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At least 1,603 records · Page 89

LLRF System Analysis for the Fermilab PIP-II LINAC

Developing long-lived quantum processing units (QPUs) capable of supporting high-fidelity quantum operations is a crucial challenge on the path toward fault-tolerant quantum computing. TESLA-shaped superconducting RF (SRF) cavities, known for photon relaxation times on the order of seconds, provide an excellent foundation for 3D QPUs and quantum memory. This talk presents a novel design that leverages TESLA cavity modes coupled to ancillary transmon qubits, optimized to preserve coherence and control. By carefully engineering the package geometry, optimizing Hamiltonian parameters, and minimizing lossy participation ratios, we achieve photon relaxation times of over 16 ms and 20 ms for the two cavity modes, representing a significant improvement over previous multimode quantum memories. Despite the reduced coupling between the qubit and cavity modes, which is necessary to preserve long lifetimes, the platform supports robust and universal control schemes that are not limited by low coupling strength. We will also discuss how this architecture can lead to scalable, modular quantum computing systems.

Varghese, P. [Fermilab]↗

X-ray mirror surface figure correction with nanometre precision controlled by layer stresses simulated by FEA

Hard X-rays with energies higher than several kiloelectronvolts can be focused to spot sizes below 10 nm with the present synchrotron beamlines, offering unique advantages for the chemical, elemental and structure analysis of matter. Nevertheless, a surface precision on the nanometre scale for the focusing optics is required and remains the main hurdle limiting X-ray analytical techniques with single-nanometre spatial resolution. On the other hand, to preserve the wavefront properties of coherent X-ray beams, precise control of the reflective mirror surface quality at the nanometre scale is demanded for X-ray free-electron laser applications. In this work, the surface shape of a multilayer-coated X-ray mirror is controlled by layer stresses. The desired surface profile of the mirror is differentiated to its second order to obtain its corresponding curvature profile. With a step size of 1 mm along the mirror length, different coating thicknesses are applied to create different layer thermal stresses from uniform temperature change. The mirror surface profile can be obtained by integrating the curvature profile to its second order and further corrected by moving constant values for the slope and height. The technical process is simulated by finite element analysis (FEA). A case study showed that the residual slope error and the residual height error between the desired shape and the FEA result are 0.22 µrad (r.m.s.) and 1.42 nm (r.m.s.), respectively.

47 OTHER INSTRUMENTATION↗

Re-evaluating probable maximum precipitation estimates: sensitivity to transposition domains and storm rotation using modern datasets

This study examines the sensitivity of Probable Maximum Precipitation (PMP) estimates to key methodological decisions embedded in the legacy approach adopted in the U.S. National Weather Service Hydrometeorological Reports No. 51 and No. 52. Although widely used for infrastructure design and risk regulation, fundamental aspects of PMP estimation—such as storm sample size, transposition domain, maximization procedures, and storm rotation—remain poorly constrained and lack formal guidance. Using the Red Rock watershed in Iowa as a case study, and leveraging the 2002–2023 NOAA Analysis of Record for Calibration (AORC) precipitation dataset, we systematically evaluate how each methodological choice, individually and in combination, influences PMP estimates. Our findings demonstrate that PMP is not a fixed physical upper bound but rather a modeling construct shaped heavily by user-defined assumptions. Notably, PMP values derived from modern gridded rainfall datasets can be substantially higher than the legacy estimate used in the original spillway design for Red Rock Dam. Decisions regarding storm sample size, domain extent, climatological window, and particularly storm rotation all contributed to higher PMP estimates. Storm rotation alone—a loosely constrained element in the current PMP practice—can amplify PMP by more than 25%. These results reveal the lack of standardized bounds in current PMP workflows and the need for systematic sensitivity and uncertainty analysis. As PMP estimation shifts toward probabilistic approaches, incorporating physically meaningful storm attributes will be key to developing more transparent, defensible methods for dam safety and climate-resilient infrastructure.

Probable maximum precipitation↗

Atom depth analysis delineates mechanisms of protein intermolecular interactions

Highlights: •3D atom depth analysis is proposed to identify different layers in protein structures. •Amino acid contents for each layers have been analyzed for a large protein dataset. •Charged amino acids in the most external layer are present at very different extents. •Atom depth indexes of K residues reflect their side chains flexibility. •Mobile surface charges can be responsible for long range protein–protein recognition. -- Abstract: The systematic analysis of amino acid distribution, performed inside a large set of resolved protein structures, sheds light on possible mechanisms driving non random protein–protein approaches. Protein Data Bank entries have been selected using as filters a series of restrictions ensuring that the shape of protein surface is not modified by interactions with large or small ligands. 3D atom depth has been evaluated for all the atoms of the 2,410 selected structures. The amino acid relative population in each of the structural layers formed by grouping atoms on the basis of their calculated depths, has been evaluated. We have identified seven structural layers, the inner ones reproducing the core of proteins and the outer one incorporating their most protruding moieties. Quantitative analysis of amino acid contents of structural layers identified, as expected, different behaviors. Atoms of Q, R, K, N, D residues are increasingly more abundant in going from core to surfaces. An opposite trend is observed for V, I, L, A, C, and G. An intermediate behavior is exhibited by P, S, T, M, W, H, F and Y. The outer structural layer hosts predominantly E and K residues whose charged moieties, protruding from outer regions of the protein surface, reorient free from steric hindrances, determining specific electrodynamics maps. This feature may represent a protein signature for long distance effects, driving the formation of encounter complexes and the eventual short distance approaches that are required for protein–protein functional interactions.

60 APPLIED LIFE SCIENCES↗

An optimization method for flexural bearing design for high-stroke high-frequency applications

A method for optimization of a high-stroke, high-frequency flexural bearing was completed. The main goal was to design a flexural bearing system as the energy restoration component of a one kW free piston linear engine alternator (LEA) operating at 90 Hz and maximum targeted displacement of 22 mm. Defined electricity output of 1 kW, with more than 30% efficiency, required engine operation under high speed and high stroke conditions. Under such challenging stroke and frequency requirements, a method of design was required to select between a wide range of parameters in flexural bearing design. A parametric CAD model was prepared and used in the optimization package of a finite element analysis (FEA) software. Four main parameters of flexural bearing geometry were identified and included the outer diameter, thickness, number of arms, and sweep angle of spiral cuts. Other design parameters including spiral gap width, shape factor and spiral start points angle were shown to be less important compared to these four main parameters in primary design and were examined separately. A neural network algorithm was used to investigate the interactions and effects of design parameters. The sensitivity of each parameter on output criteria such as maximum stress and natural frequency was examined and design charts developed. Methods for further modification of the spiral curve at end points were introduced to reduce the maximum stress level by up to 20%. Several steel alloys and a titanium-based alloy were identified as proper material candidates for high cycle applications and the final designed spring was manufactured and tested to validate the FEA results of axial stiffness and strain level throughout the flexure arms. The percent of the flexure’s moving mass was estimated to be 29% with FEA analysis and compared well with the experimental value of 31%. The stress/strain results of the FEA analysis matched with the experimental results – within ±5%.

42 ENGINEERING↗

Evidence for triaxial shape coexistence in 74 Ge

The deformation properties of the low-lying states in 74 Ge have been investigated using multistep Coulomb excitation. The measurements were carried out with the advanced 𝛾-ray tracking array, GRETINA, and the CHICO2 particle detector. A comprehensive set of 𝐸⁢2 transition and diagonal matrix elements was deduced following an analysis with the semiclassical coupled-channels code GOSIA. The data were compared with results of calculations carried out within the framework of the generalized triaxial rotor model as well as with the configuration interaction shell model and the symmetric rotor model. Results from calculations with covariant density functional theory were used to construct a five-dimensional collective Hamiltonian for further comparisons with the data. Collectively, the calculations provide an accurate reproduction of the experimental matrix elements and further support an understanding in terms of the coexistence of two axially asymmetric shapes. In conclusion, this leads to an overall interpretation of the underlying structure of 74 Ge requiring triaxiality, as is also the case in the neighboring even-mass Ge isotopes.

59 ≤ A ≤ 89↗

Diversity, taxonomy, and evolution of archaeal viruses of the class Caudoviricetes

The archaeal tailed viruses (arTV), evolutionarily related to tailed double-stranded DNA (dsDNA) bacteriophages of the class Caudoviricetes , represent the most common isolates infecting halophilic archaea. Only a handful of these viruses have been genomically characterized, limiting our appreciation of their ecological impacts and evolution. Here, we present 37 new genomes of haloarchaeal tailed virus isolates, more than doubling the current number of sequenced arTVs. Analysis of all 63 available complete genomes of arTVs, which we propose to classify into 14 new families and 3 orders, suggests ancient divergence of archaeal and bacterial tailed viruses and points to an extensive sharing of genes involved in DNA metabolism and counterdefense mechanisms, illuminating common strategies of virus–host interactions with tailed bacteriophages. Coupling of the comparative genomics with the host range analysis on a broad panel of haloarchaeal species uncovered 4 distinct groups of viral tail fiber adhesins controlling the host range expansion. The survey of metagenomes using viral hallmark genes suggests that the global architecture of the arTV community is shaped through recurrent transfers between different biomes, including hypersaline, marine, and anoxic environments.

59 BASIC BIOLOGICAL SCIENCES↗

Effects of Inorganic Antiseptic on the Properties of Zein-Based Active Films

Zein, one of corn processing byproducts, has excellent film-forming ability. However, zein does not have intrinsic antibacterial or antioxidant activity which limits its direct applicability as active food packaging material. In the present study, the rod-shaped micro-sized ZnO crystals were incorporated into zein films to construct zein-based active films as active packaging material with antibacterial property. The morphologies, structural analysis and sizes of ZnO crystals were analyzed by field emission scanning electron microscope and X-ray diffraction. Prepared zein films were evaluated for ZnO loading and distribution. Furthermore, antibacterial activities on Gram-negative bacteria and Gram-positive bacteria were tested by using the disc diffusion method. Lastly, the stability of zein-based active films under the different storage temperature and humidity was investigated. The results showed that zein based-active films had well mechanical properties, stability and antibacterial activities, which were related to the sizes of ZnO crystals in films.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

A three-dimensional meso-scale approach to concrete fracture based on combined DEM with X-ray μCT images

Highlights: • We investigate fracture in concrete beams subjected to 3-point bending. • We use a discrete element method (DEM) to capture fracture. • Concrete is described as 4-phase material. • Evolution of micro-structural phenomena is investigated. • The 3D results are carefully compared with the 2D ones. - Abstract: The paper shows three-dimensional (3D) numerical mesoscopic results on progressive concrete fracture at aggregate level in a notched concrete beam under bending. A classical particle discrete element method was used to capture fracture in concrete. Heterogeneity was taken into account with a 4-phase concrete description: aggregate, cement matrix, macro-voids and interfacial transitional zones. Both the real shape and location of aggregate particles in concrete were assumed in DEM analyses based on X-ray μCT scans. A satisfactory agreement in terms of the vertical force versus crack mouth opening displacement evolution and crack geometry was achieved between DEM analyses and own laboratory tests. The evolution of broken contacts, contact normal forces, particle rotations, internal energies was studied at the aggregate level. The 3D results were also carefully compared with the 2D ones. The 3D model proved to be a promising simulation tool in predicting concrete fracture at the mesoscopic and macroscopic level.

36 MATERIALS SCIENCE↗

A fusion relevant data-driven engineering void swelling model for 9Cr tempered martensitic steels

The UCSB database on cavity evolution in 9-12Cr tempered martensitic steels (TMS), includes the results for both dual heavy and helium ion (DII), and High Flux Isotope Reactor (HFIR) in situ helium injection (ISHI) neutron irradiations at 500°C. These results were combined with literature single ion and fission neutron irradiation data to derive a model for the void volume fraction, f v , as a function of displacements per atom (dpa) and transmutant helium concentrations in atomic parts per million (appm). The scientific foundation for the paper is described in a companion paper entitled “Cavity Evolution and Void Swelling in Dual Ion Irradiated Tempered Martensitic Steels”. Here, in this study, we show that f v (dpa, He/dpa) is described by the incubation dose, dpa i , for the onset of void growth, and the post-incubation growth rate, f v ’(%/dpa). Both dpa i and f v ’ decrease with increasing He/dpa at > ~ 5. The dpa i is also lower for the ISHI neutron irradiations at the same He/dpa. Single heavy ion and fission reactor neutron irradiations, with low He/dpa ratios, have a much larger dpa i . Based on a combined analysis of DII, single ion, ISHI and fission neutron data, we further show that the post-incubation f v data analyzed here have a common empirical curve shape, with f v ’ reaching up to ~ 0.2%/dpa at very high dpa. We also show that f v ’ can be predicted based on a physical model of defect partitioning between evolving sinks. At 500°C and fusion relevant He/dpa ≈ 10, the best-fit model predicts nominal swelling, S = f v /(1-f v ), of ~ 1.1, 4.9 and 16% at 50, 100 and 200 dpa, respectively. The physically motivated, data-driven model includes estimated uncertainties for both dpa i and f v ’.

36 MATERIALS SCIENCE↗

Structural properties of ultrafine Ba-hexaferrite nanoparticles

Crystal structure of ultrafine Ba-hexaferrite (BaFe{sub 12}O{sub 19}) nanoparticles was studied using X-ray diffractometry (XRD), high-resolution transmission electron microscopy (HRTEM), energy-dispersive X-ray spectroscopy (EDXS), X-ray absorption fine structure (XAFS), and Moessbauer spectroscopy (MS), to be compared to the structure of larger nanoparticles and the bulk. The nanoparticles were synthesized with hydrothermal treatment of an appropriate suspension of Ba and Fe hydroxides in the presence of a large excess of OH{sup -}. The ultrafine nanoparticles were formed in a discoid shape, {approx}10 nm wide and only {approx}3 nm thick, comparable to the size of the hexagonal unit cell in the c-direction. The HRTEM image analysis confirmed the hexaferrite structure, whereas EDXS showed the composition matching the BaFe{sub 12}O{sub 19} formula. XAFS and MS analyses showed considerable disorder of the structure, most probably responsible for the low magnetization. - Graphical abstract: Left: HREM image of an ultrafine Ba-hexaferrite nanoparticle (inset: TEM image of the nanoparticles); Right: the experimental HRTEM image is compared with calculated image and corresponding atomic model. Highlights: Black-Right-Pointing-Pointer Crystal structure of ultrafine Ba-hexaferrite (BaFe{sub 12}O{sub 19}) nanoparticles was compared to the structure of the bulk. Black-Right-Pointing-Pointer Thickness the discoid nanoparticles was comparable to the size of the hexagonal unit cell in the c-direction. Black-Right-Pointing-Pointer Considerable disorder of the nanoparticles' structure is most probably responsible for their low magnetization.

36 MATERIALS SCIENCE↗

Analysis of the functional gene structure and metabolic potential of microbial community in high arsenic groundwater

Microbial functional potential in high arsenic (As) groundwater ecosystems remains largely unknown. In this study, the microbial community functional composition of nineteen groundwater samples was investigated using a functional gene array (GeoChip 5.0). Samples were divided into low and high As groups based on the clustering analysis of geochemical parameters and microbial functional structures. The results showed that As related genes (arsC, arrA), sulfate related genes (dsrA and dsrB), nitrogen cycling related genes (ureC, amoA, and hzo) and methanogen genes (mcrA, hdrB) in groundwater samples were correlated with As, SO 4 2- , NH 4 + or CH 4 concentrations, respectively. Canonical correspondence analysis (CCA) results indicated that some geochemical parameters including As, total organic content, SO 4 2- , NH 4 + , oxidation-reduction potential (ORP) and pH were important factors shaping the functional microbial community structures. Alkaline and reducing conditions with relatively low SO 4 2- , ORP, and high NH 4 + , as well as SO 4 2- and Fe reduction and ammonification involved in microbially-mediated geochemical processes could be associated with As enrichment in groundwater. This study provides an overall picture of functional microbial communities in high As groundwater aquifers, and also provides insights into the critical role of microorganisms in As biogeochemical cycling.

59 BASIC BIOLOGICAL SCIENCES↗

CRAGE-RB-PI-seq reveals transcriptional dynamics of plant-associated bacteria during root colonization

Plant roots release a wide array of metabolites into the rhizosphere, shaping microbial communities and their functions. While metagenomics has expanded our understanding of these communities, little is known about the physiology of their members in host environments. Transcriptome analysis via RNA sequencing is a common approach to learning more, but its use has been challenging because of low bacterial biomass and interference from plant RNA. To overcome this, we developed a randomly-barcoded promoter-library insertion sequencing (RB-PI-seq) combined with chassis-independent recombinase-assisted genome engineering (CRAGE). Using Pseudomonas simiae WCS417 as a model rhizobacterium, this method enabled targeted amplification of barcoded transcripts, bypassing plant RNA interference and allowing measurement of thousands of promoter activities during Arabidopsis root colonization. Our analysis revealed temporally resolved transcriptional regulation, including those associated with cell growth, chemotaxis, plant immune suppression, biofilm formation, and stress responses, reflecting the coordinated physiological adaptation to the root environment. Additionally, we discovered that transcriptional activation of xanthine dehydrogenase and a lysozyme inhibitor is crucial for evading plant immune systems. This framework is scalable to other bacterial species and provides new opportunities for understanding rhizobacterial gene regulation in native environments.

59 BASIC BIOLOGICAL SCIENCES↗

Structural investigation and microwave characteristics of (Ba{sub 0.2}La{sub 0.8})Fe{sub 0.2}Mn{sub 0.4}Ti{sub 0.4}O{sub 3} absorbing materials

Synthesis and characterization of (Ba{sub 0.2}La{sub 0.8})Fe{sub 0.2}Mn{sub 0.4}Ti{sub 0.4}O{sub 3} absorbing material by mechanical alloying process has been performed. The absorbing material was prepared by oxide materials, namely BaCO{sub 3}, La{sub 2}O{sub 3}, TiO{sub 2}, Fe{sub 2}O{sub 3}, and MnCO{sub 3}. The mixture was milled for 10 h and then sintered at a temperature of 1000 ° C for 10 h. The refinement results of x-ray diffraction pattern of lanthanum manganite substituted with barium showed that the sample consisted of two phases, namely, La{sub 0.9125}MnO{sub 3} phase which has a structure monoclinic (I12/a1) with lattice parameters a = 5.527(1) Å, b = 5.572(1) Å and c = 7.810(1) Å, α = γ = 90° and β = 89.88(5)°, the unit cell volume of V = 240.57(8) Å{sup 3}, and the atomic density of ρ = 6.238 gr.cm{sup −3}. The microstructure analyses showed that the particle shapes was polygonal with the varied particle sizes of 1 ∼ 3 μm distributed homogeneously on the surface of the samples. The results of the electromagnetic wave absorption curve analysis by using a vector network analyzer (VNA) showed that the sample can absorb microwaves in the frequency range of 8-15 GHz with a very wide absorption bandwidth. It indicates that the as prepared absorber presents potential absorbing property in X and Ku-band. We concluded that the (Ba{sub 0.2}La{sub 0.8})Fe{sub 0.2}Mn{sub 0.4}Ti{sub 0.4}O{sub 3} material can be applied as a candidate absorber material of microwaves or electromagnetic wave.

36 MATERIALS SCIENCE↗

Photoemission electron microscopy of localized surface plasmons in silver nanostructures at telecommunication wavelengths

We image the field enhancement at Ag nanostructures using femtosecond laser pulses with a center wavelength of 1.55 μm. Imaging is based on non-linear photoemission observed in a photoemission electron microscope (PEEM). The images are directly compared to ultra violet PEEM and scanning electron microscopy (SEM) imaging of the same structures. Further, we have carried out atomic scale scanning tunneling microscopy on the same type of Ag nanostructures and on the Au substrate. Measuring the photoelectron spectrum from individual Ag particles shows a larger contribution from higher order photoemission processes above the work function threshold than would be predicted by a fully perturbative model, consistent with recent results using shorter wavelengths. Investigating a wide selection of both Ag nanoparticles and nanowires, field enhancement is observed from 30% of the Ag nanoparticles and from none of the nanowires. No laser-induced damage is observed of the nanostructures neither during the PEEM experiments nor in subsequent SEM analysis. By direct comparison of SEM and PEEM images of the same nanostructures, we can conclude that the field enhancement is independent of the average nanostructure size and shape. Instead, we propose that the variations in observed field enhancement could originate from the wedge interface between the substrate and particles electrically connected to the substrate.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Comparison of prestellar core elongations and large-scale molecular cloud structures in the Lupus I region

Turbulence and magnetic fields are expected to be important for regulating molecular cloud formation and evolution. However, their effects on sub-parsec to 100 parsec scales, leading to the formation of starless cores, are not well understood. We investigate the prestellar core structure morphologies obtained from analysis of the Herschel-SPIRE 350 μm maps of the Lupus I cloud. This distribution is first compared on a statistical basis to the large-scale shape of the main filament. We find the distribution of the elongation position angle of the cores to be consistent with a random distribution, which means no specific orientation of the morphology of the cores is observed with respect to the mean orientation of the large-scale filament in Lupus I, nor relative to a large-scale bent filament model. This distribution is also compared to the mean orientation of the large-scale magnetic fields probed at 350 μm with the Balloon-borne Large Aperture Telescope for Polarimetry during its 2010 campaign. Here again we do not find any correlation between the core morphology distribution and the average orientation of the magnetic fields on parsec scales. Our main conclusion is that the local filament dynamics—including secondary filaments that often run orthogonally to the primary filament—and possibly small-scale variations in the local magnetic field direction, could be the dominant factors for explaining the final orientation of each core.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmic bubble and domain wall instabilities I: parametric amplification of linear fluctuations

This is the first paper in a series where we study collisions of nucleated bubbles taking into account the effects of small initial (quantum) fluctuations in a fully 3+1-dimensional setting. In this paper, we consider the evolution of linear fluctuations around highly symmetric though inhomogeneous backgrounds. In particular, we demonstrate that a large degree of asymmetry develops over time from tiny initial fluctuations superposed upon planar and SO(2,1) symmetric backgrounds. These fluctuations are inevitable consequences of zero-point vacuum oscillations, so excluding them by enforcing a high degree of spatial symmetry is inconsistent in a quantum treatment. To simplify the analysis we consider the limit of two colliding planar walls, with mode functions for the fluctuations characterized by the wavenumber transverse to the collision direction and a longitudinal shape along the collision direction x, which we solve for. In the linear regime, the fluctuations obey a linear wave equation with a time- and space-dependent mass m{sub eff}(x,t). In situations where the walls collide multiple times, m{sub eff} oscillates in time. We use Floquet theory to study the evolution of the fluctuations and generalize the calculations familiar from the preheating literature to the case with many coupled degrees of freedom. The inhomogeneous case has bands of unstable transverse wavenumbers k{sub ⊥} whose corresponding mode functions grow exponentially. By examining the detailed spatial structure of the mode functions in x, we identify both broad and narrow parametric resonance generalizations of the homogeneous m{sub eff}(t) case of preheating. The unstable k{sub ⊥} modes are longitudinally localized, yet can be described as quasiparticles in the Bogoliubov sense. We define an effective occupation number and show they are created in bursts for the case of well-defined collisions in the background. The transverse-longitudinal coupling accompanying nonlinearity radically breaks this localized particle description, with nonseparable 3D modes arising that will be studied in subsequent papers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Angular dependence of primordial trispectra and CMB spectral distortions

Under the presence of anisotropic sources in the inflationary era, the trispectrum of the primordial curvature perturbation has a very specific angular dependence between each wavevector that is distinguishable from the one encountered when only scalar fields are present, characterized by an angular dependence described by Legendre polynomials. We examine the imprints left by curvature trispectra on the TT μ bispectrum, generated by the correlation between temperature anisotropies (T) and chemical potential spectral distortions (μ) of the Cosmic Microwave Background (CMB). Due to the angular dependence of the primordial signal, the corresponding TT μ bispectrum strongly differs in shape from TT μ sourced by the usual g {sub NL} or τ{sub NL} local trispectra, enabling us to obtain an unbiased estimation. From a Fisher matrix analysis, we find that, in a cosmic-variance-limited (CVL) survey of TT μ, a minimum detectable value of the quadrupolar Legendre coefficient is d {sub 2} ∼ 0.01, which is 4 orders of magnitude better than the best value attainable from the TTTT CMB trispectrum. In the case of an anisotropic inflationary model with a f (φ) F {sup 2} interaction (coupling the inflaton field φ with a vector kinetic term F {sup 2}), the size of the curvature trispectrum is related to that of quadrupolar power spectrum asymmetry, g {sub *}. In this case, a CVL measurement of TT μ makes it possible to measure g {sub *} down to 10{sup −3}.

79 ASTRONOMY AND ASTROPHYSICS↗