Nonlinear Instability Research Articles

Small/large amplitude vibration, snap-through and nonlinear thermo-mechanical instability of temperature-dependent FG porous circular nanoplates

Small/large amplitude vibration, snap-through and nonlinear thermo-mechanical instability of temperature-dependent FG porous circular nanoplates

A nonlinearly kinematic model of the asymmetrically turbulent premixed slit flame subjected to two-way harmonic disturbances

Transversal and longitudinal combustion instabilities typically occur in gas turbines and rocket engines. Quantifying the nonlinear flame dynamic response of turbulent premixed flames subjected to the two-way disturbances and mean bulk flows is significant to understand the complex nonlinear combustion instability phenomena. A Two-way Nonlinear Unforced Flame Speed Modeling (2W-NUFSM) approach was proposed in this study. The turbulent effects were accounted for in the flame propagation speed term and the steady flame term in the kinematic equation of the flame front; an expansion method was then used to obtain the nonlinear solutions corresponding to the transverse and longitudinal acoustic disturbances. The turbulent effect on the flame consumption speed was also considered in the heat release rate calculation of the perturbed flame. Validations of this approach were conducted by comparing its results to the former credible results obtained from other methods and good agreements were obtained. The influence of turbulent effects on the flame dynamic response in an asymmetrical premixed flame was investigated in detail. The coupling effect of the turbulence and harmonic flow disturbances on the flame nonlinear dynamic response was also quantified.

Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation

We consider the defocusing cubic nonlinear Schrödinger equation (NLS) on the twodimensional torus. The equation admits a special family of elliptic invariant quasiperiodic tori called finite gap solutions. These are inherited from the integrable 1D model (cubic NLS on the circle) by considering solutions that depend only on one variable. We study the long-time stability of such invariant tori for the 2D NLS model and show that, under certain assumptions and over sufficiently long time scales, they exhibit a strong form of transverse instability in Sobolev spaces H^s(\mathbb{T}^2)(0 < s < 1) . More precisely, we construct solutions of the 2D cubic NLS that start arbitrarily close to such invariant tori in the H^s topology and whose H^s norm can grow by any given factor. This work is partly motivated by the problem of infinite energy cascade for 2D NLS, and seems to be the first instance where (unstable) long-time nonlinear dynamics near (linearly stable) quasiperiodic tori is studied and constructed.

Development and Experimental Validation of Dissipative Embedded Column Base Connections for Enhanced Seismic Performance of Steel Moment-Resisting Frames

This paper proposes a novel embedded column base (ECB) connection that defies the current paradigm in capacity-designed steel moment-resisting frames (MRFs) where column bases have been traditionally considered as nondissipative. In the proposed concept, a dissipative zone is introduced as part of the embedded portion of the steel column. This zone features a reduced cross section and is decoupled from the concrete footing with a debonding material layer. The surrounding concrete effectively restrains the embedded section against nonlinear geometric instabilities, thereby retaining simplicity in the design process. Large-scale experiments suggest that, contrary to its conventional counterpart, the proposed dissipative ECB connection exhibits a stable hysteretic response until large lateral drift demands (i.e., 7% rad). It is also demonstrated that the dissipative ECB connection is resilient to local buckling-induced axial shortening, such that it lowers the repairability needs of slender wide-flange steel columns after earthquakes. Column twisting is also minimized throughout the loading history. The results indicate that both the elastic stiffness and flexural yield strength of the proposed ECB connection can be analytically derived for potential use in engineering design. It is found that a simple nondegrading bilinear model suffices to describe the hysteretic response of the proposed ECBs for performance-based assessment of steel MRFs.

High-peak-power pump-modulated quasi-CW fiber laser.

Quasi-continuous wave (CW) laser output with high peak power and high energy is preferred in some industrial applications. Due to the non-linear effects and transverse mode instability, such high-peak-power laser output is difficult to achieve via monolithic fiber lasers in CW mode. For diode-pumped monolithic fiber lasers, by applying overshoot pulse modulation to the pumping diodes, we obtain a pulse laser output with a peak power much higher than that in CW mode. In this paper, it has been theoretically studied that stable pulses with the width of µs level can be generated with quasi-CW operation without distortion according to our simulation. We also experimentally demonstrate a bi-directional pumped quasi-CW monolithic fiber laser operating in CW and pulse modes. In quasi-CW mode, by applying overshoot pulse modulation to the diodes, with a frequency of 1 kHz and a pulse width of 100 µs, the peak power of the output laser reached 9713 W with an average power of 898 W and M2 of 2.4 and 2.3 in the two orthogonal directions, respectively. To the best of our knowledge, this is the very first quasi-CW fiber laser of a 10-kW level with the M2 level of 2.

Study on Linear and Nonlinear Thermal Buckling Mode and Instability Characteristics for Engine Rotating Thin-Walled Blade

The thermal shock load has an important effect on the stability of thin-walled blades under high-speed operation of aircraft engines. According to the actual working conditions, the linear interpolation distribution of blade temperature is obtained by the numerical fitting method. A thermal buckling model is built to obtain the linear and nonlinear modal response of the blade through the finite element method. The results show that the blade stiffness changes under the influence of thermal buckling and the obvious torsional deformations are produced along the radial direction of the blade. Meanwhile, the largest deformation of about 1.3 mm and stress of 81 Mpa occurs on the blade tip for both the linear and nonlinear response. The buckling stress distribution and critical load factor of thermal buckling are also calculated, consistent with the rubbing part of blade. The changing radial length is the main reason for the distance reduction between the blade and casing, causing more probability of friction impact. Therefore, reasonable local thermal buckling technology is helpful to improve the design level of thermal-shock loaded blades.

Nonlinear size-dependent dynamic instability and local bifurcation of FG nanotubes transporting oscillatory fluids

Nonlinear size-dependent dynamic instability and local bifurcation of FG nanotubes transporting oscillatory fluids

Beyond the spontaneous scalarization: New fully nonlinear mechanism for the formation of scalarized black holes and its dynamical development

In the present paper, we show the existence of a fully nonlinear mechanism for the formation of scalarized black holes, which is different from the spontaneous scalarization, and demonstrate its dynamical development. We consider a class of scalar-Gauss-Bonnet gravity theories within which no tachyonic instability can occur. Although the Schwarzschild black holes are linearly stable against scalar perturbations, we show dynamically that for certain choices of the coupling function, they are unstable against nonlinear scalar perturbations. This nonlinear instability leads to the formation of new black holes with scalar hair. The fully nonlinear and self-consistent study of the equilibrium black holes reveals that the spectrum of solutions is more complicated and more than one scalarized branch can exist. We have also considered classes of scalar-Gauss-Bonnet theories where both the standard and the nonlinear scalarization can be present, and they are smoothly connected that completes in an interesting way the picture of black hole scalarization. The fully nonlinear (de)scalarization of a Schwarzschild black hole will always happen with a jump because the stable ``scalarized branch'' is not continuously connected to the Schwarzschild one that can leave clear observational signatures.

Nonlinear behavior and instabilities of a hyperelastic von Mises truss

Recent decades have witnessed a renewed interest in the field of structural stability due to new applications involving smart and deployable structures, micro- and nanocomponents and mechanical metamaterials, among others. In many of these structures multistable behavior is desirable, which can be accomplished by traditional and new materials capable of undergoing large elastic deformations. In this paper the nonlinear behavior, bifurcations and instabilities of a hyperelastic von Mises truss exhibiting multistable behavior is investigated. Most papers dealing with the von Mises truss are restricted to linear elastic materials. Here, the nonlinear equilibrium equations are derived considering elasticity in the fully non-linear range and the incompressible Mooney–Rivlin constitutive law is adopted to model the hyperelastic material. The nonlinear equations are solved by using the Newton–Raphson method and continuation techniques. Then, all equilibrium paths and bifurcation points are obtained and their stability is investigated using the energy criterion. A detailed parametric analysis of shallow and nonshallow trusses under horizontal and vertical loads is conducted. Load and geometric imperfections are considered and their influence on the bifurcation scenario and the truss load carrying capacity is clarified. The influence of the material parameters on the nonlinear response is also examined. The results show that the simultaneous presence of geometric and material nonlinearities leads to several equilibrium paths, some of which are not expected for linear elastic materials or found in the existing literature on nonlinear materials, resulting in several coexisting stable and unstable solutions and a complex potential energy landscape, thus clarifying the influence of the constitutive hyperelastic model on the results. Analytical expressions for the normalized snap-through and pitchfork bifurcation loads are derived as a function of the material parameters, truss geometry and imperfections for practical applications. The influence of Eulerian buckling on the truss load carrying capacity is also investigated and formulas to evaluate the buckling load under both vertical and horizontal loads are derived. The present results may help in the development of new engineering applications where multistability and large deformations are desired.

Rigorous proof of the slightly nonlinear Jeans instability in the expanding Newtonian universe

Due to the nonlinearity of the Euler{Poisson equations, it is possible that the nonlinear Jeans instability may lead to a faster density growing rate than the rate in the standard theory of linearized Jeans instability, which motivates us to study the nonlinear Jeans instability. The aim of this article is to develop a method proving the Jeans instability for slightly nonlinear Euler-Poisson equations in the expanding Newtonian universe. The standard proofs of the Jeans instability rely on the Fourier analysis. However, it is difficult to generalize Fourier method to a nonlinear setting, and thus there is no result in the nonlinear analysis of Jeans instability. We firstly develop a non-Fourier-based method to reprove the linearized Jeans instability in the expanding Newtonian universe. Secondly, we generalize this idea to a slightly nonlinear case. This method relies on the Cauchy problem of the Fuchsian system due to the recent developments of this system in mathematics. The fully nonlinear Jeans instability for the Euler-Poisson and Einstein-Euler equations are in progress.

Nonlinear spatiotemporal instabilities in two-dimensional electroconvective flows

This work studies nonlinear spatiotemporal stability of two-dimensional electroconvection between two flat plates subjected to a through-flow, using numerical simulations and weakly nonlinear analyses. We found that the traveling speeds of the leading and trailing edges of the wave packet in the nonlinear regime are consistent with the linear ones. We derived for the first time the Ginzburg-Landau equation (GLE) using an amplitude expansion method extending earlier work of Pham and Suslov. This GLE can predict the absolute growth rate even when the parameters are away from the linear critical conditions, outperforming the GLE derived using a multiple-scale expansion method.

Self-Induced Solutal Marangoni Flows Realize Coffee-Ring-Less Quantum Dot Microarrays with Extensive Geometric Tunability and Scalability.

Currently, quantum dot light‐emitting diodes (QD‐LEDs) are receiving extensive attention. To maximize their luminous performance, the uniformity of the QD‐LEDs is crucial. Although the spontaneously self‐induced solutal Marangoni flow of an evaporating binary mixture droplet has been widely investigated and used to suppress coffee‐ring patterns in ink‐jet printing technology, unfortunately, ring shapes are still present at the edges, and the Marangoni flow generated by the selective evaporation of volatile liquid components cannot be controlled due to its nonlinear instabilities. In this work, polygonal coffee‐ring‐less QD microarrays are created using two spontaneous and sequential solutal Marangoni flows. During the initial evaporation, internal circulating flows are controlled by polygonal‐shaped droplets. After that, sequential interfacial flows are generated by the captured volatile vapors. A theoretical model and scaling analysis are provided to explain the working mechanisms. It is expected that the newly designed printing system can be applied to the mass production of QD‐LEDs.

Generation mechanism and prediction of an observed extreme rogue wave

Rogue waves are individual ocean surface waves with crest height eta or trough-to-crest height H that are large compared to the significant wave height H_s of the underlying sea state: H/H_s>2.2 or eta /H_s>1.25. The physics of rogue wave generation and the potential of predicting the rogue wave risk are open questions. Only a few rogue waves in high sea states have been observed directly, but they can pose a danger to marine operations, onshore and offshore structures, and beachgoers. Here we report on a 17.6m high rogue wave in coastal waters with eta /H_s=1.98 and H/H_s=2.9 which are likely the largest normalized heights ever recorded. Simulations of random superposition of Stokes waves in intermediate water depth show good agreement with the observation. Non-linear wave modulational instability, a well known cause for rogue waves in laboratory settings, did not contribute significantly to the rogue wave generation. A parameter obtained from a routine spectral wave forecast provides a practical risk prediction for rogue waves. These results confirm that probabilistic prediction of oceanic rogue waves based on random superposition of steep waves are possible and should replace predictions based on modulational instability.

Investigating the impact of the latitudinal velocity profile on nonlinear gradient drift instability development in the subauroral ionosphere

Subauroral polarization streams (SAPS) are regions in the subauroral ionosphere with lower plasma density and large westward flow driven by a poleward electric field. Density irregularities have been observed in the SAPS region; these irregularities can negatively impact radio signals by causing phase and amplitude fluctuations. Previous work identified the gradient drift instability (GDI) as a generation mechanism of such ionospheric irregularities in SAPS and investigated the impact of the velocity profile on the GDI development. The turbulence spectra of the GDI are important to understand as they can provide insight into spatial scales associated with the turbulent evolution that may impact radio propagation. We hypothesize that the background electric field, through the neutral wind, and the nature of the velocity shear have an impact on the power laws from the turbulence spectra. A 2D fluid model is used to investigate the turbulence spectra of GDI in SAPS with a fixed background density profile and different latitudinal velocity profiles. Data from Super Dual Auroral Radar Network (SuperDARN) radar and Global Positioning System (GPS) provide the background ionospheric conditions. The neutral wind direction is chosen to be in the equatorward direction, which is in line with typical observations; however, this can be used to modify the electric field to consider new possibilities in the SAPS region. The angle of the electric field is manifested through the combination of the background velocity profile ( drift) and the neutral wind. The turbulence spectra of cases with no velocity profile and with different neutral wind directions are analyzed. The impact of velocity shear is studied by translating the velocity shear location relative to the density gradient. Numerical spectral analysis results are presented and compared to recent experimental observations. Results of spectral slopes of GDI simulations with no background velocity ( drift) were found to be and for the normalized density and the perturbed electric potential, respectively. Spectral slopes for simulations with different velocity shear locations were found to follow power laws of and for the normalized density and perturbed electric potential (inside SAPS region), respectively.

Instabilities of a vortex-ring-bright soliton in trapped binary three-dimensional Bose-Einstein condensates

Instabilities of vortex-ring-bright coherent structures in harmonically trapped two-component three-dimensional Bose-Einstein condensates are studied numerically within the coupled Gross-Pitaevskii equations and interpreted analytically. Interestingly, the filled vortex core with a sufficiently large amount of the bright component is observed to reduce the parametric interval of stability of the vortex ring. We have identified the mechanisms of several linear instabilities and one nonlinear parametric instability in this connection. Two of the linear instabilities are qualitatively different from ones reported earlier, to our knowledge, and are associated with azimuthal modes of $m=0$ and $m=1$, i.e., deviations of the vortex from the stationary ring shape. Our nonlinear parametric resonance instability occurs between the $m=0$ and $m=2$ modes and signals the exchange of energy between them.

On inhibition of the Rayleigh–Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping

It is still open whether the inhibition phenomenon of the Rayleigh–Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive magnetohydrodynamic (MHD) fluid in a two-dimensional (2D) horizontal slab domain, since it was roughly verified in the linearized case by Wang in [43]. In this paper, we show that this inhibition phenomenon can be rigorously verified in the (nonlinear) inhomogeneous, incompressible, inviscid case with velocity damping. More precisely, we show that there is a critical number mC, such that if the strength |m| of a horizontal magnetic field is bigger than mC, then the small perturbation solution around the magnetic RT equilibrium state is exponentially stable in time. Moreover, we also provide a nonlinear instability result for the case |m|∈(0,mC). Our instability result reveals that a horizontal magnetic field can not inhibit the RT instability, if it's strength is too small.

Optimized Filters for Stabilizing High-Order Large Eddy Simulation

High-order Flux Reconstruction (FR) schemes can be used to simulate unsteady turbulent flows using Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) in the vicinity of complex geometries. However, the application of FR can be limited by non-linear instabilities, which can arise from oscillatory behaviour of the underlying polynomial representation of the solution. In this paper, we explore filtering and its parametrization for stabilizing under-resolved simulations of the Navier–Stokes equations. A new exponential filtering operator is proposed, which is normalized by the time-step size and designed to filter high-frequency modes. Over 14,000 numerical tests are then performed to obtain an optimal set of filtering parameters, with the objective being to stabilize while maintaining high-order accuracy. We then verify that these optimal filters converge to super-accuracy for non-linear problems, and compare filtered and unfiltered simulations of the Taylor–Green vortex using both straight and curved meshes, and turbulent channel flow. These demonstrate that the filtered solutions are generally more accurate than unfiltered ones, while still stabilizing previously unstable simulations. Finally, we demonstrate the utility of these filters for more complex flows, specifically a stalled NACA 0020 airfoil.

New nonlinear instability for scalar fields

In this letter we introduce the non-linear partial differential equation (PDE) $\partial^2_{\tau} \pi \propto (\vec\nabla \pi)^2$ showing a new type of instability. Such equations appear in the effective field theory (EFT) of dark energy for the $k$-essence model as well as in many other theories based on the EFT formalism. We demonstrate the occurrence of instability in the cosmological context using a relativistic $N$-body code, and we study it mathematically in 3+1 dimensions within spherical symmetry. We show that this term dominates for the low speed of sound limit where some important linear terms are suppressed.

Nonlinear analysis of open-chain flexible manipulator with time-dependent structure

• Nonlinear dynamics analysis of time-varying structure are investigated. • The equations derived by using Hamilton’s principle. • The distinct bifurcation parameters of force & torque inputs have considered. • The effects of excitation frequency, damping coefficient have studied. The analysis of motion equations of flexible-link manipulators indicates that nonlinear terms and behavioral instability exist in their outcomes. In this system, when the differential equations possess structural time-dependent parameters, there is a higher chance for system instability, especially chaos in comparison to time-invariant ones. It is a point for abnormal behavior that is unpredictable and always accompanied by damages. Therefore, the physical parameters and system inputs that cause chaotic responses should be detected and prevented as much as possible. To this aim, the dynamic equations of flexible link manipulator with revolute-prismatic joints as a case of time-variant dynamic system are obtained by Hamilton’s principle with the assumption of nonlinear strains. The discretized motion equations are solved and the results are presented in the forms of bifurcation diagrams (for variation of torque/force amplitude), Poincaré maps, phase-plane portraits, and the largest Lyapunov exponent. Finally, the obtained results are validated with the aid of the experimental setup. The results indicate that although the system response in low torque/force amplitudes is subharmonic (amplitude of 0.01) and quasi-periodic (amplitudes of 0.02–0.03), it becomes quasi-periodic/chaotic with a mild slope with respect to time in high amplitude values. Moreover, since the behavior of modal generalized coordinate is different from the rigid ones, the quasi-periodic and chaotic vibrations do not hurt the joints.

Dust-Acoustic Nonlinear Waves in a Nanoparticle Fraction of Ultracold (2K) Multicomponent Dusty Plasma

The nonlinear dust-acoustic instability in the condensed submicron fraction of dust particles in the low-pressure glow discharge at ultra-low temperatures is experimentally and theoretically investigated. The main discharge parameters are estimated on the basisof the dust-acoustic wave analysis. In particular, the temperature and density of ions, as well as the Debye radius, are determined. It is shown that the ion temperature exceeds the temperature of the neutral gas. The drift characteristics of all plasma fractions are estimated. The reasons for the instability excitation are considered.