Velocity Perturbations Research Articles

A Bingham Plastic Fluid Solver for Turbulent Flow of Dense Muddy Sediment Mixtures

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of 1×10−4 and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results.

State and evolution of the geodynamo from numerical models reaching the physical conditions of Earth’s core

SUMMARY Our understanding of the geodynamo has recently progressed thanks to geomagnetic data of improved quality, and analyses resting on numerical simulations of increasing realism. Here, these two advances are combined in order to diagnose the state and present dynamics of Earth’s core in physically realistic conditions. A sequential, ensemble-based framework assimilates the output of geomagnetic field models covering the past 180 yr into a numerical geodynamo simulation, the physical realism of which is also advanced as data is assimilated. The internal dynamical structure estimated for the geodynamo at present reproduces previously widely documented features such as a planetary-scale, eccentric westwards gyre and localization of buoyancy release beneath the Eastern (0°E−180°E) hemisphere. Relating the typical magnetic variation timescale of the assimilated states to the power at which they operate, the present convective power of the geodynamo is estimated at 2.95 ± 0.2 TW, corresponding to an adiabatic heat flow out of the core of 14.8 ± 1 TW if the top of the core is convectively neutrally stratified at present. For the first time, morphologically and dynamically relevant trajectories are obtained by integrating the estimated states forward for a few decades of physical time using a model reaching the physical conditions of Earth’s core. Such simulations accurately account for the spatio-temporal content of high-resolution satellite geomagnetic field models and confirm earlier interpretations in terms of rapid core dynamics. The enforcement of a realistic force balance approaching a Taylor state allows for propagation of weak (velocity perturbation of about 0.6 $\mathrm{km\,yr^{-1}}$) axisymmetric torsional waves with period about 5 yr, supported by a magnetic field of root-mean-squared amplitude of 5.6 mT inside the core. Quasi-geostrophic magneto-Coriolis waves of interannual periods and significantly stronger velocity perturbation (about $7 \mathrm{km\,yr^{-1}}$) are also reproduced, with properties that converge towards those recently retrieved from the analysis of geomagnetic variations before fully achieving Earth’s core conditions. The power spectral density of magnetic variations falls off rapidly at frequencies exceeding the inverse Alfvén time (about $0.6\mathrm{yr^{-1}}$), which indicates that the excitation of hydromagnetic waves occurs preferentially at large spatial scales. The possibility to account for geomagnetic variations from years to centuries in physically realistic models opens the perspective of better constraining properties of the deep Earth through geomagnetic data assimilation.

Computation and prediction of intrinsic thermoacoustic oscillations associated with autoignition fronts

A sequential combustor architecture consists of two longitudinally staged combustion zones featuring a propagation-stabilized flame in the first stage and an autoignition-stabilized flame in the second (reheat) stage. This layout allows for increased fuel flexibility compared to single-stage systems and enables clean and efficient combustion of carbon-free fuels such as hydrogen. Interactions between the autoignition-stabilized flame and the acoustic field created by the unsteady ignition front and the surrounding boundaries can result in self-sustained (thermoacoustic) flame oscillations in the reheat stage of the sequential burner, causing performance losses and structural damage. In this paper, an intrinsic flame-acoustic feedback mechanism causing self-sustained thermoacoustic oscillations in a reheat combustor is studied. The intrinsic thermoacoustic feedback is established when an acoustic wave generated by the unsteady ignition front travels upstream and introduces local temperature, pressure and velocity perturbations in the unburnt mixture. These modulate the ignition chemistry and the front kinematics and thus, in turn, act as a new source of perturbation for the ignition front that generates heat release rate oscillations and upstream-traveling acoustic disturbances, closing the feedback loop. Compressible reactive Euler equation computations of autoignition fronts in a simple one-dimensional reheat combustor configuration with fully non-reflecting boundaries are first performed to demonstrate and characterize the intrinsic thermoacoustic oscillations associated with autoignition fronts. These computations show that the autoignition front exhibits distinct harmonic thermoacoustic oscillations which tend to become unstable at some conditions. Next, frequencies and growth rates of the intrinsic thermoacoustic oscillations in the linear regime are predicted using a hybrid approach with flame response transfer functions taken from a forced Euler calculation and using a linearized Euler equation framework to describe the combustor acoustic field. The predictions of the intrinsic thermoacoustic eigenvalue from the linearized Euler equation framework show good agreement with the linear behaviour of these oscillations observed in the Euler computations. The findings of the present work are useful both from a fundamental standpoint for prediction of intrinsic thermoacoustic instabilities and from an industrial perspective for prevention of thermoacoustic instabilities in staged combustion systems.

The response of small-scale shear layers to perturbations in turbulence

The perturbation response of small-scale shear layers in turbulence is investigated with direct numerical simulations (DNS). The analysis of shear layers in isotropic turbulence suggests that the typical layer thickness is about four times the Kolmogorov scale $\eta$ . Response for sinusoidal perturbations is investigated for an isolated shear layer, which models a mean flow around the shear layers in turbulence. The vortex formation in the shear layer is optimally promoted by the perturbation whose wavelength divided by the layer thickness is about 7. These results indicate that the small-scale shear instability in turbulence is efficiently promoted by velocity fluctuations with a wavelength of about $30\eta$ . Furthermore, DNS are carried out for decaying turbulence initialised by the artificially modified velocity field of isotropic turbulence. The vortex formation from shear layers is accelerated under the influence of external perturbations with the efficient wavelength to promote the instability. When velocity fluctuations with this wavelength are eliminated by a band-cut filter, the shear layers tend to persist for a long time without producing vortices. These behaviours affect the number of vortices in turbulence, which increases and decreases when velocity perturbations with the unstable wavelength of the instability are artificially amplified and damped, respectively. The increase in the number of vortices results in the enhancement of kinetic energy dissipation, enstrophy production and strain self-amplification. These results indicate that the perturbation response of shear layers is important in the small-scale dynamics of turbulence as well as the modulation of small-scale turbulent motions by external disturbance.

Influence of rainfall in a short-term seismic velocity monitoring at an urban landslide site in Minas Gerais, Brazil

Most high-magnitude landslides in Brazil are triggered by rainfall. The partial or total liquefaction of the soil mass is directly related to an increase in the pore pressure, which can happen after or during heavy and sustained rainfalls. Traditional near-surface geophysical methods for saturation and rigidity assessment usually involve short-duration data acquisition campaigns, reporting results representative of a specific moment. On the other hand, the cross-correlation of the ambient noise wavefield registered at different locations in continuous data streams has emerged as a promising alternative for monitoring seismic velocity variations in time. In the present study, we evaluate if the observed seismic velocity perturbations can satisfactorily relate to rainfall periods on a local scale and within minutes of resolution at a slope in Itabirito, state of Minas Gerais, Brazil, where landslide activity occurred. We calculate velocity changes in the tail portion (coda) from Green's functions retrieved from cross-correlation of seismic noise time series registered at pairs of stations from September 2022 to November 2022. In the 50 days observation period, the monitored area remained stable. We identified clear time intervals where the relative seismic velocity decreases after or during rainfall, which indicates modification in the saturation conditions of the soil. The results demonstrated that seismic velocity changes obtained from the coda of cross correlations of the ambient noise wavefield could satisfactorily constrain rainfall periods and indicate possible changes in the saturation conditions of the soil at a small local scale with a high temporal resolution.

Cased-hole reverse time migration imaging using ultrasonic pitch-catch measurement: Theory and synthetic case studies

Cement-bond evaluation is of great significance in oil/gas development, geothermal production, and CO2 storage. Advanced ultrasonic pitch-catch measurement exhibits poor performance in determining a cement-formation interface due to weak reflections from the cement-formation interface (third interface echo) in nonaxisymmetric complex ultrasonic environments. To deal with this issue, we use a reverse time migration (RTM) approach for ultrasonic pitch-catch measurements to image the cased-hole structure, especially for the cement-formation interface. To further enhance cased-hole RTM feasibility, a phase-shift interpolation technique is applied to reconstruct ultrasonic array waveforms from limited receivers in the pitch-catch measurement. Synthetic examples demonstrate that RTM is capable of imaging the cement-formation interface with a high resolution under various eccenterings of casings and tools. This study illustrates that small errors introduced by phase-shift interpolations do not greatly degrade the imaging result of RTM. Furthermore, tests for inclined cement-formation interfaces demonstrate that the RTM is able to recover the true position and geometry of the cement-formation interface when a smoothed velocity model is available. In addition, although RTM is sensitive to the velocity perturbation, it is possible to image the cased-hole structure by using a multistep strategy assuming that the position and thickness of the steel casing are unknown.

On collective nature of non-linear torsional Alfvén waves

ABSTRACT Torsional Alfvén waves in coronal plasma loops are usually considered to be non-collective, i.e. consist of cylindrical surfaces evolving independently, which significantly complicates their detection in observations. This non-collective nature, however, can get modified in the non-linear regime. To address this question, the propagation of non-linear torsional Alfvén waves in straight magnetic flux tubes has been investigated numerically using the astrophysical MHD code Athena++ and analytically, to support numerical results, using the perturbation theory up to the second order. Numerical results have revealed that there is radially uniform-induced density perturbation whose uniformity does not depend on the radial structure of the mother Alfvén wave. Our analysis showed that the ponderomotive force leads to the induction of the radial and axial velocity perturbations, while the mechanism for the density perturbation is provided by a non-equal elasticity of a magnetic flux tube in the radial and axial directions. The latter can be qualitatively understood by the interplay between the Alfvén wave perturbations, external medium, and the flux tube boundary conditions. The amplitude of these non-linearly induced density perturbations is found to be determined by the amplitude of the Alfvén driver squared and the plasma parameter β. The existence of the collective and radially uniform density perturbation accompanying non-linear torsional Alfvén waves could be considered as an additional observational signature of Alfvén waves in the upper layers of the solar atmosphere.

Perturbation-based balance training leads to improved reactive postural responses in individuals with Parkinson's disease and freezing of gait.

Perturbation-based balance training (PBT) exposes individuals to a series of sudden upright balance perturbations to improve their reactive postural responses. In this study, we aimed to evaluate the effect of a short PBT program on body balance recovery following a perturbation in individuals with freezing of gait due to Parkinson's disease. Volunteers (mean age = 64 years, SD = 10.6) were pseudorandomly assigned either to a PBT (n = 9) or to a resistance training (RT, n = 10) group. PBT was implemented through balance perturbations varying in the kind, direction, side, and magnitude of support base displacements. Both groups exercised with progressive difficulty/load activities twice a week for four weeks. Specific gains and generalization to dual-tasking and faster-than-trained support base displacements were evaluated 24 h after the end of the training, and retention was evaluated after 30 days of no training. Results showed that, compared to RT, PBT led to more stable postural responses in the 30-day retention evaluation, as indicated by decreased CoP displacement, velocity, and time to direction reversal and reduced numbers of near-falls. We found no transfer either to a dual-task or to a higher perturbation velocity. In conclusion, a training program based on diverse unpredictable balance perturbations improved the stability of reactive postural responses to those perturbations suffered during the training, without generalization to more challenging tasks.

Predictive modeling of pressurized water reactor transients using nonlinear autoregressive with exogenous input neural network

A pressurized water reactor (PWR) is a multivariable system that consists of several subsystems such as a core, steam generator, pipings, and plenums that show highly nonlinear behavior. These components are prone to critical parameters that cause potential accidents and propagate to the entire system. Therefore, the PWR needs continuous and fast pre-accident assessment through modeling and predicting by leveraging powerful intelligence technologies. In this regard, this study demonstrates the potential of the nonlinear autoregressive with exogenous inputs (NARX) neural network modeling approach. The established NARX model is evaluated using PWR transients under perturbations in control rod velocity and core inlet coolant temperature. The trained network was then applied for state estimation, future prediction, and fault detection. The simulation results verified that the NARX model predicts the target value with good accuracy as compared with the nonlinear input-output (NIO) neural network strategy. Further, it is used to forecast the step-ahead values of the targets in the defined confidence interval and fault detection. Overall, the present study gives the benefit of the NARX approach for estimation and fault detection applications in other nuclear engineering fields.

Finite-Frequency Delay Times of Phase Segments for Body Waves

ABSTRACT We propose a new way of measuring the delay times of body waves, based on the time differences between short segments of a phase. Using this proposed methodology, which we call the delay time of phase segments (DTPSs) method, we believe it is possible to (1) optimize the reduction mode that reduces finite-frequency kernels to ray-theoretical kernels, (2) reduce computation and memory storage costs by reducing the volume of finite-frequency sensitivity kernels, and (3) achieve greater linearity between delay times and velocity variations for larger velocity perturbations up to ±30%. The DTPS kernel can also be used in adjoint methods. Theory and our calculations indicate that the width of the DTPS kernel decreases as the length of the phase segment decreases from the length of the entire phase. The scattering caused by inhomogeneity is more likely to complicate the latter parts of a phase more than its beginning. For this reason, the DTPS method using a phase segment in the first quarter of a phase is robust for velocity perturbations up to ±30% from the initial model, whereas traditional methods using the entire phase are only robust for velocity perturbations up to ±10%. The DTPS method may reduce computation times by up to 70% because the size of the DTPS kernels is smaller than that of other methods by up to 70%. Synthetic tests indicate that the DTPS method produces inverse models nearly as accurate as generalized seismological data functionals.

Наиболее интересные результаты изучения Галактики по OB-звездам

A review of the main results of studying the structure and kinematics of the Galaxy obtained by various research teams using OB stars is given. The main attention is paid to the results of the authors of this work. The following questions are considered: a) the nature of the spatial distribution of OB stars in the Galaxy; b) the use of OB stars to refine the parameters of the spiral pattern of the Galaxy; c) refinement of the Galactic rotation parameters and perturbation velocities caused by the influence of the Galactic spiral density wave using OB stars; d) spatial and kinematic relationship of OB stars with galactic warp; e) analysis of the motion of some runaway OB stars.

Изучение структуры и кинематики Галактики по данным о классических цефеидах

Classical Cepheids are important for studying the properties of the galactic disk, the spiral structure of the Galaxy, its rotation, evolution, etc. This article provides an overview of the main results of studying the structure and kinematics of the Galaxy, which were obtained by various scientific teams using classical Cepheids. The main attention is paid to the results of studying the Galaxy obtained by the authors of this work. The following issues are considered: a) the nature of the spatial distribution of Cepheids in the Galaxy, both near the equatorial plane of the Galaxy and in the vertical direction; in particular, the relationship of Cepheids with the large-scale Warp of the galactic disk is considered; b) the use of young Cepheids to refine the parameters of the spiral pattern of the Galaxy; c) the use of young Cepheids to refine the rotation parameters Galaxies and perturbation velocities caused by the influence of the galactic spiral density wave.

Numerical simulations of prominence oscillations triggered by external perturbations

Context. Several energetic disturbances have been identified as triggers of large-amplitude oscillations (LAOs) in prominences. Observations show that Moreton or extreme ultraviolet waves excite prominence oscillations of the longitudinal, transverse, or mixed polarities. However, the mechanisms for the excitation of LAOs by these waves are not well understood. Aims. In this study, we aim to investigate mechanisms behind the triggering of LAOs via self-consistent perturbation produced by an eruption and via energetic waves coming from a distant energy source. Methods. We performed time-dependent numerical simulations in 2.5D and 2D setups, using the magnetohydrodynamic code MANCHA3D, involving a flux rope and dipped arcade magnetic configurations with an artificially loaded prominence mass in the magnetic dips. Two types of disturbances were applied to excite prominence oscillations. The first type involves perturbations produced self-consistently by an eruption, while the second type of perturbation is associated with the waves caused by an artificial energy release. Results. In the simulations of the eruption, we find that this eruption by itself does not produce LAOs in the prominence located in its vicinity. Its only effect is in inclining the magnetic configuration of the prominence. While the erupting flux rope rises, an elongated current sheet forms behind it. This current sheet becomes unstable and breaks into plasmoids. The downward-moving plasmoids cause perturbations in the velocity field by merging with the post-reconnection loops. This velocity perturbation propagates in the surroundings and enters the flux rope, causing the disturbance of the prominence mass. The analysis of the oscillatory motions of the prominence plasma reveals the excitation of small-amplitude oscillations (SAOs), which are a mixture of longitudinal and vertical oscillations with short and long periods. In the simulations with a distant artificial perturbation, a fast-mode shock wave is produced and it gradually reaches two flux rope prominences at different distances. This shock wave excites vertical LAOs as well as longitudinal SAOs with similar amplitudes, periods, and damping times in both prominences. Finally, in the experiment with the external triggering of LAOs of solar prominences by an artificial perturbation in a dipped arcade prominence model, we find that although the vector normal to the front of a fast-mode shock wave is parallel to the spine of the dipped arcade well before the contact, this wave does not excite longitudinal LAOs. When the wave front approaches the prominence, it pushes the dense plasma down, establishing vertical LAOs and motions due to compression and rarefaction along the magnetic field. Conclusions. The external triggering of prominence oscillations is a complex process that excites LAOs or SAOs of the longitudinal or transverse polarizations or a mix of both types. It is not an easy task to produce LAOs in prominences because the triggering event requires a sufficient amount of energy. The orientation of the prominence axis with respect to the driving event may play a crucial role in triggering a certain type of LAOs.

Effect of flow–thermodynamics interactions on the stability of compressible boundary layers: insights from Helmholtz decomposition

Helmholtz decomposition of velocity perturbations is performed in conjunction with linear stability analysis to examine the effects of flow-thermodynamics interactions on the stability of high-speed boundary layers. A corresponding decomposition of the pressure field is also proposed. The contributions of perturbation solenoidal kinetic, dilatational kinetic and internal energy to the various instability modes are examined as a function of Mach number ( $M$ ). As expected, dilatational and pressure field effects play an insignificant part in the first-mode behaviour at all Mach numbers. The second (Mack) mode, however, is dominantly dilatational in nature, and perturbation internal energy is significant compared to perturbation kinetic energy. The observed behaviour is explicated by examining the key processes of production and pressure-dilatation. Production of the second-mode dilatational kinetic energy is mostly due to the solenoidal-dilatational covariance stress tensor interacting with the mean (background) velocity gradient. This cross production component also inhibits the first mode. The dilatational pressure facilitates energy transfer from the kinetic to the internal field in the near‐wall region, whereas the energy transfer away from the wall is mostly due to the solenoidal pressure work. The dilatational characters of the fast and slow modes are also examined. The fast mode is dominantly dilatational at both $M=4$ and $M=6$ , while the nature of the slow mode is dependent on $M$ . Finally, Helmholtz decomposition of the perturbation momentum vector is performed. Interestingly, both first and second modes are dominated by solenoidal components of momentum.

Estimation of Relative Acoustic Impedance Perturbation from Reverse Time Migration Using a Modified Inverse Scattering Imaging Condition

Reverse Time Migration (RTM) is a preferred depth migration method for imaging complex structures. It solves the complete wave equation and can model all types of complex wave propagation with no dip limitation. Reverse time migration using the inverse scattering imaging condition produces structural images with an amplitude approximate to the reflectivity, which is a composite effect of the impedance and velocity changes in the acoustic media with variable velocity and density. In this study, we present a modified inverse scattering imaging condition to separate the effect of the impedance and velocity perturbations from the reflectivity. The proposed imaging condition is designed to predict the relative impedance perturbation by selecting near-angle reflections during common-shot RTM. We validate our approach on synthetic models and show that the proposed method can estimate reliable impedance perturbation.

Vibrational circular dichroism spectra of natural products by means of the nuclear velocity perturbation theory

We present the application of the recently implemented nuclear velocity perturbation theory, using the combined Gaussian and plane waves approach in CP2K, to the vibrational circular dichroism (VCD) spectra of a set of natural products. Even though the calculations were carried out for isolated molecules in the gas-phase limit, neglecting inter-molecular interactions and anharmonic effects, the match between simulated and experimental spectra is reasonable. We also study the influence of different density functionals on the conformational search and the resulting VCD spectra via group coupling matrices (GCMs). The GCM analysis reveals that the VCD signal can in some cases arise from moieties which are close to each other and in other cases from moieties far from each other. Differences in spectra obtained using different exchange–correlation density functionals can be attributed to interaction terms between different moieties in the molecules changing their sign.

Crust–Uppermost Mantle Structure beneath the Caribbean Region from Seismic Ambient Noise Tomography

ABSTRACT We present a new 3D shear velocity model for the crust–uppermost mantle structure beneath the Caribbean region from the surface down to 150 km depth. Our velocity model was derived from joint inversion of group and phase velocity dispersion data obtained from ambient noise and earthquake data. The group and phase dispersion curves estimated from ambient noise were calculated from cross correlation using up to 4 yr of continuous data. Perturbations in group and phase surfaces-wave velocities within a resolution of 1° × 1° show the relevant geotectonic units in the Caribbean plate. Plate boundaries, ocean basins, rises, rifts, and microplates are well defined by shear-wave velocity impedances. The 3D shear-wave velocity inversion along profiles shows the thickening of the crust from the ocean to continental margins. We present a new Moho interface map with depths undulating between 11 and 17 km beneath most parts of the sea and 25–45 km below the continental areas. Low-velocity zones were found in the uppermost mantle indicating a highly laterally heterogeneous area.

Rising temperatures over the Greater Mekong Subregion in CMIP6: Present-day biases and constraint future projections

This study evaluates the historical simulation of surface air temperature (SAT) over the Greater Mekong Subregion (GMS) during the period 1981–2014 with 31 models from Coupled Model Intercomparison Project phase 6 (CMIP6). The CMIP6 multi-model ensemble shows a weaker SAT growth trend than the reanalysis data in all seasons. The SAT increase is underestimated mostly in winter, by around 0.2 °C/decade. The simulated SAT climatology shows positive bias over the Gaoligong Mountain in western Yunnan, the Rakhine Mountain in Myanmar, and the Annamite Range in southern Vietnam, and negative bias elsewhere. We make a best-model ensemble to improve the representability of the GMS SAT. The range of SAT interannual variability is underestimated over most parts of GMS in boreal spring, autumn, and winter. In summer, the SAT range bias shows a dipole pattern with negative bias over the northwestern GMS and positive bias over the southeastern GMS. Dynamical diagnosis suggests that the bias in vertical velocity perturbation, manifesting as weakened regional Hadley circulation, is a major contributor to the SAT range bias in summer via vertical advection of mean potential temperature. The bias-corrected projection of the summer SAT is presented for three shared socio-economic pathways (SSPs). The SAT rising relative to the reference period 1995–2014 tends to be more spatially homogeneous under higher emission scenarios. The range of SAT interannual variability would increase over the northern GMS but decrease over the southern GMS under three SSPs scenarios. This SAT dipole variation is associated with intensified regional Hadley circulation over the GMS. The results also reiterate the urgent need for net zero emission by 2050 to maintain a sustainable environment.

Inflationary dynamics and swampland criteria for modified Gauss-Bonnet gravity compatible with GW170817

In this article we present an alternative formalism for the inflationary phenomenology of rescaled Einstein-Gauss-Bonnet models which are in agreement with the GW170817 event. By constraining the propagation velocity of primordial tensor perturbations, an approximate form for the time derivative of the scalar field coupled to the Gauss-Bonnet density is extracted. In turn, the overall degrees of freedom decrease and similar to the case of the canonical scalar field, only one scalar function needs to be designated, while the other is extracted from the continuity equation of the scalar field. We showcase explicitly that the slow-roll indices can be written in a closed form as functions of three dimensionless parameters, namely $x=\frac{1}{2\alpha}\bigg(\frac{\kappa\xi'}{\xi''}\bigg)^2$, $\beta=8H^2\xi''$ and $\gamma=\frac{\xi'\xi'''}{\xi''^2}$ and in turn, we prove that the Einstein-Gauss-Bonnet model can in fact produce a blue-tilted tensor spectral index if the condition $\beta\geq1$ is satisfied, which is possible only for Einstein-Gauss-Bonnet models with $\xi''(\phi_k)>0$. Afterwards, a brief comment on the running of the spectral indices is made where it is shown that $a_{\mathcal{S}}(k_*)$ and $a_{\mathcal{T}}(k_*)$ in the constrained case are approximately of the order $\mathcal{O}(10^{-3})$, if not smaller. Last but not least, we examine the conditions under which the Swampland criteria are satisfied. We connect the tracking condition related to scalar field theories with the present models, and we highlight the important feature of the models we propose that the tracking condition can be satisfied only if the Swampland criteria are simultaneously satisfied, however the cases with $\xi\sim1/V$ and $\xi\sim V$ are excluded, as they cannot describe the inflationary era properly.

Kinematics signature of a giant planet in the disk of AS 209

Observations of dust in protoplanetary disks with the Atacama Large Millimeter Array (ALMA) are revealing the existence of substructures such as rings, gaps, and cavities. This morphology is expected to be the outcome of dynamical interaction between the disks and (embedded) planets. However, other mechanisms are able to produce similar dust substructures. A solution to discriminate the gap formation mechanism is to look at the perturbation induced by the planet on the gas surface density and/or the kinematics. In the case of the disk around AS 209, a prominent gap has been reported in the surface density of CO atr ~100 au. A further gas gap was identified atr~ 200 au. Recently, a localized velocity perturbation was reported in the12COJ= 2−1 emission along with a clump in13COJ= 2−1 at nearly 200 au and this was interpreted as a gaseous circumplanetary disk. In this paper, we report a new analysis of ALMA archival observations of12CO and13COJ= 2−1 in AS 209. We detected a clear kinematics perturbation (kink) in multiple channels and over a wide azimuth range in both datasets. We compared the observed perturbation with a semianalytic model of velocity perturbations due to planet-disk interaction. Based on our analysis, the observed kink is not consistent with a planet at 200 au, as this would require a low gas-disk scale height (<0.05) in contradiction with the previous estimate (h/r ~0.118 atr= 100 au). When we fix the disk scale height to 0.118 (atr= 100 au), we find instead that a planet at 100 au induces a kinematics perturbation similar to the one observed. The kink amplitude in the various channels implies a planet mass of 3–5MJup. Thus, we conclude that a giant proto-planet orbiting atr~ 100 au is responsible for the large-scale kink as well as for the perturbed dust and gas surface density previously detected. The position angle of the planet is constrained to be between 60° and 100° (east of north). The 200 au gap visible in the12COJ= 2−1 moment zero map is likely due to density fluctuations induced by the spiral wake. Future observations using the high-contrast imaging technique in the near- and mid-infrared (e.g., with JWST and/or VLT/ERIS) are needed to confirm the presence and position of such a planet.