Semi-empirical Expression Research Articles

A method for constant-rate heating of milligram-sized samples

Heating a milligram-sized sample of material at a constant heating rate is usually achieved by controlling the temperature of an electric-resistance furnace with a proportional integral derivative (PID) controller. Here we present a new method for constant-rate heating that is based on a semi-empirical mathematical expression relating sample temperature, heating rate, and electric power supplied to the furnace. This method uses PID control only for second-order corrections of the heating rate. The linearity of the sample temperature vs. time curves obtained by applying this method to a simple furnace setup is the same as the linearity of the curves generated by modern commercial thermogravimetric analyzers.

Photocatalytic degradation of azo dye Metanil Yellow: Optimization and kinetic modeling using a chemometric approach

The photocatalytic degradation of an azo dye Metanil Yellow was carried out in aqueous solution using TiO2 as photocatalyst under UV irradiation. The decolorization and degradation kinetics were investigated and both followed a pseudo first order kinetic according to Langmuir–Hinshelwood model. Using HPLC/DAD and GC/MS analyses, more than 10 major reaction intermediates were identified and a tentative degradation pathway was proposed. Furthermore, ion chromatography (IC) and TOC measurements revealed a complete mineralization of Metanil Yellow into CO2, N2, H2O and inorganic ions (NH4+, NO3− and SO42−).On the other hand, an experimental design based on the surface response methodology was applied to assess the individual and interaction effects of several operating parameters (dye concentration, TiO2 concentration, pH, light flux, etc.) on the treatment efficiency (dye removal time). Based on the experimental design data, a semi-empirical expression was obtained, permitting to predict and optimize the dye removal time. This model was very consistent with experiment results (correlation factor: 99.5%). Moreover, additional experimental results obtained under near optimal conditions were found to be very close to the predicted values.This work demonstrates well the utility and benefits of the experimental design approach for screening and modeling the reaction parameters. Furthermore, it contributes significantly to the improvement and better understanding of photocatalytic processes.

Semiempirical theory of Carver rates in alkali/noble-gas systems

During an encounter between a noble-gas atom and an alkali-metal atom, the electron density at the alkali nucleus is altered, resulting in a collisional change in the alkali's hyperfine coupling (i.e., AI.S-->(A+deltaA)I.S). In the case of binary encounters, this process has been termed the Carver mechanism. The short-lived collisional change in hyperfine coupling can have very noticeable effects: it plays an important role in the loss of nuclear spin polarization in high magnetic fields, and it can be one of the dominant line broadening mechanisms for alkali hyperfine transitions (e.g., in atomic clocks). Unfortunately, though there have been measurements of the Carver relaxation rate, to date there has been little theoretical analysis of the Carver mechanism, in large part due to the very difficult problem of computing deltaA. In the present work, the author develops a theory of the Carver rate based on a semiempirical expression for deltaA(r)/A, where r is the internuclear alkali/noble-gas separation, and validates the theory by comparing to experiment. This model is then used to compute Carver and Bouchiat relaxation rates (i.e., the three-body sticking-collision analog of the Carver rate) in diverse/alkali-noble gas systems. The main conclusion of this work is that Carver rates vary by orders of magnitude across the alkalies, and in general will likely only play a significant role for Rb and Cs noble-gas systems.

NOx diesel exhaust treatment using a pulsed corona discharge: the pulse repetition rate effect

The pulsed corona offers real promise for degradation of pollutants in gas and water streams. This paper presents a study of NOx removal from diesel exhaust. Special emphasis is laid on the investigation of the dependence of the NO removal rate and efficiency on the pulse repetition rate (PRR). A nanosecond solid state power supply (45 kV, 60 ns, up to 1 kHz) was used for driving the corona reactor. A Mitsubishi 10 kW 3-cylinder diesel-generator engine with a total volume of 1300 cm3 was used as a source of exhaust gas. At an NO removal rate of 35% the NO removal efficiency was 53 g kW−1h−1 for PRR = 500 Hz and the initial NO concentration was 375 ppm. A semi-empirical expression for the corona reactor removal efficiency related both to PRR and to the residence time is presented. The removal efficiency decreases with increasing PRR at constant flow rate or constant residence time. This expression demonstrates reasonable agreement between the calculation results and the experimental data.

Noninvasive assessment of left ventricular and myocardial contractility in middle-aged men and women: disparate evolution above the age of 50?

End-systolic elastance (E(es)) is a frequently used index of left ventricular (LV) contractility. However, because of its inherent dependence on LV geometry, E(es) cannot be used to compare myocardial contractile state between ventricles with different geometries, which is the case in any cross-sectional study. Various normalization methods for E(es) have been proposed in the literature, but a standardized method is still lacking. In this study, we introduced a novel alternative normalization technique and compared it with three previously suggested methods. We tested all normalization methods to assess the age- and sex-related differences in myocardial contractility in a large population sample of 2,184 middle-aged (ages, 35-55 yr) untreated subjects free from overt cardiovascular disease. Ventricular contractility E(es) was determined using a previously validated noninvasive single-beat method, based on two-dimensional echocardiographic and brachial blood pressure measurements. Myocardial contractility was estimated as 1) E(es).end-diastolic volume (EDV); 2) E(es).LV mass (LVM); 3) 0.433.E(es).LVM/relative wall thickness (RWT), based on a theoretical LV model; and 4) 0.0941.E(es).LVM(0.455).RWT(-0.159), a novel semiempirical expression derived in this study. Because of the difference in their underlying assumptions, the various myocardial contractility indexes do not provide consistent information with respect to sex differences. Despite these discrepancies, it was found that myocardial contractility in women appears to be better preserved after the age of 50 yr compared with that in men. The physiological mechanisms behind this potentially clinically important phenomenon at population level require further investigation.

Electron cross relaxation as a function of single relaxation contributions in double‐core ionization energies and spin–orbit splitting of atoms from Ar to Ba. I. 1s−2p− double‐core holes

AbstractOn the basis of numerical ab initio, delta and multiconfiguration Breit–Dirac–Fock (ΔBDF and MCBDF) computations, we have investigated the dependence of electron “cross relaxation” on the single relaxation contributions in double‐core ionization energies and spin–orbit splitting of atoms from Ar to Ba, excluding transition elements. The cross‐relaxation variation with Z was fitted to a quadratic function of the geometric average of the single relaxation contributions. For the family of atoms AlCl, it was found that the splitting of the levels is not a straight measure of 2p spin–orbit coupling. The families of “light” atoms ArCa and CuSr yielded together a set of best‐fit coefficients, while the family of heavier atoms AgBa yielded another set. The best‐fit functions were used to predict double‐core ionization energies from single ionization data and from Koopmans' values for atoms from Ar to Ba. For molecules a semiempirical expression is proposed. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Low temperature magnetoresistance of Al-doped ZnO films

The magnetoresistances of aluminum-doped zinc oxide thin films with thickness of 463.63, 203.03, and 66.85 nm were measured at low temperatures from 2.5 to 30 K. It is found that the samples exhibit negative magnetoresistance at all measuring temperatures. However, neither the three-dimensional nor the two-dimensional weak-localization theories can reproduce the behavior of the magnetoresistance. We find that the magnetoresistance of the three films can be well described by a semiempirical expression that takes into account the third order s – d exchange Hamiltonians describing a negative part and a two-band model for the positive contribution. This strongly suggests that the negative magnetoresistance in ZnO:Al film originates from the scattering of conduction electrons due to localized magnetic moments.

DFT Study on the Intermolecular Substrate-mediated Interaction Energy in the Self-assembly of Alkanethiols on Silver

The B3LYP/LanL1MB and B3LYP/LanL2DZ methods for Ag atom in conjunction with the 6-31G(d) basis set for S, C and H atoms were used to optimize the geometries and calculate the energies for (SCH3)mAg20 (m=1-4), respectively. A single molecular adsorption energy of (SCH3)m (m=1-4) on Ag20 and the inter-molecular substrate-mediated interaction energy were evaluated. The results revealed that there is a proportional relation between the single molecular adsorption energy and the substrate-mediated intermolecular interaction energy. The results qualitatively demonstrated the semi-empirical expression for the substrate-mediated interaction energy proposed previously by us is consistent with the results of the density functional theory.

Shear strength of steel fiber reinforced concrete beams with stirrups

The present paper proposes a semi-empirical analytical expression that is capable of determining the shear strength of reinforced concrete beams with longitudinal bars, in the presence of reinforcing fibers and transverse stirrups. The expression is based on an evaluation of the strength contribution of beam and arch actions and it makes it possible to take their interaction with the fibers into account. For the strength contribution of stirrups, the effective stress reached at beam failure was considered by introducing an effectiveness function. This function shows the share of beam action strength contribution on the global strength of the beam calculated including the effect of fibers. The expression is calibrated on the basis of experimental data available in literature referring to fibrous reinforced concrete beams with steel fibers and recently obtained by the authors. It can also include the following variables in the strength previsions: - geometrical ratio of longitudinal bars in tension; - shear span to depth ratio; - strength of materials and fiber characteristics; - size effects. Finally, some of the more recent analytical expressions that are capable of predicting the shear strength of fibrous concrete beams, also in the presence of stirrups, are mentioned and a comparison is made with experimental data and with the results obtained by the authors.

Modeling particle deposition and distribution in a chamber with a two-equation Reynolds-averaged Navier–Stokes model

A Lagrangian simulation for aerosol particle transport and deposition in a chamber is developed. The eddy interaction model (EIM) is adopted to generate the instantaneous turbulent fluctuating velocity field. It is found that a satisfactory result can be obtained only when the near-wall grid is sufficiently fine and the near-wall turbulent kinetic energy is damped effectively according to its component normal to the wall. Seven particle size groups ranging from 0.01 to 10 μ m are studied. A comparison between the current numerical model and a semi-empirical expression indicates that improved deposition fraction results were obtained. The particle deposition and particle fate in the chamber are also presented.

Effect of Hydraulic Jump on Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk Analyzed by Integral Method

Flow and heat transfer in a liquid film flowing over the surface of a rotating disk was analyzed by integral technique. The integral analysis includes the prediction of the hydraulic jump and its effects on heat transfer. The results of this analysis are compared to the earlier results that did not include this effect. At low inlet Reynolds numbers and high Rossby numbers, corresponding to low film inertia and low rotation rates, respectively, a hydraulic jump appears on the disk surface. The location of the jump and the liquid film height at this location are predicted. A scaling analysis of the equations governing the film thickness provided a semi-empirical expression for these quantities that was found to be in very good agreement with numerical results. Heat transfer analysis shows that the Nusselt numbers for both constant disk surface temperature and constant disk surface heat flux boundary conditions are lowered in the vicinity of the hydraulic jump due to the thickened liquid film. This effect can be more pronounced for the constant heat flux case depending on the location of the hydraulic jump. The Nusselt number exhibits a turning point at the jump location and can have higher values downstream of the hydraulic jump compared to those obtained from the analysis that does not include the gravitational effects.

Optical and electrical transport properties of facing-target sputtered Al doped ZnO transparent film

Al doped zinc oxide thin film was prepared by dc facing-target sputtering method and its structural, optical, and electrical transport properties have been investigated. The average transmittance of the films is greater than 90% in the wavelength region of 450–700nm while the resistivity is as high as 3×10−3Ωcm. The band gap energy derived from the transmission data is 3.76eV, which is higher than that of pure ZnO thin film. This band gap growth phenomenon cannot be explained in terms of the Burstein-Moss effect. The resistivity and Hall effect measurements suggest that the interaction between the charge carriers and phonons plays a key role in the electrical transport properties of the film between 60 and 300K. The film exhibits negative magnetoresistance at low temperatures, which can be well described by a semiempirical expression that takes into account the third order s-d exchange Hamiltonians describing a negative part and a two-band model for positive contribution.

Passive optical diagnostic of Xe-propelled Hall thrusters. I. Emission cross sections

This paper presents a set of xenon apparent emission excitation cross sections for emission lines that have diagnostic value in the analysis of Xe-propelled Hall thruster plasmas. Emission cross sections are presented for three excitation processes involving ground-state xenon atoms: e−+Xe, Xe++Xe, and Xe2++Xe. The cross sections are derived from luminescence spectra produced at single-collision conditions. Apparent emission excitation cross sections are tabulated for 12 visible and 8 near-infrared lines for electron energies ranging from 10to70eV. In case of the near-infrared lines, radiation trapping effects are accounted for by measuring the detailed pressure dependence of the apparent emission cross sections and extrapolating to zero pressure. A semiempirical expression for the pressure dependence is derived that allows zero-pressure extrapolation from threshold to 70eV. Ion-induced cross sections are reported for the same emission lines at an energy per unit charge E∕q of 300eV, chosen for typical Hall thruster operating voltages. Radiation trapping effects are negligible for the ion emission excitation cross sections between 0.1 and 2.0mTorr in the present luminescence experiment.

Broadening of carbon ionic lines in a low-temperature dense plasma

The broadening of the spectral lines of singly ionized carbon obtained in a plasma jet of a capillary discharge with an evaporating wall is studied in a wide range of electron concentrations ((6.5 × 1016)−(3.5 × 1019) cm−3). With increasing plasma density, all the experimentally observed lines show a decrease in the half-width in comparison with the half-width calculated in the approximation of slight nonideality. It is experimentally established that a change in the character of the Stark broadening with increasing electron concentration is connected with a strong charge screening occurring when the distance between charged plasma particles decreases to ten diameters of the electron cloud of an emitting ion. Based on the experimentally determined applicability limits of the Griem formula for different energy states of the C II ion, a semiempirical expression for the spectral profile taking into account the Debye screening is proposed.

A closed-form charge-based expression for drain current in symmetric and asymmetric double gate MOSFET

Although both exact [Taur Y, Liang X, Wang W, Lu H. A continuous, analytic drain-current model for DG MOSFETs. IEEE Electron Dev Lett 2004;25(2):399–401] and design oriented approximate [Sallese JM, Krummenacher F, Prgaldiny F, Lallement C, Roy A, Enz C. A design oriented charge-based current model for symmetric DG MOSFET and its correlation with the EKV formalism. Solid-State Electron 2005;49(3):485–9] closed-form analytical solution of the drain current for the symmetric double gate (DG) MOST exist, a closed-form expression for asymmetric DG MOST is still lacking. In this context, this work presents a semi-empirical analytic closed-form charge-based expression for the drain current of asymmetric DG MOST that is valid from weak to strong inversion and retains the asymptotic behavior. In addition, important small-signal quantities such as the transconductance-to-current ratio are readily obtained and reveal that these are nearly insensitive to the degree of asymmetry.

Wrinkling prediction of cylindrical and conical inflated cantilever beams under torsion and bending

The combined load case of bending and torsion of a cantilever inflated beam is a load case that has not been studied extensively. When a series of inflated beams is placed parallel to each other as can be the case for an inflatable wing, each beam experiences a combination of torque and bending. A theoretical model already exist for such a load case but it is limited to membrane like materials. This paper deals with beams made of materials that need to be treated like a shell. It requires a modification for the wrinkling load due to solely bending and solely torsion. Semi-empirical expressions for both cases are presented for both cylindrical and conical shaped beams.

Heating of a fish wintering pond using low-temperature geothermal fluids, Porto Lagos, Greece

Low-enthalpy geothermal fluids are being used in Porto Lagos, Greece, to prevent freezing in an open (uncovered) pond connected to the sea where various fish species spend the winter. Despite the low temperature of the fluids and the moderate flow, the system proved to be satisfactory, increasing the pond temperature by more than 5 °C. This prevented the formation of an ice layer on the surface of the pond that would otherwise have caused a massive reduction in the fish population, as has happened in the past. A numerical model was developed and validated to simulate the thermal behavior of an open pond, based on hourly temperature measurements collected from various depths and at various sites in the pond during the last heating period. The simulator was subsequently applied to the evaluation of various alternative scenarios of exploitation. The hourly pond and ambient temperatures were also correlated in such a way as to obtain a semi-empirical expression for the heat losses from the pond and to estimate the time response of the system, so as to regulate the flow of geothermal fluids into the pond.

Monte Carlo simulations of positrons transmission and backscattering probabilities in nickel

Monte Carlo simulations for positron backscattering from the semi-infinite nickel with normal angle of incidence and the transmission through nickel foils of isotropically implanted positrons from a 22Na β + source is reported. The elastic scattering cross section, have been obtained from Rutherford differential cross section where the numerical coefficient in the atomic screening parameter and spin-relativistic correction factor is taken to be variable. Inelastic scattering model was employed to simulate the energy loss using Gryzinski’s semi-empirical expression and Liljequist and Gryzinski models to calculate the total inelastic scattering cross section. The simulated results and the available experimental data are found to be in reasonable agreement.

Anharmonic compression of the glitter lattice

A previous report has described the crystal structure of glitter, which is a dense 3-,4-connected net composed of ethylenic columns that run parallel to the c-axis of the unit cell. Such a structure invites speculation as to its relative stiffness along that axis. A semiempirical expression due to Cohen was used in a previous communication to estimate its zero-pressure bulk modulus. This estimate exceeds that of any known material at 440 GPa. Further, by treating the ethylenic units as harmonic springs, a correction was computed for the elastic deformation of the carbon-carbon double bonds along the c-axis. This correction is on the order of 300 GPa for deformations of the double bonds of approximately 0.1 angstroms. The present communication treats the ethylenic units along the c-axis of glitter as anharmonic springs obeying a Morse potential and a Morse's law force. Within the anharmonic approximation, at modest bond length deformations, x', the bulk modulus at pressure of the glitter lattice exceeds 1 TPa.

A correlation equation for calculating inclined jet penetration length in a gas-solid fluidized bed

Numerical simulation of gas-solid flow in a two-dimensional fluidized bed with an inclined jet was performed. The numerical model is based on the two-fluid model of gas and solids phase in which the solids constitutive equations are based on the kinetic theory of granular flow. The improved ICE algorithm, which can be used for both low and high-velocity fluid flow, were used to solve the model equations. The mechanism of jet formation was analyzed using both numerical simulations and experiments. The emergence and movement of gas bubbles were captured numerically and experimentally. The influences of jet velocity, nozzle diameter, nozzle inclination and jet position on jet penetration length were obtained. A semi-empirical expression was derived and the parameters were correlated from experimental data. The correlation equation, which can be easily used to obtain the inclined jet penetration length, was compared with our experimental data and published correlation equations.