Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I-100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Mathematical modeling applied to the growth of tilapia in net cages in the sub middle of the São Francisco river

This study aimed to apply mathematical models to the growth of Nile tilapia (Oreochromis niloticus) reared in net cages in the lower São Francisco basin and choose the model(s) that best represents the conditions of rearing for the region. Nonlinear models of Brody, Bertalanffy, Logistic, Gompertz, and Richards were tested. The models were adjusted to the series of weight for age according to the methods of Gauss, Newton, Gradiente and Marquardt. It was used the procedure "NLIN" of the System SAS® (2003) to obtain estimates of the parameters from the available data. The best adjustment of the data were performed by the Bertalanffy, Gompertz and Logistic models which are equivalent to explain the growth of the animals up to 270 days of rearing. From the commercial point of view, it is recommended that commercialization of tilapia from at least 600 g, which is estimated in the Bertalanffy, Gompertz and Logistic models for creating over 183, 181 and 184 days, and up to 1 Kg of mass , it is suggested the suspension of the rearing up to 244, 244 and 243 days, respectively.

Mathematical simulation parameters for drying of cassava starch pellets

Based on experimental tests, it was obtained the equations for drying, equilibrium moisture content, latent heat of vaporization of water contained in the product and the equation of specific heat of cassava starch pellets, essential parameters for realizing modeling and mathematical simulation of mechanical drying of cassava starch for a new technique proposed, consisting of preformed by pelleting and subsequent artificial drying of starch pellets. Drying tests were conducted in an experimental chamber by varying the air temperature, relative humidity, air velocity and product load. The specific heat of starch was determined by differential scanning calorimetry. The generated equations were validated through regression analysis, finding an appropriate correlation of the data, which indicates that by using these equations, can accurately model and simulate the drying process of cassava starch pellets.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Mechanisms in anti-inflammation and resolution: the role of lipoxins and aspirin-triggered lipoxins

Multicellular host responses to infection, injury or inflammatory stimuli lead to the formation of a broad range of chemical mediators by the host. The integrated response of the host is essential to health and disease; thus it is important to achieve a more complete understanding of the molecular and cellular events governing the formation and actions of endogenous mediators of resolution that appear to control the duration of inflammation. Lipoxins are trihydroxytetraene-containing lipid mediators that can be formed during cell-cell interactions and are predominantly counterregulators of some well-known mediators of inflammation. Since this circuit of lipoxin formation and action appears to be of physiological relevance for the resolution of inflammation, therapeutic modalities targeted at this system are likely to have fewer unwanted side effects than other candidates and current anti-inflammatory therapies. Here, we present an overview of the recent knowledge about the biosynthesis and bioactions of these anti-inflammatory lipid mediators.

A mathematical framework for group analysis of von Willebrand factor multimeric composition following luminography

The objective of the present study was to establish a method for quantitative analysis of von Willebrand factor (vWF) multimeric composition using a mathematical framework based on curve fitting. Plasma vWF multimers from 15 healthy subjects and 13 patients with advanced pulmonary vascular disease were analyzed by Western immunoblotting followed by luminography. Quantitative analysis of luminographs was carried out by calculating the relative densities of low, intermediate and high molecular weight fractions using laser densitometry. For each densitometric peak (representing a given fraction of vWF multimers) a mean area value was obtained using data from all group subjects (patients and normal individuals) and plotted against the distance between the peak and IgM (950 kDa). Curves were constructed for each group using nonlinear fitting. Results indicated that highly accurate curves could be obtained for healthy controls and patients, with respective coefficients of determination (r²) of 0.9898 and 0.9778. Differences were observed between patients and normal subjects regarding curve shape, coefficients and the region of highest protein concentration. We conclude that the method provides accurate quantitative information on the composition of vWF multimers and may be useful for comparisons between groups and possibly treatments.

Mathematical modeling of electro-rotation spectra of small particles in liquid solutions: Application to human erythrocyte aggregates

Electro-rotation can be used to determine the dielectric properties of cells, as well as to observe dynamic changes in both dielectric and morphological properties. Suspended biological cells and particles respond to alternating-field polarization by moving, deforming or rotating. While in linearly polarized alternating fields the particles are oriented along their axis of highest polarizability, in circularly polarized fields the axis of lowest polarizability aligns perpendicular to the plane of field rotation. Ellipsoidal models for cells are frequently applied, which include, beside sphere-shaped cells, also the limiting cases of rods and disks. Human erythrocyte cells, due to their particular shape, hardly resemble an ellipsoid. The additional effect of rouleaux formation with different numbers of aggregations suggests a model of circular cylinders of variable length. In the present study, the induced dipole moment of short cylinders was calculated and applied to rouleaux of human erythrocytes, which move freely in a suspending conductive medium under the effect of a rotating external field. Electro-rotation torque spectra are calculated for such aggregations of different length. Both the maximum rotation speeds and the peak frequencies of the torque are found to depend clearly on the size of the rouleaux. While the rotation speed grows with rouleaux length, the field frequency nup is lowest for the largest cell aggregations where the torque shows a maximum.

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 ± 2.63 years old) and 16 postmenopausal (57 ± 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg-1 min-1), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg-1 min-1) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (r s = 0.75) and VCO2 (r s = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.

Methodological approaches to planar and volumetric scintigraphic imaging of small volume targets with high spatial resolution and sensitivity

Single-photon emission computed tomography (SPECT) is a non-invasive imaging technique, which provides information reporting the functional states of tissues. SPECT imaging has been used as a diagnostic tool in several human disorders and can be used in animal models of diseases for physiopathological, genomic and drug discovery studies. However, most of the experimental models used in research involve rodents, which are at least one order of magnitude smaller in linear dimensions than man. Consequently, images of targets obtained with conventional gamma-cameras and collimators have poor spatial resolution and statistical quality. We review the methodological approaches developed in recent years in order to obtain images of small targets with good spatial resolution and sensitivity. Multipinhole, coded mask- and slit-based collimators are presented as alternative approaches to improve image quality. In combination with appropriate decoding algorithms, these collimators permit a significant reduction of the time needed to register the projections used to make 3-D representations of the volumetric distribution of target’s radiotracers. Simultaneously, they can be used to minimize artifacts and blurring arising when single pinhole collimators are used. Representation images are presented, which illustrate the use of these collimators. We also comment on the use of coded masks to attain tomographic resolution with a single projection, as discussed by some investigators since their introduction to obtain near-field images. We conclude this review by showing that the use of appropriate hardware and software tools adapted to conventional gamma-cameras can be of great help in obtaining relevant functional information in experiments using small animals.

A clinical gamma camera-based pinhole collimated system for high resolution small animal SPECT imaging

The main objective of the present study was to upgrade a clinical gamma camera to obtain high resolution tomographic images of small animal organs. The system is based on a clinical gamma camera to which we have adapted a special-purpose pinhole collimator and a device for positioning and rotating the target based on a computer-controlled step motor. We developed a software tool to reconstruct the target’s three-dimensional distribution of emission from a set of planar projections, based on the maximum likelihood algorithm. We present details on the hardware and software implementation. We imaged phantoms and heart and kidneys of rats. When using pinhole collimators, the spatial resolution and sensitivity of the imaging system depend on parameters such as the detector-to-collimator and detector-to-target distances and pinhole diameter. In this study, we reached an object voxel size of 0.6 mm and spatial resolution better than 2.4 and 1.7 mm full width at half maximum when 1.5- and 1.0-mm diameter pinholes were used, respectively. Appropriate sensitivity to study the target of interest was attained in both cases. Additionally, we show that as few as 12 projections are sufficient to attain good quality reconstructions, a result that implies a significant reduction of acquisition time and opens the possibility for radiotracer dynamic studies. In conclusion, a high resolution single photon emission computed tomography (SPECT) system was developed using a commercial clinical gamma camera, allowing the acquisition of detailed volumetric images of small animal organs. This type of system has important implications for research areas such as Cardiology, Neurology or Oncology.

Classification of brain tumor extracts by high resolution ¹H MRS using partial least squares discriminant analysis

High resolution proton nuclear magnetic resonance spectroscopy (¹H MRS) can be used to detect biochemical changes in vitro caused by distinct pathologies. It can reveal distinct metabolic profiles of brain tumors although the accurate analysis and classification of different spectra remains a challenge. In this study, the pattern recognition method partial least squares discriminant analysis (PLS-DA) was used to classify 11.7 T ¹H MRS spectra of brain tissue extracts from patients with brain tumors into four classes (high-grade neuroglial, low-grade neuroglial, non-neuroglial, and metastasis) and a group of control brain tissue. PLS-DA revealed 9 metabolites as the most important in group differentiation: γ-aminobutyric acid, acetoacetate, alanine, creatine, glutamate/glutamine, glycine, myo-inositol, N-acetylaspartate, and choline compounds. Leave-one-out cross-validation showed that PLS-DA was efficient in group characterization. The metabolic patterns detected can be explained on the basis of previous multimodal studies of tumor metabolism and are consistent with neoplastic cell abnormalities possibly related to high turnover, resistance to apoptosis, osmotic stress and tumor tendency to use alternative energetic pathways such as glycolysis and ketogenesis.

Effect of image resolution manipulation in rearfoot angle measurements obtained with photogrammetry

The aim of this study was to investigate the influence of image resolution manipulation on the photogrammetric measurement of the rearfoot static angle. The study design was that of a reliability study. We evaluated 19 healthy young adults (11 females and 8 males). The photographs were taken at 1536 pixels in the greatest dimension, resized into four different resolutions (1200, 768, 600, 384 pixels) and analyzed by three equally trained examiners on a 96-pixels per inch (ppi) screen. An experienced physiotherapist marked the anatomic landmarks of rearfoot static angles on two occasions within a 1-week interval. Three different examiners had marked angles on digital pictures. The systematic error and the smallest detectable difference were calculated from the angle values between the image resolutions and times of evaluation. Different resolutions were compared by analysis of variance. Inter- and intra-examiner reliability was calculated by intra-class correlation coefficients (ICC). The rearfoot static angles obtained by the examiners in each resolution were not different (P > 0.05); however, the higher the image resolution the better the inter-examiner reliability. The intra-examiner reliability (within a 1-week interval) was considered to be unacceptable for all image resolutions (ICC range: 0.08-0.52). The whole body image of an adult with a minimum size of 768 pixels analyzed on a 96-ppi screen can provide very good inter-examiner reliability for photogrammetric measurements of rearfoot static angles (ICC range: 0.85-0.92), although the intra-examiner reliability within each resolution was not acceptable. Therefore, this method is not a proper tool for follow-up evaluations of patients within a therapeutic protocol.

Performance assessment of the single photon emission microscope: high spatial resolution SPECT imaging of small animal organs

The single photon emission microscope (SPEM) is an instrument developed to obtain high spatial resolution single photon emission computed tomography (SPECT) images of small structures inside the mouse brain. SPEM consists of two independent imaging devices, which combine a multipinhole collimator, a high-resolution, thallium-doped cesium iodide [CsI(Tl)] columnar scintillator, a demagnifying/intensifier tube, and an electron-multiplying charge-coupling device (CCD). Collimators have 300- and 450-µm diameter pinholes on tungsten slabs, in hexagonal arrays of 19 and 7 holes. Projection data are acquired in a photon-counting strategy, where CCD frames are stored at 50 frames per second, with a radius of rotation of 35 mm and magnification factor of one. The image reconstruction software tool is based on the maximum likelihood algorithm. Our aim was to evaluate the spatial resolution and sensitivity attainable with the seven-pinhole imaging device, together with the linearity for quantification on the tomographic images, and to test the instrument in obtaining tomographic images of different mouse organs. A spatial resolution better than 500 µm and a sensitivity of 21.6 counts·s-1·MBq-1 were reached, as well as a correlation coefficient between activity and intensity better than 0.99, when imaging 99mTc sources. Images of the thyroid, heart, lungs, and bones of mice were registered using 99mTc-labeled radiopharmaceuticals in times appropriate for routine preclinical experimentation of <1 h per projection data set. Detailed experimental protocols and images of the aforementioned organs are shown. We plan to extend the instrument's field of view to fix larger animals and to combine data from both detectors to reduce the acquisition time or applied activity.

Mathematical modelling of the osmotic dehydration of cherry tomato (Lycopersicon esculentum var. cerasiforme)

Osmotic dehydration of cherry tomato as influenced by osmotic agent (sodium chloride and a mixed sodium chloride and sucrose solutions) and solution concentration (10 and 25% w/w) at room temperature (25°C) was studied. Kinetics of water loss and solids uptake were determined by a two parameter model, based on Fick's second law and applied to spherical geometry. The water apparent diffusivity coefficients obtained ranged from 2.17x10-10 to 11.69x10-10 m²/s.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.