Varying speed of light and field potential in the octonion spaces

The paper focuses on exploring the contribution of field potential on the speed of light. The octonions can be applied to study the physical quantities of electromagnetic and gravitational fields, including the transformation between two coordinate systems. In the octonion space, the radius vector can be combined with the integrating function of field potential to become one composite radius vector. The latter is considered as the radius vector in an octonion composite-space, which belongs to the function spaces. In the octonion composite-space, when there is the relative motion between two coordinate systems, it is capable of deducing the Galilean-like transformation and Lorentz-like transformation. From the two transformations, one can achieve the influence of relative speed on the speed of light (or Sagnac effect), but also the impact of electromagnetic potential on the speed of light. The study reveals that the electromagnetic potential has a direct influence on the speed of light in the optical waveguides. The paper appeals intensely to validate this inference in relevant experiments, revealing further some new physical quantities of refractive indices in the optical waveguides.Comment: 17 pages, Late

Topological Susceptibility of Yang-Mills Center Projection Vortices

The topological susceptibility induced by center projection vortices extracted from SU(2) lattice Yang-Mills configurations via the maximal center gauge is measured. Two different smoothing procedures, designed to eliminate spurious ultraviolet fluctuations of these vortices before evaluating the topological charge, are explored. They result in consistent estimates of the topological susceptibility carried by the physical thick vortices characterizing the Yang-Mills vacuum in the vortex picture. This susceptibility is comparable to the one obtained from the full lattice Yang-Mills configurations. The topological properties of the SU(2) Yang-Mills vacuum can thus be accounted for in terms of its vortex content.Comment: 12 revtex pages, 6 ps figures included using eps

First Order Static Excitation Potential: Scheme for Excitation Energies and Transition Moments

We present an approximation scheme for the calculation of the principal excitation energies and transition moments of finite many-body systems. The scheme is derived from a first order approximation to the self energy of a recently proposed extended particle-hole Green's function. A hermitian eigenvalue problem is encountered of the same size as the well-known Random Phase Approximation (RPA). We find that it yields a size consistent description of the excitation properties and removes an inconsistent treatment of the ground state correlation by the RPA. By presenting a hermitian eigenvalue problem the new scheme avoids the instabilities of the RPA and should be well suited for large scale numerical calculations. These and additional properties of the new approximation scheme are illuminated by a very simple exactly solvable model.Comment: 15 pages revtex, 1 eps figure included, corrections in Eq. (A1) and Sec. II

Detecting Generalized Synchronization Between Chaotic Signals: A Kernel-based Approach

A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several successful applications are presented, which show the capability of the kernel-based approach for detecting generalized synchronization. It is also shown that the dynamical change of the coupling coefficient between two chaotic systems can be captured by the proposed approach.Comment: 20 pages, 15 figures. massively revised as a full paper; issues on the choice of parameters by cross validation, tests by surrogated data, etc. are added as well as additional examples and figure

Method for arbitrary phase transformation by a slab based on transformation optics and the principle of equal optical path

The optical path lengths travelled by rays across a wavefront essentially determine the resulting phase front irrespective of the shape of a medium according to the principle of equal optical path. Thereupon we propose a method for the transformation between two arbitrary wavefronts by a slab, i.e. the profile of the spatial separation between the two wavefronts is taken to be transformed to a plane surface. Interestingly, for the mutual conversion between planar and curved wavefronts, the method reduce to an inverse transformation method in which it is the reversed shape of the desired wavefront that is converted to a planar one. As an application, three kinds of phase transformation are realized and it is found that the transformation on phase is able to realize some important properties such as phase reversal or compensation, focusing, and expanding or compressing beams, which are further confirmed by numerical simulations. The slab can be applied to realizing compact electromagnetic devices for which the values of the refractive index or the permittivity and permeability can be high or low, positive or negative, or near zero, depending on the choice of coordinate transformations.Comment: 8 pages, 6 figure

Application of spectral and spatial indices for specific class identification in Airborne Prism EXperiment (APEX) imaging spectrometer data for improved land cover classification

Hyperspectral remote sensing's ability to capture spectral information of targets in very narrow bandwidths gives rise to many intrinsic applications. However, the major limiting disadvantage to its applicability is its dimensionality, known as the Hughes Phenomenon. Traditional classification and image processing approaches fail to process data along many contiguous bands due to inadequate training samples. Another challenge of successful classification is to deal with the real world scenario of mixed pixels i.e. presence of more than one class within a single pixel. An attempt has been made to deal with the problems of dimensionality and mixed pixels, with an objective to improve the accuracy of class identification. In this paper, we discuss the application of indices to cope with the disadvantage of the dimensionality of the Airborne Prism EXperiment (APEX) hyperspectral Open Science Dataset (OSD) and to improve the classification accuracy using the Possibilistic c–Means (PCM) algorithm. This was used for the formulation of spectral and spatial indices to describe the information in the dataset in a lesser dimensionality. This reduced dimensionality is used for classification, attempting to improve the accuracy of determination of specific classes. Spectral indices are compiled from the spectral signatures of the target and spatial indices have been defined using texture analysis over defined neighbourhoods. The classification of 20 classes of varying spatial distributions was considered in order to evaluate the applicability of spectral and spatial indices in the extraction of specific class information. The classification of the dataset was performed in two stages; spectral and a combination of spectral and spatial indices individually as input for the PCM classifier. In addition to the reduction of entropy, while considering a spectral-spatial indices approach, an overall classification accuracy of 80.50% was achieved, against 65% (spectral indices only) and 59.50% (optimally determined principal component