Mathematical Modelling

As wind turbines more widely used with newer manufactured types and larger electrical power scales, a brief mathematical modelling for these wind turbines operating power curves is needed for optimal site matching selections. In this paper, 24 commercial wind turbines with different ratings and different manufactures are modelled using single cumulative probability density functions modelling equations. A new mean of a composite cumulative probability density function is used for better modelling accuracy. Invasive weed optimization algorithm is used to estimate different models designing parameters. The best cumulative density function model for each wind turbine is reached through comparing the RMSE of each model. Results showed that Weibull-Gamma composite is the best modelling technique for 37.5% of the reached results. 1. INTRODUCTION Modelling of renewable energy resources to maximize the best use of them can be made through using best mathematical modelling techniques which give a great effect on more describing the probabilistic nature of these resources. Wind energy is one of most commonly used renewable energy resources today especially in electrical power engineering. Wind power is transferred into electrical power by the mean of wind turbines. Mathematical modelling of wind turbines results in forecasting the generated electrical power from them and also helps to compare different turbines performance on same site location as a tool for optimal site matching. Each wind turbine has a power curve describing the relation between input wind speed and turbine output electrical power [1]. These curves are varied according to different manufacturers and different generated power ratings. The mathematical models which are used to describe the wind turbines operating power curves will be different. Each wind turbine curve has three main points cut-in speed point (2-5 m/s) at which turbine starts to operate and generate power, rated speed point (7-16 m/s) at which wind turbine generates its rated power and cutout speed (20-30 m/s) at which turbine is shutdown to prevent it from damage. These ranges of cut-in speed, rated speed and cutout speed are reached from manufacturers' tests. The most commonly used mathematical models to approximate wind speed-power characteristics curve for the turbines are linear functions [2], quadratic functions [3], cubic functions [4], spline functions [5] and logistic functions [6]. The modelling functions are categorized into piecewise continuous functions and single continuous functions. Authors in [7] reached that modelling wind turbine electrical power curve using single continuous functions is better than using piecewise continuous functions modelling where piecewise

The primary role of the cardiovascular system is to deliver a required amount of oxygen to various organs. These needs vary with time and depend on the vascular site. To maintain a required diffusion level of oxygen in the capillary networks, the cardiovascular system is controlled by regulation processes that maintain pressure and blood flow to the required physiological levels.

The biosorption of copper (II) ions onto Luffa cylindrica was investigated. Luffa cylindrica, a biomaterial with wide distribution particularly in the tropical world, is characterized with the surface area, chemical bonds, bulk density, pore size distribution, microstructures, composition, morphology and elemental composition which are determined. Biosorption studies were carried out with varying dosage and the experimental data obtained were fitted to Pseudo-Second order kinetic model. The regression value obtained from the various doses studies ranged from 0.991 to 0.999. A kinectic model was developed mathematically and as well Artificial Neural Network (ANN) was applied to develop a Multiple Input Single Output (MISO) back propagation neural network model which was validated. The RMSE value was found to be 1.2754. Artificial neural network has the capability to predict the sorption capacity quite reasonably for the model.

... Two methods have been alternatively used for the pre-selection of wavelength values, viz.: − PM1 based on three normalised ... MATLAB function corrcoef; the result is shown in Fig. ... corresponding to 30 most promising wavelength values, selected using PM1, are larger than ...

... scope of social research, as his contributions to quantum theory and other branches of physics (A. Orłowski), meteorology in the context of Chaos (M. Tempczyk), metamathematics (R ... Theory of cellular automata in simulating social processes (Katarzyna Zbiec, DLIPS-UwB) — 12 ...

... scope of social research, as his contributions to quantum theory and other branches of physics (A. Orłowski), meteorology in the context of Chaos (M. Tempczyk), metamathematics (R ... Theory of cellular automata in simulating social processes (Katarzyna Zbiec, DLIPS-UwB) — 12 ...

The membrane model describes (i) mass transport in macroporous support comprising diffusion in transition region between Knudsen and bulk diffusion superimposed on convective flow and (ii) mass transport in zeolitic phase accompanied by a parallel transport in defects of zeolitic layer. The mass transport in the support is described by Dusty Gas Model (DGM) and that in the zeolitic phase by Generalized Maxwell Stefan (GMS) approach. Parallel transport in defects of zeolitic layer is also described by DGM. Modelling is exemplified on dynamics of a semi-open Wicke-Kallenbach (W-K) cell operated with a flat silicalite-1-α-Al2O3 membrane using a CH4/N2 mixture. It appeared that measurement of dynamic responses of the semi-open W-K cell represents a rapid and precise method to characterize composite membrane quality.

The quality of apple cubes (Red Delicious and Granny Smith) maintained in pasteurised or fresh orange juice with sucrose and chemical preservatives: acidulants (citric and ascorbic acids) and potassium sorbate or sodium benzoate, packaged in plastic films of different gaseous permeability (polyethylene (PE) and EVA-SARAN-EVA (ESE)), was analysed during storage at 10 °C. Surface colour, microbial growth and instrumental texture changes were measured. Microbial flora was identified, and its growth was mathematically modelled. Shelf-life values of 10d in polyethylene and higher than 25d in ESE film, maintaining acceptable quality attributes, were obtained for both apple varieties in pasteurised juices. For Red Delicious in unpasteurised orange juice with acidulants and potassium sorbate (0.125–0.250 g/kg), shelf-life values were 7.5–8.5d in PE and higher than 15 d in ESE film. For Granny Smith apples in unpasteurised juice without potassium sorbate, shelf-life values were 10 d in PE and higher than 15 d in ESE. Higher concentrations (0.375–0.50 g/kg) of potassium sorbate adversely affected colour. Sodium benzoate was discarded as preservative because it produced severe browning in both apple varieties. All the samples showed safe sanitary conditions; coliforms microorganisms did not grow in any of the tested conditions.

Abstract The most common chemical preservatives used to inhibit both enzymatic browning and microbial growth in pre-peeled potatoes are sodium sulphite and bisulphite. Since 1987 the FDA has limited their use as food ingredients; consequently, during recent years the ...

Although artesunate, one of the potent derivatives of the qinghaosu family of drugs for treating falciparum malaria, is already in use in the field, its therapeutic protocol has only been developed empirically by hit-or-miss. A pharmacokinetic–pharmacodynamic (PK–PD) model, required for creating such a protocol, is not straightforward. Artesunate presents extremely fast pharmacokinetics. As a result the stage specificity of its action must be treated explicitly. Also, use of standard PK–PD modelling fails to explain the clinical results. Our PK–PD modelling of its activity leads us to the postulation of the existence of a novel effect: a small fraction of the parasites, as a result of chemotherapeutic pressure, become cytostatic, or ‘dormant’. At this stage, the parasite cycle is halted, making them unsusceptible to further dosing until wakening. This slows down the antimalarial activity of the drug, entailing either many frequent doses or an extended period of treatment and surveil...