Large-amplitude Perturbations Research Articles

Synchronization under saturable nonlinearity.

In this theoretical work, we introduce a nonlinear gain saturation law representative of the experimentally observed properties manifested by phenomena ranging from aeroacoustic shear layers in self-sustained cavity oscillations to flame heat release rate in thermoacoustic instabilities. Furthermore, this type of saturable gain may be relevant for a wider class of physical systems, such as active laser media in photonics. The nonlinearity discussed herein governs the fullscale behavior of a self-oscillator exhibiting linear loss under large amplitude perturbations, in contrast to the cubic damping and linear gain of the Van der Pol model. A distinctive characteristic of the proposed equation is the simple, well behaved gain term in the slow timescale dynamics.

Recursive Filtering Under Probabilistic Encoding-Decoding Schemes: Handling Randomly Occurring Measurement Outliers.

This article focuses on the recursive filtering problem for networked time-varying systems with randomly occurring measurement outliers (ROMOs), where the so-called ROMOs denote a set of large-amplitude perturbations on measurements. A new model is presented to describe the dynamical behaviors of ROMOs by using a set of independent and identically distributed stochastic scalars. A probabilistic encoding-decoding scheme is exploited to convert the measurement signal into the digital format. For the purpose of preserving the filtering process from the performance degradation induced by measurement outliers, a novel recursive filtering algorithm is developed by using the active detection-based method where the "problematic" measurements (i.e., the measurements contaminated by outliers) are removed from the filtering process. A recursive calculation approach is proposed to derive the time-varying filter parameter via minimizing such the upper bound on the filtering error covariance. The uniform boundedness of the resultant time-varying upper bound is analyzed for the filtering error covariance by using the stochastic analysis technique. Two numerical examples are presented to verify the effectiveness and correctness of our developed filter design approach.

Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation

Primordial black holes can be formed from the collapse of large-amplitude perturbation on small scales in the early Universe. Such an enhanced spectrum can be realized by introducing a flat region in the potential of single-field inflation, which makes the inflaton go into a temporary ultraslow-roll period. In this paper, we calculate the bispectrum of curvature perturbation in such a scenario. We explicitly confirm that bispectrum satisfies Maldacena’s theorem. At the end of the ultraslow-roll period, the bispectrum is generated by bulk interaction and field redefinition. At the end of inflation, bispectrum is generated only by bulk interaction. We also calculate the one-loop correction to the power spectrum from the bispectrum, called the source method. We find it consistent with the calculation of the one-loop correction from the second-order expansion of in-in perturbation theory. Published by the American Physical Society 2024

Constraining Primordial Black Hole Formation from Single-Field Inflation.

The most widely studied formation mechanism of a primordial black hole is collapse of large-amplitude perturbation on small scales generated in single-field inflation. In this Letter, we calculate one-loop correction to the large-scale power spectrum in a model with sharp transition of the second slow-roll parameter. We find that models producing an appreciable amount of primordial black holes induce nonperturbative coupling on a large scale probed by cosmic microwave background radiation. Our result implies that a small-scale power spectrum can be constrained by large-scale cosmological observations.

Evolution of weakly unstable oblique detonation in disturbed inflow

The surface instability of oblique detonation waves (ODWs) without perturbations has been extensively investigated, yet the impact of external perturbations remains under-explored. Utilizing reactive Euler equations coupled with a two-step induction-exothermic reaction model, this study conducts a numerical examination of the evolution of unstable ODW surfaces subjected to a continuous sinusoidal density/temperature perturbation inflow. The results show that, without inflow perturbations, the ODW can evolve into triple points in the downstream due to detonation instability, similar to previous work. However, a small continuous perturbation can induce a significant forward movement of the ODW unstable position. Surprisingly, as the perturbation magnitude increases, the changes in the unstable position become progressively less pronounced. By increasing the perturbation frequency, the oscillation amplitude first increases, but a decreasing period/stage occurs with a modest frequency. To investigate the response of ODW to the increase in perturbation, the frequency characteristics and numerical smoked cells of detonation surfaces are examined and analyzed using Fast Fourier Transformation. The power spectral density indicates the presence of two distinct oscillation modes within oblique detonation. Low-frequency, small-amplitude perturbations serve to amplify the instability of the detonation, and more irregular oscillations could be observed. Conversely, high-frequency, large-amplitude perturbations suppress the development of small-scale waves on the detonation wavefront and lead to a relative regular oscillation, indicating that the wavefront pressure oscillations are entirely determined by inflow perturbations and become predictable. These findings have significant implications for the control of intrinsically unstable ODWs, providing valuable insights into the regulation of ODW dynamics.

Analogue circuit realisation of surface-confined redox reaction kinetics

The literature on voltammetry and electrochemical impedance spectroscopy (EIS) recognises the importance of using large-amplitude sinusoidal perturbations to better characterise electrochemical systems. To identify the parameters of a given reaction, various electrochemical models with different sets of values are simulated and compared against the experimental data to determine the best-fit set of parameters. However, the process of solving these nonlinear models is computationally expensive. This paper proposes analogue circuit elements for synthesising surface-confined electrochemical kinetics at the electrode interface. The resultant analogue model could be used as a solver to compute reaction parameters as well as a tracker for ideal biosensor behaviour. The performance of the analogue model was verified against numerical solutions to theoretical and experimental electrochemical models. Results show that the proposed analogue model has a high accuracy of at least 97% and a wide bandwidth of up to 2 kHz. The circuit consumed an average power of 9 μW.

Registration of Nonlinear Hydrophysical Disturbances—Rogue Waves in Full-Scale Conditions

In the paper, we discuss the results of processing and analysis of field data obtained from a laser-based supersensitive detector during the registering of hydrosphere pressure variations on the seabed at various points of the Sea of Japan shelf. The main focus is the study of physical mechanisms of the occurrence of nonlinear hydrophysical disturbances in the range of gravity and infragravity sea waves classed as rogue waves, the amplitudes of which are more than twice the amplitudes of the bordering signals in this range of periods. It has been established that in the range of gravity/wind sea wave periods (2–20 s), similar disturbances were registered by the supersensitive detector of hydrosphere pressure variations. The paper explains the appearance of such nonlinear disturbances. In addition to single large-amplitude nonlinear perturbations, classical nonlinear disturbances, related to the “one sister”, “two sisters”, and “three sisters” rogue wave types were discovered. Their occurrence is associated with the interaction of gravity and infragravity sea waves in the zone of the recording equipment location. In the course of spectral processing of the obtained field data, the main modes of wind waves and infragravity sea waves responsible for the formation of the observed rogue waves were identified. The intermodal energy transfer in the observed wave packet resembles in its behavior the modified Fermi–Past–Ulam recurrence. In the lower frequency range, non-linear hydrophysical disturbances of the “sea hole” and “crest” type were found; the origin of which is associated with atmospheric processes.

Управление сетью цепочной структуры с использованием метода вспомогательного контура в условиях больших по амплитуде возмущений

The article presents a solution to the problem of controlling a network of a chain structure, where each agent is a linear plant influenced by the action of external uncontrolled large-amplitude perturbations under a priori uncertainty. For a chain network the auxiliary loop method is used. In each agent of the network the output of the previous agent is monitored, and the signal from the leading subsystem arrives only at the first agent of the network. The control systems of each agent are built using the measured data on the output of the agent and the agent preceding it. Compensation for the effect of perturbations is carried out by generating a special signal that carries information about all perturbations of the system, and then damping it by an auxiliary loop. Since the problem can be solved using only the measured scalar input and output signals, then two observers of the variables of the system. should be used to obtain estimates of the derivatives of these signals necessary for the formation of control actions. Thus, the chosen control laws in each agent of the chain ensure the achievability of the control goal with the required dynamic accuracy. An example of a chain network with four linear control plants is given. The proposed control is applied to the network plant. Computer simulation was carried out in the Matlab Simulink environment. Tracking error transients are presented for each of the four agents of the chain network. The simulation results confirmed the theoretical conclusions and showed the effectiveness of the proposed chain network control law under external uncontrolled disturbances of large amplitude.

Baroclinic Instability of a Time-Dependent Zonal Shear Flow

In the real atmosphere, the development of large-scale motion is often related to the baroclinic properties of the atmosphere. So, it is necessary to discuss the stability condition of baroclinic flow. It is advantageous to use a layered model to discuss baroclinic instability, not only to apply the potential vortex equation directly, but also to deal with shear of basic flow. The stability and oscillatory shear ability of Rossby waves are studied based on the two-layer Phillips model in the β plane; then, we summarize the baroclinic instability of time-dependent zonal shear flows. The multiscale method is used to eliminate some terms of natural frequency oscillations of nonlinear operators in the third-order expansion, thus generating an equation about the amplitude of the lowest-order Rossby wave in the long-time variable. The large amplitude perturbation begins to decrease, which produces the desired behavior. After the amplitude decreases for some time, the amplitude of Rossby waves can still be found to oscillate periodically with the time variable.

Thermal instability in the CGM of L⋆ galaxies: testing ‘precipitation’ models with the FIRE simulations

ABSTRACT We examine the thermodynamic state and cooling of the low-z circumgalactic medium (CGM) in five FIRE-2 galaxy formation simulations of Milky Way-mass galaxies. We find that the CGM in these simulations is generally multiphase and dynamic, with a wide spectrum of largely non-linear density perturbations sourced by the accretion of gas from the intergalactic medium (IGM) and outflows from both the central and satellite galaxies. We investigate the origin of the multiphase structure of the CGM with a particle-tracking analysis and find that most of the low-entropy gas has cooled from the hot halo as a result of thermal instability triggered by these perturbations. The ratio of cooling to free-fall time-scales tcool/tff in the hot component of the CGM spans a wide range of ∼1−100 at a given radius but exhibits approximately constant median values of ∼5−20 at all radii 0.1Rvir < r < Rvir. These are similar to the ≈10−20 value typically adopted as the thermal instability threshold in ‘precipitation’ models of the ICM. Consequently, a one-dimensional model based on the assumption of a constant tcool/tff and hydrostatic equilibrium approximately reproduces the number density and entropy profiles of each simulation but only if it assumes the metallicity profile and temperature boundary condition taken directly from the simulation. We explicitly show that the tcool/tff value of a gas parcel in the hot component of the CGM does not predict its probability of subsequently accreting on to the central galaxy. This suggests that the value of tcool/tff is a poor predictor of thermal stability in gaseous haloes in which large-amplitude density perturbations are prevalent.

Excitation of Shear Layer Due to Surface Roughness Near the Leading Edge: An Experiment

Abstract In this paper, a comprehensive study has been performed to address the excitation of a separated boundary layer near the leading edge due to surface roughness. Experiments are performed on a model airfoil with the semicircular leading edge at a Reynolds number (Rec) of 1.6×105, where the freestream turbulence (fst) is 1.2%. The flow features are investigated over the three rough surfaces with the roughness characteristic in the wall unit of 17, 10.5, and 8.4, which are estimated from the velocity profile at a location far downstream of reattachment. The wall roughness results in an early transition and reattachment, leading to a reduction of the laminar shear layer length apart from the bubble length. It is worthwhile to note that although the large-amplitude pretransitional perturbations are apparent from the beginning for the rough surface, the shear layer reflects the amplification of selected frequencies, where the fundamental frequency when normalized is almost the same as that of the smooth wall. The universal intermittency curve can be used to describe the transition of the shear layer, which exhibits some resemblance to the excitation of the boundary layer under fst, signifying the viscous effect.

Analytical approximation of the scalar spectrum in the ultraslow-roll inflationary models

The ultra-slow-roll (USR) inflationary models predict large-amplitude scalar perturbations at small scales which can lead to the primordial black hole production and scalar-induced gravitational waves. In general scalar perturbations in the USR models can only be obtained using numerical method because the usual slow-roll approximation breaks. In this work, we propose an analytical approach to estimate the scalar spectrum which is consistent with the numerical result. We find that the USR inflationary models predict a peak with power-law slopes in the scalar spectrum and energy spectrum of gravitational waves, and we derive the expression of the spectral indexes in terms of the inflationary potential. In turn, the inflationary potential near the USR regime can be reconstructed from the negative spectral index of the gravitational wave energy spectrum.

Morphological stability of rod-shaped continuous phases

Morphological transition of a rod-shaped phase into a string of spherical particles is commonly observed in the microstructures of alloys during solidification (Ratke and Mueller, 2006). This transition phenomenon can be explained by the classic Plateau-Rayleigh theory which was derived for fluid jets based on the surface area minimization principle. The quintessential work of Plateau-Rayleigh considers tiny perturbations (amplitude much less than the radius) to the continuous phase and for large amplitude perturbations, the breakup condition for the rod-shaped phase is still a knotty issue. Here, we present a concise thermodynamic model based on the surface area minimization principle as well as a non-linear stability analysis to generalize Plateau-Rayleigh’s criterion for finite amplitude perturbations. Our results demonstrate a breakup transition from a continuous phase via dispersed particles towards a uniform-radius cylinder, which has not been found previously, but is observed in our phase-field simulations. This new observation is attributed to a geometric constraint, which was overlooked in former studies. We anticipate that our results can provide further insights on microstructures with spherical particles and cylinder-shaped phases.

Well-directed flux of megawatt sub-mm radiation generated by a relativistic electron beam in a magnetized plasma with strong density gradients

The power of electromagnetic emission near the plasma frequency during collective electron beam-plasma interaction is found to be significantly increased in a plasma with preformed large-amplitude density perturbations. Laboratory experiments at the GOL-PET facility show that injection of a kiloampere relativistic electron beam into a magnetized plasma with strong radial density gradients is accompanied with an order of magnitude more intense generation of sub-millimeter waves than in the case of smooth density profile. As a possible mechanism for the enhanced generation of the longitudinal radiation flux observed in these experiments, we discuss the direct beam pumping of longitudinally propagating electromagnetic plasma modes due to their coupling with the Doppler shifted beam branch in the presence of oblique modulation of plasma density.

Nonlinear dynamics of dewetting thin films

Fluid films spreading on hydrophobic solid surfaces exhibit complicated dynamics that describe transitions leading the films to break up into droplets. For viscous fluids coating hydrophobic solids this process is called "dewetting". These dynamics can be represented by a lubrication model consisting of a fourth-order nonlinear degenerate parabolic partial differential equation (PDE) for the evolution of the film height. Analysis of the PDE model and its regimes of dynamics have yielded rich and interesting research bringing together a wide array of different mathematical approaches. The early stages of dewetting involve stability analysis and pattern formation from small perturbations and self-similar dynamics for finite-time rupture from larger amplitude perturbations. The intermediate dynamics describes further instabilities yielding topological transitions in the solutions producing sets of slowly-evolving near-equilibrium droplets. The long-time behavior can be reduced to a finite-dimensional dynamical system for the evolution of the droplets as interacting quasi-steady localized structures. This system yields <i>coarsening</i>, the successive re-arrangement and merging of smaller drops into fewer larger drops. To describe macro-scale applications, mean-field models can be constructed for the evolution of the number of droplets and the distribution of droplet sizes. We present an overview of the mathematical challenges and open questions that arise from the stages of dewetting and how they relate to issues in multi-scale modeling and singularity formation that could be applied to other problems in PDEs and materials science.

Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations

Primordial black holes may have formed in the radiative era of the early Universe from the collapse of large enough amplitude perturbations of the metric. These correspond to non linear energy density perturbations characterized by an amplitude larger than a certain threshold, measured when the perturbations reenter the cosmological horizon. The process of primordial black hole formation is studied here within spherical symmetry, using the gradient expansion approximation in the long wavelength limit, where the pressure gradients are small, and the initial perturbations are functions only of a time-independent curvature profile. In this regime it is possible to understand how the threshold for primordial black hole formation depends on the shape of the initial energy density profile, clarifying the relation between local and averaged measures of the perturbation amplitude. Although there is no universal threshold for primordial black hole formation, the averaged mass excess of the perturbation depends on the amplitude of the energy density peak, and it is possible to formulate a well-defined criterion to establish when a cosmological perturbation is able to form a black hole in terms of one of these two key quantities. This gives understanding of how the abundance of primordial black holes depends on the shape of the the inflationary power spectrum of cosmological perturbations.

The Distinction Between Thermal Nonequilibrium and Thermal Instability

For some forms of steady heating, coronal loops are in a state of thermal nonequilibrium and evolve in a manner that includes accelerated cooling, often resulting in the formation of a cold condensation. This is frequently confused with thermal instability, but the two are in fact fundamentally different. We explain the distinction and discuss situations where they may be interconnected. Large-amplitude perturbations, perhaps associated with MHD waves, likely play a role in explaining phenomena that have been attributed to thermal nonequilibrium but also seem to require cross-field communication.

Nonlinear Dynamics of Spinning Bosonic Stars: Formation and Stability.

We perform numerical evolutions of the fully nonlinear Einstein (complex, massive) Klein-Gordon and Einstein (complex) Proca systems, to assess the formation and stability of spinning bosonic stars. In the scalar (vector) case these are known as boson (Proca) stars. Firstly, we consider the formation scenario. Starting with constraint-obeying initial data, describing a dilute, axisymmetric cloud of spinning scalar or Proca field, gravitational collapse toward a spinning star occurs, via gravitational cooling. In the scalar case the formation is transient, even for a nonperturbed initial cloud; a nonaxisymmetric instability always develops ejecting all the angular momentum from the scalar star. In the Proca case, by contrast, no instability is observed and the evolutions are compatible with the formation of a spinning Proca star. Secondly, we address the stability of an existing star, a stationary solution of the field equations. In the scalar case, a nonaxisymmetric perturbation develops, collapsing the star to a spinning black hole. No such instability is found in the Proca case, where the star survives large amplitude perturbations; moreover, some excited Proca stars decay to, and remain as, fundamental states. Our analysis suggests bosonic stars have different stability properties in the scalar (vector) case, which we tentatively relate to its toroidal (spheroidal) morphology. A parallelism with instabilities of spinning fluid stars is briefly discussed.

Constraints on the primordial curvature power spectrum from primordial black holes

Large-amplitude density perturbations may have collapsed during the radiation dominated epoch of the Universe to form primordial black holes (PBHs). There are several constraints to the abundance of PBHs that stem from evaporation or gravitational effects. Due to the connection between primordial perturbations and the formation of PBHs, constraints on the present-day abundance of PBHs can be translated into limits on the primordial curvature power spectrum. We introduce several new observational and forecasted constraints to the amplitude of the primordial power spectrum and incorporate in our analysis uncertainties in the critical overdensity for collapse and considerations of ellipsoidal collapse. Our results provide the most stringent limits from PBHs on the primordial curvature power spectrum on small scales.

A Geometric Approach to Phase Response Curves and Its Numerical Computation Through the Parameterization Method

The Phase Response Curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper we present a new approach to PRCs based on the parameterization method. The underlying idea relies on the construction of a periodic system whose corresponding stroboscopic map has an invariant curve. We demonstrate the relationship between the internal dynamics of this invariant curve and the PRC, which yields a method to numerically compute the PRCs. Moreover, we link the existence properties of this invariant curve as the amplitude of the perturbation is increased with changes in the PRC waveform and with the geometry of isochrons. The invariant curve and its dynamics will be computed by means of the parameterization method consisting of solving an invariance equation. We show that the method to compute the PRC can be extended beyond the breakdown of the curve by means of introducing a modified invariance equation. The method also computes the amplitude response functions (ARCs) which provide information on the displacement away from the oscillator due to the effects of the perturbation. Finally, we apply the method to several classical models in neuroscience to illustrate how the results herein extend the framework of computation and interpretation of the PRC and ARC for perturbations of large amplitude and not necessarily pulsatile.