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fractal dimension

P Li, Z F Zhang
Theoretical model required for the evolution of regular dislocation pattern should simultaneously take into account both static distribution and dynamic evolution of dislocation pattern. In principle, there exists a stable uniformly moving dislocation with both core and far field advancing at the same constant velocity, which suggests the existence of the traveling waves representing moving dislocation. Therefore, one new term "dislocation wave" is defined by simultaneously consisting of both an elastic wave and a dislocation in each wavefront...
June 22, 2017: Scientific Reports
Rahul Jain, Ranga Pitchumani
This paper presents a fractal model to describe wettability on multiscale randomly rough surfaces. Hydrophobic or superhydrophobic surfaces produced using processes such as electrodeposition and etching lead to the creation of random roughness at multiple length scales on the surface. This paper considers the description of such surfaces with a fractal asperity model based on the Weierstrass-Mandelbrot (W-M) function, where the fractal parameters are uniquely determined from a power spectrum of the surface...
June 21, 2017: Langmuir: the ACS Journal of Surfaces and Colloids
Fang Zhao, Daolai Cheng
The pore size distribution is quite significant for determining the transport capacity of heat and moisture in sludge during the drying process. It is crucial to investigate the transformation of the pore size in sludge under sonication. In this paper, the microstructures of pores inside sludge before and after ultrasonic treatment with various ultrasonic conditions were observed using a microscope. Fractal geometry and image analysis were combined to quantitatively identify the evolution of pore size in sludge undergoing various acoustic energy densities and treatment times...
September 2017: Ultrasonics Sonochemistry
Rui Zhang, Shimin Liu, Jitendra Bahadur, Derek Elsworth, Yi Wang, Guanglong Hu, Yanna Liang
Microbial enhanced coalbed methane (ME-CBM) recovery is critically examined as a viable technology for natural gas recovery from coalbed methane (CBM) reservoirs. Since the majority of gas-in-place (GIP) is stored as an adsorbed phase in fine pores of coal matrix, the nano-pore structure directly influences gas storage and transport properties. Only limited studies have quantified the alteration of the nano-pore structure due to ME-CBM treatment. This study examines the evolution of the pore structure using a combination of small angle X-ray scattering (SAXS), low-pressure N2 and CO2 adsorption (LPGA) and high-pressure methane adsorption methods...
June 19, 2017: Scientific Reports
Zhiyu Huang, Jiao Chen, Xiaoyan Ai, Ruirui Li, Yingwei Ai, Wei Li
Outside soil spray seeding (OSSS) is widely used to restore cut slopes in southwest of China, and artificial soil is often sprayed onto cut slopes to establish a soil layer for revegetation. The stability of artificial soil layer and its supply of water and nutrients for plants is crucial for successful restoration. To evaluate the long-term effectiveness of OSSS, the texture, structure and nutrient availability of artificial soil were studied, various soil samples were obtained from three cut slopes with different restoration time (restored with OSSS in 1996, 2003 and 2007 respectively) and one natural developed slope (NS)...
June 14, 2017: Journal of Environmental Management
Carol Yim-Lui Cheung, Charumathi Sabanayagam, Antony Kwan-Pui Law, Neelam Kumari, Daniel Shu-Wei Ting, Gavin Tan, Paul Mitchell, Ching Yu Cheng, Tien Yin Wong
AIMS/HYPOTHESIS: We aimed to examine prospectively the association between a range of retinal vascular geometric variables measured from retinal photographs and the 6 year incidence and progression of diabetic retinopathy. METHODS: We conducted a prospective, population-based cohort study of Asian Malay individuals aged 40-80 years at baseline (n = 3280) who returned for a 6 year follow-up. Retinal vascular geometric variables (tortuosity, branching, fractal dimension, calibre) were measured from baseline retinal photographs using a computer-assisted program (Singapore I Vessel Assessment)...
June 16, 2017: Diabetologia
Lei Qin, Cheng Zhai, Shimin Liu, Jizhao Xu
Freeze-thaw induced fracturing coal by liquid nitrogen (LN2) injection exerts a significant positive effect on the fracture permeability enhancement of the coal reservoir. To evaluate the different freeze-thaw variables which modify the mechanical properties of treated coals, the effects of freezing time, number of freeze-thaw cycles, and the moisture content of coal were studied using combined uniaxial compression and acoustic emission testing systems. Freezing the samples with LN2 for increasing amounts of time degraded the strength of coal within a certain limit...
June 16, 2017: Scientific Reports
Sarah E Marzen, James P Crutchfield
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such cases, one compromises and instead seeks nearly maximally predictive features. Here, we derive upper bounds on the rates at which the number and the coding cost of nearly maximally predictive features scale with desired predictive power. The rates are determined by the fractal dimensions of a process' mixed-state distribution...
May 2017: Physical Review. E
Trifce Sandev, Alexander Iomin, Holger Kantz
We present exact analytical results for properties of anomalous diffusion on a fractal mesh. The fractal mesh structure is a direct product of two fractal sets, one belonging to a main branch of backbones, the other to the side branches of fingers. Both fractal sets are constructed on the entire (infinite) y and x axes. We suggest a special algorithm in order to construct such sets out of standard Cantor sets embedded in the unit interval. The transport properties of the fractal mesh are studied, in particular, subdiffusion along the backbones is obtained with the dispersion relation 〈x^{2}(t)〉≃t^{β}, where the transport exponent β<1 is determined by the fractal dimensions of both backbone and fingers...
May 2017: Physical Review. E
W R Heinson, A Chakrabarti, C M Sorensen
We demonstrate that kinetic aggregation forms superaggregates that have structures identical to static percolation aggregates, and these superaggregates appear as a separate phase in the size distribution. Diffusion limited cluster-cluster aggregation (DLCA) simulations were performed to yield fractal aggregates with a fractal dimension of 1.8 and superaggregates with a fractal dimension of D=2.5 composed of these DLCA supermonomers. When properly normalized to account for the DLCA fractal nature of their supermonomers, these superaggregates have the exact same monomer packing fraction, scaling law prefactor, and scaling law exponent (the fractal dimension) as percolation aggregates; these are necessary and sufficient conditions for same structure...
May 2017: Physical Review. E
Jarosław Kwapień, Paweł Oświęcimka, Marcin Forczek, Stanisław Drożdż
Based on a recently proposed q-dependent detrended cross-correlation coefficient, ρ_{q} [J. Kwapień, P. Oświęcimka, and S. Drożdż, Phys. Rev. E 92, 052815 (2015)PLEEE81539-375510.1103/PhysRevE.92.052815], we generalize the concept of the minimum spanning tree (MST) by introducing a family of q-dependent minimum spanning trees (qMSTs) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data. They inherit this ability directly from the coefficients ρ_{q}, which are processed here to construct a distance matrix being the input to the MST-constructing Kruskal's algorithm...
May 2017: Physical Review. E
J R Nicolás-Carlock, J L Carrillo-Estrada, V Dossetti
Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions have been lacking...
June 14, 2017: Scientific Reports
Ling-Jun Li, Ecosse Lamoureux, Tien Yin Wong, Ngee Lek
BACKGROUND: Poor glycemic control in Type 1 Diabetes (T1D) patients is strongly associated with an increased risk of diabetes-related microvascular complications later in life, but it is unclear whether short period of poor glycemic control in children with T1D can cause evident microvascular morphological changes long before any pathological manifestation. Our study aimed to investigate the longitudinal association between poor glycemic control and subsequent changes in retinal microvasculature, in a pilot study of 55 pediatric T1D patients from Singapore after a one-year follow-up...
June 15, 2017: BMC Ophthalmology
Shih-Cheng Liao, Chien-Te Wu, Hao-Chuan Huang, Wei-Teng Cheng, Yi-Hung Liu
Major depressive disorder (MDD) has become a leading contributor to the global burden of disease; however, there are currently no reliable biological markers or physiological measurements for efficiently and effectively dissecting the heterogeneity of MDD. Here we propose a novel method based on scalp electroencephalography (EEG) signals and a robust spectral-spatial EEG feature extractor called kernel eigen-filter-bank common spatial pattern (KEFB-CSP). The KEFB-CSP first filters the multi-channel raw EEG signals into a set of frequency sub-bands covering the range from theta to gamma bands, then spatially transforms the EEG signals of each sub-band from the original sensor space to a new space where the new signals (i...
June 14, 2017: Sensors
Zhenci Xu, Ying Tang, Thomas Connor, Dapeng Li, Yunkai Li, Jianguo Liu
Climate variability and trends have significant environmental and socioeconomic impacts. Global challenges such as food security, biodiversity loss, water scarcity and human health are affected by reference evapotranspiration, temperature, solar radiation, and precipitation together, but nonlinear dynamics of these four climatic factors have not been assessed simultaneously at the national scale. This leads to unclear climatic dynamics and limited applications. To address this knowledge gap, we analyzed the daily variability and trends of four climatic factors (reference evapotranspiration, temperature, solar radiation, and precipitation) in China simultaneously using high spatial resolution data from 1960 to 2013...
June 12, 2017: Scientific Reports
Engin Akar, Sadık Kara, Hidayet Akdemir, Adem Kırış
Chiari malformation type I (CM-I), described by a descent of the cerebellar tonsils, is assumed to be a neurological developmental disorder. The aim of the present study was to investigate morphological variance in cerebellar sub-structures, including gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF), using magnetic resonance (MR) images with three-dimensional (3D) fractal dimension (FD) analysis in patients with CM-I. MRI data of 16 patients and 15 control subjects were obtained, and structural complexity analyses were performed using a box-counting FD algorithm...
June 7, 2017: Medical & Biological Engineering & Computing
E M Anitas, A Slyamov, R Todoran, Z Szakacs
Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and scaling factors at each structural level. This is in agreement with general results deduced in the context of small-angle scattering analysis of a system of randomly oriented, non-interacting, nano-/micro-fractals...
December 2017: Nanoscale Research Letters
Sankeerti Mala, Vanita Rathod, Siddharth Pundir, Sudhanshu Dixit
CONTEXT: The unique pattern and structural diversity of fingerprints, lip prints, palatal rugae, and their occurrence in different patterns among individuals make it questionable whether they are completely unique even in a family hierarchy? Do they have any repetition of the patterns among the generations? Or is this a mere chaos theory? AIMS: The present study aims to assess the pattern self-repetition of fingerprints, lip prints, and palatal rugae among three generations of ten different families...
January 2017: Journal of Forensic Dental Sciences
Mayss Al-Sheikh, Nicholas A Iafe, Nopasak Phasukkijwatana, SriniVas R Sadda, David Sarraf
PURPOSE: To study the qualitative and quantitative features of choroidal neovascular (NV) membranes in age-related macular degeneration using optical coherence tomography angiography in patients with active and quiescent NV lesions before and after treatment with anti-vascular endothelial growth factor. METHODS: Macular optical coherence tomography angiography images were obtained using RTVue XR Avanti with AngioVue. Morphologic features and quantitative measurements of the NV lesion were analyzed using en face projection images...
May 2, 2017: Retina
Fang Yao Tang, Danny S Ng, Alexander Lam, Fiona Luk, Raymond Wong, Carmen Chan, Shaheeda Mohamed, Angie Fong, Jerry Lok, Tiffany Tso, Frank Lai, Marten Brelen, Tien Y Wong, Clement C C Tham, Carol Y Cheung
Early microvascular damage in diabetes (e.g. capillary nonperfusion and ischemia) can now be assessed and quantified with optical coherence tomography-angiography (OCT-A). The morphology of vascular tissue is indeed affected by different factors; however, there is a paucity of data examining whether OCT-A metrics are influenced by ocular, systemic and demographic variables in subjects with diabetes. We conducted an observational cross-sectional study and included 434 eyes from 286 patients with diabetes. Foveal avascular zone (FAZ) area, FAZ circularity, total and parafoveal vessel density (VD), fractal dimension (FD), and vessel diameter index (VDI) from the superficial capillary plexus OCT-angiogram were measured by a customized automated image analysis program...
May 31, 2017: Scientific Reports
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