Linear Stability Analysis of Convection in Two-Layer System with an Evaporating Vapor-Liquid Interface

Classical theories have successfully provided an explanation for convection in a liquid layer heated from below without evaporation. However, these theories are inadequate to account for the convective instabilities in an evaporating liquid layer, especially in the case when it is cooled from below. In the present paper, we study the onset of Marangoni convection in a liquid layer being overlain by a vapor layer.A new two-sided model is put forward instead of the one-sided model in previous studies. Marangoni-Bénard instabilities in evaporating liquid thin layers are investigated with a linear instability analysis. We define a new evaporation Biot number, which is different from that in previous studies and discuss the influences of reference evaporating velocity and evaporation Biot number on the vapor-liquid system. At the end, we explain why the instability occurs even when an evaporating liquid layer is cooled from below.

A Linear Stability Analysis Of Large-Prandtl-Number Thermocapillary Liquid Bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 <= Pr <= 50). We focus on the relationships between the critical Reynolds number Re-c, the azimuthal wave number m, the aspect ratio F and the Prandtl number Pr. A detailed Re-c-Pr stability diagram is given for liquid bridges with various Gamma. In the region of Pr > 1, which has been less studied previously and where Re, has been usually believed to decrease with the increase of Pr, we found Re-c exhibits an early increase for liquid bridges with Gamma around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the "effective" part of liquid bridge. (c) 2008 Published by Elsevier Ltd on behalf of COSPAR.

A Simplified Evaluation Procedure of the Scale of Fluctuation Combined Recurrence Averaging and Weighted Linear Regression

The divergence of properties from one location to another within a soil mass is termed spatial variability, which traditionally includes three parameters the mean, the standard deviation, and the scale of fluctuation, in order to stochastically describe a soil property. Among them, determining the scale of fluctuation in the evaluation of spatial variability of soil profiles is not easy due to soil condition complexity. A simplified procedure is presented in the paper to determine the scale of fluctuation combined recurrence averaging and weighted linear regression. The alternative approach utilizes widely usable spreadsheet to solve the problem more directly and efficiently.

Three-Dimensional Linear Instability Analysis of Thermocapillary Return Flow on a Porous Plane

A three-dimensional linear instability analysis of thermocapillary convection in a fluid-porous double layer system, imposed by a horizontal temperature gradient, is performed. The basic motion of fluid is the surface-tension-driven return flow, and the movement of fluid in the porous layer is governed by Darcy's law. The slippery effect of velocity at the fluid-porous interface has been taken into account, and the influence of this velocity slippage on the instability characteristic of the system is emphasized. The new behavior of the thermocapillary convection instability has been found and discussed through the figures of the spectrum.

The mean value concept in mono-linear regression of multi-variables and its application to trace studies in geosciences

IEECAS SKLLQG

Selection for variables in quantitative structure-activity/property relationship studies - Comparison between methods of orthogonal descriptors and leaps-and-bounds regression analysis

In this paper, the comparison of orthogonal descriptors and Leaps-and-Bounds regression analysis is performed. The results obtained by using orthogonal descriptors are better than that obtained by using Leaps-and-Bounds regression for the data set of nitrobenzenes used in this study. Leaps-and-Bounds regression can be used effectively for selection of variables in quantitative structure-activity/property relationship(QSAR/QSPR) studies. Consequently, orthogonalisation of descriptors is also a good method for variable selection for studies on QSAR/QSPR.

Prediction of molar absorptivities of color reagents during their color reactions with cerium using multiple regression analysis and neural network

A quantitative structure-property study has been made on the relationship between molar absorptivities (epsilon) of asymmetrical phosphone bisazo derivatives of chromotropic acid and their color reactions with cerium by multiple regression analysis and neural network. The new topological indices A(x1) - A(x3) suggested in our laboratory and molecular connectivity indices of 43 compounds have been calculated. The results obtained from the two methods are compared. The neural network model is superior to the regression analysis technique and gave a prediction which was sufficiently accurate to estimate the molar absorptivities of color reagents during their color reactions with cerium.

Quantitative structure-property relationships for colour reagents and their colour reactions with ytterbium using regression analysis and computational neural networks

In this paper, the new topological indices A(x1)-A(x3) suggested in our laboratory and molecular connectivity indices have been applied to multivariate analysis in structure-property studies. The topological indices of twenty asymmetrical phosphono bisazo derivatives of chromotropic acid have been calculated. The structure-property relationships between colour reagents and their colour reactions with ytterbium have been studied by A(x1)-A(x3) indices and molecular connectivity indices with satisfactory results. Multiple regression analysis and neural networks were employed simultaneously in this study.

QUANTITATIVE STRUCTURE-ACTIVITY-RELATIONSHIPS FOR TOXICITY OF PHENOLS USING REGRESSION-ANALYSIS AND COMPUTATIONAL NEURAL NETWORKS

Quantitative structure-toxicity models were developed that directly link the molecular structures of a et of 50 alkYlated and/or halogenated phenols with their polar narcosis toxicity, expressed as the negative logarithm of the IGC50 (50% growth inhibitor

Relationships between Testate Amoebae Assemblages (Protozoa) and Geographic Factors in Yunnan Plateau Lakes, China

Knowledge of the effect of geographic factors on the assemblages of protozoan testate amoebae is still limited, despite there having been a number of studies on this fauna. We applied statistical analyses to data on the distribution of testate amoebae from nine major lakes in the Yunnan Plateau, southwest China. Cluster analysis, based on community structure, separated the lakes into two groups - the oligotrophic/mesotrophic lakes and the hypercutrophic lakes - confirming the idea that the testate amoebae assemblages in lakes are closely related to the trophic status. Additionally, within the oligotrophic/mesotrophic lakes, there was distinct geographic clustering. Linear regression analysis and the Mantel test both revealed that similarity of species composition decreased with increasing geographic distance among the oligotrophic/mesotrophic lakes.

Modeling the effect of ozone loss on photobleaching of chromophoric dissolved organic matter in the St. Lawrence estuary

Temporal trends in total ozone for the St. Lawrence estuary were estimated from ground-based measurements at the NOAA/CMDL station in Caribou, Maine. Linear regression analysis showed that from 1979 to 1999 total ozone has decreased by about 3.3% per decade on an annual basis and ≤6.2% per decade on a monthly basis relative to unperturbed (pre-CFC) levels. The influence of increased ultraviolet-B (280–320 nm) radiation associated with ozone depletion on water column photochemical processes was evaluated by modeling the photobleaching of chromophoric dissolved organic material (CDOM). Linear regression analysis showed small (<0.5% per decade), but statistically significant upward trends in maximum noontime photobleaching rates. Most notably, positive trends in relative rates for May, June, and July, when maximum absolute rates are expected, were predicted. A global model based on TOMS ozone data revealed increases in photobleaching of ≤3% per decade at high latitudes in the Southern Hemisphere. Radiation amplification factors for increases in photochemically weighted UV (280–400 nm) in response to ozone depletion were estimated at 0.1 and 0.08 for photobleaching of CDOM absorbance at 300 and 350 nm, respectively. Application of the laboratory-based model to conditions that more closely resembled those in situ were variable with both overestimation and underestimation of measured rates. The differences between modeled rates and observed rates under quasi-natural conditions were as large or larger than the predicted increases due to ozone depletion. These comparisons suggest that biological activity and mixing play an important, but as yet ill-defined, role in modifying photochemical processes.

Applications of the method of three-dimensional projection of a molecule in quantitative structure-activity relationship of phenol derivatives

Five variables for phenol derivatives were calculated by molecular projection in three-dimensional space which were combined with eight quantum-chemical parameters and three Am indices. These variables were selected by using leaps-and-bounds regression analysis. Multiple linear regression analysis and artificial neural networks' were performed, and the results obtained by using. artificial neural networks are superior than that obtained by using multiple linear regression.

A SIMPLE METHOD FOR PREDICTION OF GAS-PERMEABILITY OF POLYMERS FROM THEIR MOLECULAR-STRUCTURE

A method for the prediction of gas permeabilities (P) through polymers from their chemical structure has been developed on the basis of the ratio of molar free volume to molar cohesive energy, V(f)/E(coh). The permeation of small gas molecules through polymer membranes is dependent on the chain packing density measured by V(f) and segmental motion of polymer chains measured by E(coh). But no simple relationship between P and V(f) or E(coh) alone was found. The permeability data of more than 60 polymers covering 7 orders of magnitude for six gases have been treated with linear regression analysis. All plots of log P vs. V(f)/E(coh) gave good straight lines. It is also found that a linear relationship holds when plotting both the intercepts and slopes of log P vs. V(f)/E(coh) lines against square of the diameters of gas molecules. Therefore, the permeabilities of all the non-swelling gases through a great variety of polymers can be estimated using two correlations above. Moreover, this method is more accurate than others in the literature and may found useful for the selection of gas separation or barrier membrane materials.

The relation between distribution of zooplankton and salinity in the Changjiang Estuary

Seasonal netzplankton samples from stations in the Changjiang (Yangtze River) Estuary were collected from May, 2004 to February, 2005. The dominant species and their contribution to the total zooplankton abundance were determined. Moreover, the relationship between the salinity and abundance was studied with stepwise linear regression. During the whole year, the salinity was positively correlated with the abundance, while the temperature, negatively. Linear regression analysis showed also a high positive correlation with salinity for total abundance in August and November, while in February and May, no obvious relations were found. The most abundant community was composed of neritic and brackish-water species. The North Passage (NP) (salinity <5) was greatly diluted by freshwater while the North Branch (NB) was brackish water with salinity range of 12-28. Consequently, clear decline in abundance of zooplankton was along the estuarine haloclines from the maximum in the area of high salinity to the minimum in the limnetic zone. Total zooplankton abundance and biomass were lower in NP than the NB in all seasons. In short, the salinity influenced the abundance of each species of zooplankton, and ultimately determined the total abundance of zooplankton. Furthermore, a winter peak in the abundance existed, which might be caused by the flourishing of Sinocalanus sinensis, a widely distributed species in the Changjiang Estuary.