Wavelength Of Instability Research Articles

Long wavelength interdomain phonons and instability of dislocations in small-angle twisted bilayers

Abstract We develop a theory for long wavelength phonons originating at dislocations separating domains in small-angle twisted homobilayers of 2D materials such as graphene and MX2 transition metal dichalcogenides (M=Mo,W; X=S,Se). We find that both partial and perfect dislocations, forming due to lattice relaxation in the twisted bilayers with parallel and anti-parallel alignment of unit cells of the constituent layers, respectively, support several one-dimensional subbands of the interdomain phonons. We show that spectrum of the lowest gapless subband is characterized by imaginary frequencies, for wave-numbers below a critical value, dependent on the dislocation orientation, which indicates an instability for long enough straight partial and perfect dislocations. We argue that pinning potential and/or small deformations of the dislocations could stabilize the gapless phonon spectra. The other subbands are gapped, with subband bottoms lying below the frequency of interlayer shear mode in domains, which facilitates their detection with the help of optical and magnetotransport techniques.

Linear stability analysis of a thin liquid film on a horizontal wall under quasi-periodic oscillation

We carry out a linear stability analysis of the flow of a thin layer of Newtonian fluid with a deformable free surface bounded at the bottom by a horizontal wall subjected to quasi-periodic oscillation in its own plane. Or's model (J. Fluid Mech., vol. 335, 1997, pp. 213–232), using a periodic oscillation, is extended to the configuration where oscillation has two incommensurate frequencies, $\omega _1$ and $\omega _2$ , with an irrational ratio $\omega ={\omega _2}/{\omega _1}$ . Using the long-wave expansion, we derive the asymptotic function involved in the long-wave instability criterion while taking into account the frequency ratio. It turns out that the maximum of this asymptotic function, as well as the frequency parameter at which long-wave instabilities occur, depend strongly on the frequency ratio. For arbitrary wavenumbers, the equations governing the problem under consideration are solved in space using Chebyshev's spectral collocation method, while the temporal resolution is performed using Floquet theory, knowing that an irrational number can be approximated by a rational number. For a large frequency ratio and for a velocity amplitude ratio equal to unity, we obtain, as in Or's work (J. Fluid Mech., vol. 335, 1997, pp. 213–232) considering the same frequency parameter interval, an alternation between the U shape and oblique shape referring respectively to instabilities of long wavelength and finite wavelength appearing in the diagram representing Reynolds number as a function of frequency parameter. By decreasing the frequency ratio towards $1/\sqrt {37}$ , the three initial U-shaped and three oblique instabilities merge into a single U-shaped and a single oblique instability. This merging phenomenon also occurs when the ratio of the amplitudes of the superimposed velocities, linked to the introduction of the second frequency, increases from small values to unity. For a fixed frequency parameter, the effect of frequency ratio and velocity amplitude ratio on the marginal stability curves in terms of Reynolds number versus wavenumber is also investigated, focusing on the appearance of long wavelength instability and finite wavelength instability.

Effect of depth ratio on frozen wave instability in immiscible liquids

In the present experimental work, a two-liquid system with comparable densities (density ratio = 0.543) undergoing lateral sinusoidal oscillation [along the length (L) of the container] has been considered. Under high forcing frequency condition (ω≫ν/L2), frozen waves appear at the interface of two-liquid system. Different depth ratios (hr) (or filling levels of liquid-1 and liquid-2) have been used to investigate the variations in the instability thresholds, wave amplitudes, wavelengths, and wave profiles of the frozen waves. Instability threshold of frozen waves shows unidirectional nature with varying depth ratios. A coefficient of relative velocity (c1) has been used to non-dimesionalize the variation of threshold amplitude (Aoc) and wave amplitude (Ar) with respect to depth ratios. Variation of normalized wave amplitude with modified Froude number shows existence of two regimes viz. gravity and surface tension dominated beyond which waves become three dimensional. A significant variation in wave profiles has been observed at high amplitude of forcing and reported in terms of radius of curvature. The three-dimensional frozen waves with temporally and spatially periodic doubling have been discussed.

Mitigating thermal burden and enhancing minor phase emission energy transfer in perovskite by introducing dopamine-mediated silver nanoparticles

Perovskite-based light-emitting diodes (PeLEDs) suffer from low wavelength and intensity instability during excited emission. This study incorporates dopamine-mediated silver nanoparticles (DA@AgNPs) into perovskite to enhance the performance of blue-light PeLEDs. Characterization studies highlight the crucial role of dopamine’s hydroxyl group in controlling the size and distribution of AgNPs. Due to the presence of amine group, dopamine acts as a “bridging linker,” facilitating precise integration of AgNPs with perovskite. DA@AgNPs–perovskite comprises a uniform cubic phase, indicating improved crystal quality and fewer defects than in pristine perovskite. DA@AgNPs prevent pinhole-defect-induced heat accumulation, reducing nonradiative energy and Joule heat. Additionally, DA@AgNPs enhance thermal conductivity and thus cooling efficiency. The energy transfer between minor and primary phase emissions is found to be highly efficient and to enhance primary phase emission through the surface plasmon resonance effect of DA@AgNPs. Finally, DA@AgNPs–perovskite is successfully employed in a high-performance blue-light PeLED (wavelength = 476 nm); the device’s external quantum efficiency is 11.2 %, luminance is 380.2 cd/m2, and emission stability is favorable (firmly maintained at 476–478 nm after strong excitation under 4.25 V for 1 h). This work provides insights into one means of improving blue-light PeLEDs, opening avenues for advancements in optoelectronics.

Self-organization of anti-aligning active particles: Waving pattern formation and chaos.

Recently, it has been shown that purely anti-aligning interaction between active particles may induce a finite wavelength instability. The formed patterns display intricate spatiotemporal dynamics, suggesting the presence of chaos. Here, we propose a quasi-one-dimensional simplification of the particle interaction model. This simplified model allows us to deduce amplitude equationsthat describe the collective motion of the active entities. We show that these equationsexhibit chaotic orbits. Furthermore, via direct numerical simulations of the particle's system, we discuss the pertinence of these amplitude equationsapproach for describing the particle's self-coordinated motions.

High–Speed Laser Modulation for Low–Noise Micro–Cantilever Array Deflection Measurement

In this paper, an innovative approach is introduced to address the noise issues associated with micro–cantilever array deflection measurement systems employing multiple lasers. Conventional systems are affected by laser mode hopping during switching, resulting in wavelength instability and beam spot fluctuations that take several hundred milliseconds to stabilize. To mitigate these limitations, a high–speed laser modulation technique is utilized, leveraging the averaging effect over multiple modulation cycles within the sampling window. By driving the lasers with a high–frequency carrier signal, a low–noise and stable output suitable for micro–cantilever beam deflection measurement is achieved. The effectiveness of this approach is demonstrated by simultaneously modulating the lasers and rapidly observing the spectral and centroid variations during high–speed switching using a custom–built high–speed spectrometer. The centroid fluctuations are also analyzed under different modulation frequencies. The experimental results confirm that the high–speed modulation method can reduce the standard deviation of beam spot fluctuations by more than 90%, leading to significant improvements in noise reduction compared to traditional laser switching methods. The proposed high–speed laser modulation approach offers a promising solution for enhancing the precision and stability of multi–laser micro–cantilever array deflection measurement systems.

Instability Compensation of Recording Interferometer in Phase-Sensitive OTDR.

In the paper, a new method of phase measurement error suppression in a phase-sensitive optical time domain reflectometer is proposed and experimentally proved. The main causes of phase measurement errors are identified and considered, such as the influence of the recording interferometer instabilities and laser wavelength instability, which can cause inaccuracies in phase unwrapping. The use of a Mach-Zender interferometer made by 3 × 3 fiber couplers is proposed and tested to provide insensitivity to the recording interferometer and laser source instabilities. It is shown that using all three available photodetectors of the interferometer, instead of just one pair, achieves significantly better accuracy in the phase unwrapping. A novel compensation scheme for accurate phase measurements in a phase-sensitive optical time domain reflectometer is proposed, and a comparison of the measurement signals with or without such compensation is shown and discussed. The proposed method, using three photodetectors, allows for very good compensation of the phase measurement errors arising from common-mode noise from the interferometer and laser source, providing a significant improvement in signal detection. In addition, the method allows the tracking of slow temperature changes in the monitored fiber/object, which is not obtainable when using a simple low-pass filter for phase unwrapping error reduction, as is customary in several systems of this kind.

Safety First: Stability and Dissipation of Line-tied Force-free Flux Tubes in Magnetized Coronae

Magnetized plasma columns and extended magnetic structures with both footpoints anchored to a surface layer are an important building block of astrophysical dissipation models. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and are expected to exist in highly magnetized neutron star magnetospheres and accretion disk coronae. For varying twist and system sizes, we investigate the stability of line-tied force-free flux tubes and the dissipation of twist energy during instabilities using linear analysis and time-dependent force-free electrodynamics simulations. Kink modes (m = 1) and efficient magnetic energy dissipation develop for plasma safety factors q ≲ 1, where q is the inverse of the number of magnetic field line windings per column length. Higher-order fluting modes (m > 1) can distort equilibrium flux tubes for q > 1 but induce significantly less dissipation. In our analysis, the characteristic pitch μ˜0 of flux-tube field lines determines the growth rate ( ∝μ˜03 ) and minimum wavelength of the kink instability ( ∝μ˜0−1 ). We use these scalings to determine a minimum flux tube length for the growth of the kink instability for any given μ˜0 . By drawing analogies to idealized magnetar magnetospheres with varying regimes of boundary shearing rates, we discuss the expected impact of the pitch-dependent growth rates for magnetospheric dissipation in magnetar conditions.

The breakup and instability structures of liquid jets in subsonic crossflows

The breakup of water and Jet A fuel jets injected transverse into elevated temperature (up to 425 °C), combustion pre-heated, subsonic crossflows was investigated by internally fluorescing the liquid jet column. The fluorescent dye seeded test liquids were illuminated by a pulsed laser light that was transmitted within the injector using a quartz rod light-guide. High-resolution images isolating the intact liquid column from light scattered by the surrounding dense spray facilitated precise measurement of the liquid column breakup position and the size and distribution of windward column instability waves. The injector geometry consisted of a 1 mm circular orifice with an orifice length of 20 mm with a tapered inlet. Liquid jet to gaseous crossflow momentum flux ratios were varied from 6 to 266 and the gas Weber number was varied from 10.7 to 228. Empirical correlations were derived for the liquid column breakup coordinates and breakup time in addition to the average and local maximum instability wavelength and amplitude on the liquid column windward surface. The reported correlations provided key insight into atomization physics and aim to support the quantitative validation of high-fidelity numerical simulations of the liquid jet in subsonic crossflow.

On corrugation mode radial wavelengths of the vertical shear instability

Abstract The vertical shear instability (VSI) is a promising mechanism to drive turbulence in protoplanetary disks. Numerical simulations in the literature demonstrate that the VSI non-linear saturation is predominated by the linear corrugation modes. These modes possess vertical wavelengths crucially longer than radial wavelengths. This paper aims to investigate the natural radial wavelength of corrugation modes upon VSI saturation, by a series of numerical simulations conducted in Athena++ at different grid resolutions, disk aspect ratios, and viscosity parameterized by ν. We find a sign of convergence emerges at 64 cells per gas scale height for fiducial simulations. Below it a continuous reduction of wavelengths with grid resolution is observed. Synthetic ALMA molecular line observations of $^{12}\rm CO(2-1)$ are performed to inspect the observability of the corrugation modes feature, which is significantly diminished with a resolution of 32 cells per scale height or above. Flared and viscous disks exhibiting longer saturation wavelengths may mitigate the observational difficulty.

The polymer diffusive instability in highly concentrated polymeric fluids

The extrusion of polymer melts is known to be susceptible to ‘melt fracture’ instabilities, which can deform the extrudate, or cause it to break entirely. Motivated by this, we consider the impact that the recently discovered polymer diffusive instability (PDI) can have on polymer melts and other concentrated polymeric fluids using the Oldroyd-B model with the effects of polymer stress diffusion included. Analytic progress can be made in the concentrated limit (when the solvent-to-total-viscosity ratio β→0), illustrating the boundary layer structure of PDI, and allowing the prediction of its eigenvalues for both plane Couette and channel flow. We draw connections between PDI and the polymer melt ‘sharkskin’ instability, both of which are short wavelength instabilities localised to the extrudate surface. Inertia is shown to have a destabilising effect, reducing the smallest Weissenberg number (W) where PDI exists in a concentrated fluid from W∼8 in inertialess flows, to W∼2 when inertia is significant.

Anti-aligning interaction between active particles induces a finite wavelength instability: The dancing hexagons.

By considering a simple model for self-propelled particle interaction, we show that anti-aligning forces induce a finite wavelength instability. Consequently, the system exhibits pattern formation. The formed pattern involves, let us say, a choreographic movement of the active entities. At the level of particle density, the system oscillates between a stripe pattern and a hexagonal one. The underlying dynamics of these density oscillations consists of two counterpropagating and purely hexagonal traveling waves. They are assembling and disassembling a global hexagonal structure and a striped lineup of particles. This self-assembling process becomes quite erratic for long-time simulations, seeming aperiodic.

Study on Marangoni explosion of binary mixtures in liquid layer

In this work, the process of forming micro-droplets due to instability and fragmentation after short chain alcohol solution spreads on the surface of oil layers is studied. Based on the free energy theory of the liquid-liquid interface, the relationship between the binary mixtures spreading on the surface of the liquid layer is derived, and the concentration range of short chain alcohol solution spreading as a thin film on the surface of the oil layer is calculated from the Hiskovsky formula. The Malangoni flow caused by the difference in evaporation rate between the center and edge of the droplet film perturbs the boundary of the liquid film, causing finger-shaped liquid columns to grow at the edge when the droplet spreads to its maximum. In this work, the expression for the critical wavelength and maximum wavelength of boundary instability are derived based on the perturbation model, and the reason for finger shaped liquid column fragmentation is explained based on the Plateau Rayleigh instability. A concentric cylindrical shell liquid column model is established to simplify the calculation and predict the location range of “droplet explosion” of droplets with different viscosity ratios on the liquid layer. Through theoretical calculations and experimental verification, it is found that the alcohol solution fragmented into small droplets within a length range of 4.51–5.98 times the width of the liquid column. This study provides theoretical guidance for existing application fields such as film forming technology and coating technology. The hypotheses, assumptions, and simplified models preliminarily verified experimentally provide solutions for some technical difficulties in the research fields of micro reactions and nanoparticle preparation in chemical industry.

Falling liquid film down a non-uniformly heated slippery inclined plane with odd viscosity effects

The study examines the impact of the odd component of the Cauchy stress tensor, linked to the breakdown of time-reversal symmetry, on the linear instability analysis of a viscous fluid layer flowing down a non-uniformly heated and slippery inclined plane. Using a long-wave series expansion within an Orr-Sommerfeld-type boundary value problem, the critical Reynolds number is derived. The results of the linear long wavelength instability in the case of infinitesimal wavenumbers reveal that odd viscosity stabilizes the flow, while wall slip destabilizes it. The noteworthy finding is that thermocapillarity significantly enhances stability, provided gas temperature matches wall temperature.

Local flow control by phononic subsurfaces over extended spatial domains

Local phonon motion underneath a surface interacting with a flow may cause the flow to passively stabilize, or destabilize, as desired within the region adjacent to the subsurface motion. This mechanism has been extensively analyzed over only a spatial region on the order of the instability wavelength along the fluid–structure interface. Here, we uncover fundamental relations between the behavior of flow instabilities and the frequency response characteristics of the phononic subsurface structure admitting the elastic motion. These relations are then utilized to demonstrate the possibility of extensive spatial expansion of the control regime along the downstream direction with minimal loss of performance—potentially covering the entire surface exposed to the flow.

Stability of diffusion flames under shear flow: Taylor dispersion and the formation of flame streets

Diffusion flame streets, observed in non-premixed micro-combustion devices, align parallel to a shear flow. They are observed to occur in mixtures with high Lewis number (Le) fuels, provided that the flow Reynolds number, or the Peclet number Pe, exceeds a critical value. The underlying mechanisms behind these observations have not yet been fully understood. In the present paper, we identify the coupling between diffusive-thermal instabilities and Taylor dispersion as a mechanism which is able to explain the experimental observations above. The explanation is largely based on the fact that Taylor dispersion enhances all diffusion processes in the flow direction, leading effectively to anisotropic diffusion with an effective (flow-dependent) Lewis number in the flow direction which is proportional to 1/Le for Pe≫1. Validation of the identified mechanism is demonstrated within a simple model by investigating the stability of a planar diffusion flame established parallel to a plane Poiseuille flow in a narrow channel. A linear stability analysis, leading to an eigenvalue problem solved numerically, shows that cellular (or finite wavelength) instabilities emerge for high Lewis number fuels when the Peclet number exceeds a critical value. Furthermore, for Peclet numbers below this critical value, longwave instabilities with or without time oscillations are obtained. Stability regime diagrams are presented for illustrative cases in a Le−Pe plane where various instability domains are identified. Finally, the linear analysis is supported and complemented by time dependent numerical simulations, describing the evolution of unstable diffusion flames. The simulations demonstrate the existence of stable cellular structures and show that the longwave instabilities are conducive to flame extinction.

Laser photo-acoustic methane sensor (7.7 µm) for use at unmanned aerial vehicles

A compact laser photo-acoustic (PA) methane sensor based on a quantum-cascade laser (∼7.7 μm; 1750 Hz; 25 mW), a resonant differential photo-acoustic detector (PAD), and a sealed-off gas-filled PA Ref-cell has been developed. Normalization of the absorption signals in the PAD is carried out according to the absorption signals in the gas-filled PA Ref-cell, which significantly reduces the measurement errors of the methane concentration in the case of instability of the laser emission wavelength. The minimum measured background signal of the PA sensor (using high purity nitrogen) is nmin≈(26.6 ± 8.4) ppb CH4 (at a bandwidth of 20 Hz), the value of normalized noise equivalent absorption (NNEA) = 8.22 × 10–10 cm−1·W/Hz1/2. A comparison of various research groups results with mid-IR PA gas analyzers is carried out. The developed PA methane sensor is adapted for placement on the UAV’s board. Device has dimensions of 315 × 165 × 110 mm, weight ∼3.1 kg, power supply from an external source (9…60 VDC), power consumption ∼20 VA.

Miniaturization and Model-Integration of the Optical Measurement System for Temperature-Sensitive Paint Investigations.

The temperature-sensitive paint (TSP) method, an optical measurement technique, is used for qualitative skin friction visualizations in a wide variety of aerodynamic applications. One such application is the visualization of the laminar-turbulent boundary-layer transition. Optical access to the surface of interest is mandatory for the measurement system, which consists of scientific cameras and LEDs. But the optical access to the area of interest is often impeded by the available windows of the wind tunnel and the wind tunnel model itself, reducing the field of view and the spatial resolution. In some cases, it is of interest to increase the flexibility of the installation of the optical measurement system by reducing its physical dimensions and placing the installation inside the plenum. The DLR Swept flat PlatE Cross-flow TRAnsition (SPECTRA-A) configuration was selected to investigate the influence of two-dimensional steps on the cross-flow-induced boundary layer transition by means of TSP, as part of the EU project Clean Sky 2. The SPECTRA-A configuration consists of two main elements: a flat plate and a displacement body mounted within a very close distance of each other, creating a narrow gap between the two elements. The surface of interest is the area on the flat plate facing the displacement body. The narrow gap limits the utilization of an external camera setup due to poor optical access. A new optical setup consisting of four miniature CMOS machine-vision cameras and five miniature high-power LEDs was integrated into the displacement body. The characteristics of the camera system were analyzed in laboratory tests, establishing that the miniature CMOS machine-vision cameras are suitable for qualitative TSP skin friction visualizations. This was confirmed by successfully measuring the laminar-turbulent boundary-layer transition on the SPECTRA-A configuration. The integrated TSP system is capable of resolving even small variations of the transition location caused by changing the amplitude of the stationary cross-flow instability. The quality of the TSP visualization with the integrated optical system allows for the measurement of the transition location and the wavelength of the stationary cross-flow instability. Overall, a cost-effective TSP visualization system with small space requirements was developed and tested for future applications in wind tunnel models, model support, or side walls of wind tunnels.

On interdependence of instabilities and average drop sizes in bag breakup

A drop exposed to cross flow of air experiences sudden accelerations, which deform it rapidly, ultimately proceeding to disintegrate into smaller fragments. In this work, we examine the breakup of a drop as a bag film with a bounding rim, resulting from acceleration-induced Rayleigh–Taylor instabilities and characterized through the Weber number, We, representative of the competition between the disruptive aerodynamic force imparting acceleration and the restorative surface tension force. Our analysis reveals a previously overlooked parabolic dependence (∼We2) of the combination of dimensionless instability wavelengths (λ¯bag2/λ¯rim4λ¯film) developing on different segments of the deforming drop. Furthermore, we extend these findings to deduce the dependence of the average dimensionless drop sizes for the rim, ⟨D¯rim⟩, and bag film, ⟨D¯film⟩, individually, on We and see them decreasing linearly for the rim (∼We−1) and quadratically for the bag film (∼We−2). The reported work is expected to have far-reaching implications as it provides unique insight on destabilization and disintegration mechanisms based on theoretical scaling arguments involving the commonly encountered canonical geometries of a toroidal rim and a curved liquid film.

Soft elastic composites: Microstructure evolution, instabilities and relaxed response by domain formation

This work provides a review of several complementary analytical methods for characterizing the macroscopic response of ‘soft’ elastic composites subjected to large deformations. For this purpose, we first recall the variational definitions of the homogenized response for hyperelastic composites with periodic and random microstructures. We distinguish between the principal solution for the ‘mesoscopic’ stored-energy function, which is based on one-cell-periodic solutions for the periodic microstructures and on the macroscopically uniform solution for the random microstructures, and the ‘relaxed’ or ‘macroscopic’ homogenized stored-energy function, which is obtained after the onset of ‘microscopic’ (periodic on multiple cells) or ‘macroscopic’ (long wavelength) instabilities. The various techniques include variational bounds of the Voigt, and generalized Reuss and Hashin–Shtrikman types, variational estimates based on the use of suitably optimized ‘linear comparison composites,’ and bounds based on the relaxation of the principal solution for the mesoscopic energy by means of a generalized Maxwell procedure consisting in the quasiconvexification of the energy and leading to domain formation. Although the methods are completely general, for simplicity, we review here illustrative results for neo-Hookean laminates and fiber-reinforced elastomers subjected to plane strain loading conditions. Among the main results, it was found that the predicted formation of twins or lamellar domains and associated soft modes of deformation for the laminates is consistent with experimental observations for thermoplastic elastomers with highly ordered lamellar microstructures. In addition, it was found that the predictions for the macroscopic instabilities by means of the relaxation of the mesoscopic energy are generally different (more conservative) and more consistent with the variational definitions of the macroscopic homogenized energy than those based on loss of ellipticity of the incremental elasticity homogenization problem.