THE ANALYTIC BASIS OF GRAVITY INTERPRETATION

Geophysics ◽  
1942 ◽  
Vol 7 (2) ◽  
pp. 169-178 ◽  
Author(s):  
D. S. Hughes
Keyword(s):  
Analytic Continuation ◽  
High Precision ◽  
Continuation Method ◽  
Resolving Power ◽  
Surface Gravity ◽  
Gravity Interpretation ◽  
Very High ◽  
Gravity Profile

One method of gravity interpretation involves the use of analytic continuation processes. In this discussion the resolving power of this method is tested numerically. Using hypothetical structures comprising single and double blocks, a surface‐gravity profile is derived. Using these values as an “observed gravity” profile, the “continuation” method is applied to compute the gravity at intermediate depths. Comparing these computed values with the actual (directly computed) gravity profile at these depth‐planes, the resolving power of the continuation method is demonstrated. It is shown that a very high precision in the observed data is necessary for very accurate resolution of structures.

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

scholarly journals Equipartition principle for Wigner matrices

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhigang Bao ◽  
László Erdős ◽  
Kevin Schnelli
Keyword(s):  
High Precision ◽  
Quantum Systems ◽  
Wigner Matrices ◽  
Very High

Abstract We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices.

Formation flying for very high precision astrometry: NEAT and micro-NEAT mission concepts

2014 ◽  
Vol 2 (1) ◽  
pp. 3 ◽  
Author(s):  
Fabien Malbet ◽  
Alexis Brandeker ◽  
Alain Léger ◽  
Bjorn Jakobsson ◽  
Renaud Goullioud ◽  
...  
Keyword(s):  
High Precision ◽  
Formation Flying ◽  
Very High ◽  
Precision Astrometry

scholarly journals Bounds on the complex permittivity of polycrystalline materials by analytic continuation

2015 ◽  
Vol 471 (2174) ◽  
pp. 20140702 ◽  
Author(s):  
A. Gully ◽  
J. Lin ◽  
E. Cherkaev ◽  
K. M. Golden
Keyword(s):  
Sea Ice ◽  
Single Crystal ◽  
Analytic Continuation ◽  
Complex Permittivity ◽  
Crystal Orientation ◽  
Fluid Transport ◽  
Continuation Method ◽  
Growth Conditions ◽  
Polycrystalline Materials ◽  
Remote Sensing Techniques

An analytic continuation method for obtaining rigorous bounds on the effective complex permittivity ε * of polycrystalline composite materials is developed. It is assumed that the composite consists of many identical anisotropic crystals, each with a unique orientation. The key step in obtaining the bounds involves deriving an integral representation for ε *, which separates parameter information from geometrical information. Forward bounds are then found using knowledge of the single crystal permittivity tensor and mean crystal orientation. Inverse bounds are also developed, which recover information about the mean crystal orientation from ε *. We apply the polycrystalline bounds to sea ice, a critical component of the climate system. Different ice types, which result from different growth conditions, have different crystal orientation and size statistics. These characteristics significantly influence the fluid transport properties of sea ice, which control many geophysical and biogeochemical processes important to the climate and polar ecosystems. Using a two-scale homogenization scheme, where the single crystal tensor is numerically computed, forward bounds for sea ice are obtained and are in excellent agreement with columnar sea ice data. Furthermore, the inverse bounds are also applied to sea ice, helping to lay the groundwork for determining ice type using remote sensing techniques.

Confined orbitals in fullerenes and quantum dots calculated by analytic continuation method

2021 ◽  
Vol 75 (3) ◽  
Author(s):  
Milagros F. Morcillo-Arencibia ◽  
José Manuel Alcaraz-Pelegrina ◽  
Antonio J. Sarsa
Keyword(s):  
Quantum Dots ◽  
Analytic Continuation ◽  
Continuation Method

Vibration-rotation bands and rotational constants of dideuteroacetylene

1955 ◽  
Vol 232 (1190) ◽  
pp. 291-309 ◽  
Keyword(s):  
Resolving Power ◽  
Vibrational States ◽  
Absorption Bands ◽  
Rotational Constants ◽  
Vibrational Assignments ◽  
Vibrational Anharmonicity ◽  
A Value ◽  
Vibrational Levels ◽  
Vibration Rotation ◽  
Very High

Nine vibrational absorption bands of dideutero-acetylene have been examined with very high resolving power. The rotational constants have been determined for the vibrational levels concerned, and the coefficients α i have been determined with more convincing accuracy than previously. In some of the bands the Q branches have been resolved, so that the l -doubling coefficients q i could be derived, and details could be established about the doublet components in some II levels. The results emphasize the need of high resolution if the vibrational assignments are to be unambiguous, and if reliable values of the rotational constants are to be derived. A value of B e has been obtained, and the vibrational anharmonicity coefficients have been considered briefly. Estimates of the centrifugal stretching constants D i in different vibrational states have been made, and one anomalous case has been found.

scholarly journals Densified Pupil Spectrograph as High-precision Radial Velocimetry: From Direct Measurement of the Universe’s Expansion History to Characterization of Nearby Habitable Planet Candidates

2022 ◽  
Vol 163 (2) ◽  
pp. 63
Author(s):  
Taro Matsuo ◽  
Thomas P. Greene ◽  
Mahdi Qezlou ◽  
Simeon Bird ◽  
Kiyotomo Ichiki ◽  
...  
Keyword(s):  
Radial Velocity ◽  
Direct Measurement ◽  
High Precision ◽  
Resolving Power ◽  
Line Of Sight ◽  
High Dispersion ◽  
Velocity Measurements ◽  
Habitable Planet ◽  
Airy Disk

Abstract The direct measurement of the universe’s expansion history and the search for terrestrial planets in habitable zones around solar-type stars require extremely high-precision radial-velocity measures over a decade. This study proposes an approach for enabling high-precision radial-velocity measurements from space. The concept presents a combination of a high-dispersion densified pupil spectrograph and a novel line-of-sight monitor for telescopes. The precision of the radial-velocity measurements is determined by combining the spectrophotometric accuracy and the quality of the absorption lines in the recorded spectrum. Therefore, a highly dispersive densified pupil spectrograph proposed to perform stable spectroscopy can be utilized for high-precision radial-velocity measures. A concept involving the telescope’s line-of-sight monitor is developed to minimize the change of the telescope’s line of sight over a decade. This monitor allows the precise measurement of long-term telescope drift without any significant impact on the Airy disk when the densified pupil spectra are recorded. We analytically derive the uncertainty of the radial-velocity measurements, which is caused by the residual offset of the lines of sight at two epochs. We find that the error could be reduced down to approximately 1 cm s−1, and the precision will be limited by another factor (e.g., wavelength calibration uncertainty). A combination of the high-precision spectrophotometry and the high spectral resolving power could open a new path toward the characterization of nearby non-transiting habitable planet candidates orbiting late-type stars. We present two simple and compact highly dispersed densified pupil spectrograph designs for cosmology and exoplanet sciences.

A HIGHLY ACCURATE BOOTSTRAPPING ALGORITHM FOR WORD SENSE DISAMBIGUATION

2001 ◽  
Vol 10 (01n02) ◽  
pp. 5-21 ◽  
Author(s):  
RADA F. MIHALCEA ◽  
DAN I. MOLDOVAN
Keyword(s):  
High Precision ◽  
Word Sense Disambiguation ◽  
Original Text ◽  
Word Sense ◽  
New Words ◽  
Input Text ◽  
Ambiguous Words ◽  
Sense Disambiguation ◽  
Very High

In this paper, we present a bootstrapping algorithm for Word Sense Disambiguation which succeeds in disambiguating a subset of the words in the input text with very high precision. It uses WordNet and a semantic tagged corpus, for the purpose of identifying the correct sense of the words in a given text. The bootstrapping process initializes a set of ambiguous words with all the nouns and verbs in the text. It then applies various disambiguation procedures and builds a set of disambiguated words: new words are sense tagged based on their relation to the already disambiguated words, and then added to the set. This process allows us to identify, in the original text, a set of words which can be disambiguated with high precision; 55% of the verbs and nouns are disambiguated with an accuracy of 92%.

CANADIAN STANDARD OF FREQUENCY

1959 ◽  
Vol 37 (1) ◽  
pp. 10-18 ◽  
Author(s):  
S. N. Kalra ◽  
C. F. Pattenson ◽  
M. M. Thomson
Keyword(s):  
High Precision ◽  
Phase Measurement ◽  
Frequency Standard ◽  
Frequency Stability ◽  
Absolute Frequency ◽  
Standard Frequency ◽  
Astronomical Observations ◽  
The Past ◽  
Time Signals ◽  
Very High

Over the past 3 years a frequency standard of very high precision has been installed in Canada. It is composed of equipment located in three different laboratories in Ottawa, Ontario, but separated by a few miles. Intercomparison of frequency between these laboratories, which is done by sending signals over telephone lines and related techniques, is briefly described. Results indicate frequency stability of about 2:1010 over short and long periods. Absolute frequency is determined from astronomical observations. International inter-comparison is carried out by phase measurement of standard frequency and by observations of time signals; some of the results are presented.

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