A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment

We present a preferential attachment growth model to obtain the distribution $P(K)$ of number of units $K$ in the classes which may represent business firms or other socio-economic entities. We found that $P(K)$ is described in its central part by a power law with an exponent $\phi=2+b/(1-b)$ which depends on the probability of entry of new classes, $b$. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution $P(K)$ is exponential. Using analytical form of $P(K)$ and assuming proportional growth for units, we derive $P(g)$, the distribution of business firm growth rates. The model predicts that $P(g)$ has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent $\zeta=3$. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.Comment: 19 pages 6 figures Applications of Physics in Financial Analysis, APFA

Photoemission study of (V1−x_{1-x}Mx_x)2_2O3_3 (M=Cr, Ti)

We present high-resolution bulk-sensitive photoemission spectra of (V$_{1-x}$M$_x$)$_2$O$_3$ (M=Cr, Ti). The measurements were made for the paramagnetic metal (PM), paramagnetic insulator (PI), and antiferromagnetic insulator (AFI) phases of (V$_{1-x}$M$_x$)$_2$O$_3$ with the samples of $x$ = 0, 0.012, and 0.028 for Cr-doping and $x$ = 0.01 for Ti-doping. In the PM phase, we observe a prominent quasiparticle peak in general agreement with theory, which combines dynamical mean-field theory with the local density approximation (LDA+DMFT). The quasiparticle peak shows a significantly larger peak width and weight than in the theory. For both the PI and AFI phases, the vanadium 3d parts of the valence spectra are not simple one peak structures. For the PI phase, there is not yet a good theoretical understanding of these structures. The size of the electron removal gap increases, and spectral weight accumulates in the energy range closer to the chemical potential, when the PI to AFI transition occurs. Spectra taken in the same phases with different compositions show interesting monotonic changes as the dopant concentration increases, regardless of the dopant species. With increased Cr-doping, the AFI phase gap decreases and the PI phase gap increases.Comment: 13 pages, 16 figures. accepted for publication in Physical Review

Effect of cation size variance on spin and orbital order in Eu1−x_{1-x}(La0.254_{0.254}Y0.746_{0.746})x_{x}VO3_3

We have investigated the $R$-ion ($R$ = rare earth or Y) size variance effect on spin/orbital order in Eu$_{1-x}$(La$_{0.254}$Y$_{0.746}$)$_{x}$VO$_3$. The size variance disturbs one-dimensional orbital correlation in $C$-type spin/$G$-type orbital ordered states and suppresses this spin/orbital order. In contrast, it stabilizes the other spin/orbital order. The results of neutron and resonant X-ray scattering denote that in the other ordered phase, the spin/orbital patterns are $G$-type/$C$-type, respectively.Comment: 4 pages, 4 figures, accepted to Rapid Communication in Physical Review

Filling of the Mott-Hubbard gap in the high temperature photoemission spectrum of (V_0.972Cr_0.028)_2O_3

Photoemission spectra of the paramagnetic insulating (PI) phase of (V_0.972Cr_0.028)_2O_3, taken in ultra high vacuum up to the unusually high temperature (T) of 800 K, reveal a property unique to the Mott-Hubbard (MH) insulator and not observed previously. With increasing T the MH gap is filled by spectral weight transfer, in qualitative agreement with high-T theoretical calculations combining dynamical mean field theory and band theory in the local density approximation.Comment: 4 pages, 4 figure

Collimated Jet or Expanding Outflow: Possible Origins of GRBs and X-Ray Flashes

We investigate the dynamics of an injected outflow propagating in a progenitor in the context of the collapsar model for gamma-ray bursts (GRBs) through two dimensional axisymmetric relativistic hydrodynamic simulations. Initially, we locally inject an outflow near the center of a progenitor. We calculate 25 models, in total, by fixing its total input energy to be 10^{51} ergs s^{-1} and radius of the injected outflow to be $7\times 10^7$ cm while varying its bulk Lorentz factor, $\Gamma_{0} = 1.05\sim 5$, and its specific internal energy, $\epsilon_0/c^2 = 0.1\sim 30$. The injected outflow propagates in the progenitor and drives a large-scale outflow or jet. We find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models. The maximum Lorentz factor is, on the other hand, sensitive to both of $\Gamma_0$ and $\epsilon_0$; roughly $\Gamma_{\rm max} \sim \Gamma_0 (1+\epsilon_0/c^2)$. Our finding will explain a smooth transition between the GRBs, X-ray rich GRBs (XRRs) and X-ray Flashes (XRFs) by the same model but with different $\epsilon_0$ values.Comment: Comments 51 pages, 21 figures. accepted for publication in ApJ high resolution version is available at http://www.mpa-garching.mpg.de/~mizuta/COLLAPSAR/collapsar.htm

Prominent quasi-particle peak in the photoemission spectrum of the metallic phase of V_2O_3

We present the first observation of a prominent quasi-particle peak in the photoemission spectrum of the metallic phase of V_2O_3 and report new spectral calculations that combine the local density approximation with the dynamical mean-field theory (using quantum Monte Carlo simulations) to show the development of such a distinct peak with decreasing temperature. The experimental peak width and weight are significantly larger than in the theory.Comment: 4 pages, 3 figures, supercedes cond-mat/010804