Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.

Attribute-Graph: A Graph based approach to Image Ranking

We propose a novel image representation, termed Attribute-Graph, to rank images by their semantic similarity to a given query image. An Attribute-Graph is an undirected fully connected graph, incorporating both local and global image characteristics. The graph nodes characterise objects as well as the overall scene context using mid-level semantic attributes, while the edges capture the object topology. We demonstrate the effectiveness of Attribute-Graphs by applying them to the problem of image ranking. We benchmark the performance of our algorithm on the 'rPascal' and 'rImageNet' datasets, which we have created in order to evaluate the ranking performance on complex queries containing multiple objects. Our experimental evaluation shows that modelling images as Attribute-Graphs results in improved ranking performance over existing techniques.Comment: In IEEE International Conference on Computer Vision (ICCV) 201

Heat Transfer in MHD Flow over A Stretching Sheet with Velocity and Thermal Slip Condition

The present work is concerned with the effects of surface slip conditions and thermal on an electrically conducting fluid over a non-isothermal stretching surface in the presence of a uniform transverse magnetic field. Similarity transformation is used to transform the partial differential equations describing the problem into a system of nonlinear ordinary differential equations which is solved analytically. The effects of various parameters on the velocity and temperature profiles as well as on the local skin-friction and the local Nusselt number are discussed in detail and displayed through graphs. Keywords: MHD; Heat transfer; Slip conditions, Kumer’s function, Similarity transformation