Taylor Equation Research Articles

A Two-source Trapezoid Model for Evapotranspiration (TTME) from satellite imagery

This study develops a Two-source Trapezoid Model for Evapotranspiration (TTME) from satellite imagery by interpreting the remotely sensed fractional vegetation cover (fc)–radiative surface temperature (Trad) space and the concept of soil surface moisture availability isopleths superimposed on the space. The theoretical upper boundary condition of TTME is determined by solving for temperatures of the driest bare surface (Ts,max) and the driest fully vegetated surface (Tc,max) both implicit in radiation budget and energy balance equations. Air temperature (Ta) constitutes the lower boundary of TTME. Trad of a pixel within the fc–Trad space is decomposed into temperature components (Tc and Ts) by interpolating the slope of the theoretical boundaries and interpreting variation in Trad with fc for each isopiestic line going across the pixel. Vegetation transpiration and soil surface evaporation are then separately parameterized. TTME was applied to the Soil Moisture-Atmosphere Coupling Experiment (SMACEX) site in central Iowa, U.S., on three days in 2002 during the period of rapid growth in corn and soybean when three scenes of Landsat Thematic Mapper (TM)/Enhanced Thematic Mapper Plus (ETM+) images and one scene of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) image were acquired. Results indicate that TTME is capable of reproducing latent heat flux (LE) with a mean absolute percentage difference (MAPD) of ~10%, and a root mean square difference (RMSD) of 45.6Wm−2 and 63.1Wm−2 for Landsat TM/ETM+ and ASTER images, respectively. Comparison of TTME with other one-source and two-source models using the same data set suggests that TTME shows comparable accuracy as the Two-Source Energy Balance (TSEB), but requires relatively fewer inputs and obviates the computation of resistance networks in the modeling domain and the overestimation of vegetation transpiration incurred by using the Priestley–Taylor equation. Sensitivity analysis suggests that TTME is most sensitive to Trad and Ta, but not sensitive to a range of meteorological observations and variables and parameters derived/specified.

Estimating and validating basin-scale actual evapotranspiration using MODIS images and hydrologic models

An algorithm for estimating daily spatial actual evapotranspiration (ET) from remotely sensed MODIS data is presented. It is based on the surface energy balance scheme and the modified Priestley–Taylor equation, and has been applied to the MODIS data acquired during growing seasons over the Laohahe River basin, northeastern China. Spatial distributed mapping of daily ET for 22 clear sky days in the year of 2000 from MODIS images over the study area were obtained. In order to validate ET values estimated from MODIS data, regional daily ET values were calculated using the lumped modified Xinanjiang hydrologic model and distributed SWAT model based on the water balance scheme, respectively. The relationship between actual daily ET estimated from MODIS images and basin-scale ET calculated from the hydrologic model were in good agreement with acceptable correlation coefficient. The results suggested that the algorithm is applicable and operational for estimating and mapping basin-scale distributed daily actual ET over the study area. In order to use the algorithm proposed by this paper for water resource management and agricultural decision making, the algorithm should be validated using more data and be tested under different environment and different land use scenario conditions in future work.

Thermal and rheological properties of the supersaturated sucrose solution in the presence of different molecular weight fractions and concentrations of dextran

In our current research work, we investigated the effects of molecular weight (Mw) and the concentration of dextran presence during cane sugar manufacturing on the rheological and glass transition properties of supersaturated sucrose solution. Three dextrans of various Mw, namely 100,000 g/mol (T100), 500,000 g/mol (T500) and 2,000,000 g/mol (T2000), were admixed in concentrations between 1,000 and 10,000 ppm with 65 and 75% w/w sucrose solution. The results indicated that both the apparent viscosity and dynamic modulus increased with an increase in dextran concentrations and they demonstrated strong dependence on its Mw. Glass transition temperature (Tg) of the samples was measured by differential scanning calorimetry, and their dependence on dextran Mw and concentration was analyzed by the Fox and expanded Gordon–Taylor mathematical models. It was found that the higher the Mw and concentration of the dextran, the greater the increase in Tg. The expanded Gordon–Taylor equation has proved useful in predicting the Tg of the sucrose solution in the presence of polymer.

Dislocation Density Based Crystal Plasticity Finite Element Simulation of Alpha-Iron

ABSTRACTFerritic/martensitic steels such as HT9 steel, is used for structural components in nuclear power plants because of its high strength and good swelling resistance. Understanding the mechanical behavior of these steels is quite important, since it will affect the strength and the life of the component. In this study, a dislocation density based crystal plasticity finite element model is developed in which different types of dislocation evolves on the activated 12 slip systems in alpha-iron. The dislocation evolves in the form of closed loop and the dislocation density is tracked as internal state variable, the generation and annihilation of dislocations are modeled based on the dislocation interaction laws. The plastic flow is calculated based on the dislocation densities and a generalized Taylor equation is used as the hardening law, and the hardening is assumed to be isotropic in this study. The evolution of polycrystal texture of alpha-iron is presented in the form of pole figures, which indicate the orientation spread and agree with the experimental result. The model also indicates the inhomogeneous dislocation distribution and stress concentration at the grain boundaries.

Novel Node Localization Algorithm Based on Nonlinear Weighting Least Square for Wireless Sensor Networks

Positioning of the location information of wireless sensor network nodes is one of the key issues in wireless sensor network applications. The traditional node positioning method based on least-square algorithm heavily depends on the ranging accuracy, and therefore cannot guarantee high precision. This paper presents a new method for wireless sensor network node positioning based on nonlinear weighting least-square algorithm. Regarding ranging equation error-weighted sum as a whole, this method starts with the initial iteration point of stepwise refinement to explore the optimal solution and further reduces the positioning computational complexity by the simplification of the Taylor equation. Experimental results demonstrate that promising results have been achieved by using this method.

State diagrams of freeze dried colostral whey powders: Effects of additives on the stability of colostral whey powders

The state diagrams of colostral whey (CW) powders with different additives were determined using freezing curve, glass transition line and maximal-freeze-concentration conditions and effects of different additives on the stability of CW powders were also investigated based on water activity and glass transition concepts. The Brunauer–Emmett–Teller (BET) and Gordon–Taylor equations were used to model water activity/moisture content and glass transition temperatures ( T g)/solids content relationships. The parameters of two models were applied for estimating water activity and T g at given moisture content. Results showed that addition with maltodextrin into CW powders increased T g of dry solids ( T gs) from 103.5 to 126.8 °C and end point of freezing ( T m ′ ) from −35.20 to −31.79 °C, whereas addition with sucrose decreased T gs to 80.1 °C and T m ′ to −36.18 °C, indicating maltodextrin was an excellent drying aid and cryoprotectant. The greater efforts were needed to make to combine the water activity and glass transition concepts for predicting the stability of food materials.

Thermal properties of agave fructans (Agave tequilana Weber var. Azul)

Abstract Thermal properties of agave ( A. tequilana Weber var. Azul) at different water contents were investigated. HP-TLC results showed a complex mixture of mono-, di-, oligo, and polysaccharides in agave fructans samples. The thermal decomposition temperatures were observed below to 200 °C. Modulated-differential scanning calorimetry studies showed a glass transition and a relaxation enthalpy processes in agave fructans. Samples with the highest moieties of monosaccharides showed the lower glass transition temperatures ( Tg ). The moisture sorption isotherm of agave fructans was determined at 20 °C and fitted to the GAB model. Gordon–Taylor equation was used to fit the Tg experimental data as a function of water content. Agave fructans was found to be an amorphous material. At low water activity ( a w ) values ( a w (0.4–0.75) collapsed and caked; and at high a w (>0.75) changed in a highly viscous liquid-like solution.

Effect of moisture content on selected physicochemical properties of two commercial hen egg white powders

After short-term storage at 23°C, selected physicochemical properties of two hen egg white powders (with and without hydrolysis) were studied. Overall, the effect of moisture content on physicochemical properties of Hydrolysed Egg White powder (HEW) was more severe than those of Dried Egg White powder (DEW). The denaturation temperature (Td) and its enthalpy change (ΔHd) of ovalbumin in DEW followed an exponential model, as well as the Td of HEW. The Gordon–Taylor equation modelled well the glass transition temperatures (Tg) of HEW and DEW. The Guggenheim–Anderson–de Boer (GAB) model fitted well to the type II moisture sorption isotherm. At the critical moisture content (12.0%, dry basis), compared with DEW, the colour of HEW began to darken dramatically and its hardness started to change significantly. These changes were closely related to the inherent characteristics of the two products. The mechanisms relevant to these physicochemical changes were discussed.

Glass transition temperatures of cassava starch–whey protein concentrate systems at low and intermediate water content

Abstract Glass transition temperatures of cassava starch (CS)–whey protein concentrate (WPC) blends were determined by means of differential scanning calorimetry (DSC) in a water content range of 8–20% (dry basis, d.b.). Water equilibration in the samples was carried out by storing them at room temperature (25 °C) during four weeks. Physical aging and phase segregation were observed in some samples after this storage period depending on the water content. Both, first DSC heating scans and tan δ curves of CS–WPC blends with intermediate water content (10–18%), showed two endothermic thermal events. The first one appeared at around 60 °C and was independent of water content. The second one was detected at higher temperatures and moved towards the low-temperature peak as the water content increased. The results can be explained by a phase segregation process that can take place when the samples are conditioned below their glass transition temperatures. The Gordon–Taylor equation described well the plasticizing effect of water on the blends. WPC was also found to decrease the glass transition temperature, at constant water content, an effect attributed to additional water produced during browning reactions in the blends.

Glass transition behavior of corn distillers dried grains with solubles (DDGS)

Distillers dried grains with solubles (DDGS), a major co-product from the corn ethanol industry, has high feed value for its chemical composition. The ratio of wet distillers grains (WDG) and condensed distillers solubles (CDS) added during the production process determines the chemical composition of DDGS. Effect of changing this ratio and the influence of moisture content on glass transition behavior of DDGS was studied. Five prediction models were evaluated to explain the glass transition of DDGS. The mixed trends in the result indicated the complex behavior of DDGS particles and revealed that both moisture content and chemical composition impact the glass transition behavior of DDGS. Onset glass transition temperature ranged from 20 to 30 °C depending on the chemical composition. Kwei equation predictions were better than the predictions by Gordon–Taylor equation. The glass transition temperature of DDGS can be mathematically explained by combining the moisture content and chemical components protein, fiber, glycerol, and sugar percent. The artificial neural network (ANN) model gave a better prediction of onset and midpoint glass transition temperature of DDGS and this might be due to the accurate mapping of the interaction between chemical components.

Wear Behaviors of PCD Tools in Turning Granite

The performance and wear mechanisms of two types of polycrystalline diamond (PCD) cutting tools (marked as PCD 010 and PCD 030) have been investigated in this paper. Continuous turning of round granite bars has been selected as the test method. The Taylor equation has been developed to describe the tool performance. The experimental results indicate that PCD 010 has a greater thermal wear resistance than PCD 030 at high cutting speeds. Scanning electron microscopy (SEM) was used to evaluate wear mechanisms of PCD tools, our results show that the dominant wear mechanisms for PCD 010 is abrasion wear while that for PCD 030 is inter-granular and cleavage wear.

CBN Tool Life Prediction by Artificial Neural Network

For economic application of CBN tools it is important to know how the tool life changes as a function of the most important technological parameters (cutting speed, feed rate, depth of cut and work piece diameter). These technological parameters have significant effects on the productivity of machining. The extended Taylor equation takes the effects of feed rate, depth of cut into account besides the cutting speed, but this equation is not valid in the whole range of cutting speed. Beyond the publicated tool life equations in the professional articles, the tool life can be determined by Artificial Neural Network (ANN). ANNs have huge flexibility and can handle different number of inputs thus they are suitable for determining tool life as a function of several cutting parameters.

Drag force on a sphere moving toward an anisotropic superhydrophobic plane

We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured superhydrophobic plane that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and φ2 (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and H (local separation). The effect of effective slip is predicted to decrease the force as compared with what is expected for two hydrophilic surfaces and described by the Taylor equation. The presence of additional length scales, L, b1, and b2, implies that a film drainage can be much richer than in the case of a sphere moving toward a hydrophilic plane. For a large (compared to L) gap the reduction of the force is small, and for all textures the force is similar to expected when a sphere is moving toward a smooth hydrophilic plane that is shifted down from the superhydrophobic wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing striped superhydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap. We show that at a thinner gap the force reduction becomes more pronounced, and that it depends strongly on the fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent force measurements in the presence of a superhydrophobic surface.

Seasonal energy and water balance of a Phragmites australis-dominated wetland in the Republican River basin of south-central Nebraska (USA)

Summary Climate and vegetation strongly influence the water cycle on local to regional scales. A change in the surface energy and water balance, especially in dry climatic regions, can have a significant impact on local water availability and, therefore, water resource management. The purpose of this study is to quantify the energy and water balance of a riparian wetland in a subhumid region of the central US, as well as the role of seasonal climate variability and vegetation phenology. The site is located in the Republican River basin in south-central Nebraska, where decreases in streamflow have been observed in recent decades. In an effort to reduce consumptive water use from evapotranspiration (ET), and thereby reclaim surface water, invasive species such as Phragmites australis have been removed throughout the riparian corridor of the river basin. In this study, we used energy/water balance monitoring stations, a Large Aperture Scintillometer (LAS), and numerous water and soil temperature probes to determine the energy and water balance during the 2009 growing season (April 11−October 3). Sensible heat flux was measured using the LAS, while ET was calculated as a residual of the energy balance (i.e., net radiation minus sensible heat flux and heat storage rates in the canopy, water, and soil). Rigorous quality control and uncertainty analyses were performed, and comparisons were also made with ET rates calculated via the simpler Priestley–Taylor method. Results of the energy budget analysis indicate that the average ET rate for the wetland during the growing season was 4.4 mm day −1 , with a maximum daily rate of 8.2 mm day −1 (occurring on June 29). Precipitation during the same 176-day period averaged 2.7 mm day −1 . Net radiation and vegetation phenology were found to be the two largest drivers of seasonal variability in ET. Sensible heat flux was significantly larger than latent heat flux early in the season, when standing vegetation in the wetland was still dry and brown. By late May and early June, however, Bowen ratios had declined well below 0.5 in response to greener and more abundant vegetation, higher transpiration rates, and reduced sensible heat flux. Heat storage rates in the wetland were dominated by changes in water temperature (as compared to soil or canopy heat storage) and comprised a significant portion of the hourly energy balance. On daily mean timescales, changes in the rate of heat storage corresponded to ∼13% of the variability in net radiation, while for the season-long average, the heat storage term was found to be essentially negligible. The Priestley–Taylor equation provided a reasonable estimate of ET during the height of the growing season but significantly overestimated ET during the beginning of the season (since it could not account for large sensible heat fluxes from the dry vegetation). Analysis of the wetland water balance showed seasonal variations in water level that were similar to changes in cumulative water inputs (i.e., precipitation minus ET). Portions of the season when the two curves had differing rates of change indicated periods of net water influx or outflux from other sources (primarily groundwater).

Thermo-physical characterization of Pharmacoat® 603, Pharmacoat® 615 and Mowiol® 4-98

Hydroxypropyl methylcellulose (HPMC) and polyvinyl alcohol (PVA) are important polymers in pharmaceutical, food and other industries being largely used as encapsulation agents. The characterization of two reference grades of HPMC (Pharmacoat® 603 and Pharmacoat® 615) and one reference grade of PVA (Mowiol® 4-98), through X-ray diffraction (XRD) and thermogravimetry (TG) is described. Specific analyses were performed by means of dynamic vapour sorption analysis of water adsorption/desorption from vapours at 10, 25, 40, 55 and 70 °C. Guggenheim–Anderson–de Boer (GAB), Brunauer–Emmett–Teller (BET), Park and n-layer BET models were successfully used to fit the experimental data. The glass transition temperature as function of water content was measured by means of differential scanning calorimetry (DSC). The experimental data were analysed according to Linear, Gordon–Taylor, Fox and Roos equations. XRD studies revealed amorphous structure for the Pharmacoat® 603 and Pharmacoat® 615 and crystalline for Mowiol® 4-98. Single and multi-step temperature degradation point was found for Pharmacoat® 603 and Pharmacoat® 615 and Mowiol® 4-98, respectively. The water uptake is higher for Pharmacoat® 603 and Pharmacoat® 615 than Mowiol® 4-98. The influence of temperature on water uptake is opposite for the two types of polymers. GAB and n-layer BET were found to better model Pharmacoat® 603 and Pharmacoat® 615 and Mowiol® 4-98 data, respectively. The water makes the glass transition to decrease quite drastically. Gordon–Taylor is better fitting the experimental data both for Pharmacoat® 603 and Pharmacoat® 615 and Mowiol® 4-98.

Effects of Thermal Denaturation on the Solid-State Structure and Molecular Mobility of Glycinin

The effects of moisture and thermal denaturation on the solid-state structure and molecular mobility of soy glycinin powder were investigated using multiple techniques that probe over a range of length and time scales. In native glycinin, increased moisture resulted in a decrease in both the glass transition temperature and the denaturation temperature. The sensitivity of the glass transition temperature to moisture is shown to follow the Gordon-Taylor equation, while the sensitivity of the denaturation temperature to moisture is modeled using Flory's melting point depression theory. While denaturation resulted in a loss of long-range order, the principal conformational structures as detected by infrared are maintained. The temperature range over which the glass to rubber transition occurred was extended on the high temperature side, leading to an increase in the midpoint glass transition temperature and suggesting that the amorphous regions of the newly disordered protein are less mobile. (13)C NMR results supported this hypothesis.

Tensile Deformation Behaviors of Ultra-Fine Subgrained Aluminum

Tensile deformation behaviors up to peak stress of the ultra-fine subgrained aluminum (2024Al) with the subgrain sizes of about 250 nm and low dislocation density inside were investigated. The results show that the ultra-fine subgrained aluminum exhibited high strain hardening and large uniform plastic strain (19.3 %), but little post-deformation hardness/dislocation density increases (99.6 HV vs. 100.3 HV and 0.79×1014 m-2 vs. 1.03×1014 m-2, respectively). The theoretical calculation based on Taylor equation demonstrated that the dislocation density increase during the tensile deformation up to peak stress was very enormous (1.64×1015 m-2). These results not only implied that the dislocations involved in the tensile deformation were in large quantities but most of them disappeared upon the unloading of the tensile deformation, but also demonstrated that high strain hardening capacity is not a sufficient factor for ultra-fine subgrained metals to store deformation dislocations leading to post-deformation hardness increases.

Effects of corn oil on glass transition temperatures of cassava starch

Glass transition temperatures of cassava starch–corn oil blends were determined by means of differential scanning calorimetry (DSC) and dynamic mechanical thermal analysis (DMTA), in a moisture content range of 4–35% (dry basis, d.b.). The samples were equilibrated at ambient temperature (25°C) during 4 weeks. A sub-Tg endothermic peak, occurring between 45 and 60°C, appeared in samples with relatively low moisture contents (less than: 14.4% (d.b.), 10.1% and 8.5% for added corn oil levels of 1.1, 4.5 and 6.6%, respectively). In correspondence with DSC measurements, secondary relaxation temperatures (Tβ) at around 55°C, measured by DMTA were also present at low moisture contents (less than: 18% (d.b.), 16% and 15% for added corn oil levels of 1.1, 4.5 and 6.6%, respectively). At intermediate moisture contents enthalpic relaxation events associated to ageing processes were evidenced by DSC first heating scans, while at higher moisture contents only the glass transition was exhibited by the samples. In all cases, increasing levels of added corn oil decreased the moisture content at which the samples exhibited the above described thermal events. The effect of water on glass transition temperatures (as determined during a DSC second heating scan and DMTA results) was well described by the Gordon–Taylor equation. It was found that cassava starch was better plasticized by water when the levels of added corn oil were decreased. The added corn oil was also found to be a plasticizer for cassava starch probably due to hydrophobic–hydrophilic type interactions with starch.

Extension of the Taylor Equation for Oil-Water-Surfactant System and Investigating the Impact of Surfactant Concentration over the Quality of Emulsion

Emulsions stand among the most important multiphase fluids, exhibiting various complicated phenomenon. To understand the process of emulsification, the Taylor equation has been extended to incorporate the parameters that depend on molecular mass of oil and their contents and the amount of surfactant added. To test the validity of the proposed equations, four well-defined short chain (n-hexane, n-heptane, n-decane, and kerosene) oils were emulsified in water and the results were compared with the experimental ones. It has been concluded that the extended Taylor equation worked well, even in the presence of surfactant. The quality of the emulsion defined and discussed in terms of size and number of droplets was best near CMC of the surfactant used. A relationship has also been derived between CMC of surfactant and its distribution coefficient, which allows the exact value of one parameter to be determined if other is known.

Magnitude and variability of land evaporation and its components at the global scale

Abstract. A process-based methodology is applied to estimate land-surface evaporation from multi-satellite information. GLEAM (Global Land-surface Evaporation: the Amsterdam Methodology) combines a wide range of remotely-sensed observations to derive daily actual evaporation and its different components. Soil water stress conditions are defined from a root-zone profile of soil moisture and used to estimate transpiration based on a Priestley and Taylor equation. The methodology also derives evaporationfrom bare soil and snow sublimation. Tall vegetation rainfall interception is independently estimated by means of the Gash analytical model. Here, GLEAM is applied daily, at global scale and a quarter degree resolution. Triple collocation is used to calculate the error structure of the evaporation estimates and test the relative merits of two different precipitation inputs. The spatial distribution of evaporation – and its different components – is analysed to understand the relative importance of each component over different ecosystems. Annual land evaporation is estimated as 67.9 × 103 km3, 80% corresponding to transpiration, 11% to interception loss, 7% to bare soil evaporation and 2% snow sublimation. Results show that rainfall interception plays an important role in the partition of precipitation into evaporation and water available for runoff at a continental scale. This study gives insights into the relative importance of precipitation and net radiation in driving evaporation, and how the seasonal influence of these controls varies over different regions. Precipitation is recognised as an important factor driving evaporation, not only in areas that have limited soil water availability, but also in areas of high rainfall interception and low available energy.