Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence

The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963-67. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, 1/f noise and LRD, concepts which are often treated as equivalent.Comment: 11 pages. Corrected and improved version of a manuscript submitted to ITISE 2016 meeting in Granada, Spai

A Comparative Numerical Study on GEM, MHSP and MSGC

In this work, we have tried to develop a detailed understanding of the physical processes occurring in those variants of Micro Pattern Gas Detectors (MPGDs) that share micro hole and micro strip geometry, like GEM, MHSP and MSGC etc. Some of the important and fundamental characteristics of these detectors such as gain, transparency, efficiency and their operational dependence on different device parameters have been estimated following detailed numerical simulation of the detector dynamics. We have used a relatively new simulation framework developed especially for the MPGDs that combines packages such as GARFIELD, neBEM, MAGBOLTZ and HEED. The results compare closely with the available experimental data. This suggests the efficacy of the framework to model the intricacies of these micro-structured detectors in addition to providing insight into their inherent complex dynamical processes

On certain finiteness questions in the arithmetic of modular forms

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3: restructered parts of the article; v4: minor corrections and change

Forbidden Transitions in a Magneto-Optical Trap

We report the first observation of a non-dipole transition in an ultra-cold atomic vapor. We excite the 3P-4P electric quadrupole (E2) transition in $^{23}$Na confined in a Magneto-Optical Trap(MOT), and demonstrate its application to high-resolution spectroscopy by making the first measurement of the hyperfine structure of the 4P$_{1/2}$ level and extracting the magnetic dipole constant A $=$ 30.6 $\pm$ 0.1 MHz. We use cw OODR (Optical-Optical Double Resonance) accompanied by photoinization to probe the transition

Magnetoelectricity at room temperature in Bi0.9-xTbxLa0.1FeO3 system

Magnetoelectric compounds with the general formula, Bi0.9-xRxLa0.1FeO3 (R =Gd, Tb, Dy, etc.), have been synthesized. These show the coexistence of ferroelectricity and magnetism, possess high dielectric constant and exhibit magnetoelectric coupling at room temperature. Such materials may be of great significance in basic as well as applied research.Comment: 11 pages of text and figure

On Penrose limit of elliptic branes

We discuss a Penrose limit of an elliptic brane configuration with $N_1$ NS5 and $N_2$ D4 branes. This background is T-dual to $N_1$ D3 branes at a fixed point of a $\mathbf{C}^3/\mathbf{Z}_{N_2}$ singularity and the T-duality survives the Penrose limit. The triple scaling limit of $N_1$ and $N_2$ gives rise to IIA pp-wave solution with a space-like compact direction. We identify the quiver gauge theory operators and argue that upon exchange of the momentum along the compact direction and the winding number these operators coincide with the operators derived in the dual type IIB description. We also find a new Penrose limit of the type IIB background and the corresponding limit in the type IIA picture. In the coordinate system we use there are two manifest space-like isometries. The quiver gauge theory operator duals of the string states are built of three bosonic fields.Comment: 25 pages with 1 figur

Function reconstruction as a classical moment problem: A maximum entropy approach

We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we reconstruct a set of functions using an iterative entropy optimization scheme, and study the convergence profile as the number of moments is increased. We consider a wide variety of functions that include a distribution with a sharp discontinuity, a rapidly oscillatory function, a distribution with singularities, and finally a distribution with several spikes and fine structure. The last example is important in the context of the determination of the natural density of the logistic map. The convergence of the method is studied by comparing the moments of the approximated functions with the exact ones. Furthermore, by varying the number of moments and iterations, we examine to what extent the features of the functions, such as the divergence behavior at singular points within the interval, is reproduced. The proximity of the reconstructed maximum entropy solution to the exact solution is examined via Kullback-Leibler divergence and variation measures for different number of moments.Comment: 20 pages, 17 figure

One-loop renormalization of heavy-light currents

We calculate the mass dependent renormalization factors of heavy-light bilinears at one-loop order of perturbation theory, when the heavy quark is treated with the Fermilab formalism. We present numerical results for the Wilson and Sheikholeslami-Wohlert actions, with and without tree-level rotation. We find that in both cases our results smoothly interpolate from the static limit to the massless limit. We also calculate the mass dependent Brodsky-Lepage-Mackenzie scale $q^*$, with and without tadpole-improvement.Comment: Lattice2001(improvement), 3 pages, 4 figure

Secular instability in quasi-viscous disc accretion

A first-order correction in the $\alpha$-viscosity parameter of Shakura and Sunyaev has been introduced in the standard inviscid and thin accretion disc. A linearised time-dependent perturbative study of the stationary solutions of this "quasi-viscous" disc leads to the development of a secular instability on large spatial scales. This qualitative feature is equally manifest for two different types of perturbative treatment -- a standing wave on subsonic scales, as well as a radially propagating wave. Stability of the flow is restored when viscosity disappears.Comment: 15 pages, 2 figures, AASTeX. Added some new material and upgraded the reference lis