Nonlinear Stage Research Articles

Research on Tensile Stress–Strain Relationship of Azide Polyether Propellant for Wide‐Temperature Range Based on Time–Temperature Superposition Principle

ABSTRACTAzide polyether propellants are emerging high‐energy solid propellants and have broad application prospects. To determine their mechanical properties under wide temperature ranges, tensile tests were conducted considering different combinations of temperature and loading rate, and the corresponding tensile stress–strain curves were plotted. The influence laws of temperature and loading rate on the materials' tensile response were revealed through qualitative and quantitative analyses. The applicability of the time–temperature superposition principle to the nonlinear deformation stage of the propellant was proved, and a stress response prediction method derived from this principle that solely relies on dynamic mechanical analysis and tensile test data was established.

The influence of geosynthetic properties on their shear behaviors at the interface with frozen soil

This paper investigates the shear properties of the interfaces between sand and short-staple nonwoven geotextile (GT1), long-staple nonwoven geotextile (GT2), and geomembrane (GM) under varying conditions of testing temperature, sand moisture content, and normal stress through temperature-controlled direct shear tests. The results reveal that the shear stress-shear displacement curves for the sand-GT1 and sand-GM interfaces can be broadly categorized into an elastic deformation stage, a nonlinear growth stage, and a stable stage. However, the sand-GT2 interface displays a continuously increasing trend throughout the experiment. The peak friction angles of the interfaces increase significantly as the temperature decreases, following the order GT1 > GT2 > GM. The average residual friction angle of sand with GT1, GT2, and GM decreased by 14.8%, 10.4%, and 31.1%, respectively, compared to the peak friction angle. The peak cohesion at the sand-GM interface is relatively weaker than that at the sand-GT1 and sand-GT2 interfaces. The shear mechanisms between frozen soil and geotextiles involve ice cementation, rolling, interlocking, and fiber tensioning, while the shear mechanisms between frozen soil and GM comprise ice cementation, rolling, indentation, and plowing.

Precise passive synchronization of dissipative soliton resonance lasers via cascaded cross-phase- and cross-absorption-modulation for mid-infrared mode-locked pulse generation

We present the first demonstration of utilizing cascaded cross-phase and cross-absorption modulation effects for synchronizing the pulse parameters of two mode-locked fiber lasers operating in the dissipative soliton resonance regime. By utilizing the cross-absorption modulation effect we achieve a significant improvement in pulse repetition frequency synchronization dynamic range (13.5 cm cavity optical path mismatch, or 1.87 kHz pulse repetition frequency mismatch) while simultaneously achieving passive pulse duration synchronization through injection of synchronization pulses into the gain fiber of one of the Slave lasers. This approach leads to a record pulse repetition frequency synchronization dynamic range. Subsequently, the synchronized DSR lasers at 1.06 µm and 1.56 µm are employed in a nonlinear difference frequency generation stage to generate mode-locked mid-infrared pulses with a pulse repetition rate of ∼ 2 MHz and an exceptional fractional instability of 3.60 × 10-13, measured for a 1000 s integration time.

Coupled wave instability in pure-quartic dispersive and noninstantaneous Kerr media in presence of walk-off

The letter explores modulational instability (MI) in birefringent optical media with pure-quartic dispersion, relaxed Kerr nonlinearity, and walk-off effects. The linear stage of MI is studied using coupled biharmonic nonlinear Schrödinger equations, and the stability of their continuous wave solutions is used to calculate the growth rate of MI. The latter is then used to characterize MI under the combined effects of nonlinear responses, group-velocity mismatch, and quartic dispersion, with a focus on the pure-quartic soliton regime. The nonlinear stage of MI is also studied through direct numerical simulations, which support the analytical predictions and emphasize the impact of quartic dispersion, relaxed Kerr nonlinearity, and the walk-off effect on the emergence of various nonlinear patterns. These findings provide valuable insights into signal generation and processing in pure-quartic optical materials and have potential applications in nonlinear optics and lasers.

Particle transport and deposition in wall-sheared thermal turbulence

We studied the transport and deposition behaviour of point particles in Rayleigh–Bénard convection cells subjected to Couette-type wall shear. Direct numerical simulations (DNSs) are performed for Rayleigh number ( $Ra$ ) in the range $10^{7} \leq Ra \leq ~10^9$ with a fixed Prandtl number $Pr = 0.71$ , while the wall-shear Reynolds number ( $Re_w$ ) is in the range $0 \leq Re_w \leq ~12\,000$ . With the increase of $Re_w$ , the large-scale rolls expanded horizontally, evolving into zonal flow in two-dimensional simulations or streamwise-oriented rolls in three-dimensional simulations. We observed that, for particles with a small Stokes number ( $St$ ), they either circulated within the large-scale rolls when buoyancy dominated or drifted near the walls when shear dominated. For medium $St$ particles, pronounced spatial inhomogeneity and preferential concentration were observed regardless of the prevailing flow state. For large $St$ particles, the turbulent flow structure had a minor influence on the particles’ motion; although clustering still occurred, wall shear had a negligible influence compared with that for medium $St$ particles. We then presented the settling curves to quantify the particle deposition ratio on the walls. Our DNS results aligned well with previous theoretical predictions, which state that small $St$ particles settle with an exponential deposition ratio and large $St$ particles settle with a linear deposition ratio. For medium $St$ particles, where complex particle–turbulence interaction emerges, we developed a new model describing the settling process with an initial linear stage followed by a nonlinear stage. Unknown parameters in our model can be determined either by fitting the settling curves or using empirical relations. Compared with DNS results, our model also accurately predicts the average residence time across a wide range of $St$ for various $Re_w$ .

Competition between merging and bifurcation in the generalized Rayleigh-Taylor instability.

The nonlinear evolution of bubble and spike fronts growing through the generalized Rayleigh-Taylor instability are studied by numerical simulations and by solving an extension of Alon's [Phys. Rev. E 48, 1008 (1993)2470-004510.1103/PhysRevE.48.1008] statistical model based on the asymptotic velocity of a single-mode bubble and the merging bubble process. In this work, the generalized Rayleigh-Taylor instability includes a frictional force due to collision with a secondary fluid. Depending on its strength the behavior during the nonlinear stage leads to two different regimes: the first is the classical inertial case where the bubble front is known to grow as h∝t^{2} and evolves towards large structures, and the second is the collisional case where the front grows as h∝t and maintains structures of relatively constant size. In this new regime, the importance of adding the bifurcation process, the opposite process of merging, is highlighted.

Racial and Ethnic Identity of Transnational Adoptees: A Model Reflecting the Lived Experience of Adult Colombian Adoptees

International and transracial adoptions have been practiced by multiple developed countries since World War II, where transracial adoptees are removed from their country of origin and raised by parents of a completely different cultural and racial background. In the United States, adoption was institutionalized after the Korean War, making adoption across races a common practice. This demographic change brings different developmental challenges to the transracial adoptee, including the task of racial and ethnic identity. In this dissertation study, the authors dived into the narratives of six Colombian transracial adoptees raised in the United States by White parents to understand their stories regarding their racial and ethnic identity process. The authors’ findings include the development of a racial and ethnic identity model that emerged from the participants’ themes and common lived experiences, including five nonlinear stages: questioning and curiosity; action-seeking behaviors; judgment and expectations; reculturation and reclaiming; and wanting to embrace both identities. Adult Colombian adoptees highlighted the fluidity of their racial and ethnic identity process and the importance of reclaiming and reconnecting with their Colombian part of self as part of this process. The ethnic and racial identity model informs mental health professionals’ clinical and professional practice by offering a guide to comprehending the process and some of the common experiences around ethnic and racial identity among transracial adoptees.

A new approach to the description of plasma Langmuir waves

After finding an exact solution to the Vlasov–Boltzmann kinetic equation (i.e., finding distribution functions for plasma particles), we consider the description of Landau damping using Poisson's equation, since with the complete distribution function, there is no need to split the kinetic equation into equilibrium and perturbed parts for the subsequent implementation of the pole bypass in the integrand expression. The found distribution function depends, in addition to velocity, on the coordinates and can be used to analytically consider different cases and configurations of the spatial confinement of the plasma. General distribution function for electrons is discussed. We consider the behavior of Langmuir waves, also at the nonlinear stage.

All-fiber supercontinuum absorption spectroscopy for mid-infrared gas sensing

The development of compact fiber-based light sources emitting over a wide wavelength range in the mid-infrared and their application to the detection of greenhouse gases and volatile organic compounds still remain of critical interest. In the present work, we make use of several dedicated infrared fibers for implementing a mid-infrared optical device pumped by a thulium doped-fiber laser around 1.965 μm that simultaneously enables a first nonlinear stage of frequency conversion and supercontinuum generation and a second linear stage of gas absorption spectroscopy. As a proof-of-principle, we carry out mid-infrared supercontinuum absorption spectroscopy of methane around 7.7 μm by means of a hollow-core fiber-based gas cell combined to a commercial Fourier-transform infrared spectrometer. Our all-fiber configuration operating in the femtosecond regime at megahertz repetition rate allows the detection of methane concentrations as low as 20 ppm.

Evaluation of the shear behavior of RC beams strengthened with prestressing BFRP grids

The shear behavior of reinforced concrete (RC) beams strengthened with prestressing basalt-fiber-reinforced polymer (BFRP) grids was experimentally evaluated. Parameters, including grid type, concrete strength, and prestress direction and level, were numerically investigated. Equations for the shear capacity of prestressing grid-strengthened beams were derived. The results showed that using BFRP grids with a 30 % prestress level increased the number of mid-span flexural cracks in the strengthened beam but reduced their length. Compared to the control beam, the load capacity under the serviceability limit state was enhanced by 48 %. The strain responses of the grids exhibited a linear stage followed by a nonlinear stage due to diagonal cracks. The maximum strains of longitudinal and transverse grid tendons in the prestressed strengthened beam decreased by 15 % and 30 %, respectively, compared to the non-prestressed beam. The BFRP grids showed a comparable strengthening effect to low-modulus carbon-fiber-reinforced polymer grids. Increasing concrete strength greatly improved the shear capacity of RC beams. The enhancement effect was greater for transverse tendons with a 30 % prestress level than for longitudinal tendons with a 60 % prestress level. The derived equation accurately predicted shear capacities in experiments or simulations within an error range from −4.7–1 %.

Experimental Study on Horizontal Resistance Parameter of Gravelly Soil Considering Slope Gradient Factor

Horizontal resistance can be significantly different for gravelly soil slope sites with different gradients. The impact of slope gradient on the horizontal resistance of soil based on a three-dimensional physical simulation test has been investigated, and the displacement of the pile top and soil pressure for four piles under various gradients (slope gradient 0–45°) was analyzed. The research reveals that ① The soil resistance exhibits a linear increase stage, non-linear steep increase stage, and gradually stabilizing stage with the increase in load. ② The ultimate soil resistance is significantly affected by depth and displacement, and hyperbolic variation characteristics related to the displacement stage. It has a slope weakening effect, and the steeper the slope gradient, the lower the ultimate soil resistance of the pile sides, which effect is negligible when the depth exceeds 0.6–0.7 times that of the pile buried depth. ③ Based on the characteristics of horizontal ultimate resistance-displacement-depth variation in soil, a gradient factor, which is only related to the slope gradient, was used to describe the impact of gradient on the soil resistance modulus (kini) and ultimate resistance (pu). kini is reduced close to the ground surface and gradually increases with depth until it becomes equal to the value of level ground. The ratio between pu in slope ground and level ground was determined for slope angles. The above horizontal resistance parameters were expressed as a function based on the test data to calculate the lateral ultimate bearing capacity of gravelly soil considering the slope gradient factor. The research results developed the theory of foundation design for building structures, promoting the reliability evaluation of pile soil systems towards a more scientific and rigorous direction.

Effect of central plasma pressure on high-order harmonics of 1/1 quasi-interchange instability in a central weak magnetic shear tokamak configuration

Abstract Numerical investigations of linear and nonlinear stages of quasi-interchange instability in a cylindrical tokamak geometry with a flat q-profile in the core region are conducted using eigenvalue and initial value codes, respectively. It is found that there exists a dependent relationship between the central plasma pressure p 0 (of the initial pressure profile) and the dominant harmonic of the quasi-interchange instability. As p 0 increases, m = n > 1 mode would be dominant in the linear stage and even in the nonlinear stage, where m and n are the poloidal and toroidal mode number, respectively. In addition, with p 0 increasing, the fast growth of other harmonics is inevitable and will deeply affect the evolution of m = n dominant quasi-interchange instability.

Breakdown of laminar regime in flat plate boundary layer seen in numerical solutions of the Navier–Stokes equations obtained with 16th-order scheme

Numerical solutions of the Navier–Stokes equations describing the onset and the development of the boundary layer instability of a subsonic flow about a finite width flat plate are described. They were obtained via exciters-free calculations with the 16th-order multioperators-based scheme optimized to resolve very small solutions scales. Some relevant details of the scheme are briefly outlined. The occurrence of the Tollmien–Schlichting waves near the leading edge, their downstream propagation and breakdowns some distance away are displayed. The role of the oblique waves seen in the solutions is emphasized. The nonlinear stage in the form of structured vortices followed by the solutions randomization are described.

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.

Observation of an Extraordinary Type V Solar Radio Burst: Nonlinear Evolution of the Electron Two-Stream Instability

Solar type V radio bursts are associated with type III bursts. Several processes have been proposed to interpret the association, electron distribution, and emission. We present the observation of a unique type V event observed by e-CALLISTO on 7 May 2021. The type V radio emission follows a group of U bursts. Unlike the unpolarized U bursts, the type V burst is circularly polarized, leaving room for a different emission process. Its starting edge drifts to higher frequency four times slower than the descending branch of the associated U burst. The type V processes seem to be ruled by electrons of lower energy. The observations conform to a coherent scenario where a dense electron beam drives the two-stream instability (causing type III emission) and, in the nonlinear stage, becomes unstable to another instability, previously known as the electron firehose instability (EFI). The secondary instability scatters some beam electrons into velocities perpendicular to the magnetic field and produces, after particle loss, a trapped distribution prone to electron cyclotron masering (ECM). A reduction in beaming and the formation of an isotropic halo are predicted for electron beams continuing to interplanetary space, possibly observable by Parker Solar Probe and Solar Orbiter.

Gravitational waves from collapse of pressureless matter in the early universe

If an early matter phase of the Universe existed after inflation with the proper power spectrum, enhanced density perturbations can decouple from the Hubble flow, turn around and collapse. In contrast towhat happens in a radiation dominated Universe where pressure nullifies deviations from sphericity in these perturbations, in a matter dominated Universe, the lack of pressure although on the one hand facilitates the gravitational collapse, it allows small deviations from sphericity to grow substantially as the collapse takes place. The subsequent collapse is complicated: initially as non-spherical deviations grow, the collapsing cloud takes the form of a “Zel'dovich pancake”. After that, the more chaotic and nonlinear stage of violent relaxation begins where shells of the cloud cross and the matter is redistributed within a factor of a few of the free fall timescale, reaching a spherical virialized state. During the whole process, strong gravitational waves are emitted due to the anisotropy of the collapse andthe small time interval that the effect takes place. The emission of gravitational waves during the stage of the violent relaxation cannot be easily estimated with an analytical model. We perform an N-body simulation to capture the behaviour of matter during this stage in order to estimate the precise spectrum of gravitational waves produced in this scenario.

Hybrid-Vlasov Modelling of Ion Velocity Distribution Functions Associated with the Kelvin–Helmholtz Instability with a Density and Temperature Asymmetry

The Kelvin–Helmholtz instability (KHI), characterized by vortices forming at a perturbed velocity shear layer, is a prominent candidate mechanism for mass, momentum, and energy transport across boundaries with velocity shear in various space plasma environments. It is of particular interest at the flanks of Earth’s magnetopause, which separates the plasma of the magnetosphere from the adjacent shocked solar wind flow in the magnetosheath. In the present study, we use local hybrid-Vlasov simulations to investigate the ion velocity distribution functions (VDFs) associated with KHI in a magnetopause-like, transverse velocity shear layer setting (magnetic field perpendicular to the shear plane). We look for signatures of ion finite Larmor radius (FLR) effects, which could be utilized in spacecraft measurements to recognize when such effects are active, influencing KHI evolution and driving plasma mixing. We show that when a density/temperature asymmetry exists across the shear layer, FLR effects produce a heat flux along the vortex edges. With a magnitude (≳0.1 mW m−2) that is a significant fraction of the total magnetosheath energy flux, the heat flux provides a distinct signature that could be measured with a single spacecraft. During the late nonlinear stage of KHI, mixed non-Maxwellian ion VDFs are additionally found within the vortices. Our results are also valid in the presence of a small magnetic shear across the magnetopause.

Gain-controlled taming of recurrent modulation instability

We show how the recurrence phenomenon characteristic of the nonlinear stage of induced modulational instability in a passive fiber is affected by forcing. An additional linear amplification, even if extremely weak, induces separatrix crossing corresponding to critical values of the gain around which the recurrence process considerably slows down, switching between dynamical orbits of different kind. We present evidence for such phenomenon in a fiber optics experiment where the gain is finely tuned by means of Raman amplification. A theoretical explanation is also provided that matches almost perfectly with our experimental results. Published by the American Physical Society 2024

Reliability of Girder Bridge System under Lateral Uneven Vehicular Overloads

Truck presence on bridges is random. Trucks may centrically or eccentrically appear on a bridge span in one or more lanes, which will cause extra load effects on girder components and eventually influence structural performance. Especially when trucks are heavily loaded, their eccentric passage is possible to induce damage in components, and, thus, the prescribed load- delivery path will be changed among components within the system. Therefore, component- and system-level structural performance of bridges subjected to aggressive vehicular overloads need to be thoroughly addressed. In this study, a WIM-based 5-axle overloaded truck model is chosen, and it is gradually applied to the finite element models of two girder bridges with different eccentric distance, considering two loading scenarios of single truck and multiple trucks. In detail, trucks are transversely loaded with an incremental eccentric distance, to investigate the impacts of eccentric loadings on structural performance, including failure sequences of components, load distribution factors among components, as well as system redundancy, as structures entering nonlinear stage. Finally, the reliability indices of the two bridges under uneven overloads are assessed at the component level and system level, respectively. The results of this study were beneficial to structural evaluation bridges subjected to overloads to ensure their serviceability and integrity.

Numerical Study of High-g Combustion Characteristics in a Channel with Backward-Facing Steps

High gravity (high-g) combustion can significantly increase flame propagation speed, thereby potentially shortening the axial length of aero-engines and increasing their thrust-to-weight ratio. In this study, we utilized the large eddy simulation model to investigate the combustion characteristics and flame morphology evolution of premixed propane–air flames in a channel with a backward-facing step. The study reveals that both the increase in centrifugal force and flow velocity can enhance pressure fluctuations during combustion and increase the turbulence intensity. The presence of centrifugal force promotes the occurrence of Rayleigh–Taylor instability (RTI) between hot and cold fluids. The combined effects of RTI and Kelvin–Helmholtz instability (KHI) enhance the disturbance between hot and cold fluids, shorten the fuel combustion time, and intensify the dissipation of large-scale vortices. The increase in fluid flow velocity can raise the flame front’s hydrodynamic stretch rate, thereby enhancing the turbulence level during combustion to a certain extent and increasing the fuel consumption rate. When a strong centrifugal force is applied, the global flame propagation speed can be more than doubled. Within a certain range, the increase in high-g field strength can enhance the intensity of RTI and accelerate the transition of RTI to the nonlinear stage.