Semi-empirical Expression Research Articles

Optimization synthesis of carbon nanotubes-anatase TiO2 composite photocatalyst by response surface methodology for photocatalytic degradation of gaseous styrene

In present study, the center composite design in response surface methodology (RSM) was firstly applied to optimize the synthesis of multi-wall carbon nanotubes (MWCNTs)–TiO2 composite photocatalyst. Twenty-eight composite photocatalysts were prepared by adjusting four operating parameters (amount of MWCNTs, amount of TiF4, hydrothermal temperature and hydrothermal time) at five levels by the method of multiple variable analysis. The structural, optical and morphological properties of the prepared composite photocatalysts were characterized by X-ray diffraction, UV–visible absorption spectra and scanning electron microscopy, respectively. Based on the experimental design, a semi-empirical expression was firstly established and subsequently applied to predict the photocatalytic degradation activity of the prepared composite photocatalysts to gaseous styrene in a cubic flow-through reactor. The results showed that the experimental photocatalytic degradation efficiencies using the differently prepared MWCNTs–TiO2 composite photocatalysts matched with the theoretically predicted values very well with a high correlation (R2=0.9790). Based on the theoretical and experimental results, the optimum synthesis parameters for the composite photocatalyst within the experimental ranges were 0.01g MWCNTs, 0.14g TiF4, and 120°C hydrothermally treated for 87.2h. The photocatalytic degradation efficiency of gaseous styrene using the MWCNTs–TiO2 composite photocatalyst synthesized under the optimum parameters reached 74.4%. All these demonstrates that the experimental design and theoretical prediction methods used in this work would have great significance in designing and developing high performance photocatalysts for environmental remediation and solar energy conversion.

Modified Mohr–Coulomb criterion for non-linear triaxial and polyaxial strength of jointed rocks

Rocks encountered in civil and mining engineering fields are invariably jointed and act under triaxial or polyaxial stress conditions. The Mohr–Coulomb shear strength criterion is the most widely used criterion for jointed rocks. In its present form there are two major limitations of this criterion; firstly it considers the strength response to be linear, and, secondly the effect of the intermediate principal stress on the strength behaviour is ignored. A modified non-linear form of Mohr–Coulomb strength criterion has been suggested in this study to overcome these limitations. Barton's concept of critical state for rocks has been imbibed in the linear Mohr–Coulomb criterion to deduce a semi-empirical expression for non-linear criterion. However, the shear strength parameters of the conventional Mohr–Coulomb criterion are used in the proposed criterion. The proposed criterion is a simple and rational nonlinear polyaxial strength criterion for anisotropic jointed rocks. In an earlier publication [1] the applicability of the criterion was evaluated for intact rocks. In present paper the criterion is extended to jointed rocks, which are anisotropic in nature. The applicability of the proposed criterion has been verified by applying it to extensive experimental data on triaxial and polyaxial test results on jointed rocks available from literature. Applicability of the criterion, to explain rock burst conditions for some Indian rocks, is also demonstrated.

Analytical and experimental evaluation on the effectiveness of upper mounted baffles with respect to commonly used baffles

In this paper, an experimental and an analytical investigation of the hydrodynamic damping due to lower and upper mounted vertical baffles as well as horizontal baffles in partially filled rectangular tanks are conducted. The analytical model earlier provided to estimate the hydrodynamic damping ratio of lower mounted vertical baffles is extended for upper mounted baffles. The semi-empirical Miles expression, which was originally developed to evaluate damping ratio of ring baffles in cylindrical tanks is also formulated for horizontal baffles in rectangular tanks. The comparisons between maximum hydrodynamic damping cased by various baffle configurations (upper and lower mounted vertical arrangements, as well as horizontal arrangements) are made and the validity of extended analytical models is discussed.

Analysis of the scaling laws for the turbulence driven panel responses

The high computational costs, associated to the numerical solution of the fluctuating pressure field generated at the wall by the turbulent boundary layer and of the induced structural response, push for the exploration of alternative methodologies of analysis. Wall pressure fluctuations spectra are often modeled using semi-empirical expressions based on the experimental evidence and on the identification of universal scaling laws. In this work the possibility to adopt a dimensionless representation, able to provide a universal expression for the structural response of plates under turbulent boundary layer excitations, is investigated with the help of pressure fluctuations and acceleration experimental data sets. The test article is a plane thin plate wetted by a fluid over one face, the boundary layer is fully developed and pressure gradient effects are negligible. The attention is devoted to the investigation and the definition of a normalization of the required axes: the excitation frequency and the power spectral density of the structural response. The analysis is initially based on analytical models for the structural response under turbulent boundary layer excitations. The proposed scaling laws are successively and successfully applied to four data sets measured in different conditions both in wind tunnels and in a towing tank.

Material Intrinsic Length in Plastic Strain Gradient Theory and Microbending Process of Metal Foils

In microbending experiments of metal foils an increase of non-dimensional bending moment with decreasing foil thickness has been observed, which indicates the obvious presence of size effects. It is attributed to plastic strain gradient. So a constitutive model taking into account plastic strain gradient together with conventional plastic strain hardening is proposed to analyze the non-dimensional bending moment in microbending process. It is confirmed that the predictions by using the proposed hardening model agree well with the experimental data, while those determined by using conventional elastoplastic model cannot capture such size effects. A semi-empirical expression is reasonable to determine the material intrinsic length as a function of shear modulus, initial yield strength, length of Burger’s vector, grain size, and macro geometrical characteristic scale of the specimen.

A semi-empirical Henry's law expression for carbon dioxide dissolution in ionic liquids

A simple model was developed to predict the solubility of carbon dioxide (CO 2) in ionic liquids under normal processing and conditioning pressures for natural gas fluids. COSMO-RS was used to predict the unsymmetrical activity coefficients for CO 2 in ILs, and the Peng–Robinson equation of state was used to calculate the CO 2 fugacity coefficient. Using these two quantities, a correlation was developed which can be used to extrapolate solubilities for ILs where experimental data is not available. This study shows that the molecular mass of the ILs is an effective parameter to correlate the Henry's constant of CO 2.

Semi-empirical description of the constant β in the equation of state for interfacial tension

A semi-empirical expression for the constant, β, in the Equation of State (EOS) for interfacial tension is proposed that exhibits a dependence on the surface area, heat capacity and thermal expansion coefficient of each of the materials involved in the three phase equilibrium (at constant temperature and pressure). The “wetting function”, which yields values between zero and unity as the contact angle, θ, varies from 0° to 180°, is also employed in the description of β. Empirical data is used to support that equation as well as the initially proposed relationship leading to its derivation that is based entirely on Classical Nucleation theory (CNT) outcomes and a “difference of the squares” correction term for the liquid–vapor and solid–vapor interfacial tensions.

Theoretical and analytical Radial Distribution Function for non-polar mixtures

The theoretical and analytical Radial Distribution Function (RDF) for non-polar mixtures is presented, and the estimation methods of model parameters (such as the minimum molecular diameter dii, mean calibration factor of volume βV and mean free path of relative motion λr,ij) are discussed. The calculated thermodynamic properties for He–H2 fluid mixtures by this RDF fit well with that of MC simulations and classical results from the Yukawa-type EOS, in which the Double Yukawa (DY) potential was used and the quantum effect was considered. Compared with the semi-empirical RDF expressions in references, the advantage of this theoretical and analytical RDF is that it can be used for all kinds of potential functions of non-polar molecules, and it covers a very wide range of temperatures and densities. The extensive practical application of this RDF for chemistry, physics and technology needs further investigation.

Electron range-energy relationships for calculating backscattering coefficients in elemental and compound semiconductors

Backscattering coefficients for electrons normally impinging on Si, Ge, GaN, GaAs and InSb targets have been calculated by using the Vicanek and Urbassek theory [M. Vicanek, H.M. Urbassek, Phys. Rev. B 44 (1991) 7234] for incident energies ≤5 keV. Electron range has been calculated from various semi-empirical analytical expressions. The cross-sections used to describe the electron transport are determined via the appropriate analytical expression given by Jablonski [A. Jablonski, Phys. Rev. B 58 (1998) 16470] whose new improved version has been recently reported by Rouabah et al. [Z. Rouabah, N. Bouarissa, C. Champion, N. Bouaouadja, Appl. Surf. Sci. 255 (2009) 6217]. The results may be seen as the first predictions for low-energy electron backscattering coefficients impinging on GaN, GaAs and InSb semiconductors. The models used in the calculation of the electron range affect both the accuracy and behaviour of the electron backscattering coefficients.

Influence of geometric and hydro-dynamic parameters of injector on calculation of spray characteristics of diesel engines

The main role in air/fuel mixture formation at the IC diesel engines has the energy introduced by fuel into the IC engine that is the characteristics of spraying fuel into the combustion chamber. The characteristic can be defined by the spray length, the spray cone angle, the physical and the chemical structure of fuel spray by different sections. Having in mind very complex experimental setups for researching in this field, the mentioned characteristics are mostly analyzed by calculations. There are two methods in the literature, the first based on use of the semi-empirical expressions (correlations) and the second, the calculations of spray characteristics by use of very complex mathematical methods. The second method is dominant in the modern literature. The main disadvantage of the calculation methods is a correct definition of real state at the end of the nozzle orifice (real boundary conditions). The majority of the researchers in this field use most frequently the coefficient of total losses inside the injector. This coefficient depends on injector design, as well as depends on the level of fuel energy and fuel energy transformation along the injector. Having in mind the importance of the real boundary conditions, the complex methods for calculation of the fuel spray characteristics should have the calculation of fuel flows inside the injector and the calculation of spray characteristics together. This approach is a very complex numerical problem and there are no existing computer programs with satisfactory calculation results. Analysis of spray characteristics by use of the semi-empirical expressions (correlations) is presented in this paper. The special attention is dedicated to the analysis of the constant in the semi-empirical expressions and influence parameters on this constant. Also, the method for definition of realistic boundary condition at the end of the nozzle orifice is presented in the paper. By use of this method completely avoid a use of the coefficient of total losses inside the injector. At the same time, semi-empirical expressions have the universal constant that does not depend on the injector design.

Thermodynamic and transport properties of nonideal systems with isotropic pair potentials

The equations of state and the structural, thermodynamic, and transport properties of the two- and three-dimensional nonideal dissipative systems consisting of particles interacting with different isotropic pair potentials are studied in a wide range of parameters typical for laboratory dusty plasma. Simple semiempirical expression for the energy density in liquid systems is considered. Comparison of the theoretical and numerical results is presented.

Electrochemical oxidation process combined with UV photolysis for the mineralization of nitrophenol in saline wastewater

As a preliminary treatment for the subsequent desalinization process, a combination of heterogeneous electrocatalysis and homogeneous photolysis is developed to mineralize bio-refractory organic pollutants in the wastewater with high salinity. A response surface methodology is used to assess the individual and interactive effects of several operating parameters (initial substrate concentration, pH, current density and Na 2SO 4 concentration) on the mineralization efficiency (the total organic carbon (TOC) removal rate) of p-nitrophenol. Based on the experimental results, a semi-empirical expression is proposed, allowing to predict and optimize the 5-h TOC removal rate. Both pH and current density are found to be the most significant positive factors that affected the combined process. With respect to the individual electrocatalysis and photolysis process, a synergetic effect on TOC removal rate is found in such a combined process. The oxygen generated by the parasite reaction of electrolysis process is recognized to play a predominant role in the synergetic effect. The degradation kinetics of PNP follows a pseudo-first-order kinetics model and features a higher degradation rate coefficient in alkaline medium and in an appropriate flowrate range. Through the LC–MS analysis of degradation products, the denitration and substitution by hydroxyl radicals on aromatic ring prove to be the first step for the degradation of PNP by the combined process.

Electron-impact-ionization cross sections for excited states ofBq+(q=0–2) and an investigation intonscaling of ionization cross sections

Nonperturbative R-matrix-with-pseudostates (RMPS) and time-dependent close-coupling (TDCC) methods are used to determine electron-impact-ionization cross sections for the excited states of B, B{sup +}, and B{sup 2+}. RMPS calculated cross sections are presented for the 1s{sup 2}2s{sup 2}3l and 1s{sup 2}2s{sup 2}4l configurations of B, the 1s{sup 2}2s3l and 1s{sup 2}2s4l configurations of B{sup +}, and the 1s{sup 2}3l, 1s{sup 2}4l, and 1s{sup 2}5l configurations of B{sup 2+}. It is shown that the TDCC-calculated cross sections for the 1s{sup 2}2s{sup 2}3s configuration of B, the 1s{sup 2}2s3s configuration of B{sup +}, and the 1s{sup 2}3s configuration of B{sup 2+} are in reasonable agreement with the RMPS results. Furthermore, n scaling of these nonperturbative cross sections is investigated and a scheme proposed to allow for the extrapolation of electron-impact-ionization cross sections to higher n shells. Two semiempirical ionization cross-section expressions are fitted to the peak of the highest n-bundled RMPS cross sections for B, B{sup +}, and B{sup 2+}. These are subsequently used for accurate evaluation of the higher n-shell ionization cross sections needed to obtain temperature- and density-dependent generalized collisional-radiative ionization coefficients for the impurity and transport modeling of magnetic fusion plasmas.

Evidence for decadal variation in global terrestrial evapotranspiration between 1982 and 2002: 1. Model development

Estimating interannual to decadal variability of terrestrial evapotranspiration (ET) requires use of standard meteorological data complemented with some high‐resolution satellite data. A semiempirical expression for this purpose is developed and validated with data from 2000 to 2007. These data were collected at 64 globally distributed sites, including the continuous measurements collected by the Atmospheric Radiation Measurement (ARM) and FLUXNET projects, and are the longest available, with continuous worldwide multisite measurements of ET, and a total of 274 site years. The sites are mainly located in North America and Asia, with the exception of three sites in Australia, two in Europe, and one in Africa. The climates of the sites vary from tropical to subarctic and from arid to humid. The land cover types of the sites vary from desert, croplands, grasslands, and shrub land to forests. On average, the 16 day average daily ET can be estimated with an error (standard deviation) of 17 W m−2 (25% in relative value), and with an average correlation coefficient of 0.94. The standard deviation of the comparison between measured and predicted site‐averaged daily ET is 9 W m−2 (14%), with a correlation coefficient of 0.93. The model is also satisfactory in reproducing the interannual variability at sites with 5 years of data in both humid and arid regions. The correlation coefficient between measured and predicted annual ET anomalies is 0.85. This simple but accurate method permits us to investigate decadal variation in global ET over the land as will be demonstrated in part two of this paper series.

Circulation of an object immersed in a bubbling fluidized bed

The motion of a large object in a bubbling fluidized bed was experimentally studied using digital image analysis (DIA). The experiments were performed in a 2-D bubbling fluidized bed with glass spheres as bed material. The object motion was measured using non-intrusive tracking techniques, while independent measurements of the dense phase velocity (using Particle Image Velocimetry (PIV)) and bubble velocity (using DIA) were carried out. The effect of the dimensionless gas velocity on the object motion was also analyzed. This work characterizes the circulation patterns of an object with a density similar to that of the bed, but much larger in size. Object size and density remained constant throughout the experiments. A comparison between the motion of sinking objects and the motion of the dense phase provided evidence of the feeble effect of buoyant forces on the motion of sinking objects. In contrast, the motion of rising objects is linked to the motion of bubbles. It was found that objects may be raised to the surface of the bed either by the action of a single bubble (one-jump) or by several passing bubbles (multiple-jumps). Based on these results, the circulation time of objects throughout the bed is a function of two parameters: the maximum depth attained by an object and the number of jumps during its rising path. This relationship is presented along and the multiple-jumps phenomenon is studied in detail. Finally, an estimate of the circulation time of an object based on semi-empirical expressions is presented for different dimensionless gas velocities. The probability density function of the circulation time shows two different modes as the object was less prone to be raised at moderate depths. The estimate of the circulation time was found to be in good agreement with our experimental data.

Bar Buckling in RC Columns Confined with Composite Materials

The onset and evolution of bar buckling at the plastic hinge of old-type reinforced concrete (RC) columns confined with composite material [fiber-reinforced polymer (FRP) and textile-reinforced mortar (TRM)] jackets was investigated experimentally and analytically in this study. The interaction between composite jacket (or concrete cover, for unconfined concrete) and embedded longitudinal compression reinforcement at the onset and evolution of bar buckling was achieved through strain measurements of the compression reinforcement. Moreover, the implementation of a recent stress-strain confinement model, which relates lateral with axial strains, allowed the description and monitoring of the axial-lateral strain relationship at the base of the columns throughout the evolution of bar buckling. Based on the aforementioned model and the experimental measurements, the postbuckling behavior of columns was related to the jacket stiffness. Finally, a semiempirical expression that gives the drift ratio of RC columns at the onset of bar buckling was modified herein for the case of FRP- or TRM-jacketed columns.

Extreme value modeling of areal rainfall from weather radar

An 11 year high‐quality radar rainfall data set is used to abstract annual maximum rainfall depths for durations of 15 min to 24 h and area sizes of 6 to 1.7 × 103 km2 for the Netherlands. Generalized extreme value (GEV) distributions are fitted to the annual maxima. A new method is presented to describe the distribution of extreme areal rainfall depths by modeling GEV parameters as a function of both duration and area size. This leads to a semiempirical expression from which quantiles of extreme rainfall depths can be obtained for a chosen duration, area size, and return period. The uncertainties in these quantiles are calculated using the bootstrap method. Radar‐based areal reduction factors (ARFs) are derived. These ARFs are comparable to those based on high‐density rain gauge networks derived from the literature. It is concluded that radar data, after careful quality control, are suitable to estimate extreme areal rainfall depths.

Residual Stiffness of Cracked Cross-Ply Composite Laminates Under Multi-Axial In-plane Loading

In this paper, the Equivalent Constraint Model (ECM) together with a 2-D shear lag stress analysis approach is applied to predict residual stiffness properties of polymer and ceramic matrix [0/90n/0] cross-ply laminates subjected to in-plane biaxial loading and damaged by transverse and longitudinal matrix cracks. It is found that the longitudinal Young’s modulus, shear modulus and major Poisson’s ratio undergo large degradation as the matrix crack density increases, with Poisson’s ratio appearing to be the most affected by transverse cracking. In cross-ply laminates with thick 90° layer strip-shaped delaminations begin to initiate and grow from the tips of matrix cracks at the 0°/90° interface. These delaminations contribute to further stiffness degradation of such laminates, and hence have to be taken into account in failure analysis models. The thickness of the 90° layer plays an important role; the thicker the 90° layer, the bigger stiffness reduction suggesting a size (volume) effect at ply level. In SiC/CAS cross-ply laminates reduction in the longitudinal modulus occurs mainly due to transverse cracks, while the shear modulus appears to be the most affected by the presence of longitudinal cracks. The shear modulus reduction ratio predicted previously by a semi-empirical formula is, in the most of cases, within 10% of the current ECM/2-D shear lag approach value. In some cases, though, the error of the semi-empirical finite element expression can be as big as 20% since it fails to capture damage mode interaction.

Experimental modelling of debris flow behaviour using a geotechnical centrifuge

Physical modelling of debris flows has been carried out in the geotechnical drum centrifuge at ETH Zürich. A new apparatus to model debris flows in the centrifuge is described. The apparatus permits the final reach of a typical debris flow to be modelled within the centrifuge, with unconsolidated material flowing down a slope to deposit as a fan around the drum. Experiments are described for both fixed base conditions and erodible bases. Tests to examine the verification (modelling) of models show that debris flow behaviour is governed mainly by friction and consolidation processes, although some resolution is required between flow behaviour downslope and flow arrest during runout. The results are compared with bulk parameters determined for field-scale debris flows. It is found that some important flow mechanisms, such as contact-dominated behaviour and high pore pressures, are developed that are closer to those developed at field-scale than tests conducted at 1g. Velocity profiles for erodible beds are compared with a semi-empirical expression derived for experimental debris flows at 1g. Normalized velocity profiles are found to be in agreement; however, absolute velocities differ from those predicted. Scaling, the limitations of the apparatus, and potential for future work are discussed.

Low-temperature magnetoresistance of Nb-doped [formula omitted] transparent conducting films

The magnetoresistance of two anatase Nb-doped TiO 2 films has been measured. The samples reveal both negative and positive magnetoresistance component at all measuring temperatures. It is indicated that the Lorentz force effect based on a two-band model can describe the positive magnetoresistance contribution well. Rather than weak localization or Kondo effect, the negative magnetoresistance behaviors follow a semiempirical expression considering the effect of localized magnetic moments. This expression, due to Khosla and Fischer in a paper published 40 years ago [R.P. Khosla, J.R. Fischer, Phys. Rev. B 2 (1970) 4084], is deduced from the s–d exchange Hamiltonian by considering the third-order perturbation. The field dependence of the magnetization curves for both samples reveals ferromagnetic characteristics, which proves the existence of localized magnetic moment in Ti 1− x Nb x O 2 compounds.