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At least 649 records · Page 36

Towards Floquet Chern insulators of light

Topological photonics explores photonic systems that exhibit robustness against defects and disorder, enabled by protection from underlying topological phases. These phases are typically realized in linear optical systems and characterized by their intrinsic photonic band structures. Here we experimentally study Floquet Chern insulators in periodically driven nonlinear photonic crystals, where the topological phase is controlled by the polarization and the frequency of the driving field. Our transient sum-frequency generation measurements reveal strong hybridization of the Floquet photonic bands. The measured spectrum remains gapless under a linearly polarized drive but becomes gapped under a circularly polarized drive. Theoretical analysis confirms that the Floquet gap is topological, characterized by a non-zero Chern number—a consequence of time-reversal symmetry breaking induced by the circularly polarized driving field. Furthermore, this work offers opportunities to explore the role of classical optical nonlinearity in topological phases and their applications in nonlinear optoelectronics.

36 MATERIALS SCIENCE↗

Evaluation of the beam-induced depolarization of the HJET target at the EIC

The Polarized Atomic Hydrogen Gas Jet Target (HJET) has played a central role in the absolute calibration of proton beam polarization at RHIC and is foreseen as a key component of the hadron polarimetry program at the future Electron–Ion Collider (EIC). The substantially higher beam current, reduced bunch spacing, and shorter bunch length planned for EIC operation motivate a careful reassessment of possible beam-induced depolarization of the jet target. In this paper, the depolarization of ground-state hydrogen atoms caused by the time-dependent magnetic field of the circulating polarized proton beam is quantitatively evaluated. The hydrogen atom is treated as a four-level hyperfine system in a holding magnetic field, and transitions driven by harmonic components of the bunch-induced magnetic field are analyzed using time-dependent quantum-mechanical evolution along atomic trajectories. Numerical tracking of hydrogen atoms through the beam region is performed using nominal EIC beam parameters. It is shown that, for a holding field of 120 mT (as used at RHIC), the resulting depolarization of the jet target at the EIC is negligibly small, ≲ 0.01 %, and well below the level relevant for EIC polarization accuracy requirements. The stability of this result with respect to plausible variations of the EIC proton beam parameters is also evaluated. In addition, possible effects under alternative experimental conditions are also examined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Weather Prediction Improvement Using Advanced Satellite Technology

We discuss in this paper some of the problems that exist today in the fall utilization of satellite data to improve weather forecasts and we propose specific recommendations to solve them. This discussion can be viewed as an aspect of the general debate on how best to organize the transition from research to operational satellites and how to evaluate the impact of a research instrument on numerical weather predictions. A method for providing this transition is offered by the National Polar-Orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP). This mission will bridge the time between the present NOAA and Department of Defense (DOD) polar orbiting missions and the initiation of the converged NPOESS series and will evaluate some of the Earth Observing System (EOS) instruments as appropriate for operational missions. Thus, this mission can be viewed as an effort to meet the operational requirements of NOAA and DOD and the research requirements of NASA. More generally, however, it can be said that the process of going from the conception of new, more advanced instruments to their operational implementation and full utilization by the weather forecast communities is not optimal. Instruments developed for research purposes may have insufficient funding to explore their potential operational capabilities. Furthermore, instrument development programs designed for operational satellites typically have insufficient funding for assimilation algorithms needed to transform the satellite observations into data that can be used by sophisticated global weather forecast models. As a result, years often go by before satellite data are efficiently used for operational forecasts. NASA and NOAA each have unique expertise in the design of satellite instruments, their use for basic and applied research and their utilization in weather and climate research. At a time of limited resources, the two agencies must combine their efforts to work toward common goals of full utilization of satellite data. This is a challenge that requires the assimilation of myriad new data into increasingly sophisticated numerical forecast models that run on increasingly sophisticated computer systems. In section II, we briefly outline the impact of satellite data on the quality of the National Centers for Environmental Prediction (NCEP) forecasts. In section III, we describe the present status of the utilization of satellite data in NCEP models and the challenges that lie ahead. In section IV, we propose solutions whose goals are summarized in section V.

Einaudi, Franco↗

Polarized-interferometer feasibility study

The feasibility of using a polarized-interferometer system as a rendezvous and docking sensor for two cooperating spacecraft was studied. The polarized interferometer is a radio frequency system for long range, real time determination of relative position and attitude. Range is determined by round trip signal timing. Direction is determined by radio interferometry. Relative roll is determined from signal polarization. Each spacecraft is equipped with a transponder and an antenna array. The antenna arrays consist of four crossed dipoles that can transmit or receive either circularly or linearly polarized signals. The active spacecraft is equipped with a sophisticated transponder and makes all measurements. The transponder on the passive spacecraft is a relatively simple repeater. An initialization algorithm is developed to estimate position and attitude without any a priori information. A tracking algorithm based upon minimum variance linear estimators is also developed. Techniques to simplify the transponder on the passive spacecraft are investigated and a suitable configuration is determined. A multiple carrier CW signal format is selected. The dependence of range accuracy and ambiguity resolution error probability are derived and used to design a candidate system. The validity of the design and the feasibility of the polarized interferometer concept are verified by simulation.

Raab, F. H.↗

Polarization Reversal Over Flooded Regions and Applications to Large-Scale Flood Mapping with Spaceborne Scatterometers

We present the polarization reversal in backscatter over flooded land regions, and demonstrate for the first time the utility of spaceborne Ku-band scatterometer for large-scale flood mapping. Scatterometer data were collected over the globe by the NASA Scatterometer (NSCAT) operated at 14 GHz on the Japanese ADEOS spacecraft from September 1996 to June 1997. During this time span, several severe floods occurred. Over most land surface, vertical polarization backscatter (Sigma(sub upsilon(upsilon)) is larger than horizontal polarization backscatter (sigma(sub hh)). Such polarization characteristics is reversed and sigma(sub upsilon(upsilon)) is smaller than sigma(sub hh) over flooded regions, except under a dense forest canopy. The total backscatter from the flooded landscape consists of direct backscatter and boundary-interaction backscatter. The direct term is contributed by direct backscattering from objects protruding above the water surface, and by backscattering from waves on the water surface. The boundary-interaction term is contributed by the forward scattering from the protruding objects and then reflected from the water surface, and also by the forward scattering from these objects after the water-surface reflection. Over flooded regions, the boundary-interaction term is dominant at large incidence angles and the strong water-surface reflection is much larger for horizontal polarization than the vertical one due to the Brewster effect in transverse-magnetic waves. These scattering mechanisms cause the polarization reversal over flooded regions. An example obtained with the Analytic Wave Theory is used to illustrate the scattering mechanisms leading to the polarization reversal. We then demonstrate the utility of spaceborne Ku-band scatterometer for large-scale flood mapping. We process NSCAT data to obtain the polarization ratio sigma(sub hh)/sigma(sub upsilon(upsilon)) with colocated data at incidence angles larger than 40 deg. The results over Asian summer monsoon regions in September-October 1996 indicate flooded areas in many countries such as Bangladesh, India, Lao, Vietnam, Cambodia, and China. Reports documented by the United Nation Department of Humanitarian Affairs (now called UN Office for the Coordination of Humanitarian Affairs) show loss of many lives and severe flood related damages which affected many million people in the corresponding flooded areas. We also map the NSCAT polarization ratio over the same regions in the "dry season" in January 1997 as a reference to confirm our results. Furthermore, we obtain concurrent ocean wind fields also derived from NSCAT data, and Asia topographic data (USGS GTOPO30) to investigate the flooded area. The results show that winds during summer monsoon season blowing inland, which perplex flood problems. Overlaying the topographic map over NSCAT results reveals an excellent correspondence between the confinement of flooded area within the relevant topographic features, which very well illustrates the value of topographic wetness index. Finally, we discuss the applications of future spaceborne scatterometers, including QuikSCAT and Seawinds, for flood mapping over the globe.

Nghiem, Son V.↗

Full-polarization millimeter wavelength variability of Sagittarius A * during the 2018 EHT campaign

Context. Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, provides a unique laboratory to study accretion dynamics and plasma processes near the event horizon. Aims. We investigated the variability and polarization properties of Sgr A* using ALMA observations during the 2018 Event Horizon Telescope campaign. Methods. We analyzed high-cadence full-polarization light curves from ALMA at millimeter wavelengths, performed time-series analysis, and investigated the temporal behavior during an X-ray flare observed by Chandra on 2018 April 24. The variability characteristics are compared with expectations from standard accretion flow models. Results. We find low variability in total intensity (σ/μ < 10%), but significantly higher variability in linear and circular polarization (∼30% and ∼50%, respectively). A time-series analysis reveals red-noise variability, with power spectral densities between −2 and −3 across all Stokes parameters. Polarized intensity shows stable intra-day timescales, while total intensity exhibits more variable timescales, suggesting distinct emission regions, with polarization likely arising from a coherent structure. On April 24, a statistically significant inter-band delay in polarized intensity coincides with a near-simultaneous X-ray and millimeter peak that deviates from the typical delayed flare scenario. This event also features enhanced millimeter variability and coherent polarization loop evolution. The observed simultaneity challenges standard models of transient synchrotron emission with cooling delays, favoring instead a scenario of continuous energy injection in an optically thin region. Conclusions. Our results offer new constraints on the physical mechanisms driving variability in Sgr A*, and provide key observational input for refining theoretical models of accretion and plasma behavior in the vicinity of supermassive black holes.

Galaxy: center↗

Variable polarization in X-ray binaries - HD 77581 (= 4U 0900-40)

Variable linear polarization has been observed from the X-ray binary system HD 77581 (= 4U 0900-40). These observations, together with observations of HD 153919 (= 4U 1700-37) and HD 152667, have been analyzed by the method of Brown et al. (1978). A polarimetric analysis should include only observations made over a time during which the scattering region producing the polarization does not change its structure. It is found that this time is typically on the order of 10 days for systems with OB supergiant primaries. An observation set compiled over a longer duration can introduce systematic errors into the derived parameters. The orbital and physical properties of HD 153919 and HD 152667 analyzed under these constraints are consistent with those derived from polarimetric observations taken 4 years earlier.

Dolan, J. F.↗

The Gravity and Extreme Magnetism Small Explorer Mission (GEMS)

Polarization is an inherently geometric quantity and provides information on source geometry inaccessible via spectroscopy or timing. To date, there have been reliable detections of X-ray polarization from only one object outside the solar system (the Crab nebula). Recent development of photoelectric polarimetry makes it possible to perform sensitive X-ray polarimetry with a modest mission. GEMS was selected by NASA to be the 13th Small Explorer mission with launch planned for 2014. GEMS will be approximately 100 times more sensitive than any previously flown X-ray polarimeter and will provide useful polarization measurements for dozens of cosmic X-ray sources. GEMS will lead to new insights into the nature of accreting black holes, magnetized neutron stars, and supernova remnants. In this talk I will review the science motivation for GEMS and describe the status of the mission implementation.

Kallman, Tim↗

Hadronic vacuum polarization using gradient flow

The gradient-flow operator product expansion for QCD current correlators including operators up to mass dimension four is calculated through NNLO. This paves an alternative way for efficient lattice evaluations of hadronic vacuum polarization functions. In addition, flow-time evolution equations for flowed composite operators are derived. Their explicit form for the non-trivial dimension-four operators of QCD is given through order $\alpha_s^3$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Probing Surface Plasmon Dynamics in Periodic Nanostructures through Ultrafast Electron Microscopy

Surface plasmon polaritons (SPPs) can be manipulated to localize and guide light in subwavelength distances, enabling them to find applications in a wide range of areas, from sensing to quantum computing. Among several methods of SPP excitation, periodic arrays of nano- and microstructures are of particular interest, as they enable engineering SPP properties through structural parameters. Here, in this study, using the photon-induced near-field electron microscopy (PINEM) technique, we investigated the mode formation, coupling, interference, and decay of SPPs in square and hexagonal arrays of circular nanoholes under both visible and near-infrared excitation. Polarization-resolved analysis revealed the key factors governing SPP localization and interference patterns, showing that the periodicity and symmetry of the array primarily determine the SPP interference patterns and their orientation, while pump polarization mainly modulates their intensity. Time-resolved PINEM measurements demonstrated the spatial dependence of the SPP temporal characteristics. In addition, cathodoluminescence (CL) spectroscopy was employed to examine the intrinsic plasmonic characteristics of the structure. Finite difference time domain (FDTD) simulations showed strong agreement with both PINEM and CL measurements on the spatial and spectral behavior of SPPs. Understanding the spatiotemporal dynamics of SPPs on nanostructures beyond the diffraction limit is crucial for optimizing plasmonic structures for advanced photonic and quantum technologies.

Plasmonics↗

High-fidelity remote entanglement of trapped atoms mediated by time-bin photons

Abstract Photonic interconnects between quantum processing nodes are likely the only way to achieve large-scale quantum computers and networks. The bottleneck in such an architecture is the interface between well-isolated quantum memories and flying photons. We establish high-fidelity entanglement between remotely separated trapped atomic qubit memories, mediated by photonic qubits stored in the timing of their pulses. Such time-bin encoding removes sensitivity to polarization errors, enables long-distance quantum communication, and is extensible to quantum memories with more than two states. Using a measurement-based error detection process and suppressing a fundamental source of error due to atomic recoil, we achieve an entanglement fidelity of 97% and show that fundamental limits due to atomic recoil still allow fidelities in excess of 99.9%.

Science & Technology - Other Topics↗

FilDReaMS: II. Application to the analysis of the relative orientations between filaments and the magnetic field in four Herschel fields

Context. Both simulations and observations of the interstellar medium show that the study of the relative orientations between filamentary structures and the magnetic field can bring new insight into the role played by magnetic fields in the formation and evolution of filaments and in the process of star formation. Aims. We provide a first application of FilDReaMS, the new method presented in the companion paper to detect and analyze filaments in a given image. The method relies on a template that has the shape of a rectangular bar with variable width. Our goal is to investigate the relative orientations between the detected filaments and the magnetic field. Methods. We apply FilDReaMS to a small sample of four Herschel fields (G210, G300, G82, G202) characterized by different Galactic environments and different evolutionary stages. First, we look for the most prevalent bar widths, and we examine the networks formed by filaments of different bar widths as well as their hierarchical organization. Second, we compare the filament orientations to the magnetic field orientation inferred from Planck polarization data and, for the first time, we study the statistics of the relative orientation angle as functions of both spatial scale and H2 column density. Results. We find preferential relative orientations in the four Herschel fields: small filaments with low column densities tend to be slightly more parallel than perpendicular to the magnetic field; in contrast, large filaments, which all have higher column densities, are oriented nearly perpendicular (or, in the case of G202, more nearly parallel) to the magnetic field. In the two nearby fields (G210 and G300), we observe a transition from mostly parallel to mostly perpendicular relative orientations at an H 2 column density ≃ 1.1 × 10 21 cm -2 and 1.4 × 10 21 cm -2 , respectively, consistent with the results of previous studies. Conclusions. Our results confirm the existence of a coupling between magnetic fields at cloud scales and filaments at smaller scale. They also illustrate the potential of combining Herschel and Planck observations, and they call for further statistical analyses with our dedicated method.

79 ASTRONOMY AND ASTROPHYSICS↗

Polarization angle requirements for CMB B-mode experiments. Application to the LiteBIRD satellite

A methodology to provide the polarization angle requirements for different sets of detectors, at a given frequency of a CMB polarization experiment, is presented. The uncertainties in the polarization angle of each detector set are related to a given bias on the tensor-to-scalar ratio r parameter. The approach is grounded in using a linear combination of the detector sets to obtain the CMB polarization signal. In addition, assuming that the uncertainties on the polarization angle are in the small angle limit (lower than a few degrees), it is possible to derive analytic expressions to establish the requirements. The methodology also accounts for possible correlations among detectors, that may originate from the optics, wafers, etc. The approach is applied to the LiteBIRD space mission. We show that, for the most restrictive case (i.e., full correlation of the polarization angle systematics among detector sets), the requirements on the polarization angle uncertainties are of around 1 arcmin at the most sensitive frequency bands (i.e., ≈ 150 GHz) and of few tens of arcmin at the lowest (i.e., ≈ 40 GHz) and highest (i.e., ≈ 400 GHz) observational bands. Conversely, for the least restrictive case (i.e., no correlation of the polarization angle systematics among detector sets), the requirements are ≈ 5 times less restrictive than for the previous scenario. At the global and the telescope levels, polarization angle knowledge of a few arcmins is sufficient for correlated global systematic errors and can be relaxed by a factor of two for fully uncorrelated errors in detector polarization angle. The reported uncertainty levels are needed in order to have the bias on r due to systematics below the limit established by the LiteBIRD collaboration.

79 ASTRONOMY AND ASTROPHYSICS↗

Cryogenic light detectors with thermal signal amplification for 0 νββ search experiments

As a step towards the realization of cryogenic-detector experiments to search for neutrinoless double-beta decay (such as CROSS, BINGO, and CUPID), we investigated a batch of 10 Ge light detectors (LDs) assisted by Neganov-Trofimov-Luke (NTL) signal amplification. Each LD was assembled with a large cubic light-emitting crystal (45 mm side) using the recently developed CROSS mechanical structure. The detector array was operated at milli-Kelvin temperatures in a pulse-tube cryostat at the Canfranc underground laboratory in Spain. We achieved good performance with scintillating bolometers from CROSS, made of Li 2 100 MoO 4 crystals and used as reference detectors of the setup, and with all LDs tested (except for a single device that encountered an electronics issue). No leakage current was observed for 8 LDs with an electrode bias up to 100 V. Operating the LDs at an 80 V electrode bias applied in parallel, we obtained a gain of around 9 in the signal-to-noise ratio of these devices, allowing us to achieve a baseline noise RMS of O(10 eV). Thanks to the strong current polarization of the temperature sensors, the time response of the devices was reduced to around half a millisecond in rise time. The achieved performance of the LDs was extrapolated via simulations of pile-up rejection capability for several configurations of the CUPID detector structure. Despite the sub-optimal noise conditions of the LDs (particularly at high frequencies), we demonstrated that the NTL technology provides a viable solution for background reduction in CUPID.

47 OTHER INSTRUMENTATION↗

Temporal coherent control of resonant two-photon double ionization of the hydrogen molecule via doubly excited states

Here, we use time-delayed, counter-rotating, circularly polarized few-cycle attosecond nonoverlapping pulses to study the temporal coherent control of the resonant process of two-photon double ionization (TPDI) of hydrogen molecule via doubly excited states for pulse propagation direction along $\hat k$ either parallel or perpendicular to the molecular axis $\hat R$. For $\hat k$∥ $\hat R$ and a pulse carrier frequency of 36 eV resonantly populating the Q 2 1 Π$^+_u$ (1) doubly excited state as well as other 1 Π$^+_u$ doubly excited states, we find that the indirect ionization pathway through these doubly excited states changes the character of the kinematical vortex-shaped momentum distribution produced by the two direct ionization pathways from fourfold to twofold rotational symmetry. This result is similar to what found in TPDI of the He atom involving 1 P$^ o_ {±1}$ doubly excited states; however, angular distributions exhibiting a quantum beat effect between the ground state and a doubly excited state seen for the He atom are observed here for its molecular counterpart with an anomaly in shape and magnitude, not in frequency. The sixfold differential probability integrated over the azimuthal angle of the photoelectron pair shows that this anomaly is due to autoionization decays and quantum beats between doubly excited states. For $\hat k$⟂$\hat R$ and a broadband pulse carrier frequency of 30 eV populating the Q 1 1 Π$^+_u$(1), Q 1 1 Σ$^+_u$(1), Q 2 1 Π$^+_u$(1) , and Q 1 1 Σ$^+_u$ (2) doubly excited states, the momentum distribution is shown to exhibit dynamical electron vortices with four spiral arms, which originates from the interplay between the 1 Δ$^+_ g$ , 1 Π$^+_ g$, and 1 Σ$^+_ g$ dynamical ionization amplitudes. Our treatment within either the adiabatic-nuclei approximation or fixed-nuclei approximation shows that the latter provides a very good account for this correlated process.

74 ATOMIC AND MOLECULAR PHYSICS↗

Ultrafast nonequilibrium evolution of excitonic modes in semiconductors

We study the time evolution of excitonic states after photoexcitation in the one-dimensional spinless extended Falicov-Kimball model. Several numerical methods are employed and benchmarked against each other: time-dependent mean-field simulations, the second-Born approximation (2BA) within the Kadanoff-Baym formalism, the generalized Kadanoff-Baym ansatz (GKBA) implemented with the 2BA, and the infinite time-evolving block decimation (iTEBD) method. It is found that the GKBA gives the best agreement with iTEBD and captures the relevant physics. Excitations to the particle-hole continuum and resonant excitations of the equilibrium exciton result in a qualitatively different dynamics. In the former case, the exciton binding energy remains positive and the frequency of the corresponding coherent oscillations is smaller than the band gap. On the other hand, resonant excitations trigger a collective mode whose frequency is larger than the band gap. We discuss the origin of these different behaviors by evaluating the nonequilibrium susceptibility using the nonthermal distribution and a random phase approximation. We note the peculiar mode with frequency larger than the band gap is associated with a partial population inversion with a sharp energy cutoff. We also discuss the effects of the cooling by a phonon bath. We demonstrate the real-time development of coherence in the polarization, which indicates excitonic condensation out of equilibrium.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ultrafast renormalization of the magnetic continuum in the proximal Kitaev quantum spin liquid H 3 LiIr 2 O 6 by tr-RIXS [Invited]

We present the first circularly polarized non-resonant pump time-resolved resonant inelastic X-ray scattering (tr-RIXS) experiment in H 3 LiIr 2 O 6 , an iridium-based Kitaev system. Our calculations and experimental results are consistent with the modification of the low-energy magnetic excitations in H 3 LiIr 2 O 6 only during illumination by the laser pulse. We discuss these results in a cooperative framework between the Floquet engineering of the exchange interactions and the dynamic renormalization of electron-electron correlations. However, the penetration length mismatch between the X-ray probe and laser pump and the intrinsic complexity of Kitaev magnets prevents us from unequivocally extracting towards which ground state H 3 LiIr 2 O 6 is driven. We outline possible solutions to these challenges for light-driven stabilization and observation of the Kitaev quantum spin liquid limit by RIXS.

Kim, Jungho [Argonne National Laboratory (ANL), Ar↗

Daytime variation in the aerosol indirect effect for warm marine boundary layer clouds in the eastern North Atlantic

Abstract. Warm boundary layer clouds in the eastern North Atlantic region exhibit significant diurnal variations in cloud properties. However, the diurnal cycle of the aerosol indirect effect (AIE) for these clouds remains poorly understood. This study takes advantage of recent advancements in the spatial resolution of geostationary satellites to explore the daytime variation in the AIE by estimating the cloud susceptibilities to changes in cloud droplet number concentration (Nd). Cloud retrievals for the month of July over 4 years (2018–2021) from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) on Meteosat-11 over this region are analyzed. Our results reveal a significant “U-shaped” daytime cycle in susceptibilities of the cloud liquid water path (LWP), cloud albedo, and cloud fraction. Clouds are found to be more susceptible to Nd perturbations at noon and less susceptible in the morning and evening. The magnitude and sign of cloud susceptibilities depend heavily on the cloud state defined by cloud LWP and precipitation conditions. Non-precipitating thin clouds account for 44 % of all warm boundary layer clouds in July, and they contribute the most to the observed daytime variation. Non-precipitating thick clouds are the least frequent cloud state (10 %), and they exhibit more negative LWP and albedo susceptibilities compared to thin clouds. Precipitating clouds are the dominant cloud state (46 %), but their cloud susceptibilities show minimal variation throughout the day. We find evidence that the daytime variation in LWP and albedo susceptibilities for non-precipitating clouds is influenced by a combination of the diurnal transition between non-precipitating thick and thin clouds and the “lagged” cloud responses to Nd perturbations. The daytime variation in cloud fraction susceptibility for non-precipitating thick clouds can be attributed to the daytime variation in cloud morphology (e.g., overcast or broken). The dissipation and development of clouds do not adequately explain the observed variation in cloud susceptibilities. Additionally, daytime variation in cloud susceptibility is primarily driven by variation in the intensity of cloud response rather than the frequency of occurrence of cloud states. Our results imply that polar-orbiting satellites with an overpass time at 13:30 LT underestimate daytime mean values of cloud susceptibility, as they observe susceptibility daily minima in the study region.

54 ENVIRONMENTAL SCIENCES↗