Different Sets Of Constants Research Articles

Analysis of the Influence of the Length Scales in a Boundary-Layer Model

We consider the Janjic (NCEP Office Note 437:61, 2001) boundary-layer model, which is one of the most widely used in numerical weather prediction models. This boundary-layer model is based on a number of length scales that are, in turn, obtained from a master length multiplied by constants. We analyze the simulation results obtained using different sets of constants with respect to measurements using sonic anemometers, and interpret these results in terms of the turbulence processes in the atmosphere and of the role played by the different length scales. The simulations are run on a virtual machine on the Chameleon cloud for low-wind-speed, unstable, and stable conditions.

An Alternative Set of Defining Constants for Use in Redefining the Four Units of the International System of Units

Different sets of constants the fixed values of which may be selected for new definitions of the four units (kilogram, mole, ampere, and kelvin) of the International System of Units are discussed. The concept of the “order of a constant” in a given system of units is proposed. Criteria for arriving at an optimal selection of defining constants as well as a set of constants consisting of Planck’s constant h, Avogadro’s constant N A, Boltzmann’s constant k, and the magnetic permeability of a vacuum (magnetic constant) μ0 are considered. The proposed set is an alternative to the base set consisting of h, e, k, and N A.

Internal consistency of the inorganic carbon system in the Arctic Ocean

AbstractHighly accurate and precise measurements of the inorganic carbon system are crucial for monitoring and assessing the uptake of anthropogenic CO2 by the ocean. The Arctic Ocean is an area of particular interest due to Arctic amplification of climate change. Internally consistent constants are essential for making high quality CO2 system measurements and for calculating the full suite of carbon parameters. Temperatures and salinities in the Arctic are near or below the valid ranges of most carbon system constants, but the applicability has never been fully assessed in the Arctic. Using measurements of all four carbon parameters (total alkalinity, total CO2, pH, and pCO2) made on the Arctic GEOTRACES/GO‐SHIP cruise in summer 2015, we evaluate the internal consistency of six different sets of constants for surface waters at in situ temperature. Five of the six sets of constants are generally internally consistent, but each is statistically significantly different from each other. Although differences among constants are generally within the uncertainty of the calculations, these results indicate caution should be used when comparing data using different constants as biases may result from the choice of constants. We also find significant uncertainty in converting measured pH to pH at in situ temperature. The uncertainty in the pH temperature conversion limits our ability to determine the accuracy of pH measurements, particularly in polar regions. Measurements in marginal ice zones indicate that dissolution of semi‐stable ikaite (CaCO3) may bias total alkalinity measurements, and should therefore be analyzed immediately upon collection or filtered before storage.

Computational fluid dynamics investigation of alternative nitric oxide emission mechanisms in a hydrogen-fueled spark-ignition engine

Abstract In the present work, the reaction mechanisms of nitric oxide (NO) are investigated in a hydrogen-fueled, spark-ignition engine during load variation by mixture leaning. As these exhaust emissions are practically the only ones emitted from such engines, there is an obvious vivid interest for their reliable prediction under different operating conditions and modes, in order to investigate the potential future use of hydrogen in engines. For that purpose, a 3D-CFD (three dimensional – computational fluid dynamics) code is applied, which has been developed by the authors and validated extensively in the past under both motoring and firing conditions, being capable to simulate in high detail the in–cylinder processes. The CFD simulation has been accomplished using different sets of constants of the thermal NO mechanism, widely known as “Zeldovich mechanism”, to provide insight into the NO production pattern at each location in the cylinder during the combustion and expansion periods. The NO emission modeling has been enhanced here with the addition of alternative production paths, such as via the NNH and N2O species formation. The NNH path has been shown to be favored at lean and low-temperature combustion conditions for hydrogen flames, whereas the N2O path becomes important for lean flames irrespectively of the fuel used. The calculations are compared with available measurements, in order to quantify the applicability of the different sets of constants and the use of these alternative production paths at such conditions and applications. For the high load cases the NO predictions have good accuracy, since the constants used have been mainly derived at such high temperature conditions where additionally the thermal NO is almost the exclusive production path. On the contrary at mid and low engine loads, when the combustion temperature is lower and leaner mixtures are used, a significant discrepancy exists between the calculations and the measured data, which is however improved especially when the NNH route is taken into consideration.

Analysis of an open-air swimming pool solar heating system by using an experimentally validated TRNSYS model

In the case of private outdoor swimming pools, seldom larger than 100 m 2, conventional auxiliary heating systems are being installed less and less. Solar heating is an option to extend the swimming season. The temperature evolution of an open-air swimming pool highly depends on the wind speed directly on the water surface, which at the same time is influenced by the surroundings of the pool. In this paper, the TRNSYS model of a private open-air pool with a 50-m 2 surface was validated by registering the water temperature evolution and the meteorological data at the pool site. Evaporation is the main component of energy loss in swimming pools. Six different sets of constants found in literature were considered to evaluate the evaporative heat transfer coefficient with the purpose of finding the most suitable one for the TRNSYS pool model. In order to do that, the evolution of the pool water temperature predicted by the TRNSYS pool model was compared with the experimentally registered one. The simulation with TRNSYS of the total system, including the swimming pool and the absorber circuit integrated into the existing filter circuit, provided information regarding the increase of the pool temperature for different collector areas during the swimming season. This knowledge, together with the economic costs, support the decision about the absorber field size.

Thoughts on a changing SI

The trend towards an International System of Units (SI) based on fundamental constants has been confirmed and recent actions could result in the redefinition of the four units still necessary to cover all the quantities of interest for physics and chemistry. In this paper some issues whose solution is becoming critical with the approach of the General Conference on Weights and Measures (CGPM) of 2011 are discussed. The traditional kinds of definition and the new proposals are considered on the basis of their mathematical expressions and the advantageous features of the most advanced proposal are pointed out. The problem of choosing the set of fundamental constants to be adopted as reference quantities for the SI units is addressed and a general rule for verifying that the set is sufficient and non-redundant is pointed out in the form of a linear system giving also expressions of all the units as functions of the reference constants. A partial application to the most important units and different sets of constants offers some comparative criteria and shows the advantages of a set including both h and me. A general condition to be fulfilled by an experiment in order to realize an SI unit is given and a procedure suitable to optimize the availability of the best relization on a global basis is outlined. Finally, the dissemination process is analysed to show that the implied comparisons of standards at any level are not affected by the realization uncertainty, so that the process can be continued with the same standards, independently of any change in the basic reference quantities of the unit system.

Constants of geodesic motion in higher-dimensional black-hole spacetimes

In [Phys. Rev. Lett. 98, 061102 (2007)], we announced the complete integrability of geodesic motion in the general higher-dimensional rotating black-hole spacetimes. In the present paper we prove all the necessary steps leading to this conclusion. In particular, we demonstrate the independence of the constants of motion and the fact that they Poisson commute. The relation to a different set of constants of motion constructed in [J. High Energy Phys. 02 (2007) 004] is also briefly discussed.

Response of boron carbide subjected to high-velocity impact

This article presents an evaluation of the response of boron carbide (B 4C) subjected to impact loading under three different conditions. Condition A is produced by plate-impact experiments where the loading condition is uniaxial strain and the stresses and pressures are high. Under plate-impact loading the material fails at the Hugoniot Elastic Limit (HEL) and the failed material undergoes high confining pressures and relatively small inelastic strains. Condition B is produced by projectile impact onto thick targets where the stresses and pressures are dependent on impact velocity, but they are generally lower than those from plate impact. Under thick-target impact/penetration most of the material fails under compression, the inelastic strains are large and the material appears to exhibit more ductility than under condition A. Lastly, condition C is produced by projectile impact and perforation of thin targets where the stresses and pressures are a combination of compression and tension. Under thin-target perforation the material fails in both tension and compression. The Johnson–Holmquist–Beissel (JHB) constitutive model is used to evaluate the material behavior for each of the three conditions, but it is not possible to accurately reproduce the experimental results of the three conditions with a single set of constants. Instead, three different sets of constants are required to accurately model the three impact conditions. These three models/constants are used to provide insight into the complex response of B 4C, and to identify possible mechanisms that are not included in the JHB model.

Celestial mechanics in Kerr spacetime

The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy E, the axial component of the angular momentum, Lz, and Carter's constant Q. These parameters are obtained by solving the Hamilton–Jacobi equation for the dynamical problem of geodesic motion. Employing the action-angle variable formalism, on the other hand, yields a different set of constants of motion, namely, the fundamental frequencies ωr, ωθ and ωϕ associated with the radial, polar and azimuthal components of orbital motion, respectively. These frequencies, naturally, determine the time scales of orbital motion and, furthermore, the instantaneous gravitational wave spectrum in the adiabatic approximation. In this paper, it is shown that the fundamental frequencies are geometric invariants and explicit formulae in terms of quadratures are derived. The numerical evaluation of these formulae in the case of a rapidly rotating black hole illustrates the behaviour of the fundamental frequencies as orbital parameters, such as the semi-latus rectum p, the eccentricity e or the inclination parameter θ− are varied. The limiting cases of circular, equatorial and Keplerian motion are investigated as well and it is shown that known results are recovered from the general formulae.

High-resolution rotational coherence spectroscopy of para-cyclohexylaniline

A high-resolution rotational coherence spectroscopy (RCS) investigation of para-cyclohexylaniline (pCHA) was performed with a solid-state picosecond laser setup, which allowed for the determination of rotational constants with unprecedented precision for a RCS experiment. The technique of time-resolved fluorescence depletion was used for the RCS measurements. The unique structural features of pCHA enabled the determination of both ground and excited state rotational constants. Three different sets of recurrences were observed in the spectrum and assigned to K″-, K′-, and J″-type transients. From a detailed analysis by a grid search procedure based on the numerical simulation of RCS spectra and a nonlinear least-squares fitting routine the following rotational constants for the ground state were obtained: A″=2406.5±0.6 MHz, (B+C)″=714.9±0.4 MHz. For the electronic excited state two different sets of constants were found to fit the experimental data within the reported uncertainties: set (I) A′=2343.6±1.3 MHz, (B+C)′=714.4±1.7 MHz and set (II) A′=2346.3±1.3 MHz, (B+C)′=719.3±2.1 MHz. From additional information set (II) was found preferable for the description of the excited state. Furthermore, the fluorescence lifetime and the alignment of the transition dipole moment in the molecular frame were obtained from the fit procedure. For a structural characterization of pCHA we performed ab initio calculations of the electronic ground and excited state using HF/6-31G(d) and CIS/6-31G(d) levels of theory, respectively. These results were compared with the experiments and used to investigate the dependence of the rotational constants on characteristic intramolecular coordinates.

Principles of sequence-dependent flexure of DNA

The curvature of a bent rod may be defined in several different, but equivalent, ways. The best way of describing the curvature of double-helical DNA is by an angle of turning per base step. Curvature comes mainly from the angle of roll between successive base-pairs, and this is defined as positive when the angle opens up on the minor groove side of the bases. DNA forms a plane curve if the roll angle values along the molecule alternate periodically between positive and negative, with a complete period equal to the helical repeat. It is known from studies of crystallized oligomers that the roll angles for particular dinucleotide steps have preferred values, or lie in preferred ranges of values. Therefore the formation of a plane curve will be easier with some base sequences of DNA than with others. We set up a computer algorithm for determining the ease with which DNA of given sequence will adopt a curved form. The algorithm has two different sets of constants: in model 1 the base step parameters come from an inspection of crystallized oligomers, and in model 2 data from a statistical survey of the incidence of dinucleotide steps in a large number of samples of chicken erythrocyte core DNA is incorporated. Both forms of the algorithm successfully locate the dyad of the nucleosome sequence (modulo 10) in a frog gene, and suggest strongly that sequence-dependent flexural properties of DNA play a part in the recognition of binding sites by nucleosome cores.

Theoretical analysis of spectroscopic constants for spherical tops: ν2, ν4 Bands of AB4 molecules

Extended analysis of the different sets of spectroscopic constants for ν 2, ν 4 bands of CH 4, CD 4, SiH 4 is performed taking into account the possibility of the unitary transformation of the corresponding effective Hamiltonians. Refined relations between different notations of tensor operators and spectroscopic constants are presented. The unitary equivalence between several different sets of constants is shown up to the λ 4 order.

Effect of modifier on three-step enzymic process: General rate equation

It is essential to know the general rate equation in order to properly interpret steady-state measurements of the following kinetic mechanism: Y is a modifier. In this paper the rate equation is derived and specialized to approximate what is known about actin-myosin hydrolysis of ATP. In general, steady-state velocities are complex functions of several rate constants. Further, the velocity measured at one modifier concentration may be a function of one set of rate constants, while at a second concentration a different set of constants may be involved. In particular, a modifier may activate at one concentration, yet strongly inhibit at a second, higher concentration.

Propagation of Rayleigh waves in a model of the cross-section of a mountain and its root

This study deals with the theoretical investigation of a model of a mountain and its root. A Gaussian function with a set of constants is used to represent the surface of a mountain and a Gaussian with a different set of constants approximates the root i.e. the crust-mantle boundary underneath the mountain. The expressions for the amplitudes of the components of strain are obtained. Also the period equation as a function of distance (x) for the propagation of Rayleigh waves is derived here.

Chromatic changes induced by changes in chromaticity of background of constant lightness.

A relatively small gray sample looks reddish when it is placed on a green background, and yellowish when it is placed on a blue background. This phenomenon is an example of the well-known contrast effect. The purpose of this paper is to make a quantitative determination of the effect, and to check whether the empirical formula previously derived for lightness contrast applies also to chromatic contrast. Two series of color samples were prepared so that, in the dominator–modulator system proposed by Judd, only one of the three fundamental responses varied. For a given member of one of these two series viewed on a surround of any member of the same series on the left side, the observer was instructed to choose, for a surround of a different member of the series on the right, the member of the series producing most nearly the same color appearance. The crispening effect which was found in lightness was also found in each of the chromatic responses, green and violet; and the empirical formula derived for lightness contrast was found to apply with fair success to the observations of each of the five observers, each with a different set of constants.

Recent Correlations of Hydrocarbon Properties With Composition

Abstract The paper presents correlations of molar volume of gaseous hydrocarbon mixtures with pressure, temperature, composition and properties of the C7-plus fraction; shrinkage of oils during flash and differential liberation of gas, including the calculation of formation volume factor under various conditions; and bubble-point pressure with temperature, composition and characteristics of C7-plus. The data on which the correlations are based comprise 1,615 measurements on 900 hydrocarbon systems, including numerous systems containing nitrogen, hydrogen sulfide and carbon dioxide. In each correlation, the number of data points covered and the accuracy is substantially greater than in previously available work. Thus, the equation yielding molar volumes of gases has an average deviation of 2.04 per cent, applied to mixtures having temperatures up to 313F and pressures up to 9,800 psia, compared to 2.37 per cent for the Benedict-Webb-Rubin equation applied to the same data, and 4.53 per cent for the method based on the law of corresponding states. The equations presented are all explicit in the dependent variable, and require no iteration on the digital computer. Introduction The ease and accuracy of determining the composition of hydrocarbon mixtures, compared to the difficulty of measuring their properties under reservoir conditions, makes it desirable to utilize composition as the key to physical behavior to the greatest possible extent. As a result, there are available correlations between composition, or easily measured characteristics dependent on composition, and practically every important engineering property of reservoir fluids. The task confronting us is one of finding more exact relationships between important variables rather than extending correlations to new properties. This paper describes new correlations of molar volumes of gases, formation volume factors, and bubble-point pressures with composition, temperature and where possible, pressure. Each correlation is obtained by employing a sufficiently large amount of data so the calculated properties are probably as least as accurate as the measurement on which they are based. MOLAR VOLUME OF GASES Although many equations of state have been proposed for pure gases, only a few methods are applicable to hydrocarbons at conditions comparable to those in petroleum reservoirs. Still fewer are useful in describing the behavior of mixtures, with which the petroleum engineer is largely concerned. The correlation presented here involves procedures similar to those of Alani and Kennedy. The van der Waals equation ....................(1) is modified to make a and b functions of temperature instead of being constants for each material. This is a cubic equation, which may have either one or three real roots. The lowest root corresponds to liquid volume, while the highest applies to gas. When the procedure was applied to 703 pressure-temperature points of 164 gases of known composition and volume, the average deviation was 12.08 per cent, and the standard deviation 8.15. The above calculations were made using the constants derived for liquids by Alani and Kennedy and the mixture equation developed by them. A closer approximation to measured molar volumes is obtained by employing different sets of constants for different areas on the pressure-temperature chart, and by changing the relationship between am and bm for mixtures and the ai and bi for individual hydrocarbons. The various sets are shown in Table 1, and the areas for which they are recommended are plotted in Figs. 1 through 7. In these figures, the area designated by zero is in the critical region for pure materials, and the values obtained for them may be unreliable. JPT P. 1105ˆ

The constants of the equation for the refractive index of air

Recent measurements at the National Bureau of Standards, the University of Texas, the National Physical Laboratory, and elsewhere have indicated that the conventional constants ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A = 79\deg</tex> K/mb, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B = 4,800\deg</tex> K) in the expression for the refractive index of moist air <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(n-1)10^{6}=\frac{A}{T}(p+\frac{B}{T})</tex> should be revised. Various laboratories appear to have arrived at this conclusion independently, with the result that there are at least four different sets of constants in current use. In much of propagation work, the absolute value of the refractive index of the atmosphere is of small moment. However, in some work it is important, and it seems highly desirable to decide upon a particular set of constants. It is also advisable to agree on the amount of future improvement in the constants which will make it worth while to respecify them. This paper attempts to give "best" values of the constants in the least squares sense and also suggests a criterion for deciding whether a future change would be worth while.