AN ASSESSMENT ON THE USE OF THE DEBYE-HUCKEL EQUATION FOR THE THERMODYNAMIC MODELING OF AQUEOUS SYSTEMS CONTAINING POLYMERS AND SALTS

In this work, a study on the role of the long-range term of excess Gibbs energy models in the modeling of aqueous systems containing polymers and salts is presented. Four different approaches on how to account for the presence of polymer in the long-range term were considered, and simulations were conducted considering aqueous solutions of three different salts. The analysis of water activity curves showed that, in all cases, a liquid-phase separation may be introduced by the sole presence of the polymer in the long-range term, regardless of how it is taken into account. The results lead to the conclusion that there is no single exact solution for this problem, and that any kind of approach may introduce inconsistencies.

An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer`s equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer`s model (combining a long-range term, based on the Debye-Huckel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid-liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems. (c) 2008 Elsevier B.V. All rights reserved.

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

Extension of a Recent Method for Obtaining Exact Solutions of the Bruce and Klute Equation

A method based on a specific power-law relationship between the hydraulic head and the Boltzmann variable was recently presented. We generalized this relationship to a range of powers and extended the solution to include the saturated zone. As a result, the new solution satisfies the Bruce and Klute equation exactly.

Estimating hourly net radiation for leaf wetness duration using the Penman-Monteith equation

Leaf wetness duration (LWD) is related to plant disease occurrence and is therefore a key parameter in agrometeorology. As LWD is seldom measured at standard weather stations, it must be estimated in order to ensure the effectiveness of warning systems and the scheduling of chemical disease control. Among the models used to estimate LWD, those that use physical principles of dew formation and dew and/or rain evaporation have shown good portability and sufficiently accurate results for operational use. However, the requirement of net radiation (Rn) is a disadvantage foroperational physical models, since this variable is usually not measured over crops or even at standard weather stations. With the objective of proposing a solution for this problem, this study has evaluated the ability of four models to estimate hourly Rn and their impact on LWD estimates using a Penman-Monteith approach. A field experiment was carried out in Elora, Ontario, Canada, with measurements of LWD, Rn and other meteorological variables over mowed turfgrass for a 58 day period during the growing season of 2003. Four models for estimating hourly Rn based on different combinations of incoming solar radiation (Rg), airtemperature (T), relative humidity (RH), cloud cover (CC) and cloud height (CH), were evaluated. Measured and estimated hourly Rn values were applied in a Penman-Monteith model to estimate LWD. Correlating measured and estimated Rn, we observed that all models performed well in terms of estimating hourly Rn. However, when cloud data were used the models overestimated positive Rn and underestimated negative Rn. When only Rg and T were used to estimate hourly Rn, the model underestimated positive Rn and no tendency was observed for negative Rn. The best performance was obtained with Model I, which presented, in general, the smallest mean absolute error (MAE) and the highest C-index. When measured LWD was compared to the Penman-Monteith LWD, calculated with measured and estimated Rn, few differences were observed. Both precision and accuracy were high, with the slopes of the relationships ranging from 0.96 to 1.02 and R-2 from 0.85 to 0.92, resulting in C-indices between 0.87 and 0.93. The LWD mean absolute errors associated with Rn estimates were between 1.0 and 1.5h, which is sufficient for use in plant disease management schemes.

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

New Specific Equation to Estimate Resting Energy Expenditure in Severely Obese Patients

Calculating the estimated resting energy expenditure (REE) in severely obese patients is useful, but there is controversy concerning the effectiveness of available prediction equations (PE) using body weight (BW). We evaluated the efficacy of REE equations against indirect calorimetry (IC) in severely obese subjects and aimed to develop a new equation based on body composition compartments. One hundred and twenty severely obese patients had their REE measured (MREE) by IC and compared to the most commonly used PE (Harris-Benedict (HB), Ireton-Jones, Owen, and Mifflin St. Jeor). In a random sample (n = 60), a new REE equation based on fat-free mass (FFM) was developed and validated. All PE studied failed to estimate REE in severe obesity (low concordance correlation coefficient (CCC) and limits of agreement of nearly 50% of the sample +/- 10% of MREE). The HB equation using actual BW exhibited good results for all samples when compared to IC (2,117 +/- 518 kcal/day by HB vs. 2,139 +/- 423 kcal/day by MREE, P > 0.01); these results were blunted when patients were separated by gender (2,771 vs. 2,586 kcal/day, P < 0.001 in males and 1,825 vs. 1,939 kcal/day, P < 0.001 in females). A new resting energy expenditure equation prediction was developed using FFM, Horie-Waitzberg, & Gonzalez, expressed as 560.43 + (5.39 x BW) + (14.14 x FFM). The new resting energy expenditure equation prediction, which uses FFM and BW, demonstrates higher accuracy, precision, CCC, and limits of agreement than the standard PE in patients when compared to MREE (2,129 +/- 45 kcal/day vs. 2,139 +/- 423 kcal/day, respectively, P = 0.1). The new equation developed to estimate REE, which takes into account both FFM and BW, provides better results than currently available equations.

Harris-Benedict equation for critically ill patients: Are there differences with indirect calorimetry?

Purpose: The aim of this study was to compare the measured energy expenditure (EE) and the estimated basal EE (BEE) in critically ill patients. Materials and Methods: Seventeen patients from an intensive care unit were randomly evaluated. Indirect calorimetry was performed to calculate patient`s EE, and BEE was estimated by the Harris-Benedict formula. The metabolic state (EE/BEE x 100) was determined according to the following criteria: hypermetabolism, more than 130%; normal metabolism, between 90% and 130%; and hypometabolism, less than 90%. To determine the limits of agreement between EE and BEE, we performed a Bland-Altman analysis. Results: The average EE of patients was 6339 +/- 1119 kJ/d. Two patients were hypermetabolic (11.8%), 4 were hypometabolic (23.5%), and 11 normometabolic (64.7%). Bland-Altman analysis showed a mean of -126 +/- 2135 kJ/d for EE and BEE. Only one patient was outside the limits of agreement between the 2 methods (indirect calorimetry and Harris-Benedict). Conclusions: The calculation of energy needs can be done with the equation of Harris-Benedict associated with lower values of correction factors (approximately 10%) to avoid overfeeding, with constant monitoring of anthropometric and biochemical parameters to assess the nutritional changing and adjust the infusion of energy. (C) 2009 Elsevier Inc. All rights reserved.

What is the best equation to estimate the basal energy expenditure of climacteric women?

Objectives The methods currently available for the measurement of energy expenditure in patients, such as indirect calorimetry and double-labelled water, are expensive and are limited in Brazil to research projects. Thus, equations for the prediction of resting metabolic rate appear to be a viable alternative for clinical practice. However, there are no specific equations for the Brazilian population and few studies have been conducted on Brazilian women in the climacteric period using existing and commonly applied equations. On this basis, the objective of the present study was to investigate the concordance between the predictive equations most frequently used and indirect calorimetry for the measurement of resting metabolic rate. Methods We calculated the St. Laurent concordance correlation coefficient between the equations and resting metabolic rate calculated by indirect calorimetry in 46 climacteric women. Results The equation showing the best concordance was that of the FAO/WHO/UNU formula (0.63), which proved to be better than the Harris & Benedict equation (0.55) for the sample studied. Conclusions On the basis of the results of the present study, we conclude that the FAO/WHO/UNU formula can be used to predict better the resting metabolic rate of climacteric women. Further studies using more homogeneous and larger samples are needed to permit the use of the FAO/WHO/UNU formula for this population group with greater accuracy.

MODELLING OF HIGH-PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG-ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng-Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition-dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO(2)-limonene, CO(2)-citral and CO(2)-linalool, and the ternary systems CO(2)-Limonene-Citral and CO(2)-Limonene-Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO(2)-limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition-dependent mixing rule to model the phase equilibrium behavior of these systems.

Heat Conduction Equation Solution in the Presence of a Change of State in a Bounded Axisymmetric Cylindrical Domain

The heat conduction problem, in the presence of a change of state, was solved for the case of an indefinitely long cylindrical layer cavity. As boundary conditions, it is imposed that the internal surface of the cavity is maintained below the fusion temperature of the infilling substance and the external surface is kept above it. The solution, obtained in nondimensional variables, consists in two closed form heat conduction equation solutions for the solidified and liquid regions, which formally depend of the, at first, unknown position of the phase change front. The energy balance through the phase change front furnishes the equation for time dependence of the front position, which is numerically solved. Substitution of the front position for a particular instant in the heat conduction equation solutions gives the temperature distribution inside the cavity at that moment. The solution is illustrated with numerical examples. [DOI: 10.1115/1.4003542]

Consistency in approximate entropy given by a volumetric estimate

Non-linear methods for estimating variability in time-series are currently of widespread use. Among such methods are approximate entropy (ApEn) and sample approximate entropy (SampEn). The applicability of ApEn and SampEn in analyzing data is evident and their use is increasing. However, consistency is a point of concern in these tools, i.e., the classification of the temporal organization of a data set might indicate a relative less ordered series in relation to another when the opposite is true. As highlighted by their proponents themselves, ApEn and SampEn might present incorrect results due to this lack of consistency. In this study, we present a method which gains consistency by using ApEn repeatedly in a wide range of combinations of window lengths and matching error tolerance. The tool is called volumetric approximate entropy, vApEn. We analyze nine artificially generated prototypical time-series with different degrees of temporal order (combinations of sine waves, logistic maps with different control parameter values, random noises). While ApEn/SampEn clearly fail to consistently identify the temporal order of the sequences, vApEn correctly do. In order to validate the tool we performed shuffled and surrogate data analysis. Statistical analysis confirmed the consistency of the method. (C) 2008 Elsevier Ltd. All rights reserved.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Positive solutions for a fourth order equation with nonlinear boundary conditions

Existence of positive solutions for a fourth order equation with nonlinear boundary conditions, which models deformations of beams on elastic supports, is considered using fixed points theorems in cones of ordered Banach spaces. Iterative and numerical solutions are also considered. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

INDEX OF AN IMPLICIT DIFFERENTIAL EQUATION

In this paper we introduce the concept of the index of an implicit differential equation F(x,y,p) = 0, where F is a smooth function, p = dy/dx, F(p) = 0 and F(pp) = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in R(5).