Journal articles: 'Метод "Differential Box Counting"'

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Ruiz de Miras, Juan. "Fast differential box-counting algorithm on GPU." Journal of Supercomputing 76, no. 1 (October 17, 2019): 204–25. http://dx.doi.org/10.1007/s11227-019-03030-1.

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Молчатский, С. Л. "Проблема структурной организации нейронных комплексов мозга человека." ТЕНДЕНЦИИ РАЗВИТИЯ НАУКИ И ОБРАЗОВАНИЯ 73, no. 1 (May 2021): 117–20. http://dx.doi.org/10.18411/lj-05-2021-31.

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Целью исследования было нахождение функции распределения структурных элементов в кластерах вентромедиального (ВМЯ) и латерального гипоталамического ядра (ЛГЯ). Метод исследования – расчета фрактального коэффициента D («box counting method»). Научная новизна – впервые был проведен компьютерный фрактальный анализ ядер ВМЯ и ЛГЯ. В результате исследованы функции распределения структурных элементов в кластерах, определены их фрактальные коэффициенты.

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He, Tao, Long Fei Cheng, Qing Hua Wu, Zheng Jia Wang, Lian Gen Yang, and Lang Yu Xie. "An Image Segmentation Calculation Based on Differential Box-Counting of Fractal Geometry." Applied Mechanics and Materials 719-720 (January 2015): 964–68. http://dx.doi.org/10.4028/www.scientific.net/amm.719-720.964.

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Differential box-counting of fractal geometry has been widely used in image processing.A method which uses the differential box-counting to segment the gathered images is discussed in this paper . It is to construct a three-dimensional gray space and use the same size boxes to contain the three dimensional space.The number of boxes needed to cover the entire image are calculated .Different sizes of boxes can receive different number of boxes, so least squares method is used to calculate the fractal dimension. According to the fractal dimension parameters, appropriate threshold is chose to segment the image by using binarization .From the handle case of bearing pictures can be seen that image segmentation based on differential box-counting method can get clear image segmentation .This method is easy to understand, to operate, and has important significance on computer image segmentation .

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Nayak, Soumya Ranjan, Jibitesh Mishra, and Pyari mohan Jena. "Fractal analysis of image sets using differential box counting techniques." International Journal of Information Technology 10, no. 1 (November 30, 2017): 39–47. http://dx.doi.org/10.1007/s41870-017-0062-3.

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Sathiya Devi, S., and S. Vidivelli. "Modified Differential Box Counting in Breast Masses for Bioinformatics Applications." Computers, Materials & Continua 70, no. 2 (2022): 3049–66. http://dx.doi.org/10.32604/cmc.2022.019917.

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YU Hai-jing, 于海晶, and 李桂菊 LI Gui-ju. "Smoke Segmentation Method Based on Improved Differential Box-Counting Fractal Dimension." Chinese Journal of Liquid Crystals and Displays 28, no. 1 (2013): 115–19. http://dx.doi.org/10.3788/yjyxs20132801.0115.

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Tzeng, Yu-Chang, Kuo-Tai Fan, and Kun-Shan Chen. "A Parallel Differential Box-Counting Algorithm Applied to Hyperspectral Image Classification." IEEE Geoscience and Remote Sensing Letters 9, no. 2 (March 2012): 272–76. http://dx.doi.org/10.1109/lgrs.2011.2166243.

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Sarkar, N., and B. B. Chaudhuri. "An efficient differential box-counting approach to compute fractal dimension of image." IEEE Transactions on Systems, Man, and Cybernetics 24, no. 1 (1994): 115–20. http://dx.doi.org/10.1109/21.259692.

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Panigrahy, Chinmaya, Angel Garcia-Pedrero, Ayan Seal, Dionisio Rodríguez-Esparragón, Nihar Mahato, and Consuelo Gonzalo-Martín. "An Approximated Box Height for Differential-Box-Counting Method to Estimate Fractal Dimensions of Gray-Scale Images." Entropy 19, no. 10 (October 10, 2017): 534. http://dx.doi.org/10.3390/e19100534.

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CHEN, WEN-SHIUNG, and SHANG-YUAN YUAN. "SOME FRACTAL DIMENSION ESTIMATE ALGORITHMS AND THEIR APPLICATIONS TO ONE-DIMENSIONAL BIOMEDICAL SIGNALS." Biomedical Engineering: Applications, Basis and Communications 14, no. 03 (June 25, 2002): 100–108. http://dx.doi.org/10.4015/s1016237202000152.

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Fractals can model many classes of time-series data. The fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales. The covering methods are a class of efficient approaches, e.g., box-counting (BC) method, to estimate the fractal dimension. In this paper, the differential box-counting (DBC) approach, originally for 2-D applications, is modified and applied to 1-D case. In addition, two algorithms, called 1-D shifting-DBC (SDBC-1D) and 1-D scanning-BC (SBC-1D), are also proposed for 1-D signal analysis. The fractal dimensions for 1-D biomedical pulse and ECG signals are calculated.

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Panigrahy, Chinmaya, Ayan Seal, and Nihar Kumar Mahato. "Image texture surface analysis using an improved differential box counting based fractal dimension." Powder Technology 364 (March 2020): 276–99. http://dx.doi.org/10.1016/j.powtec.2020.01.053.

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Liu, Yu, Lingyu Chen, Heming Wang, Lanlan Jiang, Yi Zhang, Jiafei Zhao, Dayong Wang, Yuechao Zhao, and Yongchen Song. "An improved differential box-counting method to estimate fractal dimensions of gray-level images." Journal of Visual Communication and Image Representation 25, no. 5 (July 2014): 1102–11. http://dx.doi.org/10.1016/j.jvcir.2014.03.008.

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Panigrahy, Chinmaya, Ayan Seal, Nihar Kumar Mahato, and Debotosh Bhattacharjee. "Differential box counting methods for estimating fractal dimension of gray-scale images: A survey." Chaos, Solitons & Fractals 126 (September 2019): 178–202. http://dx.doi.org/10.1016/j.chaos.2019.06.007.

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Hong, Danfeng, Zhenkuan Pan, and Xin Wu. "Improved differential box counting with multi-scale and multi-direction: A new palmprint recognition method." Optik 125, no. 15 (August 2014): 4154–60. http://dx.doi.org/10.1016/j.ijleo.2014.01.093.

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Wang, Yunqi, Mei Hui, Ming Liu, Liquan Dong, Xiaohua Liu, and Yuejin Zhao. "Edge extraction of optical subaperture based on differential box-counting dimension method with window merge replication." Optical Engineering 55, no. 9 (September 23, 2016): 093107. http://dx.doi.org/10.1117/1.oe.55.9.093107.

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Panigrahy, Chinmaya, Ayan Seal, and Nihar Kumar Mahato. "Quantitative texture measurement of gray-scale images: Fractal dimension using an improved differential box counting method." Measurement 147 (December 2019): 106859. http://dx.doi.org/10.1016/j.measurement.2019.106859.

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Myint, Soe W., Victor Mesev, and Nina Lam. "Urban Textural Analysis from Remote Sensor Data: Lacunarity Measurements Based on the Differential Box Counting Method." Geographical Analysis 38, no. 4 (October 2006): 371–90. http://dx.doi.org/10.1111/j.1538-4632.2006.00691.x.

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Liu, Cheng, You Zhan, Qiangsheng Deng, Yanjun Qiu, and Allen Zhang. "An improved differential box counting method to measure fractal dimensions for pavement surface skid resistance evaluation." Measurement 178 (June 2021): 109376. http://dx.doi.org/10.1016/j.measurement.2021.109376.

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Zhang, Le, Faning Dang, Weihua Ding, and Lin Zhu. "Quantitative study of meso-damage process on concrete by CT technology and improved differential box counting method." Measurement 160 (August 2020): 107832. http://dx.doi.org/10.1016/j.measurement.2020.107832.

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Pašić, Mervan, and Satoshi Tanaka. "Fractal Oscillations of Chirp Functions and Applications to Second-Order Linear Differential Equations." International Journal of Differential Equations 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/857410.

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We derive some simple sufficient conditions on the amplitude , the phase and the instantaneous frequency such that the so-called chirp function is fractal oscillatory near a point , where and is a periodic function on . It means that oscillates near , and its graph is a fractal curve in such that its box-counting dimension equals a prescribed real number and the -dimensional upper and lower Minkowski contents of are strictly positive and finite. It numerically determines the order of concentration of oscillations of near . Next, we give some applications of the main results to the fractal oscillations of solutions of linear differential equations which are generated by the chirp functions taken as the fundamental system of all solutions.

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Ma, Qing Lan, and Yuan Ming Huang. "Fractal Features Grown from Isotropic Melt of a Cholesterol Liquid Crystal." Materials Science Forum 663-665 (November 2010): 771–74. http://dx.doi.org/10.4028/www.scientific.net/msf.663-665.771.

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Fractal features of branch-like structures grown from isotropic melt of a cholesterol liquid crystal were investigated with differential scanning calorimetry, polarized optical microscope and computer-aided simulation, respectively. With box-counting method, we have calculated the fractal dimension to be about 2.558-2.604 for the branch-like aggregates. Our growth simulation and the calculated value of the fractal dimension suggests that the cluster-cluster aggregation model can be applied to the growing processes of branch-like structures from isotropic melt of a cholesterol liquid crystal.

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Imashev, S. A., and M. E. Cheshev. "Estimation of fractal dimension of rock samples fracture surface." Geoinformatika, no. 1 (2021): 36–44. http://dx.doi.org/10.47148/1609-364x-2021-1-36-44.

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An approach to estimate fractal dimension of a microphotograph of rock sample fracture surface using the Differential Box Counting (DBC) method is presented. The difference between this algorithm and the classical method for fractal dimension calculation is in that the grayscale levels of pixels of analyzed image are taken into account. This approach does not require initial binarization of the image, which is poorly applicable for estimation of fractal dimension of real objects, such as microphotographs of rock sample surface, which in turn does not lead to the loss of useful information. Testing the method on a set of images generated with different content of pixels of gray levels showed that there is a steady increase in fractal dimension values with increase in the number of added pixels. It is shown that fractal dimension for a set of images simulating crack propagation also demonstrates growth with increasing of fracturing. From a geometric point of view, this feature is a consequence of increase of roughness of the surface, which is a set of rectangles, the height of which corresponds to gray level of pixels of analyzed image. This approach can be used to quantify changes in sample surface structure before and after load action, as well as in real time using high-speed photography of the sample surface or radioscopy of internal cracks. Keywords: fractal analysis, fractal dimension, differential box-counting, fracture surface.

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Lee, Ju Hyun, and Michael J. Ostwald. "Fractal Dimension Calculation and Visual Attention Simulation: Assessing the Visual Character of an Architectural Façade." Buildings 11, no. 4 (April 15, 2021): 163. http://dx.doi.org/10.3390/buildings11040163.

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The design of a building façade has a significant impact on the way people respond to it physiologically and behaviourally. Few methods are available to assist an architect to understand such impacts during the design process. Thus, this paper examines the viability of using two computational methods to examine potential visual stimulus-sensation relationships in facade design. The first method, fractal analysis, is used to holistically measure the visual stimuli of a design. This paper describes both the box counting (density) and differential box counting (intensity) approaches to determining fractal dimension (D) in architecture. The second method, visual attention simulation, is used to explore pre-attentive processing and sensation in vision. Four measures—D-density (Dd), D-intensity (Di), heat map and gaze sequence—are used to provide quantitative and qualitative indicators of the ways people read different design options. Using two façade designs as examples, the results of this application reveal that the D values of a façade image have a relationship with the pre-attentive processing shown in heat map and gaze sequence simulations. The findings are framed as a methodological contribution to the field, but also to the disciplinary knowledge gap about the stimulus-sensation relationship and visual reasoning in design.

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Zhang, Tingyu, Ling Han, Jichang Han, Xian Li, Heng Zhang, and Hao Wang. "Assessment of Landslide Susceptibility Using Integrated Ensemble Fractal Dimension with Kernel Logistic Regression Model." Entropy 21, no. 2 (February 24, 2019): 218. http://dx.doi.org/10.3390/e21020218.

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The main aim of this study was to compare and evaluate the performance of fractal dimension as input data in the landslide susceptibility mapping of the Baota District, Yan’an City, China. First, a total of 632 points, including 316 landslide points and 316 non-landslide points, were located in the landslide inventory map. All points were divided into two parts according to the ratio of 70%:30%, with 70% (442) of the points used as the training dataset to train the models, and the remaining, namely the validation dataset, applied for validation. Second, 13 predisposing factors, including slope aspect, slope angle, altitude, lithology, mean annual precipitation (MAP), distance to rivers, distance to faults, distance to roads, normalized differential vegetation index (NDVI), topographic wetness index (TWI), plan curvature, profile curvature, and terrain roughness index (TRI), were selected. Then, the original numerical data, box-counting dimension, and correlation dimension corresponding to each predisposing factor were calculated to generate the input data and build three classification models, namely the kernel logistic regression model (KLR), kernel logistic regression based on box-counting dimension model (KLRbox-counting), and the kernel logistic regression based on correlation dimension model (KLRcorrelation). Next, the statistical indexes and the receiver operating characteristic (ROC) curve were employed to evaluate the models’ performance. Finally, the KLRcorrelation model had the highest area under the curve (AUC) values of 0.8984 and 0.9224, obtained by the training and validation datasets, respectively, indicating that the fractal dimension can be used as the input data for landslide susceptibility mapping with a better effect.

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Бородкин, С. В., И. Л. Батаронов, А. В. Иванов, and В. И. Ряжских. "PARAMETRIC IDENTIFICATION OF THE DIFFERENTIAL MODEL OF HEAT EXCHANGE IN A GASIFIER." ВЕСТНИК ВОРОНЕЖСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА, no. 6 (January 14, 2022): 34–42. http://dx.doi.org/10.36622/vstu.2021.17.6.005.

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На основе одномерной дифференциальной модели теплообмена в газификаторе закрытого типа сформулирована задача параметрической идентификации модели на основе измерений на штатном оборудовании промышленной газификационной установки. Модель включает в себя дополнительное интегральное условие и самосогласованно определяемую подвижную границу, отделяющую зону обледенения трубки испарителя. С применением метода сглаживания особенности разработан алгоритм итерационного решения уравнений модели, использующий метод сквозного счета для решения уравнения переноса на одной итерации. Для параметрической идентификации модели использована смешанная стратегия. Часть идентифицируемых параметров (теплоемкость испарителя, мощность нагревателя, массовая производительность насоса, коэффициент теплоотдачи в окружающую среду) определялась на основе специально организованных измерений: нагрева испарителя без прокачки сверхкритического флюида, газификации в условиях теплоизолированности корпуса испарителя, газификации в стационарном режиме работы. Остальные параметры (коэффициенты теплоотдачи в теплоноситель и сверхкритический флюид) идентифицировались в пассивных измерениях с различными производительностями насоса. Отмечено, что ввиду плохой обусловленности задачи и ограниченности вариаций коэффициентов применение регрессионных методов в данной модели неэффективно. На основе метода стрельбы разработан способ идентификации, заключающийся в определении параметров по измерениям с предельными производительностями с построением функциональной связи между идентифицируемыми параметрами, с последующей верификацией на промежуточных измерениях. Метод апробирован на примере штатной газификационной установки СГУ-7КМ-У We formulated the problem of parametric identification of the model based on measurements on the standard equipment of an industrial gasification plant on the basis of a one-dimensional differential model of heat transfer in a closed-type gasifier. The model includes an additional integral condition and a self-consistently defined movable boundary separating the icing zone of the evaporator tube. Using the method of smoothing the singularity, we developed an algorithm for iterative solution of the model equations, using the end-to-end counting method to solve the transfer equation in one iteration. We used a mixed strategy for parametric identification of the model. We determined some of the identified parameters (evaporator heat capacity, heater power, mass pump capacity, heat transfer coefficient to the environment) on the basis of specially organized measurements: heating of the evaporator without pumping supercritical fluid, gasification under conditions of thermal insulation of the evaporator body, gasification in stationary operation. We identified the remaining parameters (heat transfer coefficients to the coolant and supercritical fluid) in passive measurements with different pump capacities. We noted that due to the poor conditionality of the problem and the limited variation of coefficients, the use of regression methods in this model is ineffective. Based on the ballistic method, we developed an identification method, which consists in determining parameters by measurements with marginal performance with the construction of a functional relationship between the identified parameters, followed by verification on intermediate measurements. We tested the method on the example of a standard gasification plant SGU-7KM-U

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Peng, Shu Jing, Hui Ling Du, and Li Dan Tang. "Morphology of Cobalt Oxalate Powders Prepared with Pulsed Electromagnetic Field." Advanced Materials Research 1088 (February 2015): 295–99. http://dx.doi.org/10.4028/www.scientific.net/amr.1088.295.

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The spindle or spherical cobalt oxalate powders were prepared by conventional precipitation in the presence of pulsed electromagnetic field (PEMF). The morphology and phase structure were characterized by scanning electron microscopy (SEM) and X-ray powder diffraction (XRD). The aspect ratio and surface fractal dimension of cobalt oxalate aggregate were calculated using Image tool software and Differential Box Counting (DBC) algorithm. The results indicate that the products prepared from ammonium oxalate and cobalt chloride give rise to the formation of β-CoC2O4∙2H2O. With the increase of pulsed time, the morphology of cobalt oxalate sample varies periodically from rod-like to spheroidic. For the sample treated for 60 s, the degree of sphericity is the highest. The surface fractal dimension is 2.096 and the corresponding fractal form is tight type.

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Sangeetha, A., and R. Rajakumari. "Classification of Building Images using Fractal Features." International Journal of Recent Technology and Engineering 9, no. 5 (January 30, 2021): 183–85. http://dx.doi.org/10.35940/ijrte.e5196.019521.

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Cracks in concrete buildings may show the total extent of damage or problems of greater magnitude. Causes of cracks depend on the nature of the crack and the type of structure. Crack classification is an approach to using machine learning algorithms to find a particular type of crack. The image is preprocessed by image smoothening and removes noise using a Gaussian filter, whereas the Sobel edge detection method is used to detect the edges. By using k-means clustering, the image segmentation is carried out to identify the Region of Interest. Fractal dimension is an efficient measure for complex objects. Fractal features like fractal dimension, average, and lacunarity are calculated using a differential box-counting algorithm. The classification of the crack classifies the crack based on the characteristics derived from the crack area.

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WANG, FANG, ZONG-SHOU LI, and GUI-PING LIAO. "MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS FOR IMAGE TEXTURE FEATURE REPRESENTATION." International Journal of Pattern Recognition and Artificial Intelligence 28, no. 03 (May 2014): 1455005. http://dx.doi.org/10.1142/s0218001414550052.

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Multifractal theory has been widely used in different kinds of fields. In this paper, methods were proposed to extract two kinds of multifractal descriptors of gray series and two-dimensional surfaces for gray image based on the multifractal detrended fluctuation analysis. The proposed multifractal parameters can be well described by texture feature through the test of some textures. Three aspects of experiments have been conducted to verify the robustness of the proposed parameters, which include noise immunity, degree of image blurring and compression ratio. Comparisons were conducted between the proposed parameters and other kinds of texture feature parameters calculated by the standard multifractal analysis, the method of differential box counting and the methods of gray level co-occurrence matrix. Results demonstrate that the proposed exponents of H(2) and h(2) have great noise immunity and are robust to image compression and blurring.

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Abuzer, Amr, Ady Naber, Simon Hoffmann, Lucy Kessler, Ramin Khoramnia, and Werner Nahm. "Investigation on Non-Segmentation Based Algorithms for Microvasculature Quantification in OCTA Images." Current Directions in Biomedical Engineering 7, no. 2 (October 1, 2021): 247–50. http://dx.doi.org/10.1515/cdbme-2021-2063.

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Abstract Optical Coherence Tomography Angiography (OCTA) is an imaging modality that provides threedimensional information of the retinal microvasculature and therefore promises early diagnosis and sufficient monitoring in ophthalmology. However, there is considerable variability between experts analysing this data. Measures for quantitative assessment of the vasculature need to be developed and established, such as fractal dimension. Fractal dimension can be used to assess the complexity of vessels and has been shown to be independently associated with neovascularization, a symptom of diseases such as diabetic retinopathy. This investigation assessed the performance of three fractal dimension algorithms: Box Counting Dimension (BCD), Information Dimension (ID), and Differential Box Counting (DBC). Two of those, BCD and ID, rely on previous vessel segmentation. Assessment of the added value or disturbance regarding the segmentation step is a second aim of this study. The investigation was performed on a data set composed of 9 in vivo human eyes. Since there is no ground truth available, the performance of the methods in differentiating the Superficial Vascular Complex (SVC) and Deep Vascular Complex (DVC) layers apart and the consistency of measurements of the same layer at different time-points were tested. The performance parameters were the ICC and the Mann- Whitney U tests. The three applied methods were suitable to tell the different layers apart and showed consistent values applied in the same slab. Within the consistency test, the non-segmentation-based method, DBC, was found to be less accurate, expressed in a lower ICC value, compared to its segmentation-based counterparts. This result is thought to be due to the DBC’s higher sensitivity when compared to the other methods. This higher sensitivity might help detect changes in the microvasculature, like neovascularization, but is also more likely prone to noise and artefacts.

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Zhang, Le, Faning Dang, Weihua Ding, and Lin Zhu. "Comparative study on damage process of concrete subjected to uniaxial tensile and compression loads based on CT test and improved differential box counting method." Construction and Building Materials 285 (May 2021): 122693. http://dx.doi.org/10.1016/j.conbuildmat.2021.122693.

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Li, Li Hong, Xiu Ming Jia, and Jin Tao Zhang. "Research on Extraction and Assistant Classification of Remote Sensing for Texture Feature." Advanced Materials Research 1073-1076 (December 2014): 1881–85. http://dx.doi.org/10.4028/www.scientific.net/amr.1073-1076.1881.

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The classification precision of remote sensing image has always been one of the problems to each scholar. The traditional classification method is based on the spectral information. With the advancement of technology, the resolution of remote sensing image is gradually improving, and texture features included are getting rich, so adding texture characteristics to spectral characteristics for image classification can remedy the shortage of only relying on spectral characteristics. This paper uses experimental area of aerial image with 0.5m resolution in Datong, calculates fractal dimension using differential box-counting model, extracts the spatial texture features, and classifies precisely combining spectral characteristics in maximum likelihood method. Through comparing different classification results based on different characteristics, it show that classification accuracy based on combination of texture characteristics and spectral characteristics is more accurate (92% overall accuracy and kappa=0.91) than the one based on single spectral feature (88% overall accuracy and kappa=0.85) and texture feature (69% overall accuracy and kappa=0.65), which verifies the effectiveness of this method.

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Salhi, Khalid, El Miloud Jaara, and Mohammed Talibi Alaoui. "Texture Image Segmentation Approach Based on Neural Networks." International Journal of Recent Contributions from Engineering, Science & IT (iJES) 6, no. 1 (March 19, 2018): 19. http://dx.doi.org/10.3991/ijes.v6i1.8166.

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One of the major problems in texture analysis is segmenting images into different regions based on textures. In this paper, we present a new approach of texture segmentation, which is based on both Kohonen maps and mathematical morphology, using three different texture features, namely, Haralick features based on gray-level co-occurrence matrix (GLCM), fractal features based on fractal dimension using the differential box counting method, and wavelet features based on wavelet transform. These features are used to train the Kohonen Network, which will be represented by the underlying probability density function (PDF). The segmentation of this map’s representation is made by morphological watershed transformation. In the final part of our algorithm, this will help on the segmentation of the textural image, by assigning each pixel to a modal region extracted from the map. Our work covers the results obtained by the three extraction methods taking into consideration the execution time and the error rate.

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Басий, Р. В., Ю. В. Довгялло, and К. М. Вельма. "ФРАКТАЛЬНЫЙ АНАЛИЗ ГЕОМЕТРИИ ПОВЕРХНОСТНОГО АРТЕРИАЛЬНОГО РУСЛА БОЛЬШИХ ПОЛУШАРИЙ ГОЛОВНОГО МОЗГА." Университетская клиника, no. 4(37) (December 1, 2020): 10. http://dx.doi.org/10.26435/uc.v0i4(37).537.

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Рост частоты сосудистой патологии во всем мире заставляет искать новые методы ее ранней диагностики, в том числе на доклинической стадии. Фрактальный анализ является примером объективного метода оценки адекватности кровоснабжения того или иного органа, а значит, может служить маркером морфофункциональных отклонений со стороны артериального русла, в том числе головного мозга. Суть данного метода заключается в определении сложности организации сосудистой сети, меры заполнения пространства исследуемым объектом, в данном случае – элементами артериального русла. Актуальным для дальнейших исследований является вопрос изучения нормальных показателей фрактального индекса различных отделов поверхностного артериального русла больших полушарий у лиц мужского и женского пола, которые могли бы служить эталоном нормы и использоваться для оценки адекватности кровоснабжения той или иной области конвекситальной поверхности полушарий.Целью исследования явилось сравнение количественных характеристик поверхностной артериальной сети конвекситальной поверхности больших полушарий методом фрактального анализа у лиц мужского и женского пола. Материал и методы. В соответствии с целью работы было исследовано поверхностное артериальное русло верхнелатеральной поверхности лобной, теменной, затылочной и височной долей 24 людей обоего пола, из них 12 мужчин и 12 женщин. Для расчета фрактального индекса использовался метод box counting. Статистическая обработка полученных результатов поводилась при помощи компьютерной программы MedStat.Результаты. В ходе статистической обработки полученных результатов не было выявлено достоверных отличий между значениями фрактального индекса, характеризующего поверхностное артериальное русло лобной, теменной, затылочной и височной долей у мужчин и женщин, а значит, одно эталонное значение показателя фрактального индекса может использоваться у лиц обоего пола. Заключение. Современная медицинская наука требует использования новых прогрессивных методов исследования. При этом для получения объективных результатов рационально использовать методы, позволяющие получить количественные характеристики. Одним из таких методов является фрактальный анализ.

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Sorkin, Linda S., Tony L. Yaksh, and Carmen M. Doom. "Pain Models Display Differential Sensitivity to Ca2+-Permeable Non-NMDA Glutamate Receptor Antagonists." Anesthesiology 95, no. 4 (October 1, 2001): 965–73. http://dx.doi.org/10.1097/00000542-200110000-00028.

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Background Ca2+-permeable non-N-methyl-D-aspartate receptors are found in the spinal dorsal horn and represent a presumptive target for glutamatergic transmission in nociceptive processing. This study characterized the analgesic profile associated with the blockade of these spinal receptors by intrathecally delivered agents known to act at these receptors, the spider venom Joro toxin (JST) and philanthotoxin. Methods Philanthotoxin (0.5, 2.5, or 5 microg) or JST (5 microg) was given spinally before thermal injury to the paw. JST (5 microg) was also given 10 min before subcutaneous formalin injection, after intraplantar administration of carrageenan, and to rats that were allodynic due to tight ligation of spinal nerves. Lower doses of JST (0.25 and 1.0 microg) were given before formalin injection and testing of thermal latencies. Thermal latencies were measured using a Hargreaves box, mechanical thresholds using von Frey hairs, and formalin response by means of counting flinches. Results Both agents blocked thermal injury-induced mechanical allodynia. JST (5 microg) given 1 h after carrageenan blocked induction of thermal hyperalgesia and mechanical allodynia. JST (5 microg) had no effect in the formalin test, on allodynia after spinal nerve ligation, or when given 3 h after carrageenan. The lowest dose (0.25 microg JST) at pretreatment intervals of 60-120 min resulted in modest hypoalgesia during phase 1 formalin and thermal testing. Conclusions The behavioral effect of intrathecal Ca2+-permeable non-N-methyl-D-aspartate antagonists indicates an important role for this spinal receptor in regulating hyperalgesic states induced by tissue injury and inflammation and reveals an action that is distinct from those observed with other glutamate receptor antagonists.

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Manera, Maurizio, Bahram Sayyaf Dezfuli, Giuseppe Castaldelli, Joseph A. DePasquale, Elisa Anna Fano, Camillo Martino, and Luisa Giari. "Perfluorooctanoic Acid Exposure Assessment on Common Carp Liver through Image and Ultrastructural Investigation." International Journal of Environmental Research and Public Health 16, no. 24 (December 5, 2019): 4923. http://dx.doi.org/10.3390/ijerph16244923.

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Perfluorooctanoic acid (PFOA) poses particular concern as an emerging pollutant in both surface and ground waters. Fish, as a natural inhabitant of these waters and being highly representative of vertebrates, represents an ideal animal model to assess the toxic effects of PFOA. Hereby, liver microscopic texture was comparatively evaluated in individuals of common carp subchronically exposed to PFOA using grayscale differential box counting, a fractal analysis method. Furthermore, liver cytoplasmic glycogen areas and ultrastructure were also evaluated and compared to the image analysis findings. Redundancy Analysis was performed to assess, in summary, how much the variation of fractal dimension and lacunarity was explained by the concentration of PFOA in liver, the mass of liver and the number of proliferating cell nuclear antigen (PCNA)-immunoreactive nuclei. Treatment group ordination was better determined by fractal dimension than lacunarity. Interestingly, a significant complexity increase was associated with the modification of liver microscopic texture due to PFOA exposure. This complexity increase was related to “cloudy swelling”, possibly representing a primarily adaptive strategy against PFOA challenge, rather than a slight, reversible form of degeneration as traditionally proposed. The occurrence of endoplasmic reticulum stress, unfolded protein reaction and hormetic response was proposed and discussed.

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WANG, XING-YUAN, and YAHUI LANG. "A FAST FRACTAL ENCODING METHOD BASED ON FRACTAL DIMENSION." Fractals 17, no. 04 (December 2009): 459–65. http://dx.doi.org/10.1142/s0218348x09004491.

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In this paper a fast fractal coding method based on fractal dimension is proposed. Image texture is an important content in image analysis and processing which can be used to describe the extent of irregular surface. The fractal dimension in fractal theory can be used to describe the image texture, and it is the same with the human visual system. The higher the fractal dimension, the rougher the surface of the corresponding graph, and vice versa. Therefore in this paper a fast fractal encoding method based on fractal dimension is proposed. During the encoding process, using the fractal dimension of the image, all blocks of the given image first are defined into three classes. Then each range block searches the best match in the corresponding class. The method is based on differential box counting which is chosen specifically for texture analysis. Since the searching space is reduced and the classification operation is simple and computationally efficient, the encoding speed is improved and the quality of the decoded image is preserved. Experiments show that compared with the full search method, the proposed method greatly reduced the encoding time, obtained a rather good retrieved image, and achieved the stable speedup ratio.

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Mattos, Amilcar Castro de, João Batista Florindo, Randall L. Adam, Irene Lorand-Metze, and Konradin Metze. "The Fractal Dimension Suggests Two Chromatin Configurations in Small Cell Neuroendocrine Lung Cancer and Is an Independent Unfavorable Prognostic Factor for Overall Survival." Microscopy and Microanalysis 28, no. 2 (February 23, 2022): 522–26. http://dx.doi.org/10.1017/s1431927622000113.

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AbstractExperimental studies have shown that in small cell neuroendocrine lung carcinomas (SCLC) global opening of the chromatin structure is associated with a higher transcription activity and increase of tumor aggressiveness and metastasis. The study of the fractal characteristics (FD) of nuclear chromatin has been widely used to describe the cell nuclear texture and its changes correspond to changes in nuclear metabolic and transcription activity. Hence, we investigated whether the nuclear fractal dimension could be a prognostic factor in SCLC. Hematoxylin-eosin stained brush cytology slides from 49 patients with SCLC were retrieved from our files. The chromatin (FD) was calculated in digitalized and interactively segmented nuclei using a differential box-counting method. The 3,575 nuclei studied showed a bimodal distribution (peaks at FD1 = 2.115 and FD2 = 2.180). The 75 percentile of the FD was an independent unfavorable prognostic factor for overall survival when tested together with ECOG (Eastern Cooperative Oncology Group) performance status, tumor extension, and therapy in a multivariate Cox regression. Our study corroborates the concept of two main chromatin configurations in small cell neuroendocrine carcinomas and that globally more open chromatin indicates a higher risk of metastasis and therefore a shorter survival of the patient.

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Hall, E., S. Kessler, and S. Hanagud. "Use of Fractal Dimension in the Characterization of Chaotic Structural Dynamic Sytems." Applied Mechanics Reviews 44, no. 11S (November 1, 1991): S107—S113. http://dx.doi.org/10.1115/1.3121342.

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The purpose of this paper is to investigate the use of fractal dimensions in the characterization of chaotic systems in structural dynamics. The investigation focuses on the example of a simply-supported, Euler-Bernoulli beam which when subjected to a transverse forcing function of a particular amplitude responds chaotically. Three different nonlinear models of the system are studied: a complex partial differential equation (PDE) model, a simplified PDE model, and a Galerkin approximation to the simpler PDE model. The responses of each model are examined through zero velocity Poincare´ sections. To characterize and compare the chaotic trajectories, the box counting fractal dimension of the Poincare´ sections are computed. The results demonstrate that the fractal dimension is a spatial invariant along the length of the beam for the specific class of forcing function studied, and thus it can be used to characterize chaotic motions. In addition, the three models yield different fractal dimensions for the same forcing which indicates that fractal dimensions can also be used to quantify whether a simplification of a chaotic model accurately predicts the chaotic behavior of the full-blown model. Thus the conclusion of the paper is that fractal dimensions may play an important role in the characterization of chaotic structural dynamic systems.

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Singh, Anand Pal, Connie A. Avramis, John KG Kramer, and Alejandro G. Marangoni. "Algal meal supplementation of the cows' diet alters the physical properties of milk fat." Journal of Dairy Research 71, no. 1 (February 2004): 66–73. http://dx.doi.org/10.1017/s0022029903006642.

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A three-week algal meal supplementation of the cows' basal diet resulted in an increase in the firmness of milk fat crystallized isothermally at 5 °C for 24 h – the apparent elastic constant increased from 100 to 224 N/mm. This was accompanied by a decrease in solid fat content, from 47·7% to 44·4%. The crystallization behaviour of milk fat was also modified significantly. The rate constant of crystallization (Avrami constant) of the enriched milk fat at 19 °C was ∼20 times higher than that of control milk fat. A shorter induction time of nucleation was also observed in the temperature range [20, 27 °C]. These effects were attributed to a higher degree of supersaturation of the enriched milk fat. Enriched milk fat nucleated in a more stable β' polymorphic form at 5 °C, while control milk fat nucleated in the metastable α form, as determined by powder X-ray diffraction and differential scanning calorimetry. Changes in the microstructure of the material were observed by polarized light microscopy at 5 °C. The enriched milk fat displayed a greater amount of crystal clustering than the control. This effect was reflected in a decrease in the box-counting mass fractal dimension (Db) of the fat crystal network from 1·853 to 1·809. The decrease in Db closely predicted the observed 2·2-fold increase in the elastic constant of the fat. These changes in mechanical properties, crystallization behaviour and microstructure were driven by an increase in the 18[ratio ]1trans and a decrease in the 18[ratio ]1cis fatty acid content of the enriched milk fat.

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Cheng, Luxiao, Ruyi Feng, and Lizhe Wang. "Fractal Characteristic Analysis of Urban Land-Cover Spatial Patterns with Spatiotemporal Remote Sensing Images in Shenzhen City (1988–2015)." Remote Sensing 13, no. 22 (November 18, 2021): 4640. http://dx.doi.org/10.3390/rs13224640.

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Understanding the urban land-cover spatial patterns is of particular significance for sustainable development planning. Due to the nonlinear characteristics related to the spatial pattern for land cover, it is essential to provide a new analysis method to analyze them across remote sensing imagery. This paper is devoted to exploring the fractals and fractal dimension properties of land-cover spatial patterns in Shenzhen city, China. Land-cover information was extracted using a supervised classification method with ArcGIS technology from cloud-free Landsat TM/ETM+/OLI imagery, covering 1988–2015. The box-counting method and the least squares regression method are combined to estimate fractal dimensions of the land-cover spatial pattern. The information entropy was used to verify our fractal dimension results. The results show the fractal dimension changes for each land cover type from 1988 to 2015: (1) the land-cover spatial form of Shenzhen city has a clear fractal structure, but fractal dimension values vary in different land cover types; (2) the fractal dimension of build-up land increases and reaches a stable value, while grassland and cultivated land decrease; The fractal structure of grassland and bare land showed a bifractals trend increasing year by year; (3) the information entropy dimension growth is approaching its maximum capacity before 2011. We integrated the information entropy index and fractal dimension to analyze the complexity in land-cover spatial evolution from space-filling, space balance, and space complexity. It can be concluded that driven by policies, the land-cover spatial form in Shenzhen experienced a process from a hierarchical spatial structure with a low evolution intensity to a higher evolution intensity with multiscale differential development. The fractal dimension has been becoming better through self-organization, and its land resources are reaching the growth limits.

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"Estudio fractal de la superficie de la hoja de la especie vegetal Copaifera sp. haciendo uso del Microscopio de Fuerza Atómica-AFM." Revista ECIPeru, December 13, 2018, 10–16. http://dx.doi.org/10.33017/reveciperu2016.0002/.

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Estudio fractal de la superficie de la hoja de la especie vegetal Copaifera sp. haciendo uso del Microscopio de Fuerza Atómica-AFM Study fractal leaf surface of the plant species Copaifera sp. using the Microscope Atomic-Force-AFM Mario Omar Calla Salcedo, Robert Ronald Maguiña Zamora, y José Carlos Tavares Carvalho Universidade Federal de Amapá, Rodovia Juscelino Kubitschek de Oliveira, Km 02 - s/n, Bairro Jardim Marco Zero - Macapá -AP, CEP 68.902-280 DOI: https://doi.org/10.33017/RevECIPeru2016.0002/ Resumen Las especies de copaifera sp, que también son denominadas de copaíba y que son ampliamente utilizadas en la medicina popular debido a sus propiedades etnofarmacológicas. Este trabajo fue realizado con el objetivo de padronizar las hojas, mediante el estudio de la textura superficial da la hoja, para eso se necesita la obtención de los parámetros fractales como la dimensión Fractal, Lagunaridad y succolaridad, haciendo uso de los datos que proporciona el Microscopio de Fuerza Atómica, más conocido como AFM (por las siglas en inglés) se trabajó con la área óptima (25x25 mm2), con el procesamiento de datos y aplicando la geometría fractal, se desarrollaron los algoritmos haciendo uso del programa computacional Fortran 77, el estudio fue realizado a partir de la dificultad que se tiene al diferenciar una especie de otra de la Copaifera sp, ya que para hacer tal identificación se necesita la flor y hoja, esto es porque la planta solo florece una vez al año, y por eso se está proponiendo una manera más fácil, y efectiva da tal identificación solo haciendo uso de la hoja de la Copaifera sp, para el cálculo de la dimensión fractal se hizo uso del método de conteo de cajas (Box-Counting), se usó este método por su simplicidad y exactitud, la dimensión fractal va a servir para calcular la rugosidad y porosidad de la superficie de la hoja de la Copaifera sp., donde el valor de la rugosidad obtenido por medio de la dimensión fractal es más exacto que el cálculo de la rugosidad por medio de la geometría Euclidiana. La lagunaridad, es otro parámetro fractal, que sirve para medir el grado de uniformidad de los huecos en la superficie de la hoja de la Copaifera sp, para el cálculo de la lagunaridad se hizo uso de método conteo de Caja Diferencial (Differential Box Counting) que es un método basado en el conteo de cajá (Box-Counting), si la lagunaridad es mucho mayor que 1, existe mayor desorden de los huecos, si la lagunaridad es más próximo a 1, existe menor desorden, ahora si la lagunaridad es igual 1, la superficie es completamente uniforme, seria invariante a la rotación. La succolaridad es el último parámetro fractal que se aplicó al estudio de la superficie de la hoja, que mide la capacidad de un flujo de agua de atravesar toda la superfície en una determinada dirección, a este proceso se le llama percolación, se midió la succolaridad en las cuatro direcciones es decir de arriba hacia abajo, de abajo hacia arriba, de izquierda a la derecha, y por ultimo de derecha a la izquierda. Teniendo calculado los tres parámetros fractales: dimensión fractal, lagunaridad, y succolaridad, se tiene caracterizado completamente la superficie foliar. Descriptores: Copaifera, Dimensión Fractal, Lagunaridad, Succolaridad, Textura. Abstract The species of Copaifera sp. which are also called copal are widely used in folk medicine due to its ethnopharmacological properties. This work was accomplished with the purpose of the possibility of standardization of the leaves, on the study of the surface texture of the leaf, for this you need to obtain the fractal parameters as fractal dimension (roughness, porosity), lacunarity (rotational invariance of the holes ) and succolarity (percolation), making use of the data of the Atomic Force Microscopy (AFM) worked with the optimal area (25x25 mm2), with the data process and applying fractal mathematics, algorithms were developed with the computer program Fortran 77. The study was conducted from difficulty that one has to distinguish one species from another of Copaifera sp., and to make such identification is needed flower and leaf Copaifera sp., this is because the plant blooms only once a year. That's why it is proposing an easier and effective way to such identification, only making use of leaf Copaifera sp. for the calculation of the fractal dimension. It will make use of Box Counting method for its simplicity and exactitude, which will serve to calculate the roughness and porosity of the surface of the sheet Copaifera sp. It is expected that the value of roughness obtained by the Fractal geometry is more accurate, the calculation of roughness with Euclidean mathematics. The Lacunarity is another fractal parameter used to determine readily the uniformity of the holes for the calculation of lacunarity be made using the method of the counting boxes (Differential Box Counting) which is a method based on the counting boxes (Box-Counting), but the lacunarity is much greater than one, there is greater disorder of the holes.The lacunarity is closer to 1, there is less clutter, now the lacunarity is equal to 1, the surface is completely uniform, is down is invariant rotation, it is expected that lacunarity of Copaifera sp leaf is close to an a succolarity is the last fractal parameter that is doing applied to the study of surfaces, which measures the ability of a flow through the entire surface that serves to measure the percolation surface level. It is measured succolarity in the four directions is down from above down, bottom-up, from left to right, and finally from right to left. When it has calculated the three fractal parameters: fractal dimension, lacunarity and succolarity, it is possible to have fully characterized the leaf surface. Keywords: Copaifera. Fractal Dimension. Lacunarity. Succolarity. Texture

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Сороковая, Наталья Николаевна, and Дмитрий Николаевич Коринчук. "МАТЕМАТИЧЕСКАЯ МОДЕЛЬ И МЕТОД РАСЧЕТА ДИНАМИКИ СУШКИ И ТЕРМОДЕСТРУКЦИИ БИОМАССЫ." Scientific Works 82, no. 1 (August 23, 2018). http://dx.doi.org/10.15673/swonaft.v82i1.1008.

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Разработана математическая модель и численный метод расчета динамики тепломассопереноса, фазовых превращений и усадки при сушке коллоидных капиллярно-пористых тел цилиндрической формы в условиях равномерного обдува теплоносителем. Математическая модель строилась на базе дифференциального уравнения переноса субстанции (энергии, массы, импульса) в деформируемых системах. Проведены экспериментальные исследования кинетики обезвоживания частиц энергетической вербы в потоке воздуха с целью верификации математической модели. Обоснована возможность ее использования для расчета совместных процессов сушки и начального этапа термического разложения биомассы. С использованием ранее полученных данных по значениям энергии активации Аэф(Т) для различных видов биомассы проведено математическое моделирование динамики и кинетики высокотемпературной сушки в потоке дымовых газов энергетической вербы, которая сопровождается термодеструкцией гемиоцеллюлозы. Результаты численных экспериментов свидетельствуют об адекватности предложенного подхода, эффективности математической модели и метода ее реализации. На их основе возможно проводить исследование динамики тепломассопереноса при сушке частиц различных видов измельченной биомассы; определение температуры начала и окончания первой стадии термического разложения; момента достижения равновесного влагосодержания в зависимости от свойств материала и сушильного агента. Эти данные позволяют выбирать оптимальные с точки зрения сохранения энергии и качества высушиваемого продукта режимные параметры процесса. A mathematical model and a numerical method for calculating the dynamics of heat and mass transfer, phase transformations and shrinkage during the drying of colloidal capillary-porous cylindrical bodies under conditions of equitable winding by a coolant are developed. The mathematical model was based on the differential equation of substance (energy, mass, impulse) transfer in deformable systems. It includes the equations diffusion-filtration transfer of energy for the system as a whole, and the mass transfer of the liquid, vapor and air phases in the pores of the body. Expressions for the intensity of evaporation of a liquid, capillary pressure, and the diffusion coefficients are presented. The relative volume strain was found by means of an analytical solution of the thermoconcentration deformation equation. Based on the explicit three-layer counting difference scheme and the procedure splitting of algorithm by physical factors, a numerical method for realizing this mathematical model is developed.Experimental studies of the kinetics of dehydration of energy willow particles in the airflow were carried out to verify the mathematical model. Its applicability for calculating combined processes of drying and of the initial stage of thermal decomposition of biomass is substantiated. Using the previously obtained data on the activation energy values for various types of biomass, a mathematical simulation of the dynamics and kinetics of high-temperature drying in the flue gas flow of energy willow was carried out, which is accompanied by thermal destruction of hemiocellulose. The results of numerical experiments indicate the adequacy of the proposed approach, the effectiveness of the mathematical model and the method of its implementation. On their basis, it is possible to study the dynamics of heat and mass transfer when drying particles of different types of ground biomass; determination of the temperature of the beginning and ending of the first stage of thermal decomposition; the moment when the equilibrium moisture content is reached, depending on the properties of the material and the drying agent. These data allow choosing the process parameters that are optimal in terms of energy saving and quality of the dried product.

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Journal articles on the topic 'Метод "Differential Box Counting"'

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