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We study L q -spectra of planar self-affine measures generated by diagonal matrices. We introduce a new technique for constructing and understanding examples based on combinatorial estimates for the exponential growth of certain split binomial sums. Using this approach we disprove a theorem of Falconer and Miao from 2007 and a conjecture of Miao from 2008 concerning a closed form expression for the generalised dimensions of generic self-affine measures. We also answer a question of Fraser from 2016 in the negative by proving that a certain natural closed form expression does not generally give the L q -spectrum. As a further application we provide examples of self-affine measures whose L q -spectra exhibit new types of phase transitions. Finally, we provide new non-trivial closed form bounds for the L q -spectra, which in certain cases yield sharp results.

We study L q -spectra of planar self-affine measures generated by diagonal matrices. We introduce a new technique for constructing and understanding examples based on combinatorial estimates for the exponential growth of certain split binomial sums. Using this approach we disprove a theorem of Falconer and Miao from 2007 and a conjecture of Miao from 2008 concerning a closed form expression for the generalised dimensions of generic self-affine measures. We also answer a question of Fraser from 2016 in the negative by proving that a certain natural closed form expression does not generally give the L q -spectrum. As a further application we provide examples of self-affine measures whose L q -spectra exhibit new types of phase transitions. Finally, we provide new non-trivial closed form bounds for the L q -spectra, which in certain cases yield sharp results.

Flexible electronics products have attracted wide attention because of their excellent flexibility, conductivity and stability. In this study, the liquid phase reduction method was used to in situ reduce fractal-structured silver particles (FSSPs) on cellulose surface to prepare conductive paper with excellent conductivity, and good stability and flexibility. The experimental results show that when the mass ratio of silver to cellulose was 1.5:1, the sheet resistance of conductive paper is as low as 0.02 Ω·sq−1, and the conductivity reaches 1041.33 S cm−1, which shows excellent conductivity. In order to expand the application of conductive paper in the field of flexible wearable electronic products, the mechanical stability and oxidation resistance of conductive paper were tested. The results show that the conductive paper has good stability and is expected to replace the flexible electronics products made of plastic.

PubMedID: 26739011 This paper aimed to analyze short-term changes in landscape pattern that primarily results from building development in the east coast of Mersin Province (Turkey). Three sites were selected. Ikonos (2003) and Quickbird (2009) images for these sites were classified, and land cover transformations were quantitatively analyzed using cross-tabulation of classification results. Changes in landscape structure were assessed by comparing the calculated values of area/edge and shape metrics for the earlier and later dates. Area/edge metrics included percentage of land and edge density, while shape metrics included perimeter-area ratio, fractal dimension, and related circumscribing circle (RCC) metrics. Orchards and buildings were dominating land cover classes. Variations in patch edge, size, and shapes were also analyzed and discussed. Degradation of prime agricultural areas due to building development and implications of such development on habitat fragmentation were highlighted. © 2016, Springer International Publishing Switzerland.

We study the static and dynamic properties of networks of crumpled creases formed in hand crushed sheets of paper. The fractal dimensionalities of crumpling networks in the unfolded (flat) and folded configurations are determined. Some other noteworthy features of crumpling networks are established. The physical implications of these findings are discussed. Specifically, we state that self-avoiding interactions introduce a characteristic length scale of sheet crumpling. A framework to model the crumpling phenomena is suggested. Mechanics of sheet crushing under external confinement is developed. The effect of compaction geometry on the crushing mechanics is revealed.

Using extensive analogical simulations with square sheets of paper we investigate the influence of short-range transverse attractive interactions on the packing properties of a crumpled surface. These interactions are due to transverse connections or local bridges associated with a given number of binding sites localized on the two-dimensional surface and distributed in several patterns in the three-dimensional physical space. Geometrical relations and critical exponents describing the statistical properties of the crumpled surface are obtained as a function of the strength of the attractive interactions. Our model suggests how the presence of short-range interactions as, e.g. van der Waals forces can be important for the geometric plasticity of biological molecules, which in turn is important for biological function. The relevance of our results to the study of molecular conformation of proteins and membranes is discussed, and a comparison is also made between the behavior of the crumpled surface studied here and other important non-equilibrium fractal structures.

Objectives: Disorders of cardiovascular and other autonomic nervous system functions are often found in patients with temporal lobe epilepsy (TLE). Cardiovascular dysregulation in TLE has previously been quantified assessing traditional time and frequency domain measures of heart rate (HR) variability from short term ECG recordings. However, new complexity and fractal measures of HR variability based on non-linear dynamics and fractals ("chaos theory") may disclose certain patterns of HR dynamics that cannot be detected using only conventional measures. Methods: In addition to the traditional spectral and non-spectral components of HR variability, fractal correlation properties, approximate entropy (ApEn) of RR interval dynamics, and the slope of the power law relation were measured from 24 hour ambulatory ECG recordings to evaluate interictal autonomic cardiovascular regulatory function in 19 patients with refractory TLE, 25 patients with well controlled TLE, and in 34 healthy age and sex matched control subjects. Results: The traditional time and frequency domain measures were lower in patients with TLE than in controls (p