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Automatic selection of dispersion models in spectroscopic ellipsometry using a hierarchical genetic algorithm
No full textIn spectroscopic ellipsometry, the selection of an appropriate dispersion model is essential for accurate optical parameter extraction. Traditional approaches rely on fixed dispersion laws chosen based on prior knowledge, which can lead to suboptimal or biased results. We propose a novel Hierarchical Genetic Algorithm (HGA) framework that autonomously selects the optimal dispersion model from a set of candidates, without requiring a priori assumptions. The method maintains a computational cost comparable to that of classical genetic algorithms (CGA), while offering the added advantage of exploring multiple models simultaneously through a hierarchical structure. Simulations on a silica layer deposited on a silicon substrate under known thickness conditions demonstrate excellent agreement with theoretical values (fitness between 10−3 and 10−6, refractive index errors below 0.1%). Experimental validation on silicon samples confirms the effectiveness of the HGA, yielding results consistent with conventional methods, but without the need for predefined model selection. This approach significantly enhances the flexibility and reliability of ellipsometric characterization
Parameterisation of the interactions of waves and zonal flows taking the full Coriolis acceleration into account
No full textContext. From the Earth’s atmosphere and oceans to stellar radiation zones, inertia-gravity waves, which are called gravito-inertial waves (GIWs) in astrophysics, transport momentum and mix matter when they are damped through heat and viscous diffusions and when they break. Their short-timescale dynamics is governed by the combined action of the buoyancy force and of the Coriolis acceleration. Through the transport they trigger, they modify the long-term evolution of the large-scale planetary atmospheric (oceanic) circulation and of the structure and rotation of stars. Many current models assume the so-called traditional approximation of rotation (TAR), where the local projection of the rotation vector along the horizontal direction is neglected, is assumed.
Aims. The TAR can be adopted for very thin fluid layers or when the projection of the Coriolis acceleration along the direction of the entropy and chemical stratifications can be neglected when compared to the buoyancy force. It is often assumed when momentum fluxes, heat, and matter transported by GIWs are evaluated. We identify the applicability regime of this approximation and propose a non-traditional parameterisation of the interactions of the waves and zonal flows in planetary atmospheres (oceans) and stellar interiors, in which the full Coriolis acceleration is taken into account.
Methods. We built a prototype local non-traditional Cartesian model in which we took the full Coriolis acceleration, buoyancy, and heat and viscous diffusions into account. We studied the two channels through which GIWs exchange momentum with mean flows while transporting heat and mixing matter: their linear damping and their non-linear breaking. We did not assume any hierarchy between stratification and rotation to allow us to explore the possible large parameter space in geophysical and astrophysical flows, in particular, the cases of weak stable stratification and rapid rotation.
Results. On the one hand, the radiative and viscous dampings of GIWs increase with a decreasing ratio of the wave frequency (ω) with the inertial frequency (2Ω; Ω is the angular rotation frequency). In the sub-inertial regime (ω < 2Ω), the TAR strongly underestimates GIWs damping, especially when the buoyancy and the Coriolis acceleration are equally strong. In this regime, a non-traditional modelling must be adopted. It predicts the correct altitude at which momentum is deposited, which is closer to the excitation region of waves than the altitude predicted using the TAR. On the other hand, non-traditional modelling of GIWs convective and shear-induced breakings were proposed, and we demonstrate that the TAR overestimates the momentum flux deposited by GIWs through these channels. When the full Coriolis acceleration is taken into account, the efficiency of the convective and shear-induced overturning is reduced and the transport is weaker than predicted when the TAR is assumed. Finally, we derived a fully non-traditional parameterisation of the interaction of GIWs with mean zonal flows. This can be implemented in numerical models of the long-term evolution of the atmospheric (oceanic) general circulation and of the structure of rotating stars
Rethinking mass transfer: A unified semianalytical framework for circular and eccentric binaries
No full textMass transfer (MT) is a fundamental process in stellar evolution. While MT in circular orbits is well studied, observations indicate that it also occurs in eccentric ones, where theoretical models are limited. We present a new semianalytic framework for the secular orbital evolution of mass-transferring binaries that treats stars as either point masses or extended bodies. For the first time, a MT model is applicable to both circular and eccentric orbits and accommodates conservative and nonconservative MT across a broad range of mass ratios and stellar spins. We derived secular orbit-averaged equations describing the orbital evolution by treating MT, mass loss, and angular momentum (AM) loss as perturbations to the general two-body problem. Assuming conservative MT, we compared our results to previous models and validated them against numerical integrations. Our model predicts eccentric post-MT systems in wider orbits than classical results. Compared to other eccentric MT frameworks, the parameter space for orbital widening and eccentricity pumping we find is broader. When extended bodies are accounted for, a stronger semimajor axis and eccentricity growth are obtained at a given mass ratio, and the parameter space is further broadened for orbital widening and eccentricity pumping. Regardless of whether extended bodies are considered, eccentric MT naturally predicts higher eccentricities at longer orbital periods. This correlation has been observed in numerous post-MT systems, and thus eccentric MT provides a robust mechanism for their formation. Our model can be integrated into binary evolution and population synthesis codes to consistently treat conservative and nonconservative MT in arbitrarily eccentric orbits. The applications range from MT on the main sequence to gravitational-wave progenitors
Trivialisable control-affine systems revisited
No full textThe purpose of this paper is to explore the concept of trivial control systems, namely systems whose dynamics depends on the controls only. Trivial systems have been introduced and studied by Serres in the context of control-nonlinear systems on the plane with a scalar control. In our work, we begin by proposing an extension of the notion of triviality to control-affine systems with arbitrary number of states and controls. Next, our first result concerns two novel characterisations of trivial control-affine systems, one of them is based on the study of infinitesimal symmetries and is thus geometric. Second, we derive a normal form of trivial control-affine systems whose Lie algebra of infinitesimal symmetries possesses an almost abelian Lie subalgebra. Third, we study and propose a characterisation of trivial control-affine systems on 3-dimensional manifolds with scalar control. In particular, we complete the proof of the previous characterisation obtained by Serres. Our characterisation is based on the properties of two functional feedback invariants: the curvature (introduced by Agrachev) and the centro-affine curvature (used by Wilkens). Finally, we give several normal forms of control-affine systems, for which the curvature and the centro-affine curvature have special properties
Estimating COSMIC ionospheric radio occultation foF
No full textGNSS ionospheric radio occultation (IRO) is an important technique for remote sensing of Earth’s ionosphere. Previous validation of GNSS IRO has often been based on comparisons with ground-based observations, such as ionosondes or in-situ observations, which are assumed to be true representations of the real ionospheric state. But these reference observations commonly used for validation also have errors of their own, which are often neglected in such comparisons. In this study, we employ the three-cornered hat (3CH) method to analyze error statistics and separate errors present in Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) IRO foF2 observations. This provides a better characterization of the errors since it avoids the need to know the true value of the quantity of interest. To form the necessary triplet datasets, ionosondes, International Reference Ionosphere (IRI), NeQuick, and the Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X) data are used in addition to COSMIC. To verify the feasibility of this method under the error conditions of the data used in this paper, we initially verified the method using simulated data. The error characteristics are analyzed according to local time and geomagnetic latitude. IRO electron density error characteristics are found to be primarily related to inversion assumptions. The COSMIC IRO errors are smallest in summer and largest in winter, and the errors in high solar activity years are larger than the errors in low solar activity years. When understanding error results derived from the 3CH method, special attention should be given to the impact of error correlation and representativeness errors. The results show that the 3CH method provides a better characterization of the errors in COSMIC IRO observations, is helpful for the specification of errors in data assimilation systems, and is suitable for estimating errors in geospace observations
Wasserstein gradient flows of MMD functionals with distance kernel and Cauchy problems on quantile functions
No full textWe give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals ℱv: = MMDK2(⋅,v) towards given target measures v on the real line, where we focus on the negative distance kernel K(x, y) := − |x − y|. In one dimension, the Wasserstein-2 space can be isometrically embedded into the cone C(0,1) ⊂ L2(0, 1) of quantile functions leading to a characterization of Wasserstein gradient flows via the solution of an associated Cauchy problem on L2(0,1). Based on the construction of an appropriate counterpart of ℱv on L2(0, 1) and its subdifferential, we provide a solution of the Cauchy problem. For discrete target measures v, this results in a piecewise linear solution formula. We prove invariance and smoothing properties of the flow on subsets of C(0,1). For certain ℱv-flows this implies that initial point measures instantly become absolutely continuous, and stay so over time. Finally, we illustrate the behavior of the flow by various numerical examples using an implicit Euler scheme, which is easily computable by a bisection algorithm. For continuous targets v, also the explicit Euler scheme can be employed, although with limited convergence guarantees
SN 2016iog: A fast-declining Type II-L supernova with an ultra-faint tail persistently interacting with circumstellar material
No full textWe present optical photometric and spectroscopic observations of the rapidly declining Type IIL supernova (SN) 2016iog. SN 2016iog reached its peak ∼14 days after explosion, with an absolute magnitude in the V band of −18.64 ± 0.15 mag, followed by a steep decline of 8.85 ± 0.15 mag (100 d)−1 post-peak. Such a high decline rate makes SN 2016iog one of the fastest-declining Type IIL SNe observed to date. The rapid rise in the light curve, combined with the nearly featureless continuum observed in the spectrum at +9.3 days, suggests the presence of interaction. In the recombination phase, we observed broad Hα lines that persist at all epochs. In addition, the prominent double-peaked Hα feature observed in the late-time spectrum (+190.8 days) is likely attributable either to significant dust formation within a cool dense shell or to asymmetric circumstellar material. These features suggest the presence of a sustained interaction around SN 2016iog. We propose that the observed characteristics of SN 2016iog can be qualitatively explained by assuming a low-mass H-rich envelope surrounding a red supergiant progenitor star with low-density circumstellar material
Spiral excitation in protoplanetary disks through gap-edge illumination
No full textHigh-resolution near-infrared observations have revealed prominent two-armed spirals in a multitude of systems, such as MWC 758, SAO 206462, and V1247 Ori. Alongside the classical theory of disk–companion interaction, shadow-based driving has come into vogue as a potential explanation for such large-scale substructures. This raises the question of how these two mechanisms might be distinguished from one another in observations. To investigate this question, we ran a pair of hydrodynamical simulations with PLUTO. The first, with full radiation hydrodynamics and gas-grain collision, was designed to develop shadow-driven spirals at the outer gap edge of a subthermal Saturn-mass planet. The second simulation, with parameterized β-cooling, was set up to capture the more standard view of spiral wave excitation by a super-thermal, multi-Jupiter-mass, exterior planetary companion. Post-processing of these simulations with the Monte Carlo radiative transfer (MCRT) code RADMC3D revealed that strong vertical velocities in the shadow-driven case create a prominent two-armed feature in the moment-1 CO maps, particularly when the disk is viewed face-on in optically thicker isotopologues; this feature is not seen in the standard planet-driven case. Conversely, the presence or absence of such signatures in two-armed spiral systems would distinguish those potentially driven by exterior multi-Jupiter-mass companions, and thus help identify promising targets for future direct-imaging campaigns
Filamentary accretion flows in high-mass star-forming clouds
No full textContext. Filamentary accretion flows as gas-funneling mechanisms are a key aspect in high-mass star formation research. The kinematic properties along these structures are of particular interest.
Aims. This paper focuses on the question of whether gas is transported to dense clumps inside high-mass star-forming regions through filamentary structures, from scales of several parsecs down to the subparsec scale.
Methods. We quantified the gas flows from a scale of up to several parsecs down to the subparsec scale along filamentary structures. For this work the accretion flow mechanisms based on gas kinematic data in the three high-mass star-forming regions G75.78, IRAS21078+5211, and NGC7538 were studied with data obtained from the IRAM 30 m telescope. The analysis was carried out using the surface density derived from 1.2 mm continuum emission and velocity differences estimated from HCO+ (1 − 0) and H13CO+ (1 − 0) molecular line data.
Results. The mass flow behavior of the gas in the vicinity of high-mass star-forming clumps shows characteristic dynamical patterns, for example an increased mass flow rate toward the clumps. We assume that the velocity differences originate from filamentary-gas infall onto the high-mass star-forming clumps; however, the inclination of the filament structures along the line of sight is unknown. Nevertheless, using the velocity differences and mass surface densities, we can estimate the mean flow rates along the filamentary structures with respect to the line of sight and toward the clumps. We quantified the flow rates toward the clumps in a range from about 10−3 M⊙ yr−1 to 10−5 M⊙ yr−1, inferred from clump-centered polar plots. Slight variations in the flow rates along the filamentary structures may be caused by overdensities and velocity gradients along the filaments.
Conclusions. While the initial studies presented here already reveal interesting results such as an increasing mass flow rate toward clumps, the properties of filamentary gas flows from large to small spatial scales, as well as potential variations over the evolutionary sequence, are subject to future studies
Optimal joining strategy and pricing analysis in unreliable retrial queues with predictive maintenance
No full textThe timely improvement of systems, based on the feedback from the service data, is becoming an increasingly common practice to enhance system reliability. This generates a novel predictive maintenance policy: after each service is completed, the server performs predictive maintenance to reduce the server’s failure rate at the next service. We study an unreliable M/G/1 retrial queue with predictive maintenance. First, the stationary distribution and performance measures are analyzed using the supplementary variable method. Then, the threshold strategy of the predictive maintenance is proposed from the perspective of customers’ waiting time. Based on the linear reward-cost structure, the customer’s equilibrium strategy and socially optimal strategy are derived. Next, the optimal pricing strategy is obtained, in order to eliminate the difference between equilibrium and socially optimal strategies. Finally, numerical examples are provided to illustrate how system parameters affect customers’ strategic behavior. These examples also demonstrate the accuracy of the closed-form solution for the socially optimal joining probability using a Particle Swarm Optimization (PSO) algorithm and a Genetic Algorithm (GA)