Fundamental representations and algebraic properties of biquaternions or complexified quaternions

The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates, semi-norms, polar forms, and inner and outer products. The notation is consistent throughout, even between representations, providing a clear account of the many ways in which the component parts of a biquaternion may be manipulated algebraically

Universal properties for linelike melting of the vortex lattice

Using numerical results obtained within two models describing vortex matter (interacting elastic lines (Bose model) and uniformly frustrated XY-model) we establish universal properties of the melting transition within the linelike regime. These properties, which are captured correctly by both models, include the scaling of the melting temperature with anisotropy and magnetic field, the effective line tension of vortices in the liquid regime, the latent heat, the entropy jump per entanglement length, and relative jump of Josephson energy at the transition as compared to the latent heat. The universal properties can serve as experimental fingerprints of the linelike regime of melting. Comparison of the models allows us to establish boundaries of the linelike regime in temperature and magnetic field.Comment: Revtex, 12 pages, 2 EPS figure

Comment on "Mean First Passage Time for Anomalous Diffusion"

We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)] of the mean first passage time of a subdiffusive process to reach either end of a finite interval in one dimension. The mean first passage time is in fact infinite.Comment: To appear in Phys. Rev.

Quaternion-Octonion SU(3) Flavor Symmetry

Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group we have considered the theory of octonion variables. Accordingly, the octonion splitting of SU(3) group have been reconsidered and various commutation relations for SU(3) group and its shift operators are also derived and verified for different iso-spin multiplets i.e. I, U and V- spins. Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and models of strong and electroweak interaction

Quaternion Octonion Reformulation of Quantum Chromodynamics

We have made an attempt to develop the quaternionic formulation of Yang - Mill's field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we have discussed the field equations of SU(2) and SU(3) gauge fields for both cases of global and local gauge symmetries. It has been shown that the three quaternion units explain the structure of Yang- Mill's field while the seven octonion units provide the consistent structure of SU(3)_{C} gauge symmetry of quantum chromo dynamics

Gas turbine engine condition monitoring using Gaussian mixture and hidden Markov models

This paper investigates the problem of condition monitoring of complex dynamic systems, specifically the detection, localisation and quantification of transient faults. A data driven approach is developed for fault detection where the multidimensional data sequence is viewed as a stochastic process whose behaviour can be described by a hidden Markov model with two hidden states --- i.e. `healthy / nominal' and `unhealthy / faulty'. The fault detection is performed by first clustering in a multidimensional data space to define normal operating behaviour using a Gaussian-Uniform mixture model. The health status of the system at each data point is then determined by evaluating the posterior probabilities of the hidden states of a hidden Markov model. This allows the temporal relationship between sequential data points to be incorporated into the fault detection scheme. The proposed scheme is robust to noise and requires minimal tuning. A real-world case study is performed based on the detection of transient faults in the variable stator vane actuator of a gas turbine engine to demonstrate the successful application of the scheme. The results are used to demonstrate the generation of simple and easily interpretable analytics that can be used to monitor the evolution of the fault across time

On type-I migration near opacity transitions. A generalized Lindblad torque formula for planetary population synthesis

We give an expression for the Lindblad torque acting on a low-mass planet embedded in a protoplanetary disk that is valid even at locations where the surface density or temperature profile cannot be approximated by a power law, such as an opacity transition. At such locations, the Lindblad torque is known to suffer strong deviation from its standard value, with potentially important implications for type I migration, but the full treatment of the tidal interaction is cumbersome and not well suited to models of planetary population synthesis. The expression that we propose retains the simplicity of the standard Lindblad torque formula and gives results that accurately reproduce those of numerical simulations, even at locations where the disk temperature undergoes abrupt changes. Our study is conducted by means of customized numerical simulations in the low-mass regime, in locally isothermal disks, and compared to linear torque estimates obtained by summing fully analytic torque estimates at each Lindblad resonance. The functional dependence of our modified Lindblad torque expression is suggested by an estimate of the shift of the Lindblad resonances that mostly contribute to the torque, in a disk with sharp gradients of temperature or surface density, while the numerical coefficients of the new terms are adjusted to seek agreement with numerics. As side results, we find that the vortensity related corotation torque undergoes a boost at an opacity transition that can counteract migration, and we find evidence from numerical simulations that the linear corotation torque has a non-negligible dependency upon the temperature gradient, in a locally isothermal disk.Comment: Appeared in special issue of "Celestial Mechanics and Dynamical Astronomy" on Extrasolar Planetary System

Dilepton Spectra from Decays of Light Unflavored Mesons

The invariant mass spectrum of the $e^{+}e^{-}$ and $\mu ^{+}\mu ^{-}$ pairs from decays of light unflavored mesons with masses below the $\phi (1020)$-meson mass to final states containing along with a dilepton pair one photon, one meson, and two mesons are calculated within the framework of the effective meson theory. The results can be used for simulations of the dilepton spectra in heavy-ion collisions and for experimental searches of dilepton meson decays.Comment: 73 pages, 19 figures, 3 tables, REVTeX, new references adde

Octonion Quantum Chromodynamics

Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann \lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann \lambda matrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons