Saturation Mechanism Research Articles

Deterministic Parity‐Time Symmetry Single‐Mode Oscillation in Filterless Multimode Resonators

AbstractParity‐time symmetry has great potential for mode selection in multimode resonators. However, in a PT‐symmetry system with saturable absorption mechanisms, the random background noise can initiate single‐mode oscillation at any of the maxima within the gain spectrum, that is, potential PT frequencies. Such randomness impedes the acquisition of high‐quality signals at desired frequencies. Here, this work proposes a method to obtain deterministic PT‐symmetry single‐mode oscillation in a filterless multimode resonator through one‐shot injection. With this technique, this work changes the system's gain spectrum and enhances the gain discrepancy. Utilizing the frequency domain saturable absorption of the resonator, oscillation at desired mode can maintain its frequency after the withdrawal of the injection signal. To validate the concept, this work establishes a polarization‐division multiplexed dual‐loop optoelectronic oscillator (OEO) with a 1‐km long cavity operated under PT‐symmetry conditions. By one‐shot injecting the PT‐OEO, this work effectively eliminates the randomness arising from the relatively flat gain spectrum, facilitating oscillation at any desired potential PT frequencies from 1.8 to 9 GHz without requiring elaborate frequency tuning structures. Moreover, the one‐shot injection technique produces ultra‐low phase noise performance, achieving a remarkable −158.6 dBc Hz−1@10 kHz. This performance level stands in close comparison with the best phase noise values recorded for OEOs.

Nonlinear saturation of the ion flow driven ion sound instability in a finite length plasma

The saturation mechanism and nonlinear evolution of the ion sound instability driven by the subsonic ion flow in a finite length plasma are studied by a one-dimensional hybrid model considering kinetic ions and Boltzmann electrons. Three regimes of the instability nonlinear behavior are identified as a function of the frequency of the ion-neutral charge exchange (CX) collision fcoll. In the first (collisionless-alike) regime when the CX frequency is low, the instability is saturated by ions trapping in wave potentials leading to the formation of phase space vortexes (PSVs). One of the PSVs subsequently expands and becomes system long in the steady state. The transition to the second (medium) regime occurs when fcoll≳vp/d, where vp is the PSV expansion velocity and d is the system length. In the second regime, CX collisions convert fraction of beam ions into slow ions that can be trapped in potentials of small scale ion sound eigenmodes fluctuations. The trapping of slow ions results in the formation of a chain of small scale PSVs and the disruption of the establishment of the single system long PSV. In the third (collision-dominated) regime when fcoll≳γ (γ is the instability growth rate), CX collisions transform all beam ions into slow ions and the instability is thereby eliminated.

Chaotic magnetic disconnections trigger flux eruptions in accretion flows channeled onto magnetically saturated Kerr black holes

Magnetized accretion flow onto a black hole (BH) may lead to the accumulation of poloidal magnetic flux across its horizon, which for high BH spin can power far-reaching relativistic jets. The BH magnetic flux is subject to a saturation mechanism by means of magnetic flux eruptions involving relativistic magnetic reconnection. Such accretion flows have been described as magnetically arrested disks (MAD) or magnetically choked accretion flows (MCAF). The main goal of this work is to describe the onset of relativistic reconnection and initial development of magnetic flux eruption in accretion flow onto magnetically saturated BHs. We analyzed the results of 3D general relativistic ideal magnetohydrodynamic (GRMHD) numerical simulations in the Kerr metric, starting from weakly magnetized geometrically thick tori rotating either prograde or retrograde. We integrate d large samples of magnetic field lines in order to probe magnetic connectivity with the BH horizon. The boundary between magnetically connected and disconnected domains coincides roughly with enthalpy equipartition. The geometrically constricted innermost part of the disconnected domain develops a rigid structure of magnetic field lines -- rotating slowly and insensitive to the BH spin orientation. The typical shape of innermost disconnected lines is a double spiral converging to a sharp inner tip anchored at the single equatorial current layer. The foot points of magnetic flux eruptions are found to zip around the BH along with other azimuthal patterns. Magnetic flux eruptions from magnetically saturated accreting BHs can be triggered by minor density gaps in the disconnected domain, resulting from the chaotic disconnection of plasma-depleted magnetospheric lines. Accretion flow is effectively channeled along the disconnected lines toward the current layer, and further toward the BH by turbulent cross-field diffusion. Rotation of flux eruption foot points may contribute to the variability of BH crescent images.

Influence of reservoir water saturation on coalbed methane development: Based on multi-field coupling numerical simulation

Water in coal reservoirs serves as both the driving force of reservoir fluid and the resistance to coalbed methane (CBM) migration. However, the impact and control mechanism of water saturation on CBM development in the field have not been revealed yet. The evolution of reservoir dynamics and gas production rate under various initial water saturation conditions is simulated based on the COMSOL multiphysics numerical simulation software. The simulation results show that the reduction of initial water saturation can significantly enhance the effective permeability of the reservoir gas phase, which can be increased by up to 4764%. This increases the rate of gas production, which is the main mechanism for controlling production by water saturation in the reservoir. For high water saturation reservoirs, the positive effect of inter-well interference should be reasonably utilized, and high well network density should be used to rapidly increase gas-effective permeability. For low water saturation reservoirs, the negative effect of inter-well interference should be avoided, and low well network density should be used to increase the control of single well reserves.

Sealing Ni-Cr/Ni-Al alloys with borosilicate glass: Bonding strength, sealing interface, and fracture behavior

Encapsulation of the cold junction of sheathed thermocouples by incorporating glass-to-metal seal, which substitutes for the conventionally used organic sealants, is expected to improve the reliability of thermocouples. In this study, the sealing of borosilicate glass with thermocouple wire materials, i.e., Ni-Cr and Ni-Al alloys, was investigated. Three types of specimens were prepared for both alloys: nonoxidized, mildly preoxidized, and deeply preoxidized. High-temperature sealing with borosilicate glass was conducted for each specimen. The results revealed that grain boundaries were preferentially oxidized in both alloys and that preoxidation significantly increased the bonding strength between the alloys and borosilicate glass. However, the preoxidation conditions corresponding to the optimal bonding strength differed between the two alloys, which necessitates tailored pretreatment of the metal surface. For the Ni-Cr alloy, the sealing interfaces indicated that the deeply preoxidized specimens achieved the optimal bonding strength because of the synergistic effect of the glass saturation mechanism and mechanical interlocking mechanism, whereas the mildly preoxidized specimens were affected by unexpected chemical reactions and the consequent microscopic defects at the sealing interface. For the Ni-Al alloy, the deeply preoxidized specimens exhibited inferior bonding strengths compared with the mildly preoxidized specimens, which was attributed to their overmature intergranular oxidation, in which the grain boundaries were eroded by molten glass during sealing and trapped the glass after cooling. The glass in the grain boundaries was stressed by the cooling contraction of the metals and became prone to cracking. This study reveals the microscopic bonding mechanisms for the sealing of glass to Ni-based alloys and the causes of failure, providing a new perspective on the regulation and optimization of the sealing interface.

Examining transport and integrated modeling predictive capabilities for negative-triangularity scenarios

Abstract This paper investigates the predictive capabilities of TGYRO and TGLF models in assessing the
performance of negative triangularity (NT) plasmas compared to positive triangularity (PT) plasmas in fusion devices. TGYRO predicts kinetic profiles, while TGLF analyzes turbulent transport. The study reveals that TGYRO reasonably predicts NT profiles similar to PT, although it overpredicts the high-power scenarios where there is increased experimental MHD activity. TGLF analysis finds reduced linear growth rates in NT and altered flux spectra relative to PT. Additionally, the TGLF SAT0 saturation model is observed to predict high-k transport and a reduction of particle transport with the electron temperature gradient. These findings are further corroborated by core-pedestal modeling using the STEP (Stability Transport Equilibrium Pedestal) workflow, showing stronger confinement improvements in NT, particularly at higher power densities for the SAT0 saturation model. The study underscores the importance of accurately capturing turbulence saturation mechanisms for NT in order to project its performance accurately in fusion reactors.

Can rock surface flow derived from outcrops generate surface runoff in a rocky desertified area?

Rock surface flow, formed from exposed rock surfaces, is a unique form of runoff in rocky desertified areas with massive bedrock outcrops. The question of whether the rock surface flow promotes surface runoff formation continues to puzzle us. To address this problem, four sites with notable bedrock outcrops and different land use types were selected from a typical desertified area in Guizhou, China. Straight and concave rock-surface shapes that were the most capable of collecting rainwater were selected at each site. Soil infiltration and water storage capacity experiments were conducted to observe the infiltration and water storage properties of the soil closely adhering to the rock–soil interface (CRSI) of the bedrock outcrops by taking the soils far from the outcrops horizontally (FRSI) as the control, and to further explain the conditions for surface runoff formation via rock surface flow. Our results showed that the CRSI is more prone to producing surface runoff than the FRSI, which is attributed to its lower infiltration (stable infiltration rate of 0.2 to 192.6 mm/min) and water storage capacity (total reservoir 441.6 to 613.6 t/hm2) than that of FRSI (4.50 to 272.8 mm/min, 458.8 to 635.4 t/hm2). This phenomenon would be intensified after receiving the rock surface flow input. Concurrently, concave rock surfaces are more likely to promote surface runoff formation than straight rock surfaces, which are affected by the accumulation of rock surface shapes on rainwater. A discriminating condition for whether rock surface flow produces surface runoff at the CRSI is proposed based on the inversely proportional functional relationship between rainfall (rainfall intensity RI and amount RA) and the effective rock surface rainfall catchment area (ARS). When RI or RA exceeds the critical threshold, the surface runoff with mechanisms of excess infiltration or excess saturation is generated around bedrock outcrops. The discriminating equation will help increase surface runoff prediction accuracy in rocky desertified areas with exposed bedrock outcrops. These results help understand the importance and role of rock surface flow hydrologic processes in karst areas.

Gyrokinetic investigation of toroidal Alfvén eigenmode (TAE) turbulence

Toroidal Alfvén eigenmodes (TAEs) can transport fusion-born energetic particles out of the plasma volume, thereby decreasing plasma self-heating efficiency and possibly damaging reactor walls. Therefore, understanding TAE destabilization and identifying saturation mechanisms are crucial to achieving burning plasma. Here, a fully gyrokinetic study is employed. In the case studied, the primary drive mechanism is identified as the resonance between the magnetic drifts and the TAE, and this is seen to be disrupted by equilibrium flow shear, which can stabilize the mode by rotating it in the poloidal plane. It is found that zonal flows do not play a significant role in the saturation of these TAEs and that there are no saturation mechanisms present in the local gyrokinetic picture, which are able to saturate the mode at physically relevant transport levels in the case of TAE-only turbulence. Instead, we confirm that the global profile flattening of fast-ion density is the key saturation mechanism. The nonlinear excitation of TAEs traveling along the electron diamagnetic direction and its beating with the ion diamagnetic TAE, resulting in large amplitude oscillations that may help detect TAEs more easily in tokamaks, are also reported.

Non-linear three-mode coupling of gravity modes in rotating slowly pulsating B stars

Context. Slowly pulsating B (SPB) stars display multi-periodic variability in the gravito-inertial mode regime with indications of non-linear resonances between modes. Several have undergone asteroseismic modeling in the past few years to infer their internal properties, but only in a linear setting. These stars rotate fast, so that rotation is typically included in the modeling by means of the traditional approximation of rotation (TAR). Aims. We aim to extend the set of tools available for asteroseismology, by describing time-independent (stationary) resonant non-linear coupling among three gravito-inertial modes within the TAR. Such coupling offers the opportunity to use mode amplitude ratios in the asteroseismic modeling process, instead of only relying on frequencies of linear eigenmodes, as has been done so far. Methods. Following observational detections, we derive expressions for the resonant stationary non-linear coupling between three gravito-inertial modes in rotating stars. We assess selection rules and stability domains for stationary solutions. We also predict non-linear frequencies and amplitude ratio observables that can be compared with their observed counterparts. Results. The non-linear frequency shifts of stationary couplings are negligible compared to typical frequency errors derived from observations. The theoretically predicted amplitude ratios of combination frequencies match with some of their observational counterparts in the SPB targets. Other, unexplained observed ratios could be linked to other saturation mechanisms, to interactions between different modes, or to different opacity gradients in the driving zone. Conclusions. For the purpose of asteroseismic modeling, our non-linear mode coupling formalism can explain some of the stationary amplitude ratios of observed resonant mode couplings in single SPB stars monitored during 4 years by the Kepler space telescope.

Stability and transport of gyrokinetic critical pedestals

A gyrokinetic threshold model for pedestal width–height scaling prediction is applied to multiple devices. A shaping and aspect ratio scan is performed on National Spherical Torus Experiment (NSTX) equilibria, finding Δped=0.92A1.04κ−1.240.38δβθ,ped1.05 for the wide-pedestal branch with pedestal width Δped , aspect ratio A, elongation κ, triangularity δ, and normalized pedestal height βθ,ped . The width–transport scaling is found to vary significantly if the pedestal height is varied either with a fixed density or fixed temperature, showing how fueling and heating sources affect the pedestal density and temperature profiles for the kinetic-ballooning-mode (KBM) limited profiles. For an NSTX equilibrium, at fixed density, the wide branch is Δped=0.028(qe/Γe−1.7)1.5∼ηe1.5 and at fixed temperature Δped=0.31(qe/Γe−4.7)0.85 ∼ηe0.85 , where qe and Γe are turbulent electron heat and particle fluxes and ηe=∇ln⁡Te/∇ln⁡ne for an electron temperature Te and density ne . Pedestals close to the KBM limit are shown to have modified turbulent transport coefficients compared to the strongly driven KBMs. The role of flow shear is studied as a width–height scaling constraint and pedestal saturation mechanism for a standard and lithiated wide pedestal discharge. Finally, the stability, transport, and flow shear constraints are combined and examined for an NSTX experiment.

Towards efficiency enhancement of earth abundant Cu2BaSn(S,Se)4 chalcogenide solar cell using In2S3 as efficient electron transport layer

Cu2BaSn(S,Se)4 (CBTSSe) solar cells, are an intriguing kind of photovoltaic devices with theoretical efficiency close to 31 %. Their promise in the field of renewable energy is highlighted by their sustainable structure, as well as their low density of defects. Even with these benefits, the record efficiency for CBTSSe solar cells is now only 5.2 %. In order to identify limitations in performance and clear the path for obtaining improved practical efficiency, this emphasizes the vital requirement for deep analysis. In this work, we investigate a new structure based on Cd free In2S3/CBTSSe heterojunction in which an Indium (III) sulfide as ETL layer, and CBTSSe as absorber layer take the place of the traditional CdS/ CBTSSe structure. For the first time, an analytical model that incorporates a variety of recombination mechanisms occurred in CBTSSe solar cell, such as Auger, Shockley-Read-Hall (SRH), interface recombination, tunneling-enhanced recombination, and non-radiative recombinations is proposed. In our approach the reverse saturation mechanism is taken into account in the suggested model as a metric to identify the main recombination mechanism. Significantly, there is a good agreement between the outcomes of our model and the experiment. It is shown that CBTSSe bulk recombination, In2S3/CBTSSe interface recombination and resistances are dominating. Besides, the developed model serves as fitness function for MOGA approach to locate the optimal parameters design combination that led to optimal efficiency. We demonstrate the ability to obtain an efficiency of up to 10.12 % by carefully tuning both the CBTSSe bulk material parameters and the In2S3/CBTSSe interface features. Our findings demonstrate that the optimized design using In2S3/CBTSSe heterojunction outperforms the baseline, reaching a high JSC of 20.57 mA/cm2, VOC of 0.88 V, and FF of 55.54 %, with appropriate band alignment at the In2S3/CBTSSe interface and optimized physical and geometrical parameters. The suggested approach paves the way for additional design optimization while also making it possible to identify the degradation factors that are responsible.

Polarization Saturation in Multilayered Interfacial Ferroelectrics.

Van der Waals polytypes of broken inversion and mirror symmetries have been recently shown to exhibit switchable electric polarization even at the ultimate two-layer thin limit. Their out-of-plane polarization has been found to accumulate in a ladder-like fashion with each successive layer, offering 2D building blocks for the bottom-up construction of 3D ferroelectrics. Here, it is demonstrated experimentally that beyond a critical stack thickness, the accumulated polarization in rhombohedral polytypes of molybdenum disulfide saturates. The underlying saturation mechanism, deciphered via density functional theory and self-consistent Poisson-Schrödinger calculations, point to a purely electronic redistribution involving: 1.Polarization-induced bandgap closure that allows for cross-stack charge transfer and the emergence of free surface charge; 2. Reduction of the polarization saturation value, as well as the critical thickness at which it is obtained, by the presence of free carriers. The resilience of polar layered structures to atomic surface reconstruction, which is essentially unavoidable in polar 3D crystals, potentially allows for the design of new devices with mobile surface charges. The findings, which are of general nature, should be accounted for when designing switching and/or conductive devices based on ferroelectric layered materials.

Theoretical and global simulation analysis of collisional microtearing modes

Microtearing modes (MTMs) are suggested as a candidate for anomalous thermal transport in tokamak H-mode discharges. This study investigates MTMs in tokamak plasmas, employing simulations in the BOUT++ framework. It simplifies and linearizes the governing equations in detailed linear simulations. The study meticulously evaluates various conductivity models under diverse plasma conditions and collision regimes. The research thoroughly assesses different conductivity models across a range of plasma conditions and collision regimes. A unified dispersion relation that includes both MTM and Drift-Alfvén Wave (DAW) instabilities is derived, showing that DAW and MTM instabilities occur at varying distances from the rational surface. Specifically, MTMs become unstable near the rational surface but stabilize farther away, while drift-Alfvén instability appears farther from the rational surface. The study also re-derives MTM dispersion relations using Ohm's law and the vorticity equation, providing a thorough analysis of electromagnetic and electrostatic interactions in tokamaks. Global simulations demonstrate an inverse correlation between MTM growth rates and collisionality, and a direct correlation with temperature gradients. The nonalignment of the rational surface with the peak ω*e stabilizes the MTMs. Nonlinear simulations highlight electron temperature relaxation as the primary saturation mechanism for MTMs, with magnetic flutter identified as the dominant mode of electron thermal transport.

Temporal Clustering of Precipitation Driving Landslides Over the Italian Territory

AbstractThe occurrence of multiple precipitation events not‐independent in time, that is, a temporal clustering, is an example of a temporal compounding event. This type of forcing is of great relevance for the occurrence of different natural hazards, like floods and deep‐seated landslides, for which previous soil saturation plays an important role in shaping the associated hazard. Using ERA5‐Land data set and E‐OBS, we firstly investigate the spatial and temporal characteristics of temporal clustering of precipitation over the Italian territory, and we relate it with two oscillation patterns, namely North Atlantic Oscillation (NAO) and Mediterranean Oscillation Index (MOI), and with common synoptic conditions. Then, we explore the role of temporal compounding of precipitation in the generation of different movement types (complex, debris flow, fall, flow, and sliding) using the database of landslides from the Aree Vulnerate Italiane project (in Italian AVI, meaning Areas Affected by Landslides or Floods). From this study it emerges that below average values of NAO and MOI increase the probability of having clustered precipitation events. For all types of landslides, except rock falls, we observed that the majority of the events are preceded by a temporal clustering of precipitation, over longer time windows for complex events, shorter for debris flows. For rock falls, we found also a link with low minimum temperature and freeze‐thaw cycles for winter events and high maximum temperature for summer events. This work contributes to the investigation of temporal clustering of precipitation in connection with natural hazards characterized by a mechanism of saturation.

Nonlinear dynamics of the reversed shear Alfvén eigenmode in burning plasmas

In a tokamak fusion reactor operated at steady state, the equilibrium magnetic field is likely to have reversed shear in the core region, as the noninductive bootstrap current profile generally peaks off-axis. The reversed shear Alfvén eigenmode (RSAE) as a unique branch of the shear Alfvén wave in this equilibrium, can exist with a broad spectrum in wavenumber and frequency, and be resonantly driven unstable by energetic particles (EP). After briefly discussing the RSAE linear properties in burning plasma condition, we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels, and illustrate their potentially important role in reactor-scale fusion plasmas. By means of simplified hybrid MHD-kinetic simulations, the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP, as results of weak/vanishing magnetic shear and relatively low frequency. Through the route of wave-EP nonlinearity, the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure, and the resultant EP transport generally has a convective feature. The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations. Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory, and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE. Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode, which may effectively transfer the EP energy to fuel ions via collisionless Landau damping. Moreover, zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope, and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.

Superradiant pulse saturation in a Free Electron Laser

A study is made of the saturation mechanism of a single superradiant ‘spike’ of radiation in a Free Electron Laser. A one-dimensional (1D) computer model is developed using the Puffin, un-averaged FEL simulation code, which allows sub-radiation wavelength evolution of both the spike radiation field and the electron dynamics to be modelled until the highly non-linear saturation process of the spike is observed. Animations of the process from the start to the end of the interaction are available. The resultant saturated spike duration is at the sub-wavelength scale and has a broad spectrum. The electrons passing through the spike can both lose and gain energy many times greater than that of the ‘normal’ non-pulsed FEL interaction. A saturation mechanism is proposed and tested via a simple analysis of the 1D FEL equations. The scaling results of the analysis are seen to be in good agreement with the numerical results. A simple model of three dimensional diffraction effects of the radiation is applied to the results of the 1D simulations. This greatly reduces longer wavelengths of the power spectrum, which are seen to be emitted mainly after the electrons have propagated through the spike, and is seen to be in qualitative agreement with recent experimental results.

Preparation and interfacial microstructure of high thermal conductivity diamond/SiC composites

Diamond/SiC composites offer valuable applications in thermal management because of their exceptional thermal properties. Currently, the predominant method employed for crafting diamond/SiC composites is the reaction sintering approach. However, it encounters the challenge of a high residual silicon content. In this study, we introduced techniques such as bimodal diamond particles and high-density carbon sources (submicron diamond powder) to enhance the diamond content and reduce the residual silicon, optimizing the phase composition. The results indicated the diamond/SiC composite demonstrated a thermal conductivity of 666 W/m·K, a thermal expansion coefficient of 2.73 × 10−6 K−1, and an elastic modulus of 753 GPa. Furthermore, the meticulous assessment of the interface microstructure of diamonds in the diamond/SiC composite was conducted using transmission electron microscopy. The formation of nanocrystal-SiC and interface defects were elucidated by the mechanism of carbon dissolution saturation.

Inflows Towards Bipolar Magnetic Active Regions and Their Nonlinear Impact on a Three-Dimensional Babcock–Leighton Solar Dynamo Model

The changing magnetic fields of the Sun are generated and maintained by a solar dynamo, the exact nature of which remains an unsolved fundamental problem in solar physics. Our objective in this paper is to investigate the role and impact of converging flows toward Bipolar Magnetic Regions (BMR inflows) on the Sun’s global solar dynamo. These flows are large-scale physical phenomena that have been observed and so should be included in any comprehensive solar dynamo model. We have augmented the Surface flux Transport And Babcock–LEighton (STABLE) dynamo model to study the nonlinear feedback effect of BMR inflows with magnitudes varying with surface magnetic fields. This fully-3D realistic dynamo model produces the sunspot butterfly diagram and allows a study of the relative roles of dynamo saturation mechanisms such as tilt-angle quenching and BMR inflows. The results of our STABLE simulations show that magnetic field-dependent BMR inflows significantly affect the evolution of the BMRs themselves and result in a reduced buildup of the global poloidal field due to local flux cancellation within the BMRs, to an extent that is sufficient to saturate the dynamo. As a consequence, for the first time, we have achieved fully 3D solar dynamo solutions, in which BMR inflows alone regulate the amplitudes and periods of the magnetic cycles.

Influence of parametric forcing on Marangoni instability

We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. Although dry spots can also be avoided at larger forcing amplitudes, this comes at the expense of generating large-amplitude Faraday waves.

Saturation of spiral instabilities in disc galaxies

ABSTRACT Spiral density waves can arise in galactic discs as linear instabilities of the underlying stellar distribution function. Such an instability grows exponentially in amplitude at some fixed growth rate β before saturating non-linearly. However, the mechanisms behind saturation, and the resulting saturated spiral amplitude, have received little attention. Here, we argue that one important saturation mechanism is the non-linear trapping of stars near the spiral’s corotation resonance. Under this mechanism, we show analytically that an m-armed spiral instability will saturate when the libration frequency of resonantly trapped orbits reaches $\omega _\mathrm{lib} \sim \mathrm{a\, \, few}\times m^{1/2} \beta$. For a galaxy with a flat rotation curve, this implies a maximum relative spiral surface density $\vert \delta \Sigma /\Sigma _0\vert \sim \mathrm{a\, \, few} \times (\beta /\Omega _\mathrm{p})^2 \cot \alpha$, where Ωp is the spiral pattern speed and α is its pitch angle. This result is in reasonable agreement with recent N-body simulations, and suggests that spirals driven by internally-generated instabilities reach relative amplitudes of at most a few tens of per cent; higher amplitude spirals, like in M51 and NGC 1300, are likely caused by very strong bars and/or tidal perturbations.