Magnitude Of Various Terms Research Articles

Barycentric Corrections at 1 cm s-1 for Precise Doppler Velocities

The goal of this paper is to establish the requirements of a barycentric correction with an rms of ≲1 cm s-1, which is an order of magnitude better than necessary for the Doppler detection of true Earth analogs (∼9 cm s-1). We describe the theory and implementation of accounting for the effects on precise Doppler measurements of motion of the telescope through space, primarily from rotational and orbital motion of the Earth, and the motion of the solar system with respect to target star (i.e., the “barycentric correction”). We describe the minimal algorithm necessary to accomplish this and how it differs from a naïve subtraction of velocities (i.e., a Galilean transformation). We demonstrate the validity of code we have developed from the California Planet Survey code via comparison with the pulsar timing package, TEMPO2. We estimate the magnitude of various terms and effects, including relativistic effects, and the errors associated with incomplete knowledge of telescope position, timing, and stellar position and motion. We note that chromatic aberration will create uncertainties in the time of observation, which will complicate efforts to detect true Earth analogs. Our code is available for public use and validation.

Iupac: a report of IUPAC commission 1.2 on thermodynamics: Standard quantities in chemical thermodynamics. Fugacities, activities, and equilibrium constants for pure and mixed phases

The standard chemical potential μ° is defined in terms of a specified state of aggregation, a specified temperature, a specified standard pressure, and if needed a specified standard molality. Other standard thermodynamic quantities are obtained from μ° by the usual mathematical operations. In this report, definitions are given for the standard chemical potential of a substance B in the following states of aggregation: gas phase whether pure or mixed, condensed phase whether pure or mixed, solvent substance in solution, and solute substance in solution. Fugacities and virial coefficients are introduced in the discussion of gases, and activity, activity coefficients, and osmotic coefficients in the discussion of condensed phases. Expressions for the standard equilibrium constant are given for a reaction in the gas phase, in a condensed phase, and in a solution. Some numerical examples are given and relative magnitudes of various terms in the equations are illustrated.

Hierarchial structure theory for basic equations of fluid mechanics (BEFM) and the simplified Navier-Stokes equations (SNSE)

A hierarchial structure for the basic equations of fluid mechanics (BEFM) is found through the analysis of scales of length and time that proves a measure of the rate of change of the quantities describing the motion of the fluid as well as an estimation of the order of magnitude of various terms included in BEFM. The hierarchial structure theory shows that if (1) the characteristic Reynolds numbersRe is larger than unity and (2) the length scale in one coordinate direction is larger than that in other coordinate directions. BEFM can be classified into some levels according to the estimation of the order of magnitude of various terms included in BEFM. The hierarchial structure of BEFM has two branches: one is from BLE- to BEFM inner hierarchy, the other is from EE- to BEFM outer hierarchy, where BLE and EE are abbreviations of the boundary-layer equations and of Euler equations, respectively. The relationship between the two branches of the hierarchial structure, the characteristics, subcharacteristics and mathematical properties of the hierarchial equations are studied. A comparison between the present hierarchial equations and the Simplified Navier-Stokes equations (SNSE) appeared in literatures is also made. BLE-, EE-and Inner-outer-matched (IOM) equations hierarchies are the most important and useful three levels for solving viscous flow-fields approximately.

A Study on Dimensional Analysis for Air-Water Flow System

A simplified exposition and its consequence are given for the dimensional analysis. We have first discussed Buckingham’s π theorem, which provides a guide to the number of dimensions parameters required to specify any particular phenomenon. The influence of dimensional analysis on air-water flow system is described in details and is applied to scaling the measurements of void fraction distributions in vertical circular plunging jets. This study highlights the dimensional analysis on air-water flow system, which is a convenient technique for estimating the magnitudes of various terms in the governing equations. Key words: Dimension analysis; Buckingham’s theorem; Air-water flow; Void fraction. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 11-18 DOI: http://dx.doi.org/10.3329/ganit.v30i0.8498

A PRELIMINARY ESTIMATE OF THE ICE-SEASON ENERGY BALANCE FOR THE NIAGARA RIVER

Summary The Meteorological Service of Canada and the Ontario Hydro-Electric Power Commission are conducting an International Hydrologic Decade study of ice formation and dissipation on the upper Niagara River. As a contribution to this project, an estimate of the energy balance of the river has been made, based on long term climatological data and on hydrological observations obtained during the 1967 ice season. This paper discusses the magnitudes of various terms in the energy balance equation and suggests applications of the energy budget approach to problems of ice forecasting.

Mobility of gaseous lons in weak electric fields

Kihara's extension of the Chapman-Enskog theory of transport phenomena is used to obtain the second order and third order approximations to the mobility of gaseous ions in a weak electric field as a function of temperature and field strength. In this method it is assumed that there is no charge exchange between ions and molecules, there is no clustering, and that quantum effects can be neglected. The mobility is expressed as a series in ascending powers of the square of the field strength with coefficients which are complicated functions of the temperature, the mass ratio of the ions and molecules, and of the force law between the ions and molecules. The collision integrals which enter into the coefficients have been evaluated by numerical integration for a force law which takes into account the charge-induced dipole, charge-induced quadrupole, and the London dispersion forces, and an inverse twelfth power repulsion potential. In the potential energy function three disposable parameters specify the depth and position of the minimum, and the relative magnitudes of various terms. The results of the present calculation are then used to analyze published experimental data on mobility to obtain the disposable parameters which determine the ion-molecule force law. The agreement between theory and experiment is good except for those cases in which clustering is to be expected.