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1
Funai, J. T., and M. D. Thames. "Isochronal behavior in left ventricular systolic pressure-wall thickness relations." American Journal of Physiology-Heart and Circulatory Physiology 255, no. 5 (November 1, 1988): H1136—H1143. http://dx.doi.org/10.1152/ajpheart.1988.255.5.h1136.
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Regional left ventricular systolic pressure-thickness relations have been used to assess regional load-insensitive contractility with the assumption that they possess linear isochrones that are fundamental to the time-varying elastance model of global pressure-volume relations. We examined the shape and time-varying behavior of pressure-thickness isochrones in six open-chest canine preparations. Transmural wall thickening (sonomicrometry) and ventricular pressure were altered by abrupt preload alterations during control, dobutamine, and propranolol. In all dogs and interventions, linear isochrones (r2 mean +/- SE = 0.91 +/- 0.11) were found at 5-ms intervals. During control, linear isochrone slope rose monotonically from onset to end of systole. Thickness-axis intercepts also varied continuously in time, but peak intercept and maximal slope were asynchronous. Dobutamine caused a steeper earlier maximum slope and increased slope-intercept asynchrony. Propranolol reduced maximum slope and slope-intercept asynchrony. Isochronal data during early systole were better fitted to a parabolic than to the linear model; however, fits to linear and parabolic models were equally good near end of systole. Linear isochronal behavior exists in systolic pressure-thickness relations especially near end systole and is maintained during modest inotropic alterations.
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Krishnamurti, T. N., Anu Simon, Aype Thomas, Akhilesh Mishra, Dev Sikka, Dev Niyogi, Arindam Chakraborty, and Li Li. "Modeling of Forecast Sensitivity on the March of Monsoon Isochrones from Kerala to New Delhi: The First 25 Days." Journal of the Atmospheric Sciences 69, no. 8 (August 1, 2012): 2465–87. http://dx.doi.org/10.1175/jas-d-11-0170.1.
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Abstract This study addresses observational and modeling sensitivity on the march of the onset isochrones of the Indian summer monsoon. The first 25 days of the passage of the isochrones of monsoon onset is of great scientific interest. Surface and satellite-based datasets are used for high-resolution modeling of the impact of the motion of the onset isochrones from Kerala to New Delhi. These include the asymmetries across the isochrone such as soil moisture and its temporal variability, moistening of the dry soil to the immediate north of the isochrone by nonconvective anvil rains, and formation of newly forming cloud elements to the immediate north of the isochrone. The region immediately north of the isochrone is shown to carry a spread of buoyancy elements. As these new elements grow, they are continually being steered by the divergent circulations of the parent isochrone to the north and eventually to the northwest. CloudSat was extremely useful for identifying the asymmetric cloud structures across the isochrone. In the modeling sensitivity studies, the authors used a mesoscale Advanced Research Weather Research and Forecasting Model (ARW-WRF) to examine days 1–25 of forecasts of the onset isochrone. Prediction experiments were first modeled during normal, dry, and wet Indian monsoons using default values of model parameters. This study was extended to determine the effects of changes in soil moisture and nonconvective rain parameterizations (the parameters suggested by the satellite observations). These sensitivity experiments show that the motion of the isochrones from Kerala to New Delhi are very sensitive to the parameterization of soil moisture and nonconvective anvil rains immediately north of the isochrone.
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Schuman, Bertrand. "Une classe d’hamiltoniens polynomiaux isochrones." Canadian Mathematical Bulletin 44, no. 3 (September 1, 2001): 323–34. http://dx.doi.org/10.4153/cmb-2001-032-9.
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RésuméSoit un hamiltonien isochrone du plan . On met en évidence une classe d’hamiltoniens isochrones qui sont des perturbations polynomiales de H0. On obtient alors une condition nécessaire d’isochronisme, et un critère de choix pour les hamiltoniens isochrones. On voit ce résultat comme étant une généralisation du caractère isochrone des perturbations hamiltoniennes homogènes considérées dans [L], [P], [S].
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Engel, Hugues. "L’Hypothèse d’Isochronie Syllabique Initiale appliquée au français L2." Language, Interaction and Acquisition 11, no. 2 (November 25, 2020): 268–97. http://dx.doi.org/10.1075/lia.19009.eng.
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Résumé L’objectif principal de cette étude pilote est de tester expérimentalement ce que nous appelons l’Hypothèse d’Isochronie Syllabique Initiale. Selon cette hypothèse, les apprenants de L2 passent par une phase initiale pendant laquelle leurs productions orales présentent les caractéristiques rythmiques des langues dites à isochronie syllabique (telles que l’espagnol et le français). Pour cela, nous analysons des récits oraux d’apprenantes débutantes de français ayant le suédois pour langue maternelle (n = 6). Ces productions sont comparées à celles d’un groupe de locutrices natives du français (n = 6) et d’un groupe de locutrices natives du suédois (n = 6). Les caractéristiques rythmiques des récits en français L2, français L1 et suédois L1 sont étudiées à partir de deux mesures acoustiques, notamment le coefficient de variation de la durée syllabique, dont l’utilisation est préconisée par Patel (2008) pour déterminer si une langue est de type accentuel ou syllabique. Les mesures acoustiques employées permettent de confirmer que le français et le suédois appartiennent à des familles rythmiques distinctes. Les résultats de l’étude vont cependant à l’encontre de l’Hypothèse d’Isochronie Syllabique Initiale.
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Engel, Maximilian, and Christian Kuehn. "A Random Dynamical Systems Perspective on Isochronicity for Stochastic Oscillations." Communications in Mathematical Physics 386, no. 3 (April 8, 2021): 1603–41. http://dx.doi.org/10.1007/s00220-021-04077-z.
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AbstractFor an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be characterized as stable manifolds foliating neighborhoods of the limit cycle or as level sets of an isochron map. In recent years, there has been a lively discussion in the mathematical physics community on how to define isochrons for stochastic oscillations, i.e. limit cycles or heteroclinic cycles exposed to stochastic noise. The main discussion has concerned an approach finding stochastic isochrons as sections of equal expected return times versus the idea of considering eigenfunctions of the backward Kolmogorov operator. We discuss the problem in the framework of random dynamical systems and introduce a new rigorous definition of stochastic isochrons as random stable manifolds for random periodic solutions with noise-dependent period. This allows us to establish a random version of isochron maps whose level sets coincide with the random stable manifolds. Finally, we discuss links between the random dynamical systems interpretation and the equal expected return time approach via averaged quantities.
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Bell, Cameron P. M., Jon M. Rees, Tim Naylor, N. J. Mayne, R. D. Jeffries, Eric E. Mamajek, and John Rowe. "Pre-main-sequence isochrones – III. The Cluster Collaboration isochrone server." Monthly Notices of the Royal Astronomical Society 445, no. 4 (October 29, 2014): 3496–511. http://dx.doi.org/10.1093/mnras/stu1944.
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Nereson, Nadine A., and Edwin D. Waddington. "Isochrones and isotherms beneath migrating ice divides." Journal of Glaciology 48, no. 160 (2002): 95–108. http://dx.doi.org/10.3189/172756502781831647.
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AbstractWe use simple numerical and analytical models of ice flow and heat flow to characterize the shape of isochrones and isotherms beneath moving ice divides. Both nonlinear ice flow and reduced accumulation (wind scouring) at a divide can cause reduced downward flow in a region about one ice thickness wide under a divide. Greater downward velocities on the flanks cause isochrones and isotherms to become arched at depth. The magnitudes and shapes of these arches depend on the history of divide position. Arch amplitudes decrease by approximately e−1 for each increase in migration rate of 3–5 times the accumulation rate, the arches become asymmetric, with steeper leading edges and more gentle trailing edges, and the arch apex lags behind the divide. Isochrone and isotherm shapes can be used to infer past divide motions. In advection-dominated ice sheets, isochrone shapes record a longer history of divide position than do isotherm shapes. The opposite is true for diffusion-dominated ice sheets, in which a spatial array of ice-temperature measurements might extend the recorded history of divide position.
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Rousseau, C., and B. Toni. "Local Bifurcations of Critical Periods in the Reduced Kukles System." Canadian Journal of Mathematics 49, no. 2 (April 1, 1997): 338–58. http://dx.doi.org/10.4153/cjm-1997-017-4.
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AbstractIn this paper, we study the local bifurcations of critical periods in the neighborhood of a nondegenerate centre of the reduced Kukles system. We find at the same time the isochronous systems. We show that at most three local critical periods bifurcate from the Christopher-Lloyd centres of finite order, at most two from the linear isochrone and at most one critical period from the nonlinear isochrone. Moreover, in all cases, there exist perturbations which lead to the maximum number of critical periods. We determine the isochrones, using the method of Darboux: the linearizing transformation of an isochrone is derived from the expression of the first integral. Our approach is a combination of computational algebraic techniques (Gröbner bases, theory of the resultant, Sturm’s algorithm), the theory of ideals of noetherian rings and the transversality theory of algebraic curves.
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Li, Yang, and Pieter Vermeesch. "Short communication: Inverse isochron regression for Re–Os, K–Ca and other chronometers." Geochronology 3, no. 2 (August 2, 2021): 415–20. http://dx.doi.org/10.5194/gchron-3-415-2021.
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Abstract. Conventional Re–Os isochrons are based on mass spectrometric estimates of 187Re/188Os and 187Os/188Os, which often exhibit strong error correlations that may obscure potentially important geological complexity. Using an approach that is widely accepted in 40Ar/39Ar and U–Pb geochronology, we here show that these error correlations are greatly reduced by applying a simple change of variables, using 187Os as a common denominator. Plotting 188Os/187Os vs. 187Re/187Os produces an “inverse isochron”, defining a binary mixing line between an inherited Os component whose 188Os/187Os ratio is given by the vertical intercept, and the radiogenic 187Re/187Os ratio, which corresponds to the horizontal intercept. Inverse isochrons facilitate the identification of outliers and other sources of data dispersion. They can also be applied to other geochronometers such as the K–Ca method and (with less dramatic results) the Rb–Sr, Sm–Nd and Lu–Hf methods. Conventional and inverse isochron ages are similar for precise datasets but may significantly diverge for imprecise ones. A semi-synthetic data simulation indicates that, in the latter case, the inverse isochron age is more accurate. The generalised inverse isochron method has been added to the IsoplotR toolbox for geochronology, which automatically converts conventional isochron ratios into inverse ratios, and vice versa.
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Ichinose, Natsuhiro, Kazuyuki Aihara, and Kevin Judd. "Extending the Concept of Isochrons from Oscillatory to Excitable Systems for Modeling an Excitable Neuron." International Journal of Bifurcation and Chaos 08, no. 12 (December 1998): 2375–85. http://dx.doi.org/10.1142/s021812749800190x.
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In this paper, we study an excitable and nonoscillating neuron on the basis of a technique of extending the concept of isochrons from oscillatory to excitable systems. The extended isochrons allow reduction of an excitable system described by possibly high dimensional differential equations to a simpler system. We analytically derive a one-dimensional model of an excitable neuron stimulated by instantaneous pulses with the technique of the extended isochrons and show its similarity to an isochronal map numerically obtained from the FitzHugh–Nagumo model. Response characteristics of the one-dimensional model to periodic impulsive stimulations are also analyzed numerically.
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Xi, Yang (Luna), Eric J. Miller, and Shoshanna Saxe. "Exploring the Impact of Different Cut-off Times on Isochrone Measurements of Accessibility." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 49 (June 21, 2018): 113–24. http://dx.doi.org/10.1177/0361198118783113.
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Isochrone analysis and assessments of cumulative opportunities are a common way to quantify accessibility. However, different time cut-offs have been used by different researchers, with little investigation into what is the ‘best’ cut-off time. Outstanding questions remain concerning the most effective or predictive cut-off time and the potential implications of choosing one time limit over another. The primary objective of this paper is to explore how different cut-off times affect the calculation of isochrone-based accessibility measurements and their potential to predict travel-mode choice. Fifty dissemination areas (DAs) within the Greater Toronto and Hamilton Area (GTHA) are selected to test the impact of different isochrone cut-off times in 5-minute intervals for public transit, automobile, and walking accessibility. The relative predictive power of 30- and 45-minute isochrones in modeling mode choice is also examined. This paper finds that different cut-off times do impact the interpretability of accessibility measurements in the isochrone approach, but a defined cut-off time for general use cannot be determined based on the analysis.
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Gontcharov, George A., Maxim Yu Khovritchev, and Aleksandr V. Mosenkov. "Isochrone fitting of Galactic globular clusters – II. NGC 6205 (M13)." Monthly Notices of the Royal Astronomical Society 497, no. 3 (August 18, 2020): 3674–93. http://dx.doi.org/10.1093/mnras/staa1694.
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ABSTRACT We present new isochrone fits to colour–magnitude diagrams of the Galactic globular cluster NGC 6205 (M13). We utilize 34 photometric bands from the ultraviolet to mid-infrared by use of data from the HST, Gaia DR2, SDSS, unWISE, Pan-STARRS DR1, and other photometric sources. In our isochrone fitting we use the PARSEC, MIST, DSEP, BaSTI, and IAC-BaSTI theoretical models and isochrones, both for the solar-scaled and He–α-enhanced abundances, with a metallicity of about [Fe/H] = −1.58 adopted from the literature. The colour–magnitude diagrams, obtained with pairs of filters from different datasets but of similar effective wavelengths, show some colour offsets up to 0.04 mag between the fiducial sequences and isochrones. We attribute these offsets to systematic differences of the datasets. Some intrinsic systematic differences of the models/isochrones remain in our results: the derived distances and ages are different for the ultraviolet, optical and infrared photometry used, while the derived ages are different for the different models/isochrones, e.g. in the optical range from 12.3 ± 0.7 Gyr for He–α-enhanced DSEP to 14.4 ± 0.7 Gyr for MIST. Despite the presence of multiple stellar populations, we obtain convergent estimates for the dominant population: best-fitting distance 7.4 ± 0.2 kpc, true distance modulus 14.35 ± 0.06 mag, parallax 0.135 ± 0.004 mas, extinction AV = 0.12 ± 0.02, and reddening E(B − V) = 0.04 ± 0.01. These estimates agree with other recent estimates; however, the extinction and reddening are twice as high as generally accepted. The derived empirical extinction law agrees with the Cardelli–Clayton–Mathis extinction law with the best-fitting $R_\mathrm{V}=3.1^{+1.6}_{-1.1}$.
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Jørgensen, B. R., and L. Lindegren. "Determination of stellar ages from isochrones: Bayesian estimation versus isochrone fitting." Astronomy & Astrophysics 436, no. 1 (May 20, 2005): 127–43. http://dx.doi.org/10.1051/0004-6361:20042185.
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Spada, F., P. Demarque, Y. C. Kim, T. S. Boyajian, and J. M. Brewer. "YaPSI: a new database of evolutionary tracks and isochrones." Proceedings of the International Astronomical Union 13, S334 (July 2017): 362–63. http://dx.doi.org/10.1017/s1743921317007347.
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AbstractThe Yale–Potsdam Stellar Isochrones (YaPSI) cover the low and intermediate stellar mass regime (0.15 to 5.0 M⊙) for a wide range of solar-scaled chemical compositions (metallicity from −0.5 to +0.3; helium mass fraction from 0.25 to 0.37, assigned independently of each other). The tracks are finely spaced in mass, to allow for accurate interpolation. The models feature state-of-the-art input physics relevant to low-mass stars modeling (surface boundary conditions, equation of state), thus updating the faint end of the Yonsei-Yale (YY) isochrones. Utility codes, such as an isochrone interpolator in age, metallicity and helium content, are also provided. The YaPSI isochrones are in good agreement with the empirical mass–luminosity and mass–radius relations available to date, and provide satisfactory fitting of the color-magnitude diagrams of well-studied open clusters.
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Leysinger Vieli, G. J. M. C., R. C. A. Hindmarsh, and M. J. Siegert. "Three-dimensional flow influences on radar layer stratigraphy." Annals of Glaciology 46 (2007): 22–28. http://dx.doi.org/10.3189/172756407782871729.
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AbstractVariations in the depth of radar-detectable englacial layers (isochrones) are commonly used to assess past variability in accumulation rates, but little is known about the effect of internal and basal flow variations on isochrone deflections (e.g. bumps, troughs). In this paper, we show how the isochrones are affected by such variation using a three-dimensional flow model to investigate changes in the flow mode and in increased basal melting. We also investigate how transverse flows with lateral velocity gradients affect the development of isochrones. We use the model to visualize how such variations will be seen in radar lines which cross the flow direction. We show that in the presence of lateral gradients in the flow field we can produce bumps and troughs when viewed along transects perpendicular to the flow. The model results show that the influences of flow convergence, melting and changes in flow mode, when coupled together, affect isochrones over the whole depth of the ice sheet. Finally, changes in the near-surface layers cannot be solely attributed to spatial variation in the accumulation rate; there can also be a strong signal from changes in the flow mode.
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Sinisalo, Anna, Aslak Grinsted, and John Moore. "Dynamics of the Scharffenbergbotnen blue-ice area, Dronning Maud Land, Antarctica." Annals of Glaciology 39 (2004): 417–22. http://dx.doi.org/10.3189/172756404781814177.
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AbstractGround-penetrating radar (GPR) surveys in Scharffenbergbotnen valley, Dronning Maud Land, Antarctica, complement earlier, relatively sparse data on the ice-flow dynamics and mass-balance distribution of the area. The negative net surface mass balance in the valley appears to be balanced by the inflow. The flow regime in Scharffenbergbotnen defines four separate mass-balance areas, and about 60 times more ice enters the valley from the northwestern entrance than via the narrow western gate. We formalize and compare three methods of determining both the surface age gradient of the blue ice and the dip angles of isochrones in the firn/blue-ice transition zone: observed and dated radar internal reflections, a geometrical model of isochrones, and output from a flowline model. The geometrical analysis provides generally applicable relationships between ice surface velocity and surface age gradient or isochrone dip angle.
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Janson, Markus, Stephen Durkan, Mickaël Bonnefoy, Laetitia Rodet, Rainer Köhler, Sylvestre Lacour, Wolfgang Brandner, Thomas Henning, and Julien Girard. "Dynamical masses of M-dwarf binaries in young moving groups." Astronomy & Astrophysics 620 (November 27, 2018): A33. http://dx.doi.org/10.1051/0004-6361/201833375.
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Low-mass stars exhibit substantial pre-main sequence evolution during the first ∼100 Myr of their lives. Thus, young M-type stars are prime targets for isochronal dating, especially in young moving groups (YMGs), which contain large amounts of stars in this mass and age range. If the mass and luminosity of a star can both be directly determined, this allows for a particularly robust isochronal analysis. This motivates in-depth studies of low-mass binaries with spatially resolvable orbits, where dynamical masses can be derived. Here we present the results of an observing campaign dedicated to orbital monitoring of AB Dor Ba/Bb, which is a close M-dwarf pair within the quadruple AB Dor system. We have acquired eight astrometric epochs with the SPHERE/ZIMPOL and NACO instruments, which we combine with literature data to improve the robustness and precision for the orbital characterization of the pair. We find a system mass 0.66−0.12+0.12 M⊙ and bolometric luminosities in logL/L⊙ of −2.02 ± 0.02 and −2.11 ± 0.02 for AB Dor Ba and Bb, respectively. These measurements are combined with other YMG pairs in the literature to start building a framework of empirical isochrones in mass–luminosity space. This can be used to calibrate theoretical isochrones and to provide a model-free basis for assessing relative stellar ages. We note a tentative emerging trend where the youngest moving group members are largely consistent with theoretical expectations, while stars in older associations such as the AB Dor moving group appear to be systematically underluminous relative to isochronal expectations.
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Claessens, T. E., D. Georgakopoulos, M. Afanasyeva, S. J. Vermeersch, H. D. Millar, N. Stergiopulos, N. Westerhof, P. R. Verdonck, and P. Segers. "Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?" American Journal of Physiology-Heart and Circulatory Physiology 290, no. 4 (April 2006): H1474—H1483. http://dx.doi.org/10.1152/ajpheart.00663.2005.
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tThe linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation ( R2 < 0.75) during isovolumic relaxation and early filling; and 4) logarithmic regression is superior in estimating the fixed volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.
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Duchkov, Anton A., and Maarten V. de Hoop. "Extended isochron rays in prestack depth (map) migration." GEOPHYSICS 75, no. 4 (July 2010): S139—S150. http://dx.doi.org/10.1190/1.3459955.
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Many processes in seismic data analysis and seismic imaging can be identified with solution operators of evolution equations. These include data downward continuation and velocity continuation. We have addressed the question of whether isochrons defined by imaging operators can be identified with wavefronts of solutions to an evolution equation. Rays associated with this equation then would provide a natural way of implementing prestack map migration. Assuming absence of caustics, we have developed constructive proof of the existence of a Hamiltonian describing propagation of isochrons in the context of common-offset depth migration. In the presence of caustics, one should recast to a sinking-survey migration framework. By manipulating the double-square-root operator, we obtain an evolution equation that describes sinking-survey migration as a propagation in two-way time with surface data being a source function. This formulation can be viewed as an extension of the exploding reflector concept from zero-offset to sinking-survey migration. The corresponding Hamiltonian describes propagation of extended isochrons (fronts with constant two-way time) connected by extended isochron rays. The term extended reflects the fact that two-way time propagation now takes place in high-dimensional space with the following coordinates: subsurface midpoint, subsurface offset, and depth. Extended isochron rays can be used in a natural manner for implementing sinking-survey migration in a map-migration fashion.
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Alves, Virginia Mello, Eduardo Bica, and Daniela Borges Pavani. "Determination of astrophysical parameters of open clusters using classical and semi-automated isochrone-fitting methods." Proceedings of the International Astronomical Union 5, S266 (August 2009): 352. http://dx.doi.org/10.1017/s1743921309991268.
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AbstractWhen we use optical isochrone-fitting solutions from the literature to 2mass CMDs, they are often not the best solutions in the infrared domain. We analysed 10 open clusters with 2mass, nine of them previously studied with optical photometry (NGC 1245, NGC 1342, NGC 1502, NGC 2104, NGC 2204, NGC 2243, NGC 2281, NGC 6709 and NGC 744) and one using integrated spectroscopy (BH 132). The study involved the classical (by eye) and a semi-automated method of isochrone fitting. We used the solutions of the first method as input for the second, looking for refined solutions. The semi-automated method uses a synthetic color–magnitude diagram (CMD), based on different Padova isochrones, to compare with the observed CMDs by means of likelihood statistics. The derived astrophysical parameters are age, distance and reddening values. The present results show better fits than those implied by the optical values. We also show that the semi-automated method decreases the parameter uncertainties.
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Winter, Anna, Daniel Steinhage, Timothy T. Creyts, Thomas Kleiner, and Olaf Eisen. "Age stratigraphy in the East Antarctic Ice Sheet inferred from radio-echo sounding horizons." Earth System Science Data 11, no. 3 (July 18, 2019): 1069–81. http://dx.doi.org/10.5194/essd-11-1069-2019.
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Abstract. The East Antarctic Ice Sheet contains a wealth of information that can be extracted from its internal architecture such as distribution of age, past flow features, and surface and basal properties. Airborne radar surveys can sample this stratigraphic archive across broad areas. Here, we identify and trace key horizons across several radar surveys to obtain the stratigraphic information. We transfer the age–depth scales from ice cores to intersecting radar data. We then propagate these age scales across the ice sheet using the high fidelity continuity of the radar horizons. In Dronning Maud Land, including Dome Fuji, we mapped isochrones with ages of 38 and 74 ka. In the central region of East Antarctica around Dome Concordia, Vostok and Dome Argus, we use isochrone ages of 38, 48, 90 and 161 ka. Taking together both regions, we provide isochrone depths traced along a combined profile length of more than 40 000 km and discuss uncertainties of the obtained stratigraphy, as well as factors important to consider for further expansion. This data set is the most extensive distribution of internal horizons in East Antarctica to date. The isochrone depths presented in this study are available on PANGAEA (https://doi.org/10.1594/PANGAEA.895528; Winter et al., 2018).
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Cavitte, Marie G. P., Frédéric Parrenin, Catherine Ritz, Duncan A. Young, Brice Van Liefferinge, Donald D. Blankenship, Massimo Frezzotti, and Jason L. Roberts. "Accumulation patterns around Dome C, East Antarctica, in the last 73 kyr." Cryosphere 12, no. 4 (April 17, 2018): 1401–14. http://dx.doi.org/10.5194/tc-12-1401-2018.
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Abstract. We reconstruct the pattern of surface accumulation in the region around Dome C, East Antarctica, since the last glacial. We use a set of 18 isochrones spanning all observable depths of the ice column, interpreted from various ice-penetrating radar surveys and a 1-D ice flow model to invert for accumulation rates in the region. The shallowest four isochrones are then used to calculate paleoaccumulation rates between isochrone pairs using a 1-D assumption where horizontal advection is negligible in the time interval of each layer. We observe that the large-scale (100s km) surface accumulation gradient is spatially stable through the last 73 kyr, which reflects current modeled and observed precipitation gradients in the region. We also observe small-scale (10 s km) accumulation variations linked to snow redistribution at the surface, due to changes in its slope and curvature in the prevailing wind direction that remain spatially stationary since the last glacial.
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Iversen, Einar. "The isochron ray in seismic modeling and imaging." GEOPHYSICS 69, no. 4 (July 2004): 1053–70. http://dx.doi.org/10.1190/1.1778248.
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The isochron, the name given to a surface of equal two‐way time, has a profound position in seismic imaging. In this paper, I introduce a framework for construction of isochrons for a given velocity model. The basic idea is to let trajectories called isochron rays be associated with iso chrons in an way analogous to the association of conventional rays with wavefronts. In the context of prestack depth migration, an isochron ray based on conventional ray theory represents a simultaneous downward continuation from both source and receiver. The isochron ray is a generalization of the normal ray for poststack map migration. I have organized the process with systems of ordinary differential equations appearing on two levels. The upper level is model‐independent, and the lower level consists of conventional one‐way ray tracing. An advantage of the new method is that interpolation in a ray domain using isochron rays is able to treat triplications (multiarrivals) accurately, as opposed to interpolation in the depth domain based on one‐way traveltime tables. Another nice property is that the Beylkin determinant, an important correction factor in amplitude‐preserving seismic imaging, is closely related to the geometric spreading of isochron rays. For these reasons, the isochron ray has the potential to become a core part of future implementations of prestack depth migration. In addition, isochron rays can be applied in many contexts of forward and inverse seismic modeling, e.g., generation of Fresnel volumes, map migration of prestack traveltime events, and generation of a depth‐domain–based cost function for velocity model updating.
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Bonfanti, A., and M. Gillon. "MCMCI: A code to fully characterise an exoplanetary system." Astronomy & Astrophysics 635 (February 28, 2020): A6. http://dx.doi.org/10.1051/0004-6361/201936326.
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Context. Useful information can be retrieved by analysing the transit light curve of a planet-hosting star or induced radial velocity oscillations. However, inferring the physical parameters of the planet, such as mass, size, and semi-major axis, requires preliminary knowledge of some parameters of the host star, especially its mass or radius, which are generally inferred through theoretical evolutionary models. Aims. We seek to present and test a whole algorithm devoted to the complete characterisation of an exoplanetary system thanks to the global analysis of photometric or radial velocity time series combined with observational stellar parameters derived either from spectroscopy or photometry. Methods. We developed an integrated tool called MCMCI. This tool combines the Markov chain Monte Carlo (MCMC) approach of analysing photometric or radial velocity time series with a proper interpolation within stellar evolutionary isochrones and tracks, known as isochrone placement, to be performed at each chain step, to retrieve stellar theoretical parameters such as age, mass, and radius. Results. We tested the MCMCI on the HD 219134 multi-planetary system hosting two transiting rocky super Earths and on WASP-4, which hosts a bloated hot Jupiter. Even considering different input approaches, a final convergence was reached within the code, we found good agreement with the results already stated in the literature and we obtained more precise output parameters, especially concerning planetary masses. Conclusions. The MCMCI tool offers the opportunity to perform an integrated analysis of an exoplanetary system without splitting it into the preliminary stellar characterisation through theoretical models. Rather this approach favours a close interaction between light curve analysis and isochrones, so that the parameters recovered at each step of the MCMC enter as inputs for purposes of isochrone placement.
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Parrenin, F., R. C. A. Hindmarsh, and F. Rémy. "Analytical solutions for the effect of topography, accumulation rate and lateral flow divergence on isochrone layer geometry." Journal of Glaciology 52, no. 177 (2006): 191–202. http://dx.doi.org/10.3189/172756506781828728.
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AbstractThe effect of spatial variations in ice thickness, accumulation rate and lateral flow divergence on radar-detected isochrone geometry in ice sheets is computed using an analytical method, under assumptions of a steady-state ice-sheet geometry, a steady-state accumulation pattern and a horizontally uniform velocity shape function. By using a new coordinate transform, we show that the slope of the isochrones (with a normalized vertical coordinate) depends on three terms: a principal term which determines the sign of the slope, and two scale factors which can modify only the amplitude of the slope. The principal term depends only on a local characteristic time (ice thickness divided by accumulation rate minus melting rate) between the initial and final positions of the ice particle. For plug flow, only the initial and final values have an influence. Further applications are a demonstration of how the vertical velocity profile can be deduced from sharp changes in isochrone slopes induced by abrupt steps in bedrock or mass balance along the ice flow. We also demonstrate ways the new coordinate system may be used to test the accuracy of numerical flow models.
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Esmersoy, Cengiz, and Douglas Miller. "Backprojection versus backpropagation in multidimensional linearized inversion." GEOPHYSICS 54, no. 7 (July 1989): 921–26. http://dx.doi.org/10.1190/1.1442722.
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Seismic migration can be viewed as either backprojection (diffraction‐stack) or backpropagation (wave‐field extrapolation) (e.g., Gazdag and Sguazzero, 1984). Migration by backprojection was the view supporting the first digital methods—the diffraction and common tangent stacks of what is now called classical or statistical migration (Lindsey and Hermann, 1970; Rockwell, 1971; Schneider, 1971; Johnson and French, 1982). In this approach, each data point is associated with an isochron surface passing through the scattering object. Data values are then interpreted as projections of reflectivity over the associated isochrons. Dually, each image point is associated with a reflection‐time surface passing through the data traces. The migrated image at that point is obtained as a weighted stack of data lying on the reflection‐time surface (Rockwell, 1971; Schneider, 1971). This amounts to a weighted backprojection in which each data point contributes to image points lying on its associated isochron.
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Armstrong, Richard Lee, and Paul Ramaekers. "Sr isotopic study of Helikian sediment and diabase dikes in the Athabasca Basin, northern Saskatchewan." Canadian Journal of Earth Sciences 22, no. 3 (March 1, 1985): 399–407. http://dx.doi.org/10.1139/e85-038.
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The Athabasca Group overlies 1.8 Ga or older basement of the Churchill Province and predates uranium mineralization at 1.3 Ga. Cross-cutting diabase dikes have been dated by Rb–Sr mineral isochrons at 1.31 ± 0.07 Ga at Diabase Peninsula, Cree Lake, and 1.16 ± 0.04 Ga at Lazy Edward Bay, Cree Lake. Initial 87Sr/86Sr ratios for these dikes are 0.7040 ± 0.0005 and 0.7036 ± 0.002, respectively. Clastic sedimentary rocks of the Athabasca Group normally show limited variation in Rb/Sr and variable initial 87Sr/86Sr. Sedimentary rocks in two areas near the northern margin of the Athabasca Basin scatter about isochrons of 2.6 Ga, reflecting Archean provenance of detrital material and lack of Sr isotopic homogenization since deposition. Sediment of the tuffaceous Wolverine Point Formation, near Rumpel Lake, is much more variable in Rb/Sr and enriched in Rb relative to Sr and defines a 1.43 ± 0.03 Ga isochron with a 0.7057 ± 0.0005 initial ratio. This is possibly the age of deposition of the Athabasca Group.
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NG, Felix, and Edward C. King. "Kinematic waves in polar firn stratigraphy." Journal of Glaciology 57, no. 206 (2011): 1119–34. http://dx.doi.org/10.3189/002214311798843340.
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AbstractRadar studies of firn on the ice sheets have revealed complex folds on its internal layering that form from the interplay of snow accumulation and ice flow. A mathematical theory for these fold structures is presented, for the case where the radar cross section lies along the ice-flow direction and where the accumulation rate and ice-flow velocity are time-invariant. Our model, which accounts for firn densification, shows how ‘information’ (the depth and slope of isochrones) propagates on the radargram to govern its layer undulations. This leads us to discover universal rules behind the pattern of layer slopes on a distance–age domain and understand why the loci of layer-fold hinges curve, emerge and combine on the radargram to form closed loops that delineate areas of rising and plunging isochrones. We also develop a way of retrieving the accumulation rate distribution and layer ages from steady isochrone patterns. Analysis of a radargram from the onset zone of Bindschadler Ice Stream, West Antarctica, indicates that ice flow and accumulation rates have been steady there for the past ∼400 years, and that spatial anomalies in the latter are coupled to surface topography induced by ice flow over the undulating ice-stream bed. The theory provides new concepts for the morphological interpretation of radargrams.
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Demarque, Pierre. "Isochrones for late-type stars." Proceedings of the International Astronomical Union 4, S258 (October 2008): 383–94. http://dx.doi.org/10.1017/s1743921309032049.
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AbstractA brief summary of the history of stellar evolution theory and the use of isochrones is given. The present state of the subject is summarized. The major uncertainties in isochrone construction are considered: chemical abundances and color calibrations, and the treatment of turbulent convection in stellar interior and atmosphere models. The treatment of convection affects the modeling of stellar interiors principally in two ways: convective core overshoot which increases evolutionary lifetimes, and the depth of convection zones which determines theoretical radii. Turbulence also modifies atmospheric structure and dynamics, and the derivation of stellar abundances. The symbiosis of seismic techniques with increasingly more realistic three-dimensional radiation hydrodynamics simulations is transforming the study of late-type stars. The important case of very low mass stars, which are fully convective, is briefly visited.
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Bergbusch, Peter A., and Don A. VandenBerg. "Models for Old, Metal‐poor Stars with Enhanced α‐Element Abundances. III. Isochrones and Isochrone Population Functions." Astrophysical Journal 556, no. 1 (July 20, 2001): 322–39. http://dx.doi.org/10.1086/321571.
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Parrenin, Frédéric, and Richard Hindmarsh. "Influence of a non-uniform velocity field on isochrone geometry along a steady flowline of an ice sheet." Journal of Glaciology 53, no. 183 (2007): 612–22. http://dx.doi.org/10.3189/002214307784409298.
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The relationship between velocity field and isochrone geometry along a steady flowline of an ice sheet is examined. The method is analytical and based upon the stream function and its vertically normalized form, the normalized stream function (NSF). We show that the slope of the isochrones is the slope of the iso-NSF lines, plus a path term which is the cumulative result of the past trajectory of the ice particles. We illustrate this path term in three different examples: varying basal melting, varying basal sliding (Weertman effect) and varying velocity profile around a divide (Raymond effect). The path term generally counteracts the slope of the iso-NSF lines. In the case of the Raymond effect, it can even lead to depressions surrounding the bumps if the transition from dome to flank velocity profile is sufficiently abrupt.
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Casali, G., L. Magrini, E. Tognelli, R. Jackson, R. D. Jeffries, N. Lagarde, G. Tautvaišienė, et al. "The Gaia-ESO survey: Calibrating a relationship between age and the [C/N] abundance ratio with open clusters." Astronomy & Astrophysics 629 (September 2019): A62. http://dx.doi.org/10.1051/0004-6361/201935282.
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Context. In the era of large high-resolution spectroscopic surveys such as Gaia-ESO and APOGEE, high-quality spectra can contribute to our understanding of the Galactic chemical evolution by providing abundances of elements that belong to the different nucleosynthesis channels, and also by providing constraints to one of the most elusive astrophysical quantities: stellar age. Aims. Some abundance ratios, such as [C/N], have been proven to be excellent indicators of stellar ages. We aim at providing an empirical relationship between stellar ages and [C/N] using open star clusters, observed by the Gaia-ESO and APOGEE surveys, as calibrators. Methods. We used stellar parameters and abundances from the Gaia-ESO Survey and APOGEE Survey of the Galactic field and open cluster stars. Ages of star clusters were retrieved from the literature sources and validated using a common set of isochrones. We used the same isochrones to determine for each age and metallicity the surface gravity at which the first dredge-up and red giant branch bump occur. We studied the effect of extra-mixing processes in our sample of giant stars, and we derived the mean [C/N] in evolved stars, including only stars without evidence of extra mixing. By combining the Gaia-ESO and APOGEE samples of open clusters, we derived a linear relationship between [C/N] and (logarithmic) cluster ages. Results. We apply our relationship to selected giant field stars in the Gaia-ESO and APOGEE surveys. We find an age separation between thin- and thick-disc stars and age trends within their populations, with an increasing age towards lower metallicity populations. Conclusions. With this empirical relationship, we are able to provide an age estimate for giant stars in which C and N abundances are measured. For giant stars, the isochrone fitting method is indeed less sensitive than for dwarf stars at the turn-off. Our method can therefore be considered as an additional tool to give an independent estimate of the age of giant stars. The uncertainties in their ages is similar to those obtained using isochrone fitting for dwarf stars.
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Stevenson, Ross K., P. J. Patchett, and R. F. Martin. "Sm–Nd isochron from a granodiorite–granite complex in the Portman Lake region, Northwest Territories." Canadian Journal of Earth Sciences 26, no. 12 (December 1, 1989): 2724–29. http://dx.doi.org/10.1139/e89-232.
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Whole-rock samples for a granodiorite–granite intrusion in the Portman Lake area of the Northwest Territories yield an Sm–Nd isochron with an age of 2577 ± 36 Ma. The addition of a garnet analysis results in an age of 2562 ± 21 Ma. An Sm–Nd isochron is rare for granitic samples because of small ranges in 147Sm/144Nd values and variability in the initial Nd isotopic ratios. A wide range in 147Sm/144Nd values among samples in this study is considered a result of garnet fractionation and (or) variable concentrations of titanite in the samples. The εNd values for the initial Nd isotopic ratios of the isochrons are essentially zero or bulk Earth values. The evolution of the intrusion at 2.56 Ga reflects either the remelting of (2.7–2.8 Ga) preexisting continental crust or the mixing of depleted mantle material and crust older than 2.8 Ga. In either case, the data argue for a crustal history of at least 200 Ma prior to the intrusion of the complex in this section of the Churchill Province.
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Bossini, D., A. Vallenari, A. Bragaglia, T. Cantat-Gaudin, R. Sordo, L. Balaguer-Núñez, C. Jordi, et al. "Age determination for 269 Gaia DR2 open clusters." Astronomy & Astrophysics 623 (March 2019): A108. http://dx.doi.org/10.1051/0004-6361/201834693.
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Context. The Gaia Second Data Release provides precise astrometry and photometry for more than 1.3 billion sources. This catalog opens a new era concerning the characterization of open clusters and test stellar models, paving the way for better understanding of the disk properties. Aims. The aim of the paper is to improve the knowledge of cluster parameters, using only the unprecedented quality of the Gaia photometry and astrometry. Methods. We have made use of the membership determination based on the precise Gaia astrometry and photometry. We applied an automated Bayesian tool, BASE-9, to fit stellar isochrones on the observed G, GBP, GRP magnitudes of the high probability member stars. Results. We derive parameters such as age, distance modulus, and extinction for a sample of 269 open clusters, selecting only low reddening objects and discarding very young clusters, for which techniques other than isochrone-fitting are more suitable for estimating ages.
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Bell, Cameron P. M., Eric E. Mamajek, and Tim Naylor. "The Isochronal Age Scale of Young Moving Groups in the Solar Neighbourhood." Proceedings of the International Astronomical Union 10, S314 (November 2015): 41–48. http://dx.doi.org/10.1017/s1743921315006213.
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AbstractWe present a self-consistent, absolute isochronal age scale for young (≲ 200 Myr), nearby (≲ 100 pc) moving groups, which is consistent with recent lithium depletion boundary ages for both the β Pic and Tucana-Horologium moving groups. This age scale was derived using a set of semi-empirical pre-main-sequence model isochrones that incorporate an empirical colour-Teffrelation and bolometric corrections based on the observed colours of Pleiades members, with theoretical corrections for the dependence on logg. Absolute ages for young, nearby groups are vital as these regions play a crucial role in our understanding of the early evolution of low- and intermediate-mass stars, as well as providing ideal targets for direct imaging and other measurements of dusty debris discs, substellar objects and, of course, extrasolar planets.
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Artemiev, Dmitry, Robert Krymsky, Boris Belyatsky, and Dmitry Ashikhmin. "The age of mineralization of Mayskoe gold ore deposit (Central Chukotka): results of Re-Os isotopic dating." Journal of Mining Institute 243 (June 10, 2020): 266. http://dx.doi.org/10.31897/pmi.2020.3.266.
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The article presents the results of the sulfide mineralization dating of the Mayskoe gold ore deposit using the Re-Os isotope system and isochron age estimation method of the main sulfide minerals: arsenopyrite, pyrite, and antimonite. The complex multistage formation of the studied sulfides, as well as the close intergrowths of genetically different mineral phases, did not allow obtaining a single rhenium-osmium isochron corresponding to the formation time of sulfide mineralization. Isochrones for single minerals, collected from each sulfide sample, turned out to be the result of isotopically distinct components mixture (radiogenic crustal and non-radiogenic mantle) and do not make sense from the geochronological point of view. In terms of geology, the most significant result of the study is an age estimation of 128.8 ± 4.4 Ma, obtained for the sulfide mineralization of Mayskoe deposit using Re-Os isotope dating of single fractions of pyrite and antimonite of the ore mineralization stage. While arsenopyrite is most closely associated with gold mineralization, one of the arsenopyrite varieties corrodes framboidal pyrite of the pre-ore stage, has a maximum of the crust component in the osmium isotopic composition and forms a mixing line in the isochron diagram with an apparent formation age of 458 ± 18 Ma. The initial osmium isotopic composition of the studied sulfides indicates a mixed mantle-crust source of sulfide mineralization. The issue of simultaneous ore genesis and granitoid magmatism in the Mayskoe deposit remained unresolved (the age of granitoids according to the U-Pb zircon system is 108 Ma). However, a possible solution could be the further determination of the Re-Os isochron age of the ore mineralization sulphides from the single paragenesis of a specific sample containing both arsenopyrite and pyrite (+ antimonite) with gold.
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Ng, Felix, and Edward C. King. "Formation of RADARSAT backscatter feature and undulating firn stratigraphy at an ice-stream margin." Annals of Glaciology 54, no. 64 (2013): 90–96. http://dx.doi.org/10.3189/2013aog64a202.
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AbstractOn RADARSAT imagery, the southern margin of the onset zone of Bindschadler Ice Stream, West Antarctica, manifests a multi-banded feature, with brightness varying across the bands and oscillating along each band. Ground-based radar profiles across the margin reveal folds in the firn stratigraphy associated with this pattern and provide evidence for correlation between the depth of shallow isochrones and the RADARSAT backscatter intensity on each profile, allowing us to interpret the banded feature for firn-layer geometry in three dimensions. We use a kinematic model of isochrone depth evolution to show how layer folding and the band expression may result from deformation and advection in the near-surface flow field at ice-stream margins, even with steady flow. The model predicts the formation of longitudinally patterned bands when the ice-stream acceleration fluctuates along flow. Concerted study of the planform and stratigraphy of other RADARSAT-detected features on the ice sheets may help us understand their origin.
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Luu, Tu-Han, Edward D. Young, Matthieu Gounelle, and Marc Chaussidon. "Short time interval for condensation of high-temperature silicates in the solar accretion disk." Proceedings of the National Academy of Sciences 112, no. 5 (January 20, 2015): 1298–303. http://dx.doi.org/10.1073/pnas.1414025112.
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Chondritic meteorites are made of primitive components that record the first steps of formation of solids in our Solar System. Chondrules are the major component of chondrites, yet little is known about their formation mechanisms and history within the solar protoplanetary disk (SPD). We use the reconstructed concentrations of short-lived 26Al in chondrules to constrain the timing of formation of their precursors in the SPD. High-precision bulk magnesium isotopic measurements of 14 chondrules from the Allende chondrite define a 26Al isochron with 26Al/27Al = 1.2(±0.2) × 10−5 for this subset of Allende chondrules. This can be considered to be the minimum bulk chondrule 26Al isochron because all chondrules analyzed so far with high precision (∼50 chondrules from CV and ordinary chondrites) have an inferred minimum bulk initial (26Al/27Al) ≥ 1.2 × 10−5. In addition, mineral 26Al isochrons determined on the same chondrules show that their formation (i.e., fusion of their precursors by energetic events) took place from 0 Myr to ∼2 Myr after the formation of their precursors, thus showing in some cases a clear decoupling in time between the two events. The finding of a minimum bulk chondrule 26Al isochron is used to constrain the astrophysical settings for chondrule formation. Either the temperature of the condensation zone dropped below the condensation temperature of chondrule precursors at ∼1.5 My after the start of the Solar System or the transport of precursors from the condensation zone to potential storage sites stopped after 1.5 My, possibly due to a drop in the disk accretion rate.
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Muir Wood, David. "Analysis of consolidation with constant rate of displacement." Canadian Geotechnical Journal 53, no. 5 (May 2016): 740–52. http://dx.doi.org/10.1139/cgj-2015-0405.
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The “constant rate of strain” consolidation test has been widely used for several decades to provide a continuous load–displacement response. An exact theoretical solution can be obtained for this consolidation problem. Two other solution techniques have pedagogic advantage in their simplicity, and in their ability to (i) clarify the phases of response of the consolidating sample and (ii) be extended to incorporate additional details of material response or testing configuration. The parabolic isochrone technique imposes a particular mode shape on the isochrones at all times. Treating the sample as a single system, and applying the boundary conditions at the system level, the governing equation becomes an ordinary differential equation. For more elaborate soil properties or experimental procedures a finite difference description of the problem is readily programmed and solved. These solution techniques are used to illustrate the importance of distinguishing between the observed response of the system — the soil specimen under test — and the behaviour of the soil elements that make up this system. Examples are given of erroneous conclusions that might be drawn if this distinction is not recognised.
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Gudlaugsson, E., A. Humbert, T. Kleiner, J. Kohler, and K. Andreassen. "The influence of a model subglacial lake on ice dynamics and internal layering." Cryosphere Discussions 9, no. 4 (July 28, 2015): 3859–86. http://dx.doi.org/10.5194/tcd-9-3859-2015.
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Abstract. As ice flows over a subglacial lake, the drop in bed resistance leads to an increase in ice velocities and a subsequent draw-down of isochrones and cold ice from the surface. The ice surface flattens as it adjusts to the lack of resisting forces at the base. The rapid transition in velocity induces changes in temperature and ice viscosity, releasing deformation energy which raises the temperature locally. Recent studies of Antarctic subglacial lakes indicate that many lakes experience very fast and possibly episodic drainage, during which the lake size is rapidly reduced as water flows out. A question is what effect this would have on internal layers within the ice, and whether such past events could be inferred from isochrone structures downstream. Here, we study the effect of a subglacial lake on the dynamics of a model ice stream as well as the influence that such short timescale drainage would have on the internal layers of the ice. To this end, we use a Full–Stokes, polythermal ice flow model. An enthalpy gradient method is used to account for the evolution of temperature and water content within the ice. We find that the rapid transition between slow-moving ice outside the lake, and full sliding over the lake, releases large amounts of deformational energy, which has the potential to form a temperate layer at depth in the transition zone. In addition, we provide an explanation for a characteristic surface feature, commonly seen at the edges of subglacial lakes, a hummocky surface depression in the transition zone between little to full sliding. We also conclude that rapid changes in lake geometry or basal friction create a travelling wave at depth within the isochrone structure that transfers downstream with the advection of ice, thus indicating the possibility of detecting past events with ice penetrating radar.
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Gudlaugsson, Eythor, Angelika Humbert, Thomas Kleiner, Jack Kohler, and Karin Andreassen. "The influence of a model subglacial lake on ice dynamics and internal layering." Cryosphere 10, no. 2 (April 5, 2016): 751–60. http://dx.doi.org/10.5194/tc-10-751-2016.
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Abstract. As ice flows over a subglacial lake, the drop in bed resistance leads to an increase in ice velocities and a draw down of isochrones and cold ice. The ice surface flattens as it adjusts to the lack of resisting forces at the base. The rapid transition in velocity induces changes in ice viscosity and releases deformation energy that can raise the temperature locally. Recent studies of Antarctic subglacial lakes indicate that many lakes experience very fast and possibly episodic drainage, during which the lake size is rapidly reduced as water flows out. Questions that arise are what effect this would have on internal layers within the ice and whether such past drainage events could be inferred from isochrone structures downstream. Here, we study the effect of a subglacial lake on ice dynamics as well as the influence that such short timescale drainage would have on the internal layers of the ice. To this end, we use a full Stokes, polythermal ice flow model. An enthalpy-gradient method is used to account for the evolution of temperature and water content within the ice. We find that a rapid transition between slow-moving ice outside the lake, and full sliding over the lake, can release considerable amounts of deformational energy, with the potential to form a temperate layer at depth in the transition zone. In addition, we provide an explanation for a characteristic surface feature commonly seen at the edges of subglacial lakes, a hummocky surface depression in the transition zone between little to full sliding. We also conclude that rapid changes in the horizontal extent of subglacial lakes and slippery patches, compared to the average ice column velocity, can create a traveling wave at depth within the isochrone structure that transfers downstream with the advection of ice, thus indicating the possibility of detecting past drainage events with ice penetrating radar.
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Howes, Louise M., Lennart Lindegren, Sofia Feltzing, Ross P. Church, and Thomas Bensby. "Estimating stellar ages and metallicities from parallaxes and broadband photometry: successes and shortcomings." Astronomy & Astrophysics 622 (January 24, 2019): A27. http://dx.doi.org/10.1051/0004-6361/201833280.
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A deep understanding of the Milky Way galaxy, its formation and evolution requires observations of huge numbers of stars. Stellar photometry, therefore, provides an economical method to obtain intrinsic stellar parameters. With the addition of distance information – a prospect made real for more than a billion stars with the second Gaia data release – deriving reliable ages from photometry is a possibility. We have developed a Bayesian method that generates 2D probability maps of a star’s age and metallicity from photometry and parallax using isochrones. Our synthetic tests show that including a near-UV passband enables us to break the degeneracy between a star’s age and metallicity for certain evolutionary stages. It is possible to find well-constrained ages and metallicities for turn-off and sub-giant stars with colours including a U band and a parallax with uncertainty less than ∼20%. Metallicities alone are possible for the main sequence and giant branch. We find good agreement with the literature when we apply our method to the Gaia benchmark stars, particularly for turn-off and young stars. Further tests on the old open cluster NGC 188, however, reveal significant limitations in the stellar isochrones. The ages derived for the cluster stars vary with evolutionary stage, such that turn-off ages disagree with those on the sub-giant branch, and metallicities vary significantly throughout. Furthermore, the parameters vary appreciably depending on which colour combinations are used in the derivation. We identify the causes of these mismatches and show that improvements are needed in the modelling of giant branch stars and in the creation and calibration of synthetic near-UV photometry. Our results warn against applying isochrone fitting indiscriminately. In particular, the uncertainty on the stellar models should be quantitatively taken into account. Further efforts to improve the models will result in significant advancements in our ability to study the Galaxy.
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Cantat-Gaudin, T., A. Vallenari, R. Sordo, F. Pensabene, A. Krone-Martins, A. Moitinho, C. Jordi, et al. "Characterising open clusters in the solar neighbourhood with the Tycho-Gaia Astrometric Solution." Astronomy & Astrophysics 615 (July 2018): A49. http://dx.doi.org/10.1051/0004-6361/201731251.
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Context. The Tycho-Gaia Astrometric Solution (TGAS) subset of the first Gaia catalogue contains an unprecedented sample of proper motions and parallaxes for two million stars brighter than G ~ 12 mag. Aims. We take advantage of the full astrometric solution available for those stars to identify the members of known open clusters and compute mean cluster parameters using either TGAS or the fourth U.S. Naval Observatory CCD Astrograph Catalog (UCAC4) proper motions, and TGAS parallaxes. Methods. We apply an unsupervised membership assignment procedure to select high probability cluster members, we use a Bayesian/Markov Chain Monte Carlo technique to fit stellar isochrones to the observed 2MASS JHKS magnitudes of the member stars and derive cluster parameters (age, metallicity, extinction, distance modulus), and we combine TGAS data with spectroscopic radial velocities to compute full Galactic orbits. Results. We obtain mean astrometric parameters (proper motions and parallaxes) for 128 clusters closer than about 2 kpc, and cluster parameters from isochrone fitting for 26 of them located within a distance of 1 kpc from the Sun. We show the orbital parameters obtained from integrating 36 orbits in a Galactic potential.
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van Berkel, Kees. "Beware the isochronic fork." Integration 13, no. 2 (June 1992): 103–28. http://dx.doi.org/10.1016/0167-9260(92)90001-f.
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Bell, V. A., and R. J. Moore. "A grid-based distributed flood forecasting model for use with weather radar data: Part 1. Formulation." Hydrology and Earth System Sciences 2, no. 2/3 (September 30, 1998): 265–81. http://dx.doi.org/10.5194/hess-2-265-1998.
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Abstract. A practical methodology for distributed rainfall-runoff modelling using grid square weather radar data is developed for use in real-time flood forecasting. The model, called the Grid Model, is configured so as to share the same grid as used by the weather radar, thereby exploiting the distributed rainfall estimates to the full. Each grid square in the catchment is conceptualised as a storage which receives water as precipitation and generates water by overflow and drainage. This water is routed across the catchment using isochrone pathways. These are derived from a digital terrain model assuming two fixed velocities of travel for land and river pathways which are regarded as model parameters to be optimised. Translation of water between isochrones is achieved using a discrete kinematic routing procedure, parameterised through a single dimensionless wave speed parameter, which advects the water and incorporates diffusion effects through the discrete space-time formulation. The basic model routes overflow and drainage separately through a parallel system of kinematic routing reaches, characterised by different wave speeds but using the same isochrone-based space discretisation; these represent fast and slow pathways to the basin outlet, respectively. A variant allows the slow pathway to have separate isochrones calculated using Darcy velocities controlled by the hydraulic gradient as estimated by the local gradient of the terrain. Runoff production within a grid square is controlled by its absorption capacity which is parameterised through a simple linkage function to the mean gradient in the square, as calculated from digital terrain data. This allows absorption capacity to be specified differently for every grid square in the catchment through the use of only two regional parameters and a DTM measurement of mean gradient for each square. An extension of this basic idea to consider the distribution of gradient within the square leads analytically to a Pareto distribution of absorption capacity, given a power distribution of gradient within the square. The probability-distributed model theory (Moore, 1985) can then be used directly to obtain the integrated runoff production for the square for routing to the catchment outlet. justification for the simple linkage function is in part sought through consideration of variants on the basic model where (i) runoff production is based on a topographic index control on saturation and (ii) absorption capacity is related to the Integrated Air Capacity of the soil, as obtained from soil survey. An impervious area fraction is also introduced based on the use of Landsat classified urban areas. The Grid Model and its variants are assessed in Part 2 (Bell and Moore, 1998), first as simulation models and then as forecasting models, following the development of updating procedures to accommodate recent observations of flow so as to improve forecast performance in a real-time context.
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Chiosi, Cesare, and Luisa Pigatto. "The Distance Modulus of LMC." Symposium - International Astronomical Union 116 (1986): 513–14. http://dx.doi.org/10.1017/s0074180900149484.
Full textAbstract:
Deep CCD photometry of the star clusters NGC2162 and NGC2190 in LMC presented by Schommer et al. (1984) is used togheter with new evolutionary models computed by Bertelli et al. (1985a) which take into account overshooting from convective cores, to derive the clusters ages and the distance modulus of LMC. A preliminary analysis of the two clusters indicates that NGC 2162 and NGC 2190 belong to the same class of clusters discussed by Barbaro and Pigatto (1984). In fact, for the turn-off mass estimated by means of classical models (<2.2m⊙) these clusters should possess an extended red giant branch and a bimodal distribution of red stars (cifr. Fig.2). On the contrary they show a clump of red stars. This means that ages and other properties derived from classical models for this range of masses, may not correspond to reality. With the new models, stars of mass as low as 1.6 m⊙, ignite helium in non degenerate conditions, avoid the long lived RG phase, and burn helium as more massive stars. As consequence of it, a clump of red giants is expected. In Fig.1, we show new isochrones (Bertelli et al. 1985b) derived from models with overshooting, overlaid to the CM diagram of NGC 2162. Theoretical luminosities and Teff's are converted into Mv:(B-V)o plane by means of Teff:(B-V):BC scales based on models atmospheres collected from several authors (Chiosi, 1985). At any given age, the new isochrones run brighter than those of Ciardullo and Demarque (1977). By means of the luminosity function, a method more objective (Paczsynski, 1984) than the standard one of ZAMS and/or isochrone fitting, with a reddening of E(B-V)=0.06 and chemical composition X=0.700 and Z=0.02, we find ages of 1 109yr and a true distance modulus of (m-M)O=18.6 instead of 18.2±0.2 mag given by Schommer et al.(1984). Fig.2 shows the theoretical luminosity function at age 1 109yr, (age preliminarly assigned to the clusters by isochrone fitting) for main sequence and red giant stars obtained with Salpeter's IMF (top panel), compares it with the correspondent one of Ciardullo and Demarque(1977), and finally shows the observational LF we derive from stars counts(bottom panel) for NGC 2162. By imposing coincidence between theoretical and observational LF's at the side of main sequence fall-off and rising of the red giant clump, we derive the distance modulus (m-M)O=18.6. In conclusions, models with overshooting not only interpret the morphology of this class of clusters, but assigne LMC a distance modulus in agreement with other independent determinations (Walker, 1984; Visvanathan, 1985).
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Chiosi, Cesare, and Luisa Pigatto. "The Distance Modulus of LMC." Symposium - International Astronomical Union 116 (1986): 513–14. http://dx.doi.org/10.1017/s0074180900149575.
Full textAbstract:
Deep CCD photometry of the star clusters NGC2162 and NGC2190 in LMC presented by Schommer et al. (1984) is used togheter with new evolutionary models computed by Bertelli et al. (1985a) which take into account overshooting from convective cores, to derive the clusters ages and the distance modulus of LMC. A preliminary analysis of the two clusters indicates that NGC 2162 and NGC 2190 belong to the same class of clusters discussed by Barbaro and Pigatto (1984). In fact, for the turn-off mass estimated by means of classical models (<2.2mO) these clusters should possess an extended red giant branch and a bimodal distribution of red stars (cifr. Fig.2). On the contrary they show a clump of red stars. This means that ages and other properties derived from classical models for this range of masses, may not correspond to reality. With the new models, stars of mass as low as 1.6 mO, ignite helium in non degenerate conditions, avoid the long lived RG phase, and burn helium as more massive stars. As consequence of it, a clump of red giants is expected. In Fig.1, we show new isochrones (Bertelli et al. 1985b) derived from models with overshooting, overlaid to the CM diagram of NGC 2162. Theoretical luminosities and Teff's are converted into Mv:(B-V)o plane by means of Teff:(B-V):BC scales based on models atmospheres collected from several authors (Chiosi, 1985). At any given age, the new isochrones run brighter than those of Ciardullo and Demarque (1977). By means of the luminosity function, a method more objective (Paczsynski, 1984) than the standard one of ZAMS and/or isochrone fitting, with a reddening of E(B-V)=0.06 and chemical composition X=0.700 and Z=0.02, we find ages of 1 109yr and a true distance modulus of (m-M)O=18.6 instead of 18.2±0.2 mag given by Schommer et al.(1984). Fig.2 shows the theoretical luminosity function at age 1 109yr, (age preliminarly assigned to the clusters by isochrone fitting) for main sequence and red giant stars obtained with Salpeter's IMF (top panel), compares it with the correspondent one of Ciardullo and Demarque(1977), and finally shows the observational LF we derive from stars counts(bottom panel) for NGC 2162. By imposing coincidence between theoretical and observational LF's at the side of main sequence fall-off and rising of the red giant clump, we derive the distance modulus (m-M)O=18.6. In conclusions, models with overshooting not only interpret the morphology of this class of clusters, but assigne LMC a distance modulus in agreement with other independent determinations (Walker, 1984; Visvanathan, 1985).
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Dejonghe, Herwig. "Spherical isochrone models revisited." Monthly Notices of the Royal Astronomical Society 500, no. 1 (October 27, 2020): 1340–42. http://dx.doi.org/10.1093/mnras/staa3331.
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Bergbusch, Peter A. "Isochrone Probability Functions for Old Stellar Systems." Symposium - International Astronomical Union 190 (1999): 345–46. http://dx.doi.org/10.1017/s0074180900118170.
Full textAbstract:
The isochrone probability function (IPF) is derived from the slope of the mass–distance relation on an isochrone in where the distance along the isochrone is computed with respect to some arbitrary, well-defined point. IPFs contain the information needed to calculate both luminosity functions and color functions, and they provide a straightforward way of generating synthetic stellar populations.
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Grushka, Eli, and Ibrahim Atamna. "Isochronal optimization." Journal of Chromatography A 400 (July 1987): 5–20. http://dx.doi.org/10.1016/s0021-9673(01)81594-6.
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