Determination Of Radius Research Articles

Optical Determination of the Internal Capillary Diameter Used in Taylor Dispersion Analysis.

In this work, we describe an optical setup to determine the internal diameter of narrow bore fused silica capillary used in capillary electrophoresis and Taylor dispersion analysis (TDA). Indeed, fluctuations up to about±3-4µm on the capillary I.D. can generate important inaccuracy on the hydrodynamic radius determination by TDA. Calibration of the optical set-up, impact of the operator and of the placement of the capillary in the focal plane, and the influence of the way to cut the capillary were investigated and discussed. This optical set-up was next used to determine capillary I.D. on a 60 m long capillary spool. Relatively small variations were observed along a 60 m capillary spool (0.3µm maximum variation), while important I.D. fluctuations can be observed from capillary batch to batch. Taking three capillaries of three different nominal I.D. values, Rh values of sodium benzoate obtained by TDA were not significantly different if the capillary I.D. were optically measured, while significant variations were observed with the nominal I.D. values. A protocol based on TDA of sodium benzoate was proposed for calibrating narrow bore fused silica capillary I.D. without the use of optical measurements for researchers that would not have access to such optical equipment.

High-precision non-contact online measurement and predictive analysis of geometric parameters in large industrial components

Obtaining precise geometric parameters is fundamental in industry but often proves challenging, particularly for large-scale and irregularly shaped industrial components. This study introduces an innovative measurement method enabling precise determination of chord length, arc length, and curvature radius in curved sections of such components, even within dynamic industrial environments. Our solution relies on the implementation of a LiDAR sensor and the utilization of data processing techniques, including outlier detection and removal, as well as customized digital filters. Additionally, we incorporate analytic geometry to address specific measurement challenges. Finally, Machine Learning techniques were applied to forecast time series data of the measurements. The proposed system was validated in a real-world wind turbine tower manufacturing environment, comparing them with manual measurements performed by experienced operators. This validation confirms its effectiveness of our approach, achieving the industry-required minimum tolerances of 5 millimeters, where precise geometric data acquisition is crucial to ensure product quality.

On the use of dioxane as reference for determination of the hydrodynamic radius by NMR spectroscopy

Measuring the compaction of a protein or complex is key to our understanding of the interactions within and between biomolecules. Experimentally, protein compaction is often probed either by estimating the radius of gyration (Rg) obtained from small-angle x-ray scattering (SAXS) experiments or the hydrodynamic radius (Rh) obtained, for example, by pulsed field gradient NMR (PFG NMR) spectroscopy. PFG NMR experiments generally report on the translational diffusion coefficient, which in turn can be used to estimate Rh using an internal standard to account for sample viscosity and uncertainty about the gradient strength. 1,4-Dioxane is one such commonly used internal standard, and the reference value of Rh is therefore important. We have revisited the basis for the commonly used reference value for the Rh of dioxane (2.12 Å) that is used to convert measured diffusion coefficients into a hydrodynamic radius. We followed the same approach that was used to establish the current reference value by measuring SAXS and PFG NMR data for a set of seven different proteins and using these as standards. Our analysis shows that the current Rh reference value for dioxane Rh is underestimated, and we instead suggest a new value of 2.27 ± 0.04 Å. Using this updated reference value results in a ∼7% increase in Rh values for proteins whose hydrodynamic radii have been measured by PFG NMR. These results are particularly important when the absolute value of Rh is of interest such as when determining or validating ensemble descriptions of intrinsically disordered proteins.

Do anomalously dense hot Jupiters orbit stealth binary stars?

ABSTRACT The Wide Angle Search for Planets (WASP) survey used transit photometry to discover nearly 200 gas-giant exoplanets and derive their planetary and stellar parameters. Reliable determination of the planetary density depends on accurate measurement of the planet’s radius, obtained from the transit depth and photodynamical determination of the stellar radius. The stellar density and hence the stellar radius are typically determined in a model-independent way from the star’s reflex orbital acceleration and the transit profile. Additional flux coming from the system due to a bright, undetected stellar binary companion can, however, potentially dilute the transit curve and radial velocity signal, leading to underestimation of the planet’s mass and radius, and to overestimation of the planet’s density. In this study, we cross-check the published radii of all the WASP planet-host stars, determined from their transit profiles and radial velocity curves, against radiometric measurements of stellar radii derived from their angular diameters (via the infrared flux method) and trigonometric parallaxes. We identify eight systems showing radiometric stellar radii significantly greater than their published photodynamical values: WASPs 20, 85, 86, 103, 105, 129, 144, and 171. We investigate these systems in more detail to establish plausible ranges of angular and radial velocity separations within which such ‘stealth binaries’ could evade detection, and deduce their likely orbital periods, mass ratios, and flux ratios. After accounting for the dilution of transit depth and radial velocity amplitude, we find that, on average, the planetary densities for the identified stealth binary systems should be reduced by a factor of 1.3.

Preventing the impact of solute adsorption in Taylor dispersion analysis: Application to protein and lipid nanoparticle analysis

Taylor Dispersion Analysis (TDA) allows diffusion coefficient (D) or hydrodynamic radius (Rh) determination on a wide range of size between angstroms and about 300 nm. However, solute adsorption phenomena can affect the repeatability and reproducibility of TDA. Several numerical studies addressed the theoretical impact of solute adsorption in TDA, but very few experimental studies focus on this topic and no experimental methodologies were proposed so far to reduce the impact of adsorption in TDA. In this work, an experimental protocol, called plug-in-front TDA, consisting of adding the solute in the eluent at a lower concentration compared to the injected sample, was proposed to strongly limit the impact of adsorption on the Rh determination. This protocol was suggested based on the evidence that adsorption / desorption phenomena impacting narrow bore fused silica TDA in aqueous conditions are typically slow processes that can be counteracted by saturating the interaction sites during the experiments. Successful applications to proteins and mRNA lipid nanoparticles (LNP) in vaccine against Covid 19 and protein analysis were reported. TDA of proteins in conditions of strong interactions with the capillary surface was possible using the plug-in-front methodology. We anticipate that such experimental methodology will greatly help the experimentalist for implementing TDA in various applications.

Accurate and Model-independent Radius Determination of Single FGK and M Dwarfs Using Gaia DR3 Data

Measuring fundamental stellar parameters is key to fully comprehending the evolution of stars. However, current theoretical models overpredict effective temperatures, and underpredict radii, compared to observations of K and M dwarfs (radius inflation problem). In this work, we have developed a model-independent method to infer precise radii of single FGK and M dwarfs using Gaia DR3 parallaxes and photometry, and used it to study the radius inflation problem. We calibrated nine surface brightness–color relations for the three Gaia magnitudes and colors using a sample of stars with angular diameter measurements. We achieved an accuracy of 4% in our angular diameter estimations, which Gaia’s parallaxes allow us to convert to physical radii. We validated our method by comparing our radius measurements with literature samples and the Gaia DR3 catalog, which confirmed the accuracy of our method and revealed systematic offsets in the Gaia measurements. Moreover, we used a sample with measured Hα equivalent width (Hα EW), a magnetic activity indicator, to study the radius inflation problem. We demonstrated that active stars have larger radii than inactive stars, showing that radius inflation is correlated with magnetic activity. We found a correlation between the radius inflation of active stars and Hα EW for the mass bin 0.5 < M[M ⊙] ≤ 0.6, but we found no correlation for lower masses. This could be due to lack of precision in our radius estimation or a physical reason. Radius measurements with smaller uncertainties are necessary to distinguish between the two scenarios.

Neutron radius determination of 133Cs and its impact on the interpretation of CEνNS-CsI measurement

Proton-133Cs elastic scattering at low momentum transfer is performed using an in-ring reaction technique at the Cooler Storage Ring at the Heavy Ion Research Facility in Lanzhou. Recoil protons from the elastic collisions between the internal H2-gas target and the circulating 133Cs ions at 199.4 MeV/u are detected by a silicon-strip detector. The matter radius of 133Cs is deduced by describing the measured differential cross sections using the Glauber model. Employing the adopted proton distribution radius, a point-neutron radius of 4.86(21) fm for 133Cs is obtained. With the newly determined neutron radius, the weak mixing angle sinθW2 is independently extracted to be 0.227(28) by fitting the coherent elastic neutrino-nucleus scattering data. Our work limits the sinθW2 value in a range smaller than the ones proposed by the previous independent approaches, and would play an important role in searching new physics via the high precision CEνNS-CsI cross section data in the future.

Neutron Skins: Weak Elastic Scattering and Neutron Stars

The recently completed PREX-2 campaign measured the density distribution of neutrons in the lead nucleus as a function of momentum transfer (the form factor), confirmed a relatively large extent of the neutrons beyond the protons in the nucleus (the neutron skin), and provided a precise determination of the density of protons and neutrons at the center of a heavy nucleus. In turn, the measured form factor can be related to various nuclear and neutron star properties. The NICER X-ray telescope has inferred the masses and radii of some X-ray pulsars (neutron stars), although complications arise when determining these quantities independently. Further improvements in NICER have enabled simultaneous mass–radius determinations that had not previously been possible. During the next decade, measurements in astrophysics, gravitational-wave astronomy, and nuclear physics are expected to provide a wealth of more precise data. In this review, we present an overview of the current state of neutron skin measurements and offer insights into prospects for the future.

Influence of Orbit and Mass Constraints on Reflected Light Characterization of Directly Imaged Rocky Exoplanets

Survey strategies for upcoming exoplanet direct imaging missions have considered varying assumptions of prior knowledge. Precursor radial velocity surveys could have detected nearby exo-Earths and provided prior orbit and mass constraints. Alternatively, a direct imaging mission performing astrometry could yield constraints on the orbit and phase angle of target planets. Understanding the impact of prior mass and orbit information on planetary characterization is crucial for efficiently recognizing habitable exoplanets. To address this question, we use a reflected-light retrieval tool to infer the atmospheric and bulk properties of directly imaged Earth-analogs while considering varying levels of prior information and signal-to-noise ratio (S/N). Because of the strong correlation between the orbit-related parameters and the planetary radius, prior information on the orbital distance and planetary phase angle yield much tighter constraints on the planetary radius: from Rp=2.95−1.95+2.69R⊕ without prior knowledge, to Rp=1.01−0.19+0.33R⊕ with prior determination of the orbit for S/N = 20 in the visible/near-infrared spectral range, thus allowing size determination from reflected light observations. However, additional knowledge of planet mass does not notably enhance radius ( Rp=0.98−0.14+0.17R⊕ ) or atmospheric characterization. Also, prior knowledge of the mass alone does not yield a tight radius constraint ( Rp=1.64−0.80+1.29R⊕ ) nor improves atmospheric composition inference. By contrast, because of its sensitivity to gas column abundance, detecting a Rayleigh scattering slope or bounding Rayleigh opacity helps to refine gas mixing ratio inferences without requiring prior mass knowledge. Overall, apart from radius determination, increasing the S/N is more beneficial than additional prior observations.

Mechanism of temporal interface evolution and internal circulations during the droplet formation in a planar slit T-microchannel

The present study has numerically explored the mechanism of interface evolution and internal flow circulations during the droplet formation in two-phase flow through a planar T-microchannel. The two-dimensional unsteady form of the conservative level set equation coupled with Navier–Stokes equations has been solved using the finite element method. The range of parameters include the contact angle (θ) from 120° to 180°, and the flow rate ratio (Qr) from 0.1 to 10 for the low capillary number (Cac≤10−2). The present study indicates that surface wettability plays a crucial role in influencing the temporal evolution of the interface. The internal flow circulation in the droplet is controlled by the axial and radial velocities primarily influenced by shear stress. The newly introduced novel “interface-to-neck ratio” parameter has provided another platform to investigate the pinch-off dynamics of droplets. Moreover, the phenomenon of droplet pinch-off is primarily initiated and driven by the Laplace pressure, defined by three distinct approaches: the pressure difference method, the determination of the minimum local radius of curvature on the rear side, and a calculation of the neck width. The predictive correlations have been established to estimate the droplet characteristics as a function of the flow rate ratio and contact angle. The findings reported have significant implications for the design of droplet dispensing systems that depend on surface wettability as a critical regulating parameter.

MFFC-SDN: multi-level feature fusion codec-based ship detection network in SAR images

ABSTRACT In recent years, with the development of deep learning, SAR image-based ship target-detection technology has become a current research hotspot. SAR images are characterized by complex backgrounds, significant speckle noise interference, and poor interpretability. To address this challenge, this study proposes a new Gaussian circle radius determination strategy and a multi-level feature fusion codec-based ship detection network (MFFC-SDN) for SAR images. Differing from CenterNet’s corner-oriented Gaussian circle strategy, the Gaussian circle strategy proposed in this paper takes the centre point coordinates of the real target as the origin to define a circular region. This approach allows for more precise supervision of the training model. Meanwhile, we propose MFFC-SDN to solve the problem of the poor performance of CenterNet in SAR ship detection. MFFC-SDN is an anchor-free, single-stage target-detection method with a low computation cost. In MFFC-SDN, we introduce a Multilevel Feature Recapture Codec Module (MFR-CM) to enhance the feature extraction capability of the network by using the features of the encoding stage twice because of the easy loss of image features in the lengthy codec process of the CenterNet network backbone. A Residual Attention Pyramid Feature Fusion Module (RA-PFFM) is designed to enhance the feature map and obtain multi-scale features. Experimental results on the SSDD and SAR-ship-dataset show that MFFC-SDN significantly enhances SAR image target-detection performance, effectively addressing detection challenges related to large target size variations and complex environmental conditions. Compared with existing algorithms, MFFC-SDN achieves the highest A P 50 .

Momentum dependent flavor radiative corrections to the coherent elastic neutrino-nucleus scattering for the neutrino charge-radius determination

Despite being neutral particles, neutrinos can have a non-zero charge radius, which represents the only non-null neutrino electromagnetic property in the standard model theory. Its value can be predicted with high accuracy and its effect is usually accounted for through the definition of a radiative correction affecting the neutrino couplings to electrons and nucleons at low energy, which results effectively in a shift of the weak mixing angle. Interestingly, it introduces a flavour-dependence in the cross-section. Exploiting available neutrino-electron and coherent elastic neutrino-nucleus scattering (CEνNS) data, there have been many attempts to measure experimentally the neutrino charge radius. Unfortunately, the current precision allows one to only determine constraints on its value. In this work, we discuss how to properly account for the neutrino charge radius in the CEνNS cross-section including the effects of the non-null momentum-transfer in the neutrino electromagnetic form factor, which have been usually neglected when deriving the aforementioned limits. We apply the formalism discussed to a re-analysis of the COHERENT cesium iodide and argon samples and the NCC-1701 germanium data from the Dresden-II nuclear power plant. We quantify the impact of this correction on the CEνNS cross-section and we show that, despite being small, it can not be neglected in the analysis of data from future high-precision experiments. Furthermore, this momentum dependence can be exploited to significantly reduce the allowed values for the neutrino charge radius determination.

Energy induced carbon nanotube rapidly assemble variable interweaving networks at the carbon fiber interface

Regulating carbon fiber with carbon nanotubes (CNTs) is important to improve the interface mechanical properties of composite materials. Therefore, a “thermotropic flash assembly (TFA)” process for the synthesis of CNTs in liquid phase is proposed. This work achieves the continuous and controllable formation of a micro-nano interweaving network of CNTs, with predictions made from a thermal perspective through enhancements to the process. Firstly, 12 working conditions and a large number of sample data are established by microcontrolling carbon fiber energy, and the growth thickness of CNTs is predicted by self-learning algorithm. Secondly, the “liquid-solid-solid” thermotropic growth of CNTs is proposed for the first time, which is different from the existing “gas-liquid-solid” and “gas-solid-solid” growth mechanisms of CNTs. Theoretical deductions and calculations are made for the interfacial temperature, exothermic, and endothermic energies during the growth process, which leads to the determination of a thermal growth space radius of 2.4 μm at the interface. Finally, it is found that the shear strength is increased by at least 27.7 %, although some tensile strength is sacrificed. This work not only points out the direction for low-cost, large-scale and customized control of interface properties, but also lays a theoretical foundation for exploring the growth mechanism of CNTs in an open environment at low temperature.

The mass-radius relation of exoplanets revisited

Determining the mass-radius ($M$-$R$) relation of exoplanets is important for exoplanet characterization. Here, we present a re-analysis of the $M$-$R$ relations and their transitions using exoplanetary data from the PlanetS catalog, which accounts only for planets with reliable mass and radius determination. We find that "small planets" correspond to planets with masses of up to $ M_ (within 17&lt;!PCT!&gt;) where $R $. Planets with masses between $ and $127 M_ (within 5&lt;!PCT!&gt;) can be viewed as "intermediate-mass" planets, where $R $. Massive planets, or gas giant planets, are found to have masses beyond $127 M_ and an $M$-$R$ relation of $R $. By analyzing the radius-density relation we also find that the transition from "small" to "intermediate" planets occurs at a planetary radius of $ R_ (within 3&lt;!PCT!&gt;). Our results are consistent with previous studies' results and provide an ideal fit for the current measured planetary population.

Geodesic structure, shadow and optical appearance of black hole immersed in Chaplygin-like dark fluid

In this study, we focus on a black hole immersed in a cosmological Chaplygin-like dark fluid (CDF), characterized by the equation of state p = -B/ρ and an additional parameter q influencing the energy density of the fluid. We investigate the geodesic structure, shadow, and optical appearance of such a black hole. Through analysis on the effective potential and the epicyclic frequencies, it is found that the existence of innermost/outermost stable circular orbits for a timelike particle is governed by the CDF parameters. The behaviors of the orbital conserved quantities and Keplerian frequency are also examined. Due to the existence of pseudo-cosmological horizon, the determination of the shadow radius depends significantly on the position of the observer. By placing the static observer at an approximately flat position between the event and pseudo-cosmological horizons, we constrain the CDF parameters using EHT observations. We investigate the effect of CDF on the shadows and optical images of the black hole, surrounded by various profiles of accretions. For the thin disk accretion, the light trajectories are categorized into direct emission, lensing ring, and photon ring based on impact parameters. Due to the existence of outermost stable circular orbits, outer edges could exist in the direct and lensing ring images. The observed brightness is mainly due to direct emission, with a minor contribution from the lensing ring, while the contribution from the photon ring is negligible due to extreme demagnetization. In the case of spherical accretion, we consider both static and infalling accretion models. The images obtained under infalling accretion are slightly darker than those under static accretion, attributed to the Doppler effect. Throughout the study, we analyze the influence of the parameters B and q on the results.

Analysis of a Novel Method for Generating 3D Mesh at Contact Points in Packed Beds

This study comprehensively analyzes the impact of the novel HybridBridge method, developed by the authors, for generating a 3D mesh at contact points within packed beds within the effective thermal conductivity. It compares HybridBridge with alternative methodologies, highlights its superiority and outlines potential applications. The HybridBridge employs two independent geometry parameters to facilitate optimal flow mapping while maintaining physically accurate effective thermal conductivity and ensuring high mesh quality. A method is proposed to estimate the HybridBridge radius for a defined packed bed and cap height, enabling a presimulative determination of a suitable radius. Numerical analysis of a body-centered-cubic unit cell with varied HybridBridges is conducted alongside previous simulations involving a simple-cubic unit cell. Additionally, a physically based resistance model is introduced, delineating effective thermal conductivity as a function of the HybridBridge geometry and porosity. An equation for the HybridBridge radius, tailored to simulation parameters, is derived. Comparison with the unit cells and a randomly packed bed reveals an acceptable average deviation between the calculated and utilized radii, thereby streamlining and refining the implementation of the HybridBridge methodology.

Study of solar brightness profiles in the 18–26 GHz frequency range with INAF radio telescopes

Context. The Sun is an extraordinary workbench, on which several fundamental astronomical parameters can be measured with high precision. Among these parameters, the solar radius R⊙ plays an important role in several aspects, for instance, in evolutionary models. Moreover, it conveys information about the structure of the different layers that compose the solar interior and its atmosphere. Despite the efforts to obtain accurate measurements of R⊙, the subject is still debated, and measurements are puzzling and/or lacking in many frequency ranges. Aims. We determine the mean, equatorial, and polar radii of the Sun (Rc, Req, and Rpol) in the frequency range 18.1 − 26.1 GHz. We employed single-dish observations from the newly appointed Medicina Gavril Grueff Radio Telescope and the Sardinia Radio Telescope (SRT) in five years, from 2018 to mid-2023, in the framework of the SunDish project for solar monitoring. Methods. Two methods for calculating the radius at radio frequencies were employed and compared: the half-power, and the inflection point. To assess the quality of our radius determinations, we also analysed the possible degrading effects of the antenna beam pattern on our solar maps using two 2D models (ECB and 2GECB). We carried out a correlation analysis with the evolution of the solar cycle by calculating Pearson’s correlation coefficient ρ in the 13-month running means. Results. We obtained several values for the solar radius, ranging between 959 and 994 arcsec, and ρ, with typical errors of a few arcseconds. These values constrain the correlation between the solar radius and solar activity, and they allow us to estimate the level of solar prolatness in the centimeter frequency range. Conclusions. Our R⊙ measurements are consistent with the values reported in the literature, and they provide refined estimates in the centimeter range. The results suggest a weak prolateness of the solar limb (Req &gt; Rpol), although Req and Rpol are statistically compatible within 3σ errors. The correlation analysis using the solar images from the Grueff Radio Telescope shows (1) a positive correlation between solar activity and the temporal variation in Rc (and Req) at all observing frequencies, and (2) a weak anti-correlation between the temporal variation of Rpol and solar activity at 25.8 GHz.

Determination of Effective Radius under the Condition of Nonuniform Gas Occurrence and Borehole Plastic Failure.

In order to solve the problem of the blindness of borehole layout when the nonuniform occurrence of gas and the neglect of plastic failure around the borehole will underestimate the gas production, a gas-solid coupling model is established for considering plastic failure. The finite element software COMSOL Multiphysics is used to investigate the evolution of the effective radius during the nonuniform occurrence of gas, and the relationship between the effective radius and the borehole spacing is determined. The results show that the permeability around the borehole increases significantly when plastic failure is considered and the rising area is butterfly shaped, with a maximum increase of 94 times. Not only does the peak value of the gas drainage flow increase but the time of its occurrence is also delayed. The maximum gas drainage flow rate increases by 40.7%, and the cumulative drainage volume increases by 37%. The relationship between the effective radius and reasonable borehole spacing in nonuniform gas occurrence is obtained. This research can provide a reference for the selection of borehole spacing under the condition of nonuniform distribution of coal seam gas.

Design of a microwave spectrometer for high-precision Lamb shift spectroscopy of antihydrogen atoms

We have developed a microwave spectrometer for a measurement of the 2S1/2-2P1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{2S_{1/2}-2P_{1/2}}$$\\end{document} Lamb shift of antihydrogen atoms towards the determination of the antiproton charge radius. The spectrometer consists of two consecutive apparatuses, of which the first apparatus, Hyperfine Selector (HFS), filters out 2S1/2(F=1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{2S_{1/2}(F=1)}$$\\end{document} hyperfine states and pre-selects the 2S1/2(F=0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{2S_{1/2}(F=0)}$$\\end{document} state, and the second apparatus, MicroWave Scanner (MWS), sweeps the frequency around the target transition to obtain the spectrum. We optimized the geometry of the apparatuses by evaluating the S-parameter that represents the ratio of the reflected microwave signal over the input, utilizing microwave simulations based on the finite element method. The HFS was designed to obtain a resonant property at 1.1 GHz for an efficient removal of the 2S1/2(F=1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{2S_{1/2}(F=1)}$$\\end{document} hyperfine states, and the MWS was designed to realize weak frequency-dependency in the signal reflection. Also, the spatial distributions of microwave electric field were simulated. We report the design of the spectrometer and discuss an expected precision of the first measurement.

Isothermal compressibility, internal pressure studies of aqueous rare earth nitrate solutions at 298.15 K: An attempt to estimate ionic radii and understand inner– and outer–sphere exchange water structural interactions

In this communication, we report our analysis and results concerning the determination of ionic radii in aqueous solution phase for Lanthanum (La+3), Neodymium (Nd+3), Erbium (Er+3) and Ytterbium (Yb+3) ions in presence of nitrate (NO3-) anion at 298.15 K. The literature data for density, adiabatic compressibility, and specific heat capacity of solutions at constant pressure have been used to compute isothermal compressibility, internal pressure of solutions in limiting concentration range. The apparent molar isothermal compressibility of electrolytes and hydration numbers have been obtained. The electrostriction for rare earth cations and intrinsic volumes have been calculated using thermodynamic equations. The ionic radii of cations have been obtained using the ionic partial molar volume data of NO3- ions and the results are compared with those obtained for rare earth chlorides. The two series affect is also observed for ionic radii and internal pressure. The results have been explained on the basis of water structural effects due to electrostatic field and water dipole interaction between the inner– and outer–sphere water exchange reaction.