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DOE OSTI2016

Spectroscopic determination of masses (and implied ages) for red giants

The mass of a star is arguably its most fundamental parameter. For red giant stars, tracers luminous enough to be observed across the Galaxy, mass implies a stellar evolution age. It has proven to be extremely difficult to infer ages and masses directly from red giant spectra using existing methods. From the Kepler and apogee surveys, samples of several thousand stars exist with high-quality spectra and asteroseismic masses. Here we show that from these data we can build a data-driven spectral model using The Cannon, which can determine stellar masses to ∼0.07 dex from apogee dr12 spectra of red giants; these imply age estimates accurate to ∼0.2 dex (40%). We show that The Cannon constrains these ages foremost from spectral regions with CN absorption lines, elements whose surface abundances reflect mass-dependent dredge-up. We deliver an unprecedented catalog of 70,000 giants (including 20,000 red clump stars) with mass and age estimates, spanning the entire disk (from the Galactic center to R∼20 kpc). We show that the age information in the spectra is not simply a corollary of the birth-material abundances [Fe/H] and [α/Fe], and that, even within a monoabundance population of stars, there are age variations that vary sensibly with Galactic position. Such stellar age constraints across the Milky Way open up new avenues in Galactic archeology.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

Testing SO(10)-inspired leptogenesis with low energy neutrino experiments

We extend the results of a previous analysis of ours showing that, when both heavy and light flavour effects are taken into account, successful minimal (type I + thermal) leptogenesis with SO(10)-inspired relations is possible. Barring fine tuned choices of the parameters, these relations enforce a hierarchical RH neutrino mass spectrum that results into a final asymmetry dominantly produced by the next-to-lightest RH neutrino decays (N{sub 2} dominated leptogenesis). We present the constraints on the whole set of low energy neutrino parameters. Allowing a small misalignment between the Dirac basis and the charged lepton basis as in the quark sector, the allowed regions enlarge and the lower bound on the reheating temperature gets relaxed to values as low as ∼ 10{sup 10} GeV. It is confirmed that for normal ordering (NO) there are two allowed ranges of values for the lightest neutrino mass: m{sub 1} ≅ (1−5) × 10{sup −3} eV and m{sub 1} ≅ (0.03−0.1) eV. For m{sub 1}∼<0.01 eV the allowed region in the plane θ{sub 13}-θ{sub 23} is approximately given by θ{sub 23}∼<49°+0.65 (θ{sub 13}−5°), while the neutrinoless double beta decay effective neutrino mass falls in the range m{sub ee} = (1−3) × 10{sup −3} eV for θ{sub 13} = (6°−11.5°). For m{sub 1}∼>0.01 eV, one has quite sharply m{sub ee} ≅ m{sub 1} and an upper bound θ{sub 23}∼<46°. These constraints will be tested by low energy neutrino experiments during next years. We also find that inverted ordering (IO), though quite strongly constrained, is not completely ruled out. In particular, we find approximately θ{sub 23} ≅ 43°+12° log (0.2 eV/m{sub 1}), that will be fully tested by future experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Ultra high energy cosmic rays: implications of Auger data for source spectra and chemical composition

We use a kinetic-equation approach to describe the propagation of ultra high energy cosmic ray protons and nuclei and calculate the expected spectra and mass composition at the Earth for different assumptions on the source injection spectra and chemical abundances. When compared with the spectrum, the elongation rate X{sub max}(E) and dispersion σ(X{sub max}) as observed with the Pierre Auger Observatory, several important consequences can be drawn: a) the injection spectra of nuclei must be very hard, ∼ E{sup -γ} with γ∼ 1- 1.6; b) the maximum energy of nuclei of charge Z in the sources must be ∼ 5Z× 10{sup 18} eV, thereby not requiring acceleration to extremely high energies; c) the fit to the Auger spectrum can be obtained only at the price of adding an ad hoc light extragalactic component with a steep injection spectrum ∼ E{sup -2.7}). In this sense, at the ankle E{sub A}≈ 5× 10{sup 18} eV) all the components are of extragalactic origin, thereby suggesting that the transition from Galactic to extragalactic cosmic rays occurs below the ankle. Interestingly, the additional light extragalactic component postulated above compares well, in terms of spectrum and normalization, with the one recently measured by KASCADE-Grande.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Observation of Two Excited Bc+ States and Measurement of the Bc+ (2S) Mass in pp Collisions at s =13 TeV

Signals consistent with the Bc+(2S) and Bc∗+(2S) states are observed in proton-proton collisions at s=13 TeV, in an event sample corresponding to an integrated luminosity of 143 fb-1, collected by the CMS experiment during the 2015-2018 LHC running periods. These excited bc states are observed in the Bc+π+π- invariant mass spectrum, with the ground state Bc+ reconstructed through its decay to J/ψπ+. The two states are reconstructed as two well-resolved peaks, separated in mass by 29.1±1.5(stat)±0.7(syst) MeV. The observation of two peaks, rather than one, is established with a significance exceeding five standard deviations. The mass of the Bc+(2S) meson is measured to be 6871.0±1.2(stat)±0.8(syst)±0.8(Bc+) MeV, where the last term corresponds to the uncertainty in the world-average Bc+ mass. © 2019 CERN for the CMS Collaboration. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1974

Organic synthesis in a simulated Jovian atmosphere. III - Synthesis of aminonitriles

The products from spark and semicorona discharges through mixtures simulating the Jovian atmosphere were analyzed by gas chromatography combined with mass spectrometry. When the reaction was performed at -80 C, 3-ethylaminopropionitrile and a number of higher homologs were formed. On the other hand, at +20 C, higher molecular-weight material appeared which yielded aminonitrile-derived fragments on mass spectrometry. Although the spectra were not identical, there were notable similarities between these and the mass spectra of some compounds present in the Murray and Orgeuil meteorites. Aminonitriles may occur as minor constituents of the Jovian atmosphere and perhaps by cyclization may produce pyrimidines.

Molton, P. M.↗

DOE OSTI2013

Active and sterile neutrino mass effects on beta decay spectra

We study the spectra of the emitted charged leptons in charge current weak nuclear processes to analyze the effect of neutrino masses. Standard active neutrinos are studied here, with masses of the order of 1 eV or lower, as well as sterile neutrinos with masses of a few keV. The latter are warm dark matter (WDM) candidates hypothetically produced or captured as small mixtures with the active neutrinos. We compute differential decay or capture rates spectra in weak charged processes of different nuclei ({sup 3}H, {sup 187}Re, {sup 107}Pd, {sup 163}Ho, etc) using different masses of both active and sterile neutrinos and different values of the mixing parameter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

On spectral temperatures of negative pions produced in d{sup 12}C, {sup 4}He{sup 12}C, and {sup 12}C{sup 12}C collisions at 4.2 A GeV/c

The experimental transverse momentum distributions of negative pions produced in d{sup 12}C, {sup 4}He{sup 12}C, and {sup 12}C{sup 12}C collisions at 4.2 A GeV/c were analyzed in the framework of Hagedorn Thermodynamic Model. The spectral temperatures of {pi}{sup -} mesons as well as their relative contributions to the total multiplicity of {pi}{sup -} mesons were extracted from fitting the p{sub t} spectra by two-temperature Hagedorn function. The results were compared systematically with the earlier results obtained from analysis of non-invariant center-of-mass energy spectra of negative pions produced in the analyzed collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2010

AKARI OBSERVATIONS OF BROWN DWARFS. I. CO AND CO{sub 2} BANDS IN THE NEAR-INFRARED SPECTRA

Near-infrared medium-resolution spectra of seven bright brown dwarfs are presented. The spectra were obtained with the Infrared Camera on board the infrared astronomical satellite AKARI, covering 2.5-5.0 {mu}m with a spectral resolution of approximately 120. The spectral types of the objects range from L5 to T8 and enable us to study the spectral evolution of brown dwarfs. The observed spectra are in general consistent with predictions from previous observations and photospheric models; spectra of L-type dwarfs are characterized by continuum opacity from dust clouds in the photosphere, while very strong molecular absorption bands dominate the spectra in T-type dwarfs. We find that the CO fundamental band around 4.6 {mu}m is clearly seen even in the T8 dwarf 2MASS J041519 - 0935, confirming the presence of a non-equilibrium chemical state in the atmosphere. We also identify the CO{sub 2} fundamental stretching-mode band at 4.2 {mu}m for the first time in the spectra of late-L- and T-type brown dwarfs. As a preliminary step towards interpretation of the data obtained by AKARI, we analyze the observed spectra by comparing with those predicted by the unified cloudy model (UCM). Although overall spectral energy distributions can be reasonably fitted with the UCM, observed CO and CO{sub 2} bands in late-L and T dwarfs are unexpectedly stronger than the model predictions assuming local thermodynamical equilibrium. We examine the vertical mixing model and find that this model explains the CO band at least partly in the T dwarfs 2MASS J041519 - 0935 and 2MASS J055919 - 1404. The CO fundamental band also shows excess absorption against the predicted one in the L9 dwarf SDSS J083008+4828. Since CO is already highly abundant in the upper photospheres of late-L dwarfs, the extra CO due to vertical mixing has little effect on the CO band strengths, and the vertical mixing model cannot be applied to this L dwarf. A more serious problem is that the significant enhancement of the CO{sub 2} 4.2 {mu}m band in both the late-L and T dwarfs cannot be explained at all by the vertical mixing model. The cause of this enhancement of the CO{sub 2} band remains to be explained.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Exotic fermions in Kadyshevsky’s theory and the possibility to detect them

As it is known, the principal research interest of V.G. Kadyshevsky was the development of a geometric approach to quantum field theory with a constraint imposed on the mass spectrum of elementary particles. Non-Hermitian operators arising in this case seemed to be a major obstacle to the development of a consistent theory. These issues have been resolved recently, and the introduction of the pseudo-Hermitian algebraic approach to the construction of quantum theory was a major advance in this physical research. The central point of such theories is the construction of PT -symmetric non-Hermitian Hamiltonians with real eigenvalues. It is important to note that both purely theoretical and experimental studies (e.g., in non-Hermitian optics) are found among the many published papers on this subject. Therefore, we believe that the development of pseudo-Hermitian relativistic quantum theory with a maximal mass may provide favorable opportunities to discuss the possible experimental verification of theoretical results obtained in this field. Kadyshevsky himself regarded the hypothesis of existence of new particles, which he called exotic fermions, as an important prediction of his theory. The possibility of discovery of exotic neutrinos in precision experiments on the determination of the neutrino mass is discussed in the present study.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2011

SPECTRAL INDEX AS A FUNCTION OF MASS ACCRETION RATE IN BLACK HOLE SOURCES: MONTE CARLO SIMULATIONS AND AN ANALYTICAL DESCRIPTION

We present herein a theoretical study of correlations between spectral indexes of X-ray emergent spectra and mass accretion rate ( m-dot ) in black hole (BH) sources, which provide a definitive signature for BHs. It has been firmly established, using the Rossi X-ray Timing Explorer (RXTE) in numerous BH observations during hard-soft state spectral evolution, that the photon index of X-ray spectra increases when m-dot increases and, moreover, the index saturates at high values of m-dot . In this paper, we present theoretical arguments that the observationally established index saturation effect versus mass accretion rate is a signature of the bulk (converging) flow onto the BH. Also, we demonstrate that the index saturation value depends on the plasma temperature of converging flow. We self-consistently calculate the Compton cloud (CC) plasma temperature as a function of mass accretion rate using the energy balance between energy dissipation and Compton cooling. We explain the observable phenomenon, index- m-dot correlations using a Monte Carlo simulation of radiative processes in the innermost part (CC) of a BH source and we account for the Comptonization processes in the presence of thermal and bulk motions, as basic types of plasma motion. We show that, when m-dot increases, BH sources evolve to high and very soft states (HSS and VSS, respectively), in which the strong blackbody(BB)-like and steep power-law components are formed in the resulting X-ray spectrum. The simultaneous detections of these two components strongly depends on sensitivity of high-energy instruments, given that the relative contribution of the hard power-law tail in the resulting VSS spectrum can be very low, which is why, to date RXTE observations of the VSS X-ray spectrum have been characterized by the presence of the strong BB-like component only. We also predict specific patterns for high-energy e-fold (cutoff) energy (E{sub fold}) evolution with m-dot for thermal and dynamical (bulk) Comptonization cases. For the former case, E{sub fold} monotonically decreases with m-dot , in the latter case, the E{sub fold} decrease is followed by its increase at high values of m-dot . The observational evolution of E{sub fold} versus m-dot can be another test for the presence of a converging flow effect in the formation of the resulting spectra in the close vicinity of BHs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2010

A NEAR-INFRARED SPECTROSCOPIC SURVEY OF CLASS I PROTOSTARS

We present the results of a near-IR spectroscopic survey of 110 Class I protostars observed from 0.80 {mu}m to 2.43 {mu}m at a spectroscopic resolution of R = 1200. This survey is unique in its selection of targets from the whole sky, its sample size, wavelength coverage, depth, and sample selection. We find that Class I objects exhibit a wide range of lines and the continuum spectroscopic features. Eighty-five percent of Class I protostars exhibit features indicative of mass accretion, and we found that the veiling excess, CO emission, and Br {gamma} emission are closely related. We modeled the spectra to estimate the veiling excess (r{sub k} ) and extinction to each target. We also used near-IR colors and emission line ratios, when available, to also estimate extinction. In the course of this survey, we observed the spectra of 10 FU Orionis-like objects, including 2 new ones, as well as 3 Herbig Ae-type stars among our Class I young stellar objects. We used photospheric absorption lines, when available, to estimate the spectral type of each target. Although most targets are late-type stars, there are several A- and F-type stars in our sample. Notably, we found no A or F class stars in the Taurus-Auriga or Perseus star-forming regions. There are several cases where the observed CO and/or water absorption bands are deeper than expected from the photospheric spectral type. We find a correlation between the appearance of the reflection nebula, which traces the distribution of material on very large scales, and the near-IR spectrum, which probes smaller scales. All of the FU Orionis-like objects are associated with reflection nebulae. The spectra of the components of spatially resolved protostellar binaries tend to be very similar. In particular both components tend to have similar veiling and H{sub 2} emission, inconsistent with random selection from the sample as a whole. There is a strong correlation between [Fe II] and H{sub 2} emission, supporting previous results showing that H{sub 2} emission in the spectra of young stars is usually shock excited by stellar winds.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

DUST AND THE TYPE II-PLATEAU SUPERNOVA 2004dj

We present mid-infrared (MIR) spectroscopy of a Type II-plateau supernova, SN 2004dj, obtained with the Spitzer Space Telescope, spanning 106-1393 days after explosion. MIR photometry plus optical/near-IR observations are also reported. An early-time MIR excess is attributed to emission from non-silicate dust formed within a cool dense shell (CDS). Most of the CDS dust condensed between 50 days and 165 days, reaching a mass of 0.3 x 10{sup -5} M{sub sun}. Throughout the observations, much of the longer wavelength (>10 {mu}m) part of the continuum is explained as an IR echo from interstellar dust. The MIR excess strengthened at later times. We show that this was due to thermal emission from warm, non-silicate dust formed in the ejecta. Using optical/near-IR line profiles and the MIR continua, we show that the dust was distributed as a disk whose radius appeared to be shrinking slowly. The disk radius may correspond to a grain destruction zone caused by a reverse shock which also heated the dust. The dust-disk lay nearly face-on, had high opacities in the optical/near-IR regions, but remained optically thin in the MIR over much of the period studied. Assuming a uniform dust density, the ejecta dust mass by 996 days was (0.5 {+-} 0.1) x 10{sup -4} M{sub sun} and exceeded 10{sup -4} M{sub sun} by 1393 days. For a dust density rising toward the center the limit is higher. Nevertheless, this study suggests that the amount of freshly synthesized dust in the SN 2004dj ejecta is consistent with that found from previous studies and adds further weight to the claim that such events could not have been major contributors to the cosmic dust budget.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

YOUNG STELLAR CLUSTERS CONTAINING MASSIVE YOUNG STELLAR OBJECTS IN THE VVV SURVEY

The purpose of this research is to study the connections of the global properties of eight young stellar clusters projected in the Vista Variables in the Via Lactea (VVV) ESO Large Public Survey disk area and their young stellar object (YSO) populations. The analysis is based on the combination of spectroscopic parallax-based reddening and distance determinations with main-sequence and pre-main-sequence ishochrone fitting to determine the basic parameters (reddening, age, distance) of the sample clusters. The lower mass limit estimations show that all clusters are low or intermediate mass (between 110 and 1800 M {sub ⊙}), the slope Γ of the obtained present-day mass functions of the clusters is close to the Kroupa initial mass function. The YSOs in the cluster’s surrounding fields are classified using low resolution spectra, spectral energy distribution fits with theoretical predictions, and variability, taking advantage of multi-epoch VVV observations. All spectroscopically confirmed YSOs (except one) are found to be massive (more than 8 M {sub ⊙}). Using VVV and GLIMPSE color–color cuts we have selected a large number of new YSO candidates, which are checked for variability and 57% are found to show at least low-amplitude variations. In few cases it was possible to distinguish between YSO and AGB classifications on the basis of light curves.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

DISK EVOLUTION IN W5: INTERMEDIATE-MASS STARS AT 2-5 Myr

We present the results of a survey of young intermediate-mass stars (age < 5 Myr, 1.5 M{sub sun} <M{sub *}{<=} 15 M{sub sun}) in the W5 massive star-forming region. We use combined optical, near-infrared, and Spitzer Space Telescope photometry and optical spectroscopy to define a sample of stars of spectral types A and B and examine their infrared excess properties. We find objects with infrared excesses characteristic of optically thick disks, i.e., Herbig AeBe stars. These stars are rare: <1.5% of the entire spectroscopic sample of A and B stars, and absent among stars more massive than 2.4 M{sub sun}. 7.5% of the A and B stars possess infrared excesses in a variety of morphologies that suggest their disks are in some transitional phase between an initial, optically thick accretion state and later evolutionary states. We identify four morphological classes based on the wavelength dependence of the observed excess emission above theoretical photospheric levels: (1) the optically thick disks; (2) disks with an optically thin excess over the wavelength range 2-24 {mu}m, similar to that shown by Classical Be stars; (3) disks that are optically thin in their inner regions based on their infrared excess at 2-8 {mu}m and optically thick in their outer regions based on the magnitude of the observed excess emission at 24 {mu}m; (4) disks that exhibit empty inner regions (no excess emission at {lambda} {<=} 8 {mu}m) and some measurable excess emission at 24 {mu}m. A sub-class of disks exhibit no significant excess emission at {lambda}{<=} 5.8 {mu}m, have excess emission only in the Spitzer 8 {mu}m band and no detection at 24 {mu}m. We discuss these spectral energy distribution types, and suggest physical models for disks exhibiting these emission patterns and additional observations to test these theories.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2010

The Search for a π 1 (1400) Exotic Meson in the gammap-->Δ ++ ηπ - System with CLAS

Several experiments have reported evidence for the π 1 (1400) using pion production but the results have been controversial and its existence has yet to be seen in photoproduction. Theoretical works have implied that the production amplitude will be greatly increased in photoproduction in comparison to the pion production. The reaction gammap-->Λ ++ X-->pπ + π - (η) is being studied in the photon energy range 4.4 to 5.4 GeV as a possible method of producing the π1(1400) resonance. Data were collected at Jefferson Lab in Hall B. This reaction is being investigated by detecting the pπ + π - 2gamma and reconstructing the eta through the missing-mass of the p π + π - , and comparing the results to the 2γ composite. These data have yielded a 0 (980) and a 2 (1320) in the π - eta invariant mass spectrum. Further analysis is needed to untangle the possible π1(1400) resonance from the a2(1320).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

Leptogenesis from first principles in the resonant regime

The lepton asymmetry generated by the out-of-equilibrium decays of heavy Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly enhanced. In this work, we study this scenario within a first-principle approach. The quantum field theoretical treatment is applicable for mass splittings of the order of the width of the Majorana neutrinos, for which the enhancement is maximally large. The non-equilibrium evolution of the mixing Majorana neutrino fields is described by a formal analytical solution of the Kadanoff-Baym equations, that is obtained by neglecting the back-reaction. Based on this solution, we derive approximate analytical expressions for the generated asymmetry and compare them to the Boltzmann result. We find that the resonant enhancement obtained from the Kadanoff-Baym approach is smaller compared to the Boltzmann approach, due to additional contributions that describe coherent transitions between the Majorana neutrino species. We also discuss corrections to the masses and widths of the degenerate pair of Majorana neutrinos that are relevant for very small mass splitting, and compare the approximate analytical result for the lepton asymmetry with numerical results. - Highlights: Black-Right-Pointing-Pointer Treatment of leptogenesis in the resonant regime by a first-principle approach. Black-Right-Pointing-Pointer Applicable for mass differences of the order of the width. Black-Right-Pointing-Pointer Non-equilibrium evolution described by Kadanoff-Baym equations. Black-Right-Pointing-Pointer Analytical solution can be obtained neglecting backreaction. Black-Right-Pointing-Pointer Resonant enhancement is smaller compared to the classical Boltzmann approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2013

Low temperature oxidation mechanisms of nanocrystalline magnetite thin film

A detailed investigation of the mechanisms related to the low temperature oxidation of nanocrystalline magnetite thin films into maghemite is presented. Despite strong differences in the functional properties of these two phases, structural similarities make it difficult to distinguish between them, and to quantify the oxidation process, particularly in the case of nanostructured polycrystalline layers. Contrary to the case of bulk materials or monocrystalline films and particles, the oxidation processes in nanocrystalline thin film have only scarcely been studied. In this work, structural and optical techniques, including X-ray diffraction (XRD), EXAFS/X-ray absorption near edge structure, FTIR, and Raman scattering, have been used to estimate the oxidation rate of magnetite. The overall oxidation reaction rates are discussed in the framework of two limiting cases corresponding to intra grain diffusion and to grain boundary diffusion. SIMS profiling and electrical measurements were also carried out to better assess the oxidation quantification in order to conclude on the predominant oxidation mechanisms in this heterogeneous material. We propose a qualitative model for the structure, in terms of insulating zone distribution, for partially oxidized films.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Hyperfine interactions of constituent quarks and the mass spectrum of tetraquark states

The simplest form of the Hyperfine Interaction (HFI) of quarks is a color-spin interaction, sometimes called Fermi-Breit (FB) HFI. For conventional hadrons, this HFI for quark-antiquark (qq) pairs is twice as strong as the same HFI for quark-quark (qq or qq) pairs, but this difference is absorbed into the different HFI constants for mesons and baryons, which are free parameters of the fits. For tetraquarks, however, qqHFI is only half as strong as the qq/qqHFI and both kinds of pairs coexist within the same state. Hence it is worth investigating a model with different fit constants for qq and qq/q pairs. We have investigated 3 models of spin-color HFI for light scalar tetraquarks: 2 models with single constants for both kinds of pairs and one model with different fit constants. The light scalar nonet is chosen because of a lack of other experimentally observed multiplets interpretable as pure exotic states. Since even the nonet contains only 3 particles with distinct masses (i. e. 3 fit points), the constituent quark masses had to be taken from conventional hadron fits obtained in our previous work. The two-constant model did not prove to be a viable alternative to the one-constant models. © 2019 Author(s).

60 APPLIED LIFE SCIENCES↗