Unstable entropies and dimension theory of partially hyperbolic systems

In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carathéodory–Pesin dimension characteristic, motivated by the work of Bowen and Pesin etc. We then establish some basic results in dimension theory for Bowen unstable topological entropy, including an entropy distribution principle and a variational principle in general setting. As applications of this new concept, we study unstable topological entropy of saturated sets and extend some results in Bowen (1973 Trans. Am. Math. Soc. 184 125–36); Pfister and Sullivan (2007 Ergod. Theor. Dynam. Syst. 27 929–56). Our results give new insights to the multifractal analysis for partially hyperbolic systems.

Experimental Investigation of Piezoelectric Micropumps with Single, Series or Parallel Pump Chambers

Three types of piezoelectric micropumps following different configurations: single, series, and parallel connection, are developed and investigated. All the micropumps are fabricated by wet etching technology and sealed by high temperature glass bonding. They share the same dimension characteristic of diffuser/nozzle microchannels. Verifying the impact of adding series or parallel connected pump chambers on single chambers, as well as verifying the performance of the flow rate, pressure and piezoelectric transducer vibration of three micropumps have been examined. Through the comparisons between three kinds of micropumps, the results show that the flow rate of the micropumps with parallel connected pump chambers have a higher flow rate than that of micropumps with single and serial connected pump chambers under the same driving conditions. In addition, both the flow rate and pressure with the serial micropump are the lowest. The pressure of the micropump with single pump chamber is larger than other kinds of micropumps at certain driving frequencies. Consequently, increasing the pump chambers cannot always increase the performance of the micropump. This coincides with the theory analysis. Finally, the vibration performance of piezoelectric transducers with three micropumps have been carried out. The parallel transducer has a higher vibration displacement than the other two kinds of micropumps. These results have great potentials for integration into labs with a chip or microfluidic driven systems.

Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

Fractal analysis relies on scale invariance and the concept of fractal dimension enables one to characterize and quantify the space filled by a geometrical set exhibiting complex and tortuous patterns. Fractal tools have been widely used in hydrology but seldom in the specific context of urban hydrology. In this paper, fractal tools are used to analyse surface and sewer data from 10 urban or peri-urban catchments located in five European countries. The aim was to characterize urban catchment properties accounting for the complexity and inhomogeneity typical of urban water systems. Sewer system density and imperviousness (roads or buildings), represented in rasterized maps of 2 m × 2 m pixels, were analysed to quantify their fractal dimension, characteristic of scaling invariance. The results showed that both sewer density and imperviousness exhibit scale-invariant features and can be characterized with the help of fractal dimensions ranging from 1.6 to 2, depending on the catchment. In a given area consistent results were found for the two geometrical features, yielding a robust and innovative way of quantifying the level of urbanization. The representation of imperviousness in operational semi-distributed hydrological models for these catchments was also investigated by computing fractal dimensions of the geometrical sets made up of the sub-catchments with coefficients of imperviousness greater than a range of thresholds. It enables one to quantify how well spatial structures of imperviousness were represented in the urban hydrological models.

Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

Fractal analysis relies on scale invariance and the concept of fractal dimension enables to characterise and quantify the space filled by a geometrical set exhibiting complex and tortuous patterns. Fractal tools have been widely used in hydrology but seldom in the specific context of urban hydrology. In this paper fractal tools are used to analyse surface and sewer data from 10 urban or peri-urban catchments located in 5 European countries. The aim was to characterise urban catchment properties accounting for the complexity and inhomogeneity typical of urban water systems. Sewer system density and imperviousness (roads or buildings), represented in rasterized maps of 2 m × 2 m pixels, were analysed to quantify their fractal dimension, characteristic of scaling invariance. The results showed that both sewer density and imperviousness exhibit scale invariant features and can be characterized with the help of fractal dimensions ranging from 1.6 to 2, depending on the catchment. In a given area consistent results were found for the two geometrical features, yielding a robust and innovative way of quantifying the level of urbanization. The representation of imperviousness in operational semi-distributed hydrological models for these catchments was also investigated by computing fractal dimensions of the geometrical sets made up of the sub-catchments with coefficients of imperviousness greater than a range of thresholds. It enabled to quantify how well spatial structures of imperviousness were represented in the urban hydrological models.

Vehicles Categorization in Complex Background

This paper presents a novel approach to categorize multi-view vehicles in complex background using only two dimension characteristic vectors instead of high dimension vectors. Vehicles have large variability of models and the view-point makes the appearance change dramatically. Significant characteristics should be chosen as the evidence to categorize. In this paper, we categorize the vehicles into two categories – cars and lorries. Line detection method is used and calculating the average line length and the number of parallel lines as the two characteristics. A linear classifier is trained using 30 different view cars and lorries as the training set and an 10 additional different cars and lorries as the testing set.

Correlation Coefficient Matrix Based PD Feature Dimensional Reduction

The abstraction of diagnostic feature from field condition monitoring data is a significant research challenge. A new dimension reduction method based on correlation coefficient matrix is proposed aimed at the high-dimension characteristic parameters in the process of pattern recognition for partial discharge in power transformer. The CCM is constructed by parameters extracted from partial discharge signature in power transformer. The parameters that have similar classification characters are reduced directed by the correlation analysis result. The reduced PD features are inputted to the pattern classifiers of probabilistic neural networks (PNN). The results show that the parameter dimension is reduced and the classifier construction is simplified, and the recognition effect is better than that of the traditional back propagation neural network (BPNN) in the condition of small samples.

In-Cylinder Heat Transfer Model for Diesel Engine Based on Improved Woschni Correlation

Based on the Woschni correlation, a three dimensional in-cylinder heat transfer model is proposed, which develops Woschni correlation from zero dimension to three dimension. Characteristic parameters are proposed as transient flow and heat transfer parameters from in-cylinder CFD simulation, with further consideration of the influence of thermal conductivity, viscosity and Prandtl number. According to test data, the new correlation can be regressed. The new model costs little more calculation time, and it can satisfy the engineering demand.

Dose Verification in Intensity Modulation Radiation Therapy: A Fractal Dimension Characteristics Study

Purpose.This study describes how to identify the coincidence of desired planning isodose curves with film experimental results by using a mathematical fractal dimension characteristic method to avoid the errors caused by visual inspection in the intensity modulation radiation therapy (IMRT).Methods and Materials.The isodose curves of the films delivered by linear accelerator according to Plato treatment planning system were acquired using Osiris software to aim directly at a single interested dose curve for fractal characteristic analysis. The results were compared with the corresponding planning desired isodose curves for fractal dimension analysis in order to determine the acceptable confidence level between the planning and the measurement.Results.The film measured isodose curves and computer planning curves were deemed identical in dose distribution if their fractal dimensions are within some criteria which suggested that the fractal dimension is a unique fingerprint of a curve in checking the planning and film measurement results. The dose measured results of the film were presumed to be the same if their fractal dimension was within 1%.Conclusions.This quantitative rather than qualitative comparison done by fractal dimension numerical analysis helps to decrease the quality assurance errors in IMRT dosimetry verification.

Road Damage Feature Extraction in Image Based on Fractal Dimension

This paper studies the basic principle of the fractal theory, and analyses fractal characteristics of the road crack external form. The fractal dimension characteristic construction algorithm is designed by self-similarity of fractal dimensional and its mathematical expression form. Then road crack texture fractal extraction and analysis is highlighted based on one dimensional fractal. At last, it is compared with regional division combined methods segmentation by testing. The results show that the fractal dimension is a kind of effective quantitative method to depict road crack characteristics, and the algorithm can extract various road crack feature effectively and improve the fracture identification precision and intelligence.