Low-order Resonances Research Articles

(Invited) Mie Resonant Silicon Nanosphere Nanoantenna for Fluorescence Enhancement

A nanoantenna is a device that manipulates light propagation and enhances light-matter interaction at the nanoscale. Integration of an emitter into a nanoantenna capable of increasing local density of photonic states at the emission wavelength results in the enhancement of the spontaneous emission rate (Purcell effect) and modifies the emission spectrum. A nanoantenna can also control the directionality and radiation pattern of an emitter. Traditionally, plasmonic nanoantennas made from gold or silver nanostructures supporting localized surface plasmon resonances had been the main stream of the nanoantenna research. Recently, high refractive index nanoparticles having low-order Mie resonances have been attracting attention as a new type of dielectric nanoantennas. Advantages of a dielectric nanoantenna compared to a plasmonic one are the smaller loss and the possession of magnetic type Mie resonances arising from light-induced displacement current. By properly controlling the overlap of the magnetic and electric multipole resonances, radiation patters of an emitter placed nearby can be tailored with high degree of freedom. Furthermore, magnetic-type Mie resonances can couple with higher-order optical transitions of an emitter such as a magnetic-dipole transition, and thus can enhance and control radiation from otherwise weak forbidden transitions.Recently, we have succeeded in producing perfectly spherical nanoparticles of crystalline silicon (Si) in 100-300 nm in diameters. These Si nanospheres exhibit the electric and magnetic multipole resonances at the optical frequency [1]. In this presentation, we first show scattering and absorption properties of the Mie resonant Si nanospheres. Especially, we show that solutions of size-purified Si nanospheres exhibit vivid structural color and the solutions can be used as structural color inks. We then show that the solutions can preserve helicity of incoming circularly-polarized light and can enhance local chiral fields around nanospheres [2, 3]. This property can be used to improve the sensitivity of enantiomer-selective chiral molecular sensing. We then show some examples of enhanced light-matter interaction by Si nanoparticles. These include enhancement of magnetic dipole transitions of an emitter by magnetic-type Mie resonances of Si nanospheres (magnetic Purcell effect) [4, 5], enhancement of excitation and emission processes of in-plane dipoles of monolayer transition metal dichalcogenides (TMDC) [6], and enhancement of a spin forbidden singlet-to-triplet absorption transition of a molecule by Si nanodisks [7, 8].

Multi-condition stability analysis and lightweight research of mining wide-body dump truck compartment

This paper proposes a multi-condition optimization method based on single condition optimization and weight. This method analyzes and discusses various working states of the wide-body dump truck and optimize its structure. Firstly, the modal shape and natural frequency of the carriage under modal conditions are analyzed using the finite element method. Combined with the mechanic’s theory, the carriage’s force, deformation, and stress are studied under the turning and partial load conditions. This part provides a basis for subsequent stability analysis and lightweight research. According to the filtering white noise method and differential equation method, the f-class road model and the vehicle system dynamics model are established in MATLAB to study the influence of road vibration on the stability of the dump truck during operation. The carriage vibration data prove that the road vibration causes the low order resonance of the carriage and affects the stability of the dump truck. This part provides a basis for the subsequent stability optimization. Based on the above analysis, a multi-objective genetic algorithm based on the response surface is used to optimize the structural parameters of the carriage under partial load conditions, turning conditions and modal conditions, to realize the optimization of stability, mass, stress and deformation of the carriage. Finally, the entropy weight method is used to fuse the optimization results of the three working conditions. The correctness of the comprehensive optimization results is verified, and the wide-body dump truck carriage optimization is realized, proving the feasibility of the proposed method.

Kepler-discovered Multiple-planet Systems near Period Ratios Suggestive of Mean-motion Resonances Are Young

Before the launch of the Kepler Space Telescope, models of low-mass planet formation predicted that convergent type I migration would often produce systems of low-mass planets in low-order mean-motion resonances. Instead, Kepler discovered that systems of small planets frequently have period ratios larger than those associated with mean-motion resonances and rarely have period ratios smaller than those associated with mean-motion resonances. Both short-timescale processes related to the formation or early evolution of planetary systems and long-timescale secular processes have been proposed as explanations for these observations. Using a thin disk stellar population’s Galactic velocity dispersion as a relative age proxy, we find that Kepler-discovered multiple-planet systems with at least one planet pair near a period ratio suggestive of a second-order mean-motion resonance have a colder Galactic velocity dispersion and are therefore younger than both single-transiting and multiple-planet systems that lack planet pairs consistent with mean-motion resonances. We argue that a nontidal secular process with a characteristic timescale no less than a few hundred Myr is responsible for moving systems of low-mass planets away from second-order mean-motion resonances. Among systems with at least one planet pair near a period ratio suggestive of a first-order mean-motion resonance, only the population of systems likely affected by tidal dissipation inside their innermost planets has a small Galactic velocity dispersion and is therefore young. We predict that period ratios suggestive of mean-motion resonances are more common in young systems with 10 Myr ≲ τ ≲ 100 Myr and become less common as planetary systems age.

Tidal Dissipation Regimes among the Short-period Exoplanets

The efficiency of tidal dissipation provides a zeroth-order link to a planet’s physical properties. For super-Earth and sub-Neptune planets in the range R ⊕ ≲ R p ≲ 4R ⊕, particularly efficient dissipation (i.e., low tidal quality factors) may signify terrestrial-like planets capable of maintaining rigid crustal features. Here, we explore global constraints on planetary tidal quality factors using a population of planets in multiple-planet systems whose orbital and physical properties indicate susceptibility to capture into secular spin–orbit resonances. Planets participating in secular spin–orbit resonance can maintain large axial tilts and significantly enhanced heating from obliquity tides. When obliquity tides are sufficiently strong, planets in low-order mean-motion resonances can experience resonant repulsion (period ratio increase). The observed distribution of period ratios among transiting planet pairs may thus depend nontrivially on the underlying planetary structures. We model the action of resonant repulsion and demonstrate that the observed distribution of period ratios near the 2:1 and 3:2 commensurabilities implies Q values spanning from Q ≈ 101–107 and peaking at Q ≈ 106. This range includes the expected range in which super-Earth and sub-Neptune planets dissipate (Q ≈ 103–104). This work serves as a proof of concept for a method of assessing the presence of two dissipation regimes, and we estimate the number of additional multitransiting planetary systems needed to place any bimodality in the distribution on a strong statistical footing.

Turning whispering-gallery-mode responses through Fano interferences in coupled all-dielectric block-disk cavities.

Here, we theoretically demonstrate a strategy for efficiently turning whispering-gallery-mode (WGM) responses of a subwavelength dielectric disk through their near-field couplings with common low-order electromagnetic resonances of a dielectric block. Both simulations and an analytical coupled oscillator model show that the couplings are Fano interferences between dark high-quality WGMs and bright modes of the block. The responses of a WGM in the coupled system are highly dependent on the strengths and the relative phases of the block modes, the coupling strength, and the decay rate of the WGM. The WGM responses of coupled systems can exceed that of the individual disk. In addition, such a configuration will also facilitate the excitation of WGMs by a normal incident plane wave in experiments. These results could enable new applications for enhancing light-matter interactions.

Dynamic Responses of the Planetary Gear Mechanism Considering Dynamic Wear Effects

Gear wear is unavoidable and results in vibrations and decreased performance in a planetary gear system. In this work, the wear phenomenon of the gear teeth surface and the dynamic responses of the planetary gear mechanism are investigated through a computational methodology. Dynamic responses are presented by considering the dynamic wear effects. First, the model of the planetary gear mechanism dynamics is established by considering the nonlinear stiffness and friction of gear surfaces. The dynamic wear model of the gear is then established based on Archard’s wear model. Further, the coupling between the dynamics and wear characteristics of the planetary gear mechanism is presented by considering the dynamic wear effects. Finally, a numerical investigation is conducted. The simulation results reveal severe wear between the sun and planet gears. The wear depth and meshing vibration responses exhibit prominent nonlinear characteristics. The low-order resonance of the meshing frequency becomes more marked as the mesh times and wear increase.

Enhanced energy transfer and multimodal vibration mitigation in an electromechanical acoustic black hole beam

Owing to their unique energy focusing capability and high-frequency damping effects, Acoustic Black Hole (ABH) structures show promise for numerous engineering applications. However, conventional ABH structures are mostly effective only above the so-called cut-on frequency, a bottlenecking deficiency that needs to be addressed if low-frequency problems are of concern. Meanwhile, achieving simultaneous high frequency ABH effects and low-frequency vibration reduction is also a challenge. In this paper, electrical linear and nonlinear shunts are intentionally added to an ABH beam via PZT patches to tactically influence its dynamics through electromechanical coupling. Both numerical and experimental results confirm that the effective frequency range of the ABH can be broadened as a result of the electrical nonlinearity induced energy transfer (ET) from low to high frequencies inside the beam. However, increased nonlinearity strength, albeit beneficial to energy transfer, jeopardizes the linear dynamic absorber (DA) effects acting on the lower-order resonances. Solutions are exploited to tackle this problem, exemplified by the use of negative capacitance in the nonlinear shunts with the embodiment of parallel linear electrical branches. On top of the nonlinear ET effects, simultaneous DA effect is also achieved for the low-frequency resonant vibration mitigation. Studies finally end up with a design methodology which embraces the principle of ET and DA to tactically cope with different frequency bands. The final outcome is the broadband multi-modal vibration reduction and the breaking down of the frequency barrier existing in conventional linear ABH structures.

Vibroacoustic Transfer Characteristics of Underwater Cylindrical Shells Containing Complex Internal Elastic Coupled Systems

Cylindrical shells containing complex elastic coupling systems are the main structural form of underwater vehicles. Therefore, in this paper, the vibroacoustic radiation problem of underwater cylindrical shells containing complex internal elastic coupling systems is studied. Firstly, the dynamics model of the complex elastic coupled system is established through the method of integrated conductivity. The sound pressure distribution law and the general magnitude relationship between the performance index of hydroacoustic radiation and vibration isolation are investigated through numerical simulation. A strategy of global sensitivity analysis and related parameter optimization is carried out, by applying the Sobol’ method to the dynamics model. It could be concluded that the main flap of sound pressure at low and medium frequencies appears in the direction of the excitation force or the perpendicular to the excitation force, the magnitudes correspondence between the vibration level drop—power flow—hydroacoustic radiation at low frequencies can be expressed as a relatively simple function, and the vibroacoustic transmission of the system at lower order resonance frequencies is dominated by the parameter configuration of the vibration isolation device, while at higher frequencies is more influenced by the modalities of the base structure. The transfer power flow and the level drop are used as objective functions to optimise the acoustic radiation index of the coupled system, with the best results obtained when the transfer power flow and the level drop are used together as objective functions.

Non-perturbative investigation of low-eccentricity exterior mean motion resonances

ABSTRACT Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel properties in the low-eccentricity regime for interior mean motion resonances of Jupiter in the fundamental model of the circular planar restricted three-body model. Here, we extend the non-perturbative investigation to exterior mean motion resonances in the low-eccentricity regime (up to about 0.1) and for perturber mass in the range of ∼5 × 10−5 to 1 × 10−3 (in units of the central mass). Our results demonstrate that first-order exterior resonances have two branches at low eccentricity as well as low-eccentricity bridges connecting neighbouring first-order resonances. With increasing perturber mass, higher order resonances dissolve into chaos, whereas low-order resonances persist with larger widths in their radial extent but smaller azimuthal widths. For low-order resonances, we also detect secondary resonances arising from small-integer commensurabilities between resonant librations and the synodic frequency. These secondary resonances contribute significantly to generating the chaotic sea that typically occurs near mean motion resonances of higher mass perturbers.

Circumbinary planets: migration, trapping in mean-motion resonances, and ejection

Context. Most of the planetary systems discovered around binary stars are located at approximately three semi-major axes from the barycentre of their system, curiously close to low-order mean-motion resonances (MMRs). The formation mechanism of these circumbinary planets is not yet fully understood. In situ formation is extremely challenging because of the strong interaction with the binary. One possible explanation is that, after their formation, the interactions between these planets and the surrounding protoplanetary disc cause them to migrate at velocities dependent on the nature of the disc and the mass of the exoplanet. Although extensive data can be obtained with direct hydrodynamical simulations, their computational cost remains too high. On the other hand, the direct N-body simulations approach allows us to model a large variety of parameters at much lower cost. Aims. We analyse the planetary migration around a wide variety of binary stars using Stokes-like forces that mimic planetary migration at a constant rate. Our goal is to identify the main parameters responsible for the ejection of planets at different resonances with the inner binary. Methods. We performed 4200 N-body simulations with Stokes-like forces and analysed their evolution and outcome as a function of the properties of each system. For each simulated exoplanet, we applied an ensemble learning method for classification in order to clarify the relationship between the inspected parameters and the process of MMR capture. Results. We identify the capture probability for different N/1 MMRs, 4/1 being the most prone to capture exoplanets, with 37% probability, followed by MMR 5/1 with ~23% of probability. The eccentricity of the binary is found to be the most important parameter in determining the MMR capture of each circumbinary exoplanet, followed by the mass ratio of the binary and the initial eccentricity of the planet.

Scattering by circularly symmetric structured optical fields in stratified media

Structured optical fields (SOFs) with spatially inhomogeneous phase, amplitude, or polarization can excite substantially different optical responses in nanoscale scattering particles. Inhibition of low-order multipolar resonances, excitation of dark modes and anapoles, and spin and orbital angular momenta dichroism have been demonstrated, broadening the scope of nanoscale manipulations of optical resonances by using these engineered external SOFs. However, studying scattering effects illuminated by SOFs is more complicated than conventional plane wave illuminations, and the difficulty increases for scattering particles on a substrate. In this paper, we present explicit expressions of SOFs propagating through stratified media, or multilayered systems, and provide their beam-shape coefficients. Specifically, simple analytic expressions are provided for circularly symmetric Bessel beams passing through an interface. Then, scattering calculations for a dielectric sphere on a substrate illuminated by an evanescent optical vortex are performed via the $T$-matrix method, which yields accurate and efficient results as compared with finite element analysis. This paper will find practical applications in modeling SOFs for realistic configurations of scattering of particles on a substrate at nonplanar nonparaxial external light source illuminations.

A Control Strategy of LCL-Type Grid-Connected Inverters for Improving the Stability and Harmonic Suppression Capability

The conventional inverter-side current single-loop feedback control scheme is weak in suppressing the grid-side current harmonics, posing a challenge for an inverter to inject high-quality current under distorted grid voltage. With capacitor current compensation added, the control scheme achieves controllability of the grid-side current harmonics so that it can effectively suppress some specific harmonic components. However, due to the stability requirements, only a few low-order harmonic resonance controllers can be applied, which limits the mitigation of high-order harmonics. To tackle this problem, the grid-side current feedback control with inductor–capacitor–inductor (LCL) resonance damping is proposed in this paper. In this case, a higher LCL resonance frequency can be set compared to the inverter-side current single-loop feedback control scheme. Thereby, more resonance controllers can be applied to suppress high-order grid-side current harmonics. The active damping method of capacitor current proportional feedback plus capacitor voltage proportional feedback is adopted because of its high robustness to grid impedance variations. Furthermore, this paper reveals that the applied active damping method has a limitation in that it only considers a single inverter under inductive grid impedance, which cannot eliminate the risk of resonance caused by the interaction of multiple inverters and the grid. To address this issue, a phase lead compensator (PLC) is proposed, eliminating the resonance risk by removing the non-passive region of the inverter output admittance. To retain the advantage of the inverter-side current single-loop feedback control scheme, i.e., only a few measuring devices are required, a digital differentiator is used to calculate the capacitor current from the capacitor voltage. The difference between the measured inverter-side current and the calculated capacitor current is taken to approximate the grid-side current for the feedback control. The control performance is comparable to using the grid-side current for feedback. Simulation and experimental results demonstrate that the proposed control scheme endows the inverter with good stability and current quality without extra measurement devices.

Tuning the higher to lower order resonance frequency ratio and implementing the tunable THz MIMO/self-diplexing antenna

The frequency ratio of higher to lower order mode can be electronically tuned in a terahertz (THz) antenna with metallic radiator using a graphene loop. Antenna is designed with slotted metallic radiator to obtain the dual-band response with fundamental and second order transverse magnetic mode providing the directional and bi-directional radiation pattern in the lower and upper band, respectively. The insertion of graphene loop and varying its chemical potential (μc) provides two resonances until 0.4eV and four resonances for further greater values of μc. The desired impedance matching can be achieved at the frequencies of any two resonances at a time by selecting an appropriate value of μc. Antenna can operate with higher/lower order mode centred at frequency 3.77/3.02 THz and 4.39/2.86 THz for the values of μc as 0.9 and 0.3eV , respectively. The frequency ratio of higher to lower order mode can be tuned within the range of 1.22–1.59 with the variation in μc. Also, application of graphene loop confines the radiated power in a single direction at the frequency of higher order mode making the radiation pattern consistent. Antenna can be utilized in future THz wireless applications which require the utilization of adjacent channels with different frequencies in communication. Also, a two-port antenna is designed which can offer the tunable multi-input–multi-output (MIMO) and self-diplexing capability with pattern diversity. The MIMO parameters; envelope correlation coefficient (ECC) and diversity gain (DG) is evaluated and their values are found within acceptable limits as ECC<0.06 and DG>9.9 in the operating bands.

Passivity-Based Design of a Fractional-Order Virtual Capacitor for Active Damping of Multiparalleled Grid-Connected Current-Source Inverters

Current-source inverters (CSIs) have advantages, such as voltage boosting capability and direct current controllability, in high-power conversion applications with low switching frequency. However, inadequate damping of the passive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$CL$</tex-math></inline-formula> filter gives rise to low-order harmonic resonance. The recent research regarding active damping techniques generally focuses on resonance mitigation of single grid-connected inverters. However, multiple resonances that arise from dynamic interactions among paralleled grid-connected inverters compromise system stability and power quality. This article presents the delay-dependent passivity-based analysis and design of a lossless fractional-order virtual capacitor for resonance damping of multiparalleled grid-connected CSI-based systems. Fractional-order capacitors provide a higher degree of freedom that enhances the frequency behavior and robustness of the control. Simulation and experimental results demonstrate the effectiveness of the proposed active damping control even with variations in the grid impedance and the number of paralleled CSIs.

Shape- and Size-Dependent Refractive Index Sensing and SERS Performance of Gold Nanoplates.

Plasmonic sensors are promising for ultrasensitive chemical and biological analysis. Gold nanoplates (Au NPLs) show unique geometrical structures with high ratios of surface to bulk atoms, which display fascinating plasmonic properties but require optimization. This study presented a systematic investigation of the influence of different parameters (shape, aspect ratio, and resonance mode) on localized surface plasmon resonance properties, refractive index (RI, n) sensitivities, and surface-enhanced Raman scattering (SERS) enhancement ability of different types of Au NPLs through finite-difference time-domain (FDTD) simulations. As a proof of concept, triangular, circular, and hexagonal Au NPLs with varying aspect ratios were fabricated via a three-step seed-mediated growth method by the experiment. Both FDTD-simulated and measured experimental results confirm that the RI sensitivities increase with the aspect ratio. Furthermore, choosing a lower order resonance mode of Au NPLs benefits higher RI sensitivities. The SERS enhancement abilities of Au NPLs also predicted to be highly dependent on the shape and aspect ratio. The triangular Au NPLs showed the highest SERS enhancement ability, while it drastically decreased for circular Au NPLs after the rounding process. The SERS enhancement ability gradually became more intense as the hexagonal Au NPLs overgrown on circular Au NPLs with increasing volumes of HAuCl4 solution. The results are expected to help develop effective biosensors.

Web of resonances and possible path of evolution of the small Uranian satellites

Satellite systems around giant planets are immersed in a region of complex resonant configurations. Understanding the role of satellite resonances contributes to comprehending the dynamical processes in planetary formation and posterior evolution. Our main goal is to analyse the resonant structure of small moons around Uranus and propose different scenarios able to describe the current configuration of these satellites. We focus our study on the external members of the regular satellites interior to Miranda, namely Rosalind, Cupid, Belinda, Perdita, Puck, and Mab, respectively. We use N-body integrations to perform dynamical maps to analyse their dynamics and proximity to two-body and three-body mean-motion resonances (MMR). We found a complicated web of low-order resonances amongst them. Employing analytical prescriptions, we analysed the evolution by gas drag and type-I migration in a circumplanetary disc (CPD) to explain different possible histories for these moons. We also model the tidal evolution of these satellites using some crude approximations and found possible paths that could lead to MMRs crossing between pairs of moons. Finally, our simulations show that each mechanism can generate significant satellite radial drift leading to possible resonant capture, depending on the distances and sizes.

TOI-1670 b and c: An Inner Sub-Neptune with an Outer Warm Jupiter Unlikely to Have Originated from High-eccentricity Migration

We report the discovery of two transiting planets around the bright (V = 9.9 mag) main-sequence F7 star TOI-1670 by the Transiting Exoplanet Survey Satellite. TOI-1670 b is a sub-Neptune ( R ⊕) on a 10.9 day orbit, and TOI-1670 c is a warm Jupiter ( R Jup) on a 40.7 day orbit. Using radial velocity observations gathered with the Tull Coudé Spectrograph on the Harlan J. Smith telescope and HARPS-N on the Telescopio Nazionale Galileo, we find a planet mass of M Jup for the outer warm Jupiter, implying a mean density of g cm−3. The inner sub-Neptune is undetected in our radial velocity data (M b < 0.13 M Jup at the 99% confidence level). Multiplanet systems like TOI-1670 hosting an outer warm Jupiter on a nearly circular orbit () and one or more inner coplanar planets are more consistent with “gentle” formation mechanisms such as disk migration or in situ formation rather than high-eccentricity migration. Of the 11 known systems with a warm Jupiter and a smaller inner companion, eight (73%) are near a low-order mean-motion resonance, which can be a signature of migration. TOI-1670 joins two other systems (27% of this subsample) with period commensurabilities greater than 3, a common feature of in situ formation or halted inward migration. TOI-1670 and the handful of similar systems support a diversity of formation pathways for warm Jupiters.

Magnetic field sensing based on multi-order resonances of atomic spins.

Broad-dynamic-range magnetometers are demanded in practical applications and fundamental research. We experimentally demonstrate a parametrically modulated atomic magnetometer with a large dynamic range by taking advantage of the high-order resonance effects. With the increase of the strength of the modulation field, both low-order and high-order resonances are well resolved and used to measure the DC or AC magnetic fields. The experimentally demonstrated sensitivity of the magnetometer based on the zeroth-order resonance is 1.5 pT/Hz, and those based on the high-order resonances are below 3 pT/Hz, making the measurement of high magnetic fields feasible under an open-loop operation. Moreover, we also demonstrated the measurement of high-frequency large AC magnetic field with the high-order resonances, and the sensitivity for the AC magnetic field based on the first-order resonance is 7 pT/Hz. Our scheme provides a new path for the development of broad-dynamic-range and miniaturized atomic magnetometers.

Влияние эффекта Ярковского на орбитальные резонансы астероидов с малыми перигелийными расстояниями

The paper presents the study results of the Yarkovsky effect influence on the resonant characteristics of asteroids with small perihelion distances. Out of 52 studied objects, 27 asteroids were identified that move in the vicinity of stable and unstable low-order mean motion resonances with major planets. The evolution of the asteroids orbits is constructed with and without the Yarkovsky effect, and the behavior of the resonance characteristics in both cases is analyzed. The effect was taken into account by including the perturbation from the transversal acceleration A2, the values of which for the presented objects were obtained earlier by the authors of this work. It is shown that the Yarkovsky effect influence on stable resonances is insignificant and leads to small changes in the libration amplitude of the resonance characteristics. The stability of the resonance is preserved. With unstable resonant interaction, the number of passages through the exact commensurability changes, and for some asteroids the resonance becomes more stable.

Transit timings variations in the three-planet system: TOI-270

ABSTRACT We present ground- and space-based photometric observations of TOI-270 (L231-32), a system of three transiting planets consisting of one super-Earth and two sub-Neptunes discovered by TESS around a bright (K-mag = 8.25) M3V dwarf. The planets orbit near low-order mean-motion resonances (5:3 and 2:1) and are thus expected to exhibit large transit timing variations (TTVs). Following an extensive observing campaign using eight different observatories between 2018 and 2020, we now report a clear detection of TTVs for planets c and d, with amplitudes of ∼10 min and a super-period of ∼3 yr, as well as significantly refined estimates of the radii and mean orbital periods of all three planets. Dynamical modelling of the TTVs alone puts strong constraints on the mass ratio of planets c and d and on their eccentricities. When incorporating recently published constraints from radial velocity observations, we obtain masses of $M_{\mathrm{b}}=1.48\pm 0.18\, M_\oplus$, $M_{\mathrm{c}}=6.20\pm 0.31\, M_\oplus$, and $M_{\mathrm{d}}=4.20\pm 0.16\, M_\oplus$ for planets b, c, and d, respectively. We also detect small but significant eccentricities for all three planets : eb = 0.0167 ± 0.0084, ec = 0.0044 ± 0.0006, and ed = 0.0066 ± 0.0020. Our findings imply an Earth-like rocky composition for the inner planet, and Earth-like cores with an additional He/H2O atmosphere for the outer two. TOI-270 is now one of the best constrained systems of small transiting planets, and it remains an excellent target for atmospheric characterization.