Semi-empirical mass

From the semi-empirical mass formula Eq. (2.2), neglecting the last two terms, the gain in B.E. for a nucleus splitting into two equal fragments is... 

It has long been recognized that the liquid-drop model semi-empirical mass equation cannot calculate the correct masses in the vicinity of neutron and proton magic numbers. More recently it was realized that it is less successful also for very deformed nuclei midway between closed nucleon shells. Introduction of magic numbers and deformations in the liquid drop model improved its predictions for deformed nuclei and of fission barrier heights. However, an additional complication with the liquid-drop model arose when isomers were discovered which decayed by spontaneous fission. Between uranium and... 

These competing forces helped form the semi-empirical mass formula (SEMF) shown in the following equation ... 

Beta stability is thought to be known reasonably well, with use being made of the semi-empirical mass formula. Johansson et al. think it unlikely that an error of more than one or two units of N for a given Z will result from the prediction of the beta-stability line. Electron capture in superheavy elements has been considered by Morovic and by Grumann, Morovic, and Greiner. ... 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

Having obtained the value of the limiting viscosity number, we can calculate relative molar mass using the semi-empirical equation ... 

In the SF models, all of the terms in the droplet and gas conservation equations are retained. Therefore, the SF models are the more general models for spray calculations. The models account for mass, momentum and energy exchanges between droplets and gas. To formulate the exchange terms, the nature of the conditions at droplet-gas interface is of importance. The exchange processes are typically modeled by means of semi-empirical correlations. 

Next we consider the compact star in the low mass X-ray binary 4U 1728-34. In a very recent paper Shaposhnikov et al. (2003) (hereafter STH) have analyzed a set of 26 Type-I X-ray bursts for this source. The data were collected by the Proportional Counter Array on board of the Rossi X-ray Timing Explorer (RXTE) satellite. For the interpretation of these observational data Shaposhnikov et al. 2003 used a model of the X-ray burst spectral formation developed by Titarchuk (1994) and Shaposhnikov Titarchuk (2002). Within this model, STH were able to extract very stringent constrain on the radius and the mass of the compact star in this bursting source. The radius and mass for 4U 1728-34, extracted by STH for different best-fits of the burst data, are depicted in Fig. 6 by the filled squares. Each of the four MR points is relative to a different value of the distance to the source (d = 4.0, 4.25, 4.50, 4.75 kpc, for the fit which produces the smallest values of the mass, up to the one which gives the largest mass). The error bars on each point represent the error contour for 90% confidence level. It has been pointed out (Bombaci 2003) that the semi-empirical MR relation for the compact star in 4U 1728-34 obtained by STH is not compatible with models pure hadronic stars, while it is consistent with strange stars or hybrid stars. 

Diffusion coefficients may be estimated using the Wilke-Chang equation (Danckwerts, 1970), the Sutherland-Einstein equation (Gobas et al., 1986), or the Hayduk-Laudie equation (Tucker and Nelken, 1982), which state that Dw values decrease with the molar volume (Vm) to the power 0.3 to 0.6. Alternatively, the semi-empirical Worch relation may be used (Worch, 1993), which predicts diffusion coefficients to decrease with increasing molar mass to the power of 0.53. These four equations yield very similar D estimates (factor of 1.2 difference). Using the estimates from the most commonly used Hayduk-Laudie equation... 

Overview of Semi-Empirical and Ab Initio Molecular Orbital Methods. 2.2 Applications of Molecular Mechanics. 3 Experimental Structural Methods. 3.1 X-Ray Diffraction. 3.2 NMR Spectroscopy and. 3.3 Mass Spectrometry. 3.4 UV/Fluorescence. 3.5 IR Spectroscopy. 3.6 Redox Potentials. 4 Thermodynamic Aspects. 4.1 Melting Points. 5 Reactivity of Fully Conjugated Rings 6 Reactivity of Nonconjugated Rings... 

Bjarnholt and coworkers (Refs 13 and 21) used a semi-empirical approach to estimate the useful energy of HE via underwater expln energy measurements. In essence, their approach involves computation of a shock toss factor, ft > 1, to estimate the shock energy at the HE/water boundary from measured shock energies at some distance from the HE. This is coupled with the assumption that the measured bubble energy at some distance from the HE equals the bubble energy at the HE/water boundary. Then the total underwater expansion work per unit mass of HE, A0, is given by ... 

Models in general are a mathematical representation of a conceptual picture. Rate equations and mass balances for the oxidants and their reactants are the basic tools for the mathematical description. As Levenspiel (1972, p.359) pointed out the requirement for a good engineering model is that it be the closest representation of reality which can be treated without too many mathematical complexities. It is of little use to select a model which closely mirrors reality but is so complicated that we cannot do anything with it. In cases where the complete theoretical description of the system is not desirable or achievable, experiments are used to calculate coefficients to adjust the theory to the observations this procedure is called semi-empirical modeling. 

Semi-Empirical Model Based on the Mass Balance... 

In the following first example the liquid ozone concentration and the OH-radical concentration are calculated with semi-empirical formula from the mass balance for ozone (Laplanche et al., 1993). For ozonation in a bubble column, with or without hydrogen peroxide addition, they developed a computer program to predict the removal of micropollutants. The main influencing parameters, i. e. pH, TOC, U V absorbance at 254 nm (SAC254), inorganic carbon, alkalinity and concentration of the micropollutant M are taken into consideration. 

Due to the fact that protein adsorption in fluidized beds is accomplished by binding of macromolecules to the internal surface of porous particles, the primary mass transport limitations found in packed beds of porous matrices remain valid. Protein transport takes place from the bulk fluid to the outer adsorbent surface commonly described by a film diffusion model, and within the pores to the internal surface known as pore diffusion. The diffusion coefficient D of proteins may be estimated by the semi-empirical correlation of Poison [65] from the absolute temperature T, the solution viscosity rj, and the molecular weight of the protein MA as denoted in Eq. (16). 

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