Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

A pore-size-dependent equation of state for multilayer adsorption in cylindrical mesopores

The chemical potential of adsorbed film inside cylindrical mesopores is dependent on the attractive interactions between the adsorbed molecules and adsorbent, the curvature of gas/adsorbed phase interface, and surface tension. A state equation of the adsorbed film is proposed to take into account the above factors. Nitrogen adsorption on model adsorbents, MCM-41, which exhibit uniform cylindrical channels, are used to verify the theoretical analysis. The proposed theory is capable of describing the important features of adsorption processes in cylindrical mesopores. According to this theory, at a given relative pressure, the smaller the pore radius is, the thicker the adsorbed film will be. The thickening of adsorbed films in the pores as the vapor pressure increases inevitably causes an increase in the interface curvature, which consequently leads to capillary condensation. Besides, this study confirmed that the interface tension depends substantially on the interface curvature in small mesopores. A quantitative relationship between the condensation pressure and the pore radius can be derived from the state equation and used to predict the pore radius from a condensation pressure, or vice versa.

Continuity of care and readmission in two service systems: a comparative Victorian and Groningen case-register study

Objective: We compared service consumption, continuity of care and risk of readmission in a record linkage follow-up study of cohorts of patients with schizophrenia and related disorders in Victoria (Australia) and in Groningen (The Netherlands). These areas are interesting to compare because mental health care is in a different stage of deiustitutionalization. More beds are available in Groningen and more community resources are available in Victoria. Method: The cohorts were followed for 4 years, since discharge from inpatient services using record linkage data available in the psychiatric case-registers in both areas. Survival analysis was used to study continuity of care and risk of readmission. Results: Available indicators showed a higher level of continuity of care in Victoria. While the relative risk of readmission was the same in both areas and not affected by aftercare contact after discharge, the number of days spent in hospital was much higher in the Groningen register area. Conclusion: These findings provide further support for earlier reports that the risk of readmission is predominantly affected by attributes of mental illness. However, the duration of admissions, is strongly affected by service system variables, including the provision of continuity of care.

Groundwater waves in a coastal aquifer: A new governing equation including vertical effects and capillarity

Groundwater waves, that is, water table fluctuations, are a natural phenomenon in coastal aquifers. They represent an important part of the interaction between the ocean and aquifer and affect the mass exchange between them. This paper presents a new groundwater wave equation. Because it includes the effects of vertical flows and capillarity, the new equation is applicable to both intermediate-depth aquifers and high-frequency waves. Compared with the wave equation derived by Nielsen ed al. [1997], the present equation provides a closer representation of groundwater waves. In particular, it predicts high-frequency water table fluctuations as observed in the field. A validation of the new equation has been carried out by comparing the analytical solutions to it with predictions from direct simulations using the numerical model SUTRA. The effects of various physical parameters and their relative importance are also discussed.

Asymptotic solutions to the Gross-Pitaevskii gain equation: Growth of a Bose-Einstein condensate

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature.

Interpretation of negative values of the interaction parameter in the adsorption equation through the effects of surface layer heterogeneity

The problem of the negative values of the interaction parameter in the equation of Frumkin has been analyzed with respect to the adsorption of nonionic molecules on energetically homogeneous surface. For this purpose, the adsorption states of a homologue series of ethoxylated nonionic surfactants on air/water interface have been determined using four different models and literature data (surface tension isotherms). The results obtained with the Frumkin adsorption isotherm imply repulsion between the adsorbed species (corresponding to negative values of the interaction parameter), while the classical lattice theory for energetically homogeneous surface (e.g., water/air) admits attraction alone. It appears that this serious contradiction can be overcome by assuming heterogeneity in the adsorption layer, that is, effects of partial condensation (formation of aggregates) on the surface. Such a phenomenon is suggested in the Fainerman-Lucassen-Reynders-Miller (FLM) 'Aggregation model'. Despite the limitations of the latter model (e.g., monodispersity of the aggregates), we have been able to estimate the sign and the order of magnitude of Frumkin's interaction parameter and the range of the aggregation numbers of the surface species. (C) 2004 Elsevier B.V All rights reserved.

Non-diagonal solutions of the reflection equation for the trigonometric A((1)) (n-1) vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.

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.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

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.