Search results for "equation"
showing 10 items of 4219 documents
Some insights on the description of gradient elution in reversed-phase liquid chromatography
2014
The so-called "fundamental equation for gradient elution" has been used for modeling the retention in gradient elution. In this approach, the instantaneous retention factor (k) is expressed as a function of the change in the modifier content (φ(ts )), ts being the time the solute has spent in the stationary phase. This approach can only be applied at constant flow rate and with gradients where the elution strength depends on the column length following a f(t-l/u) function, u being the linear mobile phase flow rate, and l the distance from the column inlet to the location where the solute is at time t measured from the beginning of the gradient. These limitations can be solved by using the h…
Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method
2015
Abstract Freezing processes are characterised by sharp changes in specific heat capacity and thermal conductivity for temperatures close to the freezing point. This leads to strong nonlinearities in the governing PDE that may be difficult to resolve using traditional numerical methods. In this work we present a meshless numerical method, based on a local Hermite radial basis function collocation approach in finite differencing mode, to allow the solution of freezing problems. By introducing a Kirchhoff transformation and solving the governing equations in Kirchhoff space, the strength of nonlinearity is reduced while preserving the structure of the heat equation. In combination with the hig…
A reaction engineering approach to kinetic analysis of photocatalytic reactions in slurry systems
2016
Abstract The knowledge of the rate equation is fundamental for the assessment of the activity of the photocatalytic material and for the study, design and optimization of photocatalytic reactors. In the case of photocatalytic reactions, the local volumetric rate of photon absorption (LVRPA) affects the reaction rate and its inherently uneven distribution within a “slurry” reactor makes complex a correct kinetic analysis. In the present work it is shown which are the critical aspects of the kinetic analysis in slurry reactors and how to carry out photocatalytic experiments to minimize the misinterpretations of the experimental results. In particular, the influence of the type of illumination…
A mathematical tool for describing the behaviour of a dense effluent discharge
2009
In many cases a dense effluent has to be discharged in the environment with possible harmful consequences. The preferred design for the relevant discharge unit is that of a simple or multi-port diffuser issuing jets at a given inclination above the horizontal. This work presents the follow-on developments of a model previously proposed to predict the behaviour of inclined dense jets issuing in a stagnant environment. It consists of a set of three ordinary differential equations that can be solved by standard numerical methods. Model outputs include information on the trajectory, spreading and dilution of inclined dense jets, return point position and concentration. Interestingly the model a…
Modelling and simulation of gas-liquid hydrodynamics in mechnically stirred tanks
2007
Abstract Computational fuid dynamics (CFD) is an increasingly important tool for carrying out realistic simulations of process equipment. In the case of multiphase systems the development of CFD models is less advanced than for single-phase systems. In the present work CFD simulations of gas–liquid stirred tanks are reported. An Eulerian–Eulerian multi-fluid approach is used in conjunction with the simplest two-phase extension of the k–ɛ turbulence model. All bubbles are assumed to share the same size. The effect of inter-phase forces on simulation results is separately considered. As concerns drag, it is shown that the sole parameter needed to characterize the dispersed phase behaviour is …
Heterogeneous kinetics: from solid–gas reaction to solid–liquid dissolution
2002
Abstract The extension of the formal kinetics of solid–gas reactions to solid–liquid dissolution is investigated theoretically. The work is based on modelling the dissolution of a solid in a closed system by a stoichiometrically simple chemical reaction A solid ⇄A liquid proceeding up to either an equilibrium state if the solid phase is initially in excess or exhaustion in the reverse situation. The initial amount of solid compared to the capacity of the liquid phase appears as a major factor of complexity. First, the rate equation is formulated in terms of the intensive variables without any assumption about the mechanism and the rate-limiting step. The resulting equations are compared to …
Job Characteristics, Recovery Experiences and Occupational Well-being: Testing Cross-lagged Relationships across 1 Year
2013
The aim of the present study conducted among 274 Finnish employees was to examine the relationships between job characteristics, recovery experiences and occupational well-being across 1 year. We hypothesized that these relationships would follow normal causation, that is, job characteristics at T1 predict recovery experiences (detachment, relaxation, mastery and control at off-job time) and well-being (fatigue at work and work engagement) at T2, and recovery experiences at T1 predict well-being at T2. The structural equation modelling analyses lent support to the hypothesized normal causation model compared with the reversed causation and reciprocal models. However, only the longitudinal r…
Positive parenting and parenting stress among working mothers in Finland, the UK and the Netherlands : Do working time patterns matter?
2017
This study explored the effects of working time patterns on positive parenting and parenting stress, and the moderating effects of working hours, the unpredictability of work schedules, and autonomy over working time in a European context. This cross-national survey study compared Finnish (n = 337), Dutch (n = 283) and British (n = 317) mothers with children under the age of 13, using structural equation modeling with a multigroup procedure. We found a connection between working time patterns and positive parenting but the nature of the connection differed between countries. In all three countries, no relationship was found between working time pattern and parenting stress, while unpredict…
Wronskian representation of solutions of NLS equation, and seventh order rogue wave.
2012
This work is a continuation of a recent paper in which we have constructed a multi-parametric family of the nonlinear Schrodinger equation in terms of wronskians. When we perform a special passage to the limit, we get a family of quasi-rational solutions expressed as a ratio of two determinants. We have already construct Peregrine breathers of orders N=4, 5, 6 in preceding works; we give here the Peregrine breather of order seven.
Spatial Bayesian Modeling Applied to the Surveys of Xylella fastidiosa in Alicante (Spain) and Apulia (Italy)
2020
The plant-pathogenic bacterium Xylella fastidiosa was first reported in Europe in 2013, in the province of Lecce, Italy, where extensive areas were affected by the olive quick decline syndrome, caused by the subsp. pauca. In Alicante, Spain, almond leaf scorch, caused by X. fastidiosa subsp. multiplex, was detected in 2017. The effects of climatic and spatial factors on the geographic distribution of X. fastidiosa in these two infested regions in Europe were studied. The presence/absence data of X. fastidiosa in the official surveys were analyzed using Bayesian hierarchical models through the integrated nested Laplace approximation (INLA) methodology. Climatic covariates were obtained from …