Perturbation Frequency Research Articles

Dynamic instability of two-step continuous crystallization with applications to beta-lactoglobulin, lysozyme and insulin crystal growth

Abstract This study is concerned with a continuous operation mode of bulk crystallization from a supersaturated solution with allowance for the two-step mechanism of nucleation and growth of crystals. The integro-differential system of governing equations for the crystal-size distribution function and liquid supersaturation is formulated accounting for mass input into the saturated solution and withdrawal rate of product crystals from the crystallizer (mass exchange with the environment). This system contains the particles growth rate for the two-step nucleation mechanism, which is only a function of crystal radius when considering $\beta$-lactoglobulin, lysozyme and insulin crystal growth. The steady-state analytical solutions of this system are found for the Weber-Volmer-Frenkel-Zel'dovich and Meirs nucleation kinetics. The crystal-size distribution function for unsteady crystallization mode is found by means of the integral Laplace transform method. This function enables us to derive a single unsteady integro-differential equation for the liquid supersaturation. A linear instability analysis based on this equation is carried out. The amplification rate and frequency of small perturbations following from this analysis enable us to find the neutral stability curve and the domains of stable and unstable crystallization. We show that the frequency of perturbations stabilizes near the neutral stability curve when dealing with the stable mode of continuous crystallization.

Cascaded Integral Minus Tilt Integral Derivative With Filter for Frequency Stabilization of V2G/G2V Enabled Hybrid Microgrid

ABSTRACTRenewable generation plays an important part in today's power system. With the inclusion of the inverter interfaced renewable energy sources (RESs) into a microgrid, the total system inertia decreases and it leads to increased frequency deviation in presence of a disturbance. This paper proposes a cascaded Integral Minus Tilt Integral Derivative with Filter (I–TDN)‐Proportional‐Integral (PI), [(I‐TDN)‐PI] controller for frequency stabilization of a hybrid microgrid in presence of electric vehicles (EV). The microgrid model includes reheated thermal power plant with high degree of non‐linear system such as inverter based RESs like photovoltaic and wind generation systems. A diesel engine generator is incorporated for load frequency control during perturbation in the system frequency. Virtual inertia controller (VIC) with inverter based energy storage system (ESS) is commonly used to improve system inertia and frequency stability of the microgrid. In addition to the ESS, this paper proposes inclusion of the EVs in this VIC. The optimal gains of the proposed cascaded I‐TDN‐PI controller are determined using Mountain Gazelle Optimizer (MGO), a modern metaheuristic optimization algorithm. Sensitivity of the proposed controller is investigated in presence of system nonlinearities, load perturbations, time delay, system parameter variation and RES power fluctuations. The simulation results justify the robustness of the proposed control structure for frequency stabilization of the microgrid.

Measurement and Identification of Flame Describing Function (FDF) Based on Parallel Subsystem Model

Because of the need for low pollutant emissions, industrial gas turbines typically use partially premixed gases for combustion. However, the nonlinear dynamic characteristics of partially premixed flames have not been studied sufficiently. Therefore, this study focuses on the dynamics of a partially premixed flame generated by a swirler with fuel holes on its surface and designs a flame describing function (FDF) identification method based on the parallel subsystem model. This method can separate the flame dynamic characteristics into a parallel connection of the nonlinear and linear models. The nonlinear model is related to the disturbance frequency and velocity perturbation amplitude, whereas the linear model depends only on the disturbance frequency. This method is verified using a simulation. Finally, experimental research on partially premixed flames is conducted. Based on the experimental data, the identification method successfully separates the FDF into a nonlinear model with saturation characteristics and a linear model with Gaussian distribution characteristics. The flame model obtained by the identification method is the foundation for the analysis of combustion thermoacoustic stability and active/passive control strategy.

Self-selection of flow instabilities by acoustic perturbations around rectangular cylinder in cross-flow

This work experimentally investigates the flow structure around a rectangular cylinder with an aspect ratio of 2 under varying incidence angles to examine how acoustic perturbations modify and modulate the unsteady flow instabilities. In the absence of acoustic excitation, the angle of incidence is found to markedly influence the flow topology and the natural shedding pattern altering the vortex formation length and wake dynamics. With acoustic perturbations, it is observed that for incidence angles $\alpha = 0^{\circ }$ and $\alpha = 5^{\circ }$ , the masked impinging leading-edge vortex (ILEV)/trailing-edge vortex shedding (TEVS) instability modes of $n= 1$ and $n= 2$ become evident when their frequencies coincide with the frequencies of the acoustic perturbations (i.e. resonant condition). Both trailing-edge and leading-edge vortices were found to be modulated by the acoustic pressure cycle. These instability modes, which are naturally present under non-resonant conditions for significantly higher aspect ratios, highlight the role of incidence angle and self-excited acoustic resonance in virtually augmenting the streamwise length of the cylinder, thereby facilitating the emergence and sustenance of the ILEV/TEVS shedding pattern.

Modulation instability of whistler wave with electron loss cone distribution in magnetized plasma

Abstract The modulation instability of whistler mode waves caused by thermal electron anisotropy is studied. Based on MHD equations, the nonlinear Schrödinger equation (NLSE) that describes the nonlinear modulation of whistler waves is derived by using the Krylov-Bogoliubov-Mitropolsky (KBM) method. The condition for wave modulation instability is obtained from the loss cone distribution function of thermal electron anisotropy, revealing that the nonlinear growth of the waves tends towards electron perpendicular temperature anisotropy. By setting up continuous background waves and introducing small ion low frequency perturbations, we find that the change in the amplitude of the modulated wave is related with wave number. This finding has been validated through simulations that align with our analytical results. Additionally, we also calculate the maximum amplitude of the wave with loss cone angle and times, which revealed that the electron vertical temperature anisotropy will lead to the modulation instability of the whistler wave. This further confirms the occurrence of the modulation instability of the whistler wave in laboratory plasmas and strengthens their credibility.

Dominance reversal protects large-effect resistance polymorphisms in temporally varying environments.

A central challenge in evolutionary biology is to uncover mechanisms maintaining functional genetic variation in heterogeneous environments 1,2 . Population genetics theory suggests that beneficial reversal of dominance, where alleles are dominant when beneficial and recessive when deleterious, can help maintain such variation in temporally varying environments 3,4 . However, empirical examples are scarce 5 due to difficulties in measuring dominance in fitness in field experiments 6 . Here we quantify the selective effects and dominance of large-effect insecticide-resistant alleles at the Ace enzymatic locus in Drosophila melanogaster 7 . In laboratory assays, we identify a beneficial reversal of dominance of the Ace alleles for fitness-associated phenotypes under selection in the presence and absence of malathion, a widely used organophosphate insecticide. Using highly replicated field mesocosms, we show that resistant Ace alleles fluctuate rapidly in response to a pulse of malathion, but are maintained in its absence. We show that this pattern is only consistent with beneficial reversal of dominance, where the resistant Ace alleles are dominant and beneficial for resistance and recessive and deleterious for enzymatic function. Moreover, we find that seasonally fluctuating selection due to insecticide resistance can generate fluctuating chromosome-scale genomic perturbations of allele frequencies. We propose an extension to Wright's physiological theory of dominance 8 , arguing that under fluctuating selection the currently deleterious allele should often behave as loss-of-function and thus recessive to the currently beneficial allele. Overall, our results suggest that beneficial reversals of dominance can be common and can help both maintain genetic variation and allow for rapid evolutionary responses to environmental shifts.

Smoothed Cepstral Peak Prominence: A Comparison Between Dysphonic and Non-dysphonic Mexican Adults Employing the Praat Software.

Background Acoustic vocal analysis provides objective and measurable values for various voice parameters, such as fundamental frequency (F0), shimmer, jitter, and the noise-to-harmony ratio (NHR). In severely dysphonic patients, who present increased variability in glottic cycles and abnormalities in vocal intensity, conventional acoustic analysis is an unreliable predictor of dysphonia. The logarithmic transformation of the vocal spectrum (cepstrum) allows capturing the signal without relying on recording technique, frequency, or vocal intensity. Smoothed cepstral peak prominence (CPPS) is a variable in cepstral analysis that serves as a reliable predictor of dysphonia, being directly proportional to its severity. Objective To determine the mean value of CPPS in continuous speech and sustained vowels in dysphonic and non-dysphonic Mexican adults, with or without laryngeal pathology. Materials and methods Sustained vowel and continuous speech analysis was performed using the Praat software (Version 6.1.15, developed by Paul Boersma and David Weenink, Phonetic Sciences, University of Ámsterdam, https://www.praat.org/) to obtain the smoothed cepstral peak prominence (CPPS) in 51 dysphonic patients with laryngeal pathology and 24 non-dysphonic patients without underlying laryngeal pathology. Frequency perturbation variables such as shimmer, jitter, and NHR were collected. Quality of life was assessed using the 30-item Voice Handicap Index (VHI-30). Results We found significantly lower median CPPS values in patients with laryngeal pathology, both in sustained vowel (6.59, IQR 4.09-9.38, p < 0.001) and in connected speech (4.82, IQR 3.57-6.03, p < 0.001), compared with the non-dysphonic population (sustained phonation: 11.69, IQR 9.26-12.81, p < 0.001; connected speech: 6.38, IQR 0.90-7.09, p < 0.001). Conclusions A low CPPS value is a reliable predictor of underlying laryngeal pathology in dysphonic voices and could be considered for routine screening and diagnosis in patients with vocal pathology.

Analysis of therapeutic effect of fibrocystic degeneration of vocal folds

Objective:To explore the differences in clinical presentation and therapeutic outcomes between vocal fold fibrocystic degeneration and other common benign lesions, such as vocal fold polyp and cyst. Methods:Vocal function was assessed before and after surgery in 10 cases of vocal fold fibrocystoids, 30 cases of vocal fold polyps and 10 cases of vocal fold cysts at Department of Voice Medicine, Xiamen University Zhongshan Hospital. The voice Assessments included GRBAS（G-scale）, VHI-10 scale, Reflux Symptom Index（RSI） scale, stroboscope, acoustic objective analysis, and aerodynamics measurements. The acoustice analysis parameters included fundamental frequency（F0）, fundamental frequency perturbation（Jitter）, amplitude perturbation（Shimmer） and voice disturbance severity index（DSI）, while the maximum phonation time（MPT） was assessed for aerodynamics. Stroboscopic parameters included vocal fold straightness, vocal fold color, glottic closure and mucosal wave. All three groups underwent phonomicrosurgery and a follow-up review was conducted one month later. Pre-and post-operative function assessment parameters were compared across the three groups. Results:Significant differences were founded in the G grade, Jitter, Shimmer, DSI, glottic closure and mucosal wave between the vocal fold fibrocystic degeneration group and the vocal fold polyp and vocal fold cyst group（P<0.05）. Most voice function parameters in all three groups showed significant improvement after surgery（P<0.05）. The improvement of VHI（10）, RSI and mucosal wave scores in the vocal fold fibrocystic lesion group was significantly different from that of the vocal fold polyp group（P<0.05）. Conclusion:Vocal fold fibrocystic degeneration is a more severe than that of vocal fold polyps and cysts, which are two common benign vocal fold lesions. Phonomicrosurgery is an effective treatment for vocal fold fibrocystic degeneration, but its curative effect are less favorable compared to those for vocal fold polyps and vocal fold cysts. Therefore, a detailed preoperative evaluation is essential for predicting surgical outcomes.

The effect of hydrogen enrichment on the conical premixed methane–air flame response and thermoacoustic modes coupling

This paper investigates the thermoacoustic dynamic responses of hydrogen-enriched laminar premixed conical methane–air flames under dual-mode coupling. Utilizing the level set method and the G-equation model, one meticulously derives the flame describing function (FDF) in relation to variations in hydrogen enrichment levels (ηH). This precisely derived FDF is then integrated into the low-order network model of the Rijke tube to analyze the thermoacoustic unstable modes of the system. Finally, dual-frequencies incoming flow velocity perturbations are reintroduced as inputs to obtain the flame response under thermoacoustic modes coupling. Results show that while keeping the unstretched steady flame aspect ratio constant, an increase in ηH not only raises the FDF’s cut-off frequency but also enhances the FDF gain within the nonlinear frequency region, leading to more unstable modes, especially high frequency modes within the Rijke tube system. Furthermore, the flame response is further altered under the excitation of dual unstable modes. When both modes are within the linear frequency region of the FDF, the flame response is co-controlled by the two modes, predominantly by the mode with a larger velocity perturbation amplitude, with weaker modes coupling leading to the additional frequency perturbation having a suppressive effect on the flame response at the original frequency. Conversely, when one or two modes are within the nonlinear frequency region of the FDF, the flame response is dominated by the lower-frequency mode, with higher nonlinear modes coupling allowing the additional frequency perturbation to both promote and suppress the response at the original frequency and also couple to produce a significant difference frequency response. Novelty and significance The novelty of this paper lies in the determination of the flame describing function (FDF) with varying hydrogen enrichment levels and the stability of thermoacoustic systems, and more significantly, conducting an in-depth and comprehensive investigation into the nonlinear dynamic responses of hydrogen-enriched flames to different types of dual-mode coupling perturbations. The dual-mode perturbations result in either attenuation or amplification of the flame response, depending on whether the corresponding frequencies lie within the linear or nonlinear frequency regions of the FDF, which innovatively incorporates the influence of the FDF phase and examines the responses at the difference frequencies generated by the coupling. This lays a foundation for further exploration into the mechanisms of modes coupling in hydrogen-enriched and other thermoacoustic systems.

Hybrid intelligent framework for designing band gap-rich 2D metamaterials

An artificial intelligence machine learning-based design framework is proposed to design lattice-based metamaterials with hexagonal symmetry that deliver wide band gaps at user-desired frequency ranges between 0 and 1000 kHz. The design approach starts by selecting a traditional, easy-to-manufacture parent lattice-based material that does not necessarily exhibit wide or functional band gaps. Subsequently, the parent lattice is transformed into a band-gap-rich lattice by superposing periodic triangular-shaped perturbations (i.e., zigzag-sine-based curvatures) with controllable frequencies and magnitudes on its ligaments. Finally, the frequency and magnitude parameters needed to deliver a specific band gap between 0 and 1000 kHz are determined using a hybrid intelligent framework, developed based on an Adaptive Neuro-Fuzzy Inference Systems (ANFIS). The ANFIS network integrates fuzzy logic expert models and artificial neural networks’ machine learning capabilities. Such a hybrid network is known for its ability to model strongly nonlinear and complex data. The data used in training the ANFIS models is generated using parametric finite element-based simulations where band gaps corresponding to a wide range of perturbation frequencies and magnitudes are computationally determined. The parametric study showed a nonlinear and complex topology-band gap characteristic relation; however, the Adaptive Neuro-Fuzzy Inference System (ANFIS) proved capable of modeling the observed complex topology-band gap behavior efficiently. The accuracy of the ANFIS models exceeded 99 % in several design ranges (i.e., perturbation parameters ranges). These were designated as high-accuracy design regions and were highlighted in the proposed design approach. Using multiple case studies with different band gap requirements, the ANFIS-based design framework proved effective in delivering customized lattice-based metamaterials with user-defined band gap frequencies.

Flame transfer functions of asymmetric conical and V-shaped flames

Transfer functions of asymmetric flames subjected to incident flow perturbations are explored using the classical kinematic model, the G-equation, parameterized by flame tip angle α, flame-base incline angle β, and eccentricity e. With perturbations of various frequencies, we analyze perturbed asymmetric flames and derive analytical formulations of Flame Transfer Functions (FTF) for various flame conditions. It is observed that the gain of the asymmetric conical flame is increased compared to the symmetric case. Meanwhile, the amplification effect of the V-shaped flame is considerably suppressed as the flame becomes asymmetric. That means with a proper asymmetric geometry setting, the V-shaped flame no longer tends to amplify the perturbation and in other words becomes less susceptible to combustion instability. These findings have significant value for the future design and optimization of propulsion systems, where improving flame stability and reducing thermoacoustic instabilities are critical. Subsequently, a numerical study is conducted to verify the FTF results and examine the response of asymmetric flames under various perturbation levels. It has been demonstrated that the asymmetric conical flame is minimally affected by the amplitude of these perturbations, and the asymmetric V-shaped flame is highly sensitive to the convective amplitudes.

Weak time-scale separation at the onset of oscillatory magnetoconvection in rapidly rotating fluids

Convective instabilities are one of the integral parts of the dynamics of flows driven by thermal buoyancy. Naturally, physical phenomena exhibit a wide disparity in the length and timescales of the field variables in numerical simulations and experimental observations. Such variations are not represented in the traditional normal mode stability analysis attempting to understand the onset of convection. This study attempts to incorporate different time constants for different perturbation variables in the linear stability analysis with the help of a Taylor series expansion. The infinite horizontal layer model is chosen for simplicity. Apart from the classical Rayleigh-Bénard system, additional physical effects such as background rotation and magnetic field have been considered with plausible implications for geophysical flow applications. The time scale separation is implemented by considering a slight change in the frequency of temperature perturbation compared to that for other physical quantities. Both analytical and numerical methods have been utilised for the investigation. The threshold buoyancy force is reduced when the temperature perturbation has a smaller frequency than the frequencies of other variables. Besides that, the onset wavenumber and frequency of the oscillatory modes are modified due to weak scale separation from the onset characteristics of the reference case. In particular, enhanced frequency of temperature perturbations leads to smaller-scaled magnetically controlled convective rolls and larger-scaled viscously controlled instabilities at the onset. A robust dependence of the onset characteristics with the parameter quantifying the timescale separation is obtained. Additionally, two transitions in the convective onset modes with scale separation have been identified.

Empowering offshore wind with ES-STATCOM for stability margin improvement and provision of grid-forming capabilities

Offshore wind power plants (WPPs) play a pivotal role in achieving a CO2-neutral electricity sector. However, their grid connection presents significant challenges and costs. High-voltage alternating current (HVAC) offers a cost-effective solution, but it may necessitate the installation of a static synchronous compensator (STATCOM) at the onshore bus to ensure stability and compliance with connection requirements. Integrating energy storage into the STATCOM (ES-STATCOM) enables the provision of ancillary services, such as inertial response and frequency support, which require active power. This paper utilizes the generalized Nyquist criterion to demonstrate that operating the ES-STATCOM with grid-forming control enhances the stability margin of the grid-connected WPP when compared to operating it with grid-following control. Furthermore, it illustrates through network frequency perturbation (NFP) plots that the overall WPP, comprising grid-following wind turbines and a grid-forming ES-STATCOM, imparts grid-forming behavior at the grid-connection point.

Unified framework of forced magnetic reconnection and Alfvén resonance

A unified linear theory that includes forced reconnection as a particular case of Alfvén resonance is presented. We consider a generalized Taylor problem in which a sheared magnetic field is subject to a time-dependent boundary perturbation oscillating at frequency ω0. By analyzing the asymptotic time response of the system, the theory demonstrates that the Alfvén resonance is due to the residues at the resonant poles, in the complex frequency plane, introduced by the boundary perturbation. Alfvén resonance transitions towards forced reconnection, described by the constant-psi regime for (normalized) times t≫S1/3, when the forcing frequency of the boundary perturbation is ω0≪S−1/3, allowing the coupling of the Alfvén resonances across the neutral line with the reconnecting mode, as originally suggested in Uberoi and Zweibel, (1999). Additionally, it is shown that even if forced reconnection develops for finite, albeit small, frequencies, the reconnection rate and reconnected flux are strongly reduced for frequencies ω0≫S−3/5.

Recommendations on setup in simulating atmospheric gravity waves under conventionally neutral boundary layer conditions

Wind farm-induced atmospheric gravity waves have been the subject of recent research as they can impact wind farm performance. Pressure variations associated with gravity waves can contribute to the global blockage effect and wind farm wake recovery. Therefore, accurate numerical simulation of flow fields, where wind-farm-induced gravity waves may be produced, is important. Three main considerations in such simulations are the overall domain size, the use of Rayleigh damping near domain boundaries to dampen gravity waves, and advection damping at the inlet to prevent spurious oscillations. Often these considerations are treated ad hoc rather than systematically. This work aims to test and extend the systematic modelling of internal gravity waves proposed in a preliminary investigation to modelling of both internal and trapped gravity waves. The preliminary study identifies the length scales to set the domain and damping layer sizes and the time scale to configure the Rayleigh damping coefficient but under linearly stratified conditions. Large eddy simulations of flow through a wind farm canopy are performed under conventionally neutral boundary layer (CNBL) conditions to test the validity of proposed setups for CNBL conditions. Background atmospheric parameters, such as Froude number (Fr), inversion height (Hi ), and inversion layer Froude number (Fri ) control most of the atmospheric gravity wave characteristics. We validated for CBNL conditions that the effective wavelengths of the internal gravity waves are the correct length scale to configure the domain size and damping layer thickness. Likewise, the optimum damping coefficient to dampen the internal gravity waves relates to the free atmosphere’s buoyancy frequency or buoyant perturbations’ time scale. We infer that the damping coefficient in the inversion layer may relate to the inversion buoyancy frequency to effectively dampen the trapped gravity waves. Moreover, the advection damping length is linked to the horizontal wavelength of the trapped gravity waves in the inversion layer to prevent spurious waves at the inlet by retaining wave energy accumulation.

Experimental study of multiscale dynamic characterization of the gas-solid phase in a disturbing rotary centrifugal air classifier using pressure signal testing and analysis methods

This study investigates the complex dynamic characteristics of the flow field inside a disturbing rotary centrifugal air classifier through experimental analysis. To this end, micro-pressure sensors are employed to measure pressure signals in different spatial regions under various operating conditions. The analysis includes time-frequency characterization, complexity assessment, and multi-scale energy analysis. The time-domain fluctuation characteristics of the air classifier's pressure signal are closely tied to operating parameters, with the most intense pressure fluctuations occurring in the middle and back region of the air classifier. The loaded condition intensifies the fluctuations, with particle presence exacerbating low-frequency pressure variations and affecting the cyclone's vortex stability. Additionally, the internal installation of the screen cage structure exhibits maximum complexity and randomness in the internal flow field when Rf = 45 Hz, f = 0.4 kg/s, and β = 0°, showing higher randomness and reflecting fine-scale interactions between gas and particles. Conversely, larger scale characteristics are revealed by DET values in higher detail signal levels. Changes in operational parameters, such as perturbation frequency and feeding time, significantly affect the axial distribution of multi-scale energy in the air classifier, with a greater influence on pressure fluctuation at the macroscopic scale, indicating intensified turbulent behavior between gas and particles. This study reveals the influencing mechanisms of various operating parameters on the multiscale dynamic characteristics and complexity of the flow field inside the rotary centrifugal air classifier.

Theoretical analysis and numerical validation of the mechanisms controlling composition noise

A new definition of entropy fluctuation is provided in this paper, that allows properly separating entropy and mixture composition fluctuations. This decomposition into linearly independent variables prevents from overestimating compositional noise in indirect noise prediction. When considering quasi one-dimensional flow in nozzles, a new resulting system of linearized Euler equations is obtained. Two analytical solutions of this system of equations are investigated in this study, one dedicated to low-frequency perturbations and another one for all frequency perturbations. This new theory is then validated by comparing the model predictions with direct numerical simulation of nozzle flows in which composition fluctuations are pulsed. To do so, new Navier–Stokes characteristics boundary conditions to account for the new properly defined entropy wave are provided. Furthermore, non-reflecting inlet boundary conditions have been newly derived, relaxing on the axial mass-flow rate, static temperature and species mass fractions. Finally, a parametric study based on an air-kerosene (equivalent C10H20) mixture and an ideal framework shows that composition noise can reach a maximum of 10% of entropy noise for lean combustion and choked nozzle while for rich combustion, composition noise and entropy noise show comparable levels.

On the Origin of “Rotating Instabilities”—Stability and Frequency Studies of Channel Flows

Abstract A group of unsteady flow phenomena in turbomachinery is often referred to as “rotating instabilities.” They occur at flow conditions with very asymmetric velocity profiles, as found downstream of blade rows in axial compressors with large rotor tip clearance in stable operating points close to compressor stall or off-design operating points in steam turbines. In the present work, it is shown that such instabilities do not depend on the blading but also occur in blading-free flow channels. The theoretical proof is carried out with the tools and computational programs of spatial stability theory and Reynolds number dependent jumps in the transverse wavelengths at characteristic perturbation frequencies of the present asymmetric turbulent channel flow are discovered. Experimental investigations in a straight flow channel confirm the calculated frequency field and other characteristics of the perturbations. In agreement to theoretical results, a very asymmetric velocity profile across the channel height was found to trigger disturbances within a limited range of frequencies and not bound to the existence of blading. The notion of rotating instability is misleading in the characterization of this disturbance.

Integral field spectroscopy supports atmospheric optics to reveal the finite outer scale of the turbulence

The spatial coherence wavefront outer scale ( characterizes the size of the largest turbulence eddies in Earth's atmosphere, determining low spatial frequency perturbations in the wavefront of the light captured by ground-based telescopes. Advances in adaptive optics (AO) techniques designed to compensate for atmospheric turbulence emphasize the crucial role of this parameter for the next generation of large telescopes. The motivation of this work is to introduce a novel technique for estimating \ from seeing-limited integral field spectroscopic (IFS) data. This approach is based on the impact of a finite \ on the light collected by the pupil entrance of a ground-based telescope. We take advantage of the homogeneity of IFS observations to generate band filter images spanning a wide wavelength range, enabling the assessment of image quality (IQ) at the telescope's focal plane. Comparing the measured wavelength-dependent IQ variation with predictions derived from a first-order analytical approach based on turbulence statistics simplifications using the von Kármán model provides valuable insights into the prevailing \ parameter during the observations. We applied the proposed technique to observations from the Multi-Unit Spectroscopic Explorer (MUSE) in the wide-field mode obtained at the Paranal Observatory. Our analysis successfully validates the first-order analytical expression, which combines the seeing ($ $) and the \ parameters, to predict the IQ variations with the wavelength in ground-based astronomical data. However, we observed some discrepancies between the measured and predictions of the IQ that are analyzed in terms of uncertainties in the estimated $ $ and dome-induced turbulence contributions. This work constitutes the empirical validation of the analytical expression for estimating IQ at the focal plane of ground-based telescopes under specific $ $ and finite \ conditions. Additionally, we provide a simple methodology to characterize the \ and dome-seeing ($ dome $) as by-products of IFS observations routinely conducted at major ground-based astronomical observatories.

Linear stability analysis of a solidification process with convection in a bounded region of space

The morphological/dynamic instability of crystallization process in a bounded region in the presence of intense convection in liquid is studied. The paper considers a linear theory of morphological instability with a flat solid-liquid interface on the example of molten metal and magma. The mathematical model includes heat transfer equations and convective type boundary conditions at the interface. The equations for perturbations of the temperature field and interfacial boundary are found, allowing to obtain the dispersion relation. Its analysis has shown the existence of morphological instability of the flat interfacial boundary for a wide range of wavenumbers. Dynamic perturbations (perturbations of the quasi-stationary crystallization velocity) were also analyzed and two solutions for the perturbation frequency were obtained. One of them is stable and the other one is unstable. The system selects one of them depending on the action of convection. The result of morphological and dynamic instability is the appearance of a two-phase region in front of a flat solid-liquid interface. Therefore, the paper also considers the dynamic instability of stationary crystallization with a two-phase region replaced by a discontinuity surface. In this case, the dynamic instability was also found for a wide range of crystallization velocities.