Fractal dimensions of time sequences

We present a simple and efficient way for calculating the fractal dimension $D$ of any time sequence sampled at a constant time interval. We calculated the error of a piecewise interpolation to $N+1$ points of the time sequence with respect to the next level of ($2N+1$)-point interpolation. This error was found to be proportional to the scale (i.e., $1/N$) to the power of $1?D$. A simple analysis showed that our method is equivalent to the inverse process of the method of random midpoint displacement widely used in generating fractal Brownian motion for a given $D$. The efficiency of our method makes the fractal dimension a practical tool in analyzing the abundant data in natural, economic, and social sciences.     

Fundamental mode in advanced technology optical fibres by two-point quasi-rational approximations

An analytic approximant is found for the fundamental guided mode of advanced technology optical fibres using a two-point quasi-rational approximation method. Very accurate results are obtained particularly in the linearly varying refractive index core, the maximum error being less than $1\times {10}^{\mathrm{-6}}$. The fractional power transport across the fibre is also given.     

Dynamical quantum Fisher information in the Ising model

In terms of quantum Fisher information, we discuss the dynamics of quantity ${\chi }^2$ of the Ising model. The inequality ${\chi }^2<1$ detects the class of entangled states which are useful for sub-shot-noise sensitivity. All the exact dynamics of the expectations of collective spin operators are derived. The minimum ${\chi }^2$ in the plane perpendicular to the mean spin direction is analytically given. We find that ${\chi }^2$ does not depend on the system size $N$ when $N\ge 4$. Except for the periodic points, the evolution states are always entangled and useful for the sub-shot-noise phase estimation.     

Application of medium energy plasma focus device in study of radioisotopes

Pulsed neutrons generated in a plasma focus device are used for the thermal neutron activation analysis (TNAA) of selected three elements having widely different half-lives varying from a few seconds to a few days [Dysprosium (Dy), Manganese (Mn) and Gold (Au)]. Neutron pulse having strength of $(1.2\pm 0.3)\times {10}^9$ neutrons/pulse with a pulse width of $46\pm 5\text{ns}$ is produced by “MEPF-12” device operated at a filling gas (deuterium + 0.5% krypton) pressure of 3 mbar. The fast 2.45 MeV D–D neutrons are thermalized before irradiating the sample. The decay gammas from the radioisotopes ^165mDy ($T_{1/2}=1.26\text{min.}$), ⁵⁶Mn ($T_{1/2}=2.58\text{hrs.}$), and ¹⁹⁸Au ($T_{1/2}=2.69\text{days}$) produced via reactions, ¹⁶⁴Dy($n,\gamma$)^165mDy, ⁵⁵Mn($n,\gamma$) ⁵⁶Mn, and ¹⁹⁷Au($n,\gamma$) ¹⁹⁸Au respectively are counted off-line in a lead shielded well type $76\times 76{\text{mm}}^2$ NaI(Tl) detector coupled to a calibrated 2048 channel analyzer. The values of half-lives evaluated from the measured decay gammas, $1.43\pm 0.3\text{min.}$, $2.56\pm 0.5\text{hrs.}$ and $2.84\pm 0.6\text{days}$ respectively for the radioisotopes of Dy, Mn and Au, are seen to be close to the values reported in literature.     

First order flows for N=2 extremal black holes and duality invariants

We derive explicitly the superpotential W for the non-BPS branch of $N=2$ extremal black holes in terms of duality invariants of special geometry. Although this is done for a one-modulus case (the $t^3$ model), the example gives $Z\ne 0$ black holes and captures the basic distinction from previous attempts on the quadratic series (vanishing C tensor) and from the other $Z=0$ cases. The superpotential W turns out to be a non-polynomial expression (containing radicals) of the basic duality invariant quantities. These are the same which enter in the quartic invariant $I_4$ for $N=2$ theories based on symmetric spaces. Using the flow equations generated by W, we also provide the analytic general solution for the warp factor and for the scalar field supporting the non-BPS black holes.