Temporal Amplification Research Articles

Drop breakup in bag regime under the impulsive condition

This study experimentally investigates the spatiotemporal evolution and associated local instabilities of a drop subjected to a weak shock wave. The front and side views of the drop are captured to understand its three-dimensional evolution and breakup. The interaction of shock causes the windward side of the drop to compress and generate a surface wave over it. Its temporal amplification is found to be governed by Kelvin–Helmholtz instability. The core of the deformed drop expands in a stream-wise direction, forming a Rayleigh–Taylor instability-driven bag structure. Consistent pressure gradients across the bag cause its continuous elongation until the pressure gradient overcomes the surface tension. This continuous elongation leads the sheet to undergo kinematic thinning, which causes the sheet to destabilize and nucleate the hole. This hole recedes and gathers liquid from upstream to thicken its interface, called the bag rim. The accelerating receding motion of the bag rim triggers Rayleigh–Taylor instability, and the corrugation that forms over it grows into ligaments and destabilizes to shed droplets through end pinching and ligament merging. Additionally, the accelerating rim undergoes radial expansion, with its further destabilization governed by the coupled effect of Rayleigh–Taylor and Rayleigh–Plateau instabilities, as well as the collision of the receding bag rim. This leads to the formation of corrugations, which grow into ligaments and further destabilize to shed drops via end pinching. Nonlinear effects dominate ligament dynamics and increase with the Weber number. The asymmetric ejection of the daughter drop from the rim causes it to evolve into a bag, undergoing tertiary breakup.

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

Effect of dilute nitride GaNAs quantum well thickness on spin amplification dynamics of tunnel-coupled InAs quantum dots

Electron spin dynamics of dilute nitride GaNAs quantum well (QW)-InAs quantum dots (QDs) tunnel-coupled structures having different QW thicknesses were studied via circularly polarized time-resolved photoluminescence. The rate equation fitting considering a capture of QD electron spins by the GaNAs localized states via tunnel transfer revealed that the spin amplification dynamics of the QDs depended on the QW thickness. For the QW thickness of 5 nm, although the temporal amplification of QD electron spin polarization was slow owing to the weak wavefunction coupling between the QW and QD, the long duration of high electron spin polarization was observed because of the suppressed capture of QD majority spins relative to the efficient removal of QD minority spins. When the QW thickness increased from 5 to 20 nm, the strong spin filtering in GaNAs and strong wavefunction coupling led to the fast amplification of QD electron spin polarization with high initial spin polarization. However, the spin polarization rapidly decays after the amplification owing to the removal of both QD majority and minority spins, originating from many effective localized states. These results indicate that the time-dependent QD electron spin polarization and the resultant spin amplification can be widely tuned by changing the thickness of the tunnel-coupled GaNAs QW.

Temporal and Spatial Amplification of Extreme Rainfall and Extreme Floods in a Warmer Climate

Abstract This work explores the relationship between catchment size, rainfall duration, and future streamflow increases on 133 North American catchments with sizes ranging from 66.5 to 9886 km2. It uses the outputs from a high spatial (0.11°) and temporal (1-h) resolution single model initial-condition large ensemble (SMILE) and a hydrological model to compute extreme rainfall and streamflow for durations ranging from 1 to 72 h and for return periods of between 2 and 300 years. Increases in extreme precipitation are observed across all durations and return periods. The projected increases are strongly related to duration, frequency, and catchment size, with the shortest durations, longest return periods, and smaller catchments witnessing the largest relative rainfall increases. These increases can be quite significant, with the 100-yr rainfall becoming up to 20 times more frequent over the smaller catchments. A similar duration–frequency–size pattern of increases is also observed for future extreme streamflow, but with even larger relative increases. These results imply that future increases in extreme rainfall will disproportionately impact smaller catchments, and particularly so for impervious urban catchments which are typically small, and whose stormwater drainage infrastructures are designed for long-return-period flows, both being conditions for which the amplification of future flow will be maximized.

Optical signal denoising through temporal passive amplification

Mitigating the stochastic noise introduced during the generation, transmission, and detection of temporal optical waveforms remains a significant challenge across many applications, including radio-frequency photonics, light-based telecommunications, spectroscopy, etc. The problem is particularly difficult for the weak-intensity signals often found in practice. Active amplification worsens the signal-to-noise ratio, whereas noise mitigation based on optical bandpass filtering attenuates further the waveform of interest. Additionally, current optical filtering approaches are not optimal for signal bandwidths narrower than just a few GHz. We propose a versatile concept for simultaneous amplification and noise mitigation of temporal waveforms, here successfully demonstrated on optical signals with bandwidths spanning several orders of magnitude, from the kHz to GHz scale. The concept is based on lossless temporal sampling of the incoming coherent waveform through Talbot processing. By reaching high gain factors (>100), we show the recovery of ultra-weak optical signals, with power levels below the detector threshold, additionally buried under a much stronger noise background. The method is inherently self-tracking, a capability demonstrated by simultaneously denoising four data signals in a dense wavelength division multiplexing scheme.

Non-modal stability analysis in viscous fluid flows with slippery walls

A study of optimal temporal and spatial disturbance growths is carried out for three-dimensional viscous incompressible fluid flows with slippery walls. The non-modal temporal stability analysis is performed under the framework of normal velocity and normal vorticity formulations. A Chebyshev spectral collocation method is used to solve the governing equations numerically. For a free surface flow over a slippery inclined plane, the maximum temporal energy amplification intensifies with the effect of wall slip for the spanwise perturbation, but it attenuates with the wall slip when perturbation considers both streamwise and spanwise wavenumbers. It is found that the boundary for the regime of transient growth appears far ahead of the boundary for the regime of exponential growth, which raises a question on the critical Reynolds number for the shear mode predicted from the eigenvalue analysis. Furthermore, the eigenvalue analysis or the modal stability analysis reveals that the unstable region for the shear mode decays rapidly in the presence of wall slip, which is followed by the successive amplification of the critical Reynolds number for the shear mode and ensures the stabilizing effect of slip length on the shear mode. On the other hand, for a channel flow with slippery bounding walls, the maximum spatial energy amplification intensifies with the effect of wall slip in the absence of angular frequency, but it reduces with the wall slip if the angular frequency is present in the disturbance. Furthermore, the maximum spatial energy disturbance growth can be achieved if the disturbance excludes the angular frequency. Furthermore, it is observed that the angular frequency plays an essential role in the pattern formation of optimal response. In addition, the pseudo-resonance phenomenon occurs due to external temporal and spatially harmonic forcings, where the pseudo-resonance peak is much higher than the resonance peak.

Layer-selective spin amplification in size-modulated quantum nanocolumn

The optical spin properties of size-modulated quantum nanocolumns (QNCs), which are composed of 9 layers of vertically coupled InGaAs quantum dots (QDs), have been studied by circularly polarized time-resolved photoluminescence spectroscopy of QD excited states with barrier excitation. High spin polarization at the emissive state is one of the essential elements in the development of spin-functional optical devices. Coupling of QD excited states can enhance the spin polarization if only minority spins are effectively removed from the emissive excited states. In this study, size-modulated QNCs with the increasing size toward the upper layer were grown, and we revealed that the combination of QD size modulation and electron wavefunction coupling in the stacking direction can greatly enhance spin polarization during light emission from the smaller-sized QD layers. We observed a temporal spin amplification of more than 80% at coupled excited states. This enhancement is derived from the size-modulation-induced selective transfer of minority spins to the larger-sized QD layers, which have abundant excited states where electron spins are transferred. In addition, we found that QNCs can retain high spin polarization even at high excitation spin density. Our findings of spin amplification during light emission will provide QNC systems suitable for spin-functional optical devices.

Tunable gallium nitride-based devices for ultrafast signal processing

In this paper, we propose a micro-ring resonator model based on gallium nitride (GaN) and graphene, which exhibits tunable properties of nonlinearity. It provides a great bandwidth covering from visible to telecommunication band. Especially, based on the characteristic of GaN, it has unique advantages in shorter wavelength, which is used for demonstrating the ultrafast signal processing including wavelength conversion, temporal amplification and pulse compression. Moreover, the tunable signal processing is achieved via the method of applying additional bias voltage to graphene without changing the geometric dimension of the device. These results have significant potential applications of nonlinear optics and optical communications.

Noise-induced temporal regularity and signal amplification in an optomechanical system with parametric instability.

Noise usually has an unwelcome influence on system performance. For instance, noise inevitably affects the low-frequency mechanical freedom in optomechanical experiments. However, we investigate here the beneficial effects of thermal noise on a basic optomechanical system with parametric instability. In a regime near parametric instability, it is found that thermal noise in the mechanical freedom can sustain long-term quasi-coherent oscillations when the system would otherwise remain in the equilibrium state. In an overlapping regime of parametric instability and bistability, intermittent switching between a self-sustained oscillating state and an equilibrium can be induced by adding a certain amount of noise. When a subthreshold periodic signal is applied to the mechanics, the switching between the self-sustained oscillations and the equilibrium exhibits good periodicity at a rate that is synchronized to the signal frequency, resulting in a significant amplification of the signal. Our results deepen the understanding of the interplay between optomechanical nonlinearity and noise and provide theoretical guidance for experimental observation of noise-induced beneficial phenomena in optomechanics.

Glacial Erosion Driven by Variations in Meltwater Drainage

AbstractThe subglacial processes of abrasion and quarrying are thought to be primarily responsible for bedrock erosion by glaciers. While theory points to sliding speed as the dominant control on abrasion, rates of quarrying are likely scaled by a more complex combination of sliding speed, effective pressure, bed roughness, and short‐term water‐pressure fluctuations. Here we pair a model for quarrying based on statistical characterization of bedrock strength with a model for subglacial hydrology that describes the temporal evolution of cavities under the influence of variations in sliding speed and effective pressure. Using a finite element model, we simulate the evolution of the hydrological system at the base of a glacier and compute rates of abrasion and quarrying. Cavity lengths and channel cross sections evolve through time, causing temporal shifts in ice‐bed contact area, which in turn govern the differential stress that influences erosion over the course of a year. Our results demonstrate how variations in meltwater production amplify rates of subglacial erosion relative to the case of steady meltwater generation. The level of amplification depends on how the variations control the ice‐bed contact area. Seasonal variations are most effective in boosting mean rates of basal sliding and hence subglacial abrasion, whereas shorter‐term variations (monthly‐weekly) most strongly influence rates of subglacial quarrying through temporal amplification of differential bedrock stress around cavities. This influence of transient hydrology on subglacial erosion processes may explain why glaciers in temperate climates with strong variations in temperature and precipitation erode faster than similar‐type glaciers in polar environments.

Prominence oscillations: Effect of a time-dependent background temperature

Context. Small amplitude oscillations in prominences have been known about for a long time, and from a theoretical point of view, these oscillations have been interpreted in terms of standing or propagating linear magnetohydrodynamic (MHD) waves. In general, these oscillations were studied by producing small perturbations in a background equilibrium with stationary physical properties. Aims. Taking into account that prominences are dynamic plasma structures, the assumption of a stationary equilibrium is not realistic. Therefore, our main aim is to study the effects produced by a non-stationary background on slow MHD waves, which could be responsible for prominence oscillations. Methods. Assuming that the radiation term is proportional to temperature and constant external heating, we have derived an expression for the temporal variation of the background temperature, which depends on the imbalance between heating and cooling processes. Furthermore, radiative losses, together with parallel thermal conduction, have also been included as damping mechanisms for the waves. Results. As temperature increases with time, the period of slow waves decreases and the amplitude of the velocity perturbations is damped. The inclusion of radiative losses enhances the damping. As temperature decreases with time, the period of slow waves increases and the amplitude of velocity perturbations grows while, as expected, the inclusion of radiative losses contributes to the damping of oscillations. Conclusions. There is observational evidence that, in different locations of the same prominence, oscillations are damped or amplified with time. This temporal damping or amplification can be obtained by a proper combination of a variable background temperature, together with radiative damping. Furthermore, decayless oscillations can also be obtained with an appropriate choice of the characteristic radiation time.

Compact Analog Temporal Edge Detector Circuit With Programmable Adaptive Threshold for Neuromorphic Vision Sensors

This paper presents a low-power compact analog circuit for processing time varying signals. The proposed circuit implements temporal differentiation, amplification and rectification, i.e., separation of outputs into on and off pathways. It is based on a hysteretic differentiator circuit, commonly used in neuromorphic vision sensors to implement temporal edge detection. This paper presents a thorough analysis of the original circuit and identifies the source of the problems and limitations it has for processing real-world sensory signals. The steps required to solve this problem are presented as well as an extended circuit with tunable gain and adaptable threshold that allows thresholding of small temporal changes (noise) and high-pass filtering of large temporal changes. The new circuit proposed is particularly suited for focal plane implementation of both gradient based and token based motion algorithms that require robust detection of temporal discontinuities. The circuit has been designed and successfully integrated into a 64 × 1 test prototype motion chip, fabricated in standard 350 nm CMOS technology. The paper provides extensive experimental characterization results.

Stabilizing effect of optimally amplified streaks in parallel wakes

AbstractWe show that optimal perturbations artificially forced in parallel wakes can be used to completely suppress the absolute instability and to reduce the maximum temporal growth rate of the inflectional instability. To this end we compute optimal transient energy growths of stable streamwise uniform perturbations supported by a parallel wake for a set of Reynolds numbers and spanwise wavenumbers. The maximum growth rates are shown to be proportional to the square of the Reynolds number and to increase with spanwise wavelengths with sinuous perturbations slightly more amplified than varicose ones. Optimal initial conditions consist of streamwise vortices and the optimally amplified perturbations are streamwise streaks. Families of nonlinear streaky wakes are then computed by direct numerical simulation using optimal initial vortices of increasing amplitude as initial conditions. The stabilizing effect of nonlinear streaks on temporal and spatiotemporal growth rates is then determined by analysing the linear impulse response supported by the maximum amplitude streaky wakes profiles. This analysis reveals that at $\mathit{Re}= 50$, streaks of spanwise amplitude ${A}_{s} \approx 8\hspace{0.167em} \% {U}_{\infty } $ can completely suppress the absolute instability, converting it into a convective instability. The sensitivity of the absolute and maximum temporal growth rates to streak amplitudes is found to be quadratic, as has been recently predicted. As the sensitivity to two-dimensional (2D, spanwise uniform) perturbations is linear, three-dimensional (3D) perturbations become more effective than the 2D ones only at finite amplitudes. Concerning the investigated cases, 3D perturbations become more effective than the 2D ones for streak amplitudes ${A}_{s} \gtrsim 3\hspace{0.167em} \% {U}_{\infty } $ in reducing the maximum temporal amplification and ${A}_{s} \gtrsim 12\hspace{0.167em} \% {U}_{\infty } $ in reducing the absolute growth rate. However, due to the large optimal energy growths they experience, 3D optimal perturbations are found to be much more efficient than 2D perturbations in terms of initial perturbation amplitudes. Despite their lower maximum transient amplification, varicose streaks are found to be always more effective than sinuous ones in stabilizing the wakes, in accordance with previous findings.

Absolute and convective instabilities and their roles in the forecasting of large frontal meanderings

[1] Frontal meanderings are generally difficult to predict. In this study, we demonstrate through an exercise with the Iceland-Faeroe Front (IFF) that satisfactory predictions may be achieved with the aid of hydrodynamic instability analysis. As discovered earlier on, underlying the IFF meandering is a convective instability in the western boundary region followed by an absolute instability in the interior; correspondingly the disturbance growth reveals a switch of pattern from spatial amplification to temporal amplification. To successfully forecast the meandering, the two instability processes must be faithfully reproduced. This sets stringent constraints for the tunable model parameters, e.g., boundary relaxation, temporal relaxation, eddy diffusivity, etc. By analyzing the instability dispersion properties, these parameters can be rather accurately set and their respective ranges of sensitivity estimated. It is shown that too much relaxation inhibits the front from varying; on the other hand, too little relaxation may have the model completely skip the spatial growth phase, leading to a meandering way more upstream along the front. Generally speaking, dissipation/diffusion tends to stabilize the simulation, but unrealistically large dissipation/diffusion could trigger a spurious absolute instability, and hence a premature meandering intrusion. The belief that taking in more data will improve the forecast does not need to be true; it depends on whether the model setup admits the two instabilities. This study may help relieve modelers from the laborious and tedious work of parameter tuning; it also provides us criteria to distinguish a physically relevant forecast from numerical artifacts.

Vortex formation and vortex breakup in a laminar separation bubble

AbstractThe convective primary amplification of a forced two-dimensional perturbation initiates the formation of essentially two-dimensional large-scale vortices in a laminar separation bubble. These vortices are then shed from the bubble with the forcing frequency. Immediately downstream of their formation, the vortices get distorted in the spanwise direction and quickly disintegrate into small-scale turbulence. The laminar–turbulent transition in a forced laminar separation bubble is dominated by this vortex formation and breakup process. Using numerical and experimental data, we give an in-depth characterization of this process in physical space as well as in Fourier space, exploiting the largely periodic character of the flow in time as well as in the spanwise direction. We present evidence that a combination of more than one secondary instability mechanism is active during this process. The first instability mechanism is the elliptic instability of vortex cores, leading to a spanwise deformation of the cores with a spanwise wavelength of the order of the size of the vortex. Another mechanism, potentially an instability of flow in between two consecutive vortices, is responsible for three-dimensionality in the braid region. The corresponding disturbances possess a much smaller spanwise wavelength as compared to those amplified through elliptic instability. The secondary instability mechanisms occur for both fundamental and subharmonic frequency, respectively, even in the absence of continuous forcing, indicative of temporal amplification in the region of vortex formation.

Ultra-short photon pulse generation in relativistic laser-plasmas

Optical pulse compression by the linear reflection of a laser pulse from a relativistically moving plasma is studied. Using Lorentz transformations, covariance of Maxwell's equations and the principle of phase invariance to transform between the rest frame and the moving frame, analytics can be exactly performed in the moving frame. Closed-form formulae for reflected waveforms as a function of incident angle show temporal compression and intensity amplification by a factor of 2γ and 4γ2, respectively, where γ is the Lorentz factor of the relativistic electron plasma. As an independent test, fully relativistic electromagnetic particle simulations agree well with analytical results, predicting pulse compression and large amplification to be of relevance to the generation of attosecond optical pulses.

Calcium Signaling: Deciphering the Calcium–NFAT Pathway

Rapid cellular calcium oscillations activate gene expression hours later. How this temporal response amplification is achieved has until now been largely a mystery. An elegant combination of experimental strategies and a model that encompasses non-linear inputs and outputs now sheds new light on this long-standing problem.

Elucidating the Design Principles of Signal Transduction Networks – application to Dopamine and Calcium signaling in reinforcement learning

AbstractThe biochemical networks underlying biological functions are in general highly complex. An important aim of systems biology is to provide mechanistic insight into how the different interactions within the network give rise to specific behaviors and properties. In this paper we consider the use of structured dynamic perturbations applied to the network nodes and edges for elucidating the most important interactions in signal transduction networks. Signal transduction networks mediate extracellular and intracellular signals to the nucleus, resulting in an appropriate response by the gene regulatory network. The most important characteristic of signal transduction networks is usually the specific temporal amplification of stimuli signals. As a case study we consider the intracellular signaling pathways that underlie reinforcement learning in striatum neuronal cells of the brain. It has recently been found that these networks respond to Dopamine and Calcium signals in a fashion which is strongly dependent on the signal shape, and the hypothesis is that this is related to the existence of a resonant feedback loop within the network. By systematically perturbing the nodes and edges of the network using general dynamic perturbations, affecting both the strength and phase lag of the direct interactions within the network, we are able to identify the most important components and interactions underlying the “resonant” signal amplification. Based on this we derive a reduced order model of the network, with retained physical states, from which we can show that the apparent resonance is caused by two parallel pathways with opposing effects and widely different time-constants. We postulate that this is a sound architecture for signal amplification of mid-frequency signals based on the fact that the robustness can be made almost arbitrarily large, as compared to resonant feedback loops that are inherently unrobust.

PERTURBATION AND STABILITY ANALYSIS OF THE MULTI-ANTICIPATIVE INTELLIGENT DRIVER MODEL

This paper discusses three kinds of IDM car-following models that consider both the multi-anticipative behaviors and the reaction delays of drivers. Here, the multi-anticipation comes from two ways: (1) the driver is capable of evaluating the dynamics of several preceding vehicles, and (2) the autonomous vehicles can obtain the velocity and distance information of several preceding vehicles via inter-vehicle communications. In this paper, we study the stability of homogeneous traffic flow. The linear stability analysis indicates that the stable region will generally be enlarged by the multi-anticipative behaviors and reduced by the reaction delays. The temporal amplification and the spatial divergence of velocities for local perturbation are also studied, where the results further prove this conclusion. Simulation results also show that the multi-anticipative behaviors near the bottleneck will lead to a quicker backwards propagation of oscillations.

Sensitivity analysis of a streamwise corner flow

The stability of the flow formed by the intersection of two perpendicular flat plates is revisited through a study of the sensitivity to base-flow variations. After a brief presentation of the asymptotic regime, sensitivity functions underlying corner mode (concentrated close to the intersection) and Tollmien–Schlichting modes, with different obliqueness angles, are computed. Taking this into consideration, associated mechanisms as well as active regions are identified, which further confirm the sensitivity area of the corner mode along the intersection of two flat plates. Furthermore, the concept of ΔU-pseudospectra indicates that under a small base-flow modification, a certain range of frequencies underlying the corner mode could become unstable. Then, an optimization technique tracking the worst-case scenario, i.e., the deviation leading to a maximum temporal amplification rate, shows that a small variation in the reference field in the area of uncertainty leads to a significant decrease in the critical Reynolds number as observed in experiments. A hypothesis based on the onset of an inflectional mechanism is thus proposed to explain the experimental results.