introduced to detect complex coastlines and ensure robust simulations near the coast. The algorithm is compatible with structured grid arrangement in the horizontal plane and allows for high-order discretisation schemes for the free surface boundary conditions for an accurate representation of complex free surfaces. A parallelised solver for the Laplace equation is utilised to ensure fast simulations for large domains with multi-core infrastructures.The proposed model is validated against theories and experiments for various two- and three-dimensional nonlinear wave propagation and transformation cases that represent typical coastal conditions. The simulations show a good representation of nonlinear waves, and the results compare well with experiments. Furthermore, two large-scale engineering scenarios are simulated, where the applicability of the coastline algorithm and the parallel commutation capability of the model are demonstrated.

Identification of Acoustic Wave Signatures in the Ionosphere From Conventional Surface Explosions Using MF/HF Doppler Sounding

AbstractWe present an experiment to detect one ton TNT‐equivalent chemical explosions using pulsed Doppler radar observations of isodensity layers in the ionospheric E region during two campaigns. The first campaign, conducted on 15 October 2019, produced potential detections of all three shots. The detections closely resemble the temporal and spectral properties predicted using the InfraGA ray tracing and weakly nonlinear waveform propagation model. Here the model predicts that within 6.5–7.25 min of each shot a waveform peaking between 0.9 and 0.4 Hz will impact the ionosphere at 100 km. As the waves pass through this region, they will imprint their signal on an isodensity layer, which is detectable using a Doppler radar operating at the plasma frequency of the isodensity. Within the time windows of each of the three shots in the first campaign, we detect enhanced wave activity peaking near 0.5 Hz. These waves were imprinted on the Doppler signal probing an isodensity layer at 2.785 MHz near 100 km altitude. Despite these detections, the method appears to be unreliable as none of the six shots from the second campaign, conducted on 10 July 2020 were detected. The observations from this campaign were characterized by an increased acoustic noise environment in the microbarom band and persistent scintillation on the radar returns. These effects obscured any detectable signal from these shots and the baseline noise was well above the detection levels of the first campaign.

Intermixed Time-Dependent Self-Focusing and Defocusing Nonlinearities in Polymer Solutions.

Low-power visible light can lead to spectacular nonlinear effects in soft-matter systems. The propagation of visible light through transparent solutions of certain polymers can experience either self-focusing or defocusing nonlinearity, depending on the solvent. We show how the self-focusing and defocusing responses can be captured by a nonlinear propagation model using local spatial and time-integrating responses. We realize a remarkable pattern formation in ternary solutions and model it assuming a linear combination of the self-focusing and defocusing nonlinearities in the constituent solvents. This versatile response of solutions to light irradiation may introduce a new approach for self-written waveguides and patterns.

Weakly nonlinear propagation of focused ultrasound in bubbly liquids with a thermal effect: Derivation of two cases of Khokolov–Zabolotskaya–Kuznetsoz equations

A physico-mathematical model composed of a single equation that consistently describes nonlinear focused ultrasound, bubble oscillations, and temperature fluctuations is theoretically proposed for microbubble-enhanced medical applications. The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation that has been widely used as a simplified model for nonlinear propagation of focused ultrasound in pure liquid is extended to that in liquid containing many spherical microbubbles, by applying the method of multiple scales to the volumetric averaged basic equations for bubbly liquids. As a result, for two-dimensional and three-dimensional cases, KZK equations composed of the linear combination of nonlinear, dissipation, dispersion, and focusing terms are derived. Especially, the dissipation term depends on three factors, i.e., interfacial liquid viscosity, liquid compressibility, and thermal conductivity of gas inside bubbles; the thermal conduction is evaluated by using four types of temperature gradient models. Finally, we numerically solve the derived KZK equation and show a moderate temperature rise appropriate to medical applications.

Oil–Water Two-Phase Flow Volume Fraction Measurement Based on Nonlinear Ultrasound Technique

Ultrasonic techniques have been widely used to determine the volume fractions of liquid components in oil&#x2013;water two-phase flow. The two major ultrasonic interactions amenable to volume fraction estimation are the sound speed and attenuation. Instead of using these two linear ultrasound parameters, this study explores the use of ultrasound nonlinear parameter to measure the volume fraction of oil&#x2013;water two-phase flow. Based on the theoretical modeling of ultrasound nonlinear propagation and nonlinearity measurement principle using finite amplitude insertion substitution (FAIS), we established a relationship between volume fraction and the amplitude of the second harmonic components in the received ultrasound waveform. With the use of high-intensity ultrasonic excitation, two-end calibration, and second harmonic amplitude extraction, the volume fraction of water can be calculated. The performance of the proposed method is validated by the numerical simulations and experimental studies in a lab-scale flow loop. Good qualitative agreement between the model and results shows that the nonlinear ultrasonic measurement technique has good quantitative accuracy and high measurement sensitivity, which make it well suited for industrial applications.

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

This paper presents the approximate solution of the nonlinear acoustic wave propagation model is known as the modified Camassa–Holm (mCH) equation with the Caputo fractional derivative. We examine this study utilizing the Laplace transform (ℒ T) coupled with the homotopy perturbation method (HPM) to construct the strategy of the Laplace transform homotopy perturbation method (ℒ T‐HPM). Since the Laplace transform is suitable only for a linear differential equation, therefore ℒ T‐HPM is the suitable approach to decompose the nonlinear problems. This scheme produces an iterative formula for finding the approximate solution of illustrated problems that leads to a convergent series without any small perturbation and restriction. Graphical results demonstrate that ℒ T‐HPM is simple, straightforward, and suitable for other nonlinear problems of fractional order in science and engineering.

On some novel bright, dark and optical solitons to the cubic-quintic nonlinear non-paraxial pulse propagation model

On some novel bright, dark and optical solitons to the cubic-quintic nonlinear non-paraxial pulse propagation model

Reduced order model for nonlinear multi-directional ocean wave propagation

In this paper, we introduce a reduced order model (ROM) for the propagation of nonlinear multi-directional ocean wave-fields. The ROM relies on Galerkin projection of Zakharov equations embedded in the high-order spectral (HOS) method, which describes the evolution of nonlinear waves. The dominant flow features of wave evolution are computed from proper orthogonal decomposition (POD) and these modes are used for the projection. The HOS scheme to compute the vertical velocity is treated in a novel way for an efficient implementation of POD-based ROM. We refer to this alternative formalism of HOS as HOS-simple. The final reduced order model (ROM) is derived from the Galerkin projection of HOS-simple. For the case of irregular waves, where the number of modes required are in the range of 200, the ROM has no significant advantage since both HOS and HOS-simple are much faster than real-time. The real advantage is demonstrated in multi-directional (or short-crested) irregular waves, where the ROM is the only model capable of achieving real-time computation, a major improvement to the standard HOS method. The potential use of the ROM in propagating short-crested waves from far-field to near-field for real-world applications involving wave probes in a wave tank/controlled environment as well as X-band radar in open ocean is also demonstrated.

A new family of 𝒜− acceptable nonlinear methods with fixed and variable stepsize approach

Solving stiff, singular, and singularly perturbed initial value problems (IVPs) has always been challenging for researchers working in different fields of science and engineering. In this research work, an attempt is made to devise a family of nonlinear methods amongst which second- to fourth-order methods are not only — stable but — acceptable as well under order stars’ conditions. These features make them more suitable for solving stiff and singular systems in ordinary differential equations. Methods with remaining orders are either zero- or conditionally stable. The theoretical analysis contains local truncation error, consistency, and order of accuracy of the proposed nonlinear methods. Furthermore, both fixed and variable stepsize approaches are introduced wherein the latter improves the performance of the devised methods. The applicability of the methods for solving the system of IVPs is also described. When used to solve problems from physical and real-life applications, including nonlinear logistic growth and stiff model for flame propagation, the proposed methods are found to have good results.

Analytical simulations of the Fokas system; extension (2 + 1)-dimensional nonlinear Schrödinger equation

This paper studies novel analytical solutions of the extended [Formula: see text]-dimensional nonlinear Schrödinger (NLS) equation which is also known with [Formula: see text]-dimensional complex Fokas ([Formula: see text]D–CF) system. Fokas derived this system in 1994 by using the inverse spectral method. This model is considered as an icon model for nonlinear pulse propagation in monomode optical fibers. Many novel computational solutions are constructed through two recent analytical schemes (Ansatz and Projective Riccati expansion (PRE) methods). These solutions are represented through sketches in 2D, 3D, and contour plots to demonstrate the dynamical behavior of pulse propagation in breather, rogue, periodic, lump, and solitary characteristics. The stability property of the obtained solutions is examined based on the Hamiltonian system’s properties. The obtained solutions are checked by putting them back into the original equation through Mathematica 12 software.