Money in Gas-Like Markets: Gibbs and Pareto Laws

We consider the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, we introduce saving propensity $\lambda$ of agents, such that each agent saves a fraction $\lambda$ of its money and trades with the rest. We show the steady-state money or wealth distribution in a market is Gibbs-like for $\lambda=0$, has got a non-vanishing most-probable value for $\lambda \ne 0$ and Pareto-like when $\lambda$ is widely distributed among the agents. We compare these results with observations on wealth distributions of various countries.Comment: 4 pages, 2 eps figures, in Conference Procedings of International Conference on "Unconventional Applications of Statistical Physics", Kolkata, India, March 2003; paper published in Physica Scripta T106 (2003) 3

Renormalization group approach to an Abelian sandpile model on planar lattices

One important step in the renormalization group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer algorithm to carry out such exact enumeration for cells of planar lattices in RG approach to Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. {\bf 59}, 381 (1987)] and consider both the reduced-high RG equations proposed by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. {\bf 72}, 1690 (1994)] and the real-height RG equations proposed by Ivashkevich [Phys. Rev. Lett. {\bf 76}, 3368 (1996)]. Using this algorithm we are able to carry out RG transformations more quickly with large cell size, e.g. $3 \times 3$ cell for the square (sq) lattice in PVZ RG equations, which is the largest cell size at the present, and find some mistakes in a previous paper [Phys. Rev. E {\bf 51}, 1711 (1995)]. For sq and plane triangular (pt) lattices, we obtain the only attractive fixed point for each lattice and calculate the avalanche exponent $\tau$ and the dynamical exponent $z$. Our results suggest that the increase of the cell size in the PVZ RG transformation does not lead to more accurate results. The implication of such result is discussed.Comment: 29 pages, 6 figure

Enhanced grain surface effect on magnetic properties of nanometric La0.7Ca0.3MnO3 manganite : Evidence of surface spin freezing of manganite nanoparticles

We have investigated the effect of nanometric grain size on magnetic properties of single phase, nanocrystalline, granular La0.7Ca0.3MnO3 (LCMO) sample. We have considered core-shell structure of our LCMO nanoparticles, which can explain its magnetic properties. From the temperature dependence of field cooled (FC) and zero-field cooled (ZFC) dc magnetization (DCM), the magnetic properties could be distinguished into two regimes: a relatively high temperature regime T > 40 K where the broad maximum of ZFC curve (at T = Tmax) is associated with the blocking of core particle moments, whereas the sharp maximum (at T = TS) is related to the freezing of surface (shell) spins. The unusual shape of M (H) loop at T = 1.5 K, temperature dependent feature of coercive field and remanent magnetization give a strong support of surface spin freezing that are occurring at lower temperature regime (T < 40 K) in this LCMO nanoparticles. Additionally, waiting time (tw) dependence of ZFC relaxation measurements at T = 50 K show weak dependence of relaxation rate [S(t)] on tw and dM/dln(t) following a logarithmic variation on time. Both of these features strongly support the high temperature regime to be associated with the blocking of core moments. At T = 20 K, ZFC relaxation measurements indicates the existence of two different types of relaxation processes in the sample with S(t) attaining a maximum at the elapsed time very close to the wait time tw = 1000 sec, which is an unequivocal sign of glassy behavior. This age-dependent effect convincingly establish the surface spin freezing of our LCMO nanoparticles associated with a background of superparamagnetic (SPM) phase of core moments.Comment: 41 pages, 10 figure

A generalized family of anisotropic compact object in general relativity

We present model for anisotropic compact star under the general theory of relativity of Einstein. In the study a 4-dimensional spacetime has been considered which is embedded into the 5-dimensional flat metric so that the spherically symmetric metric has class 1 when the condition $e^{\lambda}=\left(\,1+C\,e^{\nu} \,{\nu'}^2\,\right)$ is satisfied ($\lambda$ and $\nu$ being the metric potentials along with a constant $C$). A set of solutions for the field equations are found depending on the index $n$ involved in the physical parameters. The interior solutions have been matched smoothly at the boundary of the spherical distribution to the exterior Schwarzschild solution which necessarily provides values of the unknown constants. We have chosen the values of $n$ as $n=2$ and $n$=10 to 20000 for which interesting and physically viable results can be found out. The numerical values of the parameters and arbitrary constants for different compact stars are assumed in the graphical plots and tables as follows: (i) LMC X-4 : $a=0.0075$, $b=0.000821$ for $n=2$ and $a=0.0075$, $nb=0.00164$ for $n\ge 10$, (ii) SMC X-1: $a=0.00681$, $b=0.00078$ for $n=2$, and $a=0.00681$, $nb=0.00159$ for $n \ge 10$. The investigations on the physical features of the model include several astrophysical issues, like (i) regularity behavior of stars at the centre, (ii) well behaved condition for velocity of sound, (iii) energy conditions, (iv) stabilty of the system via the following three techniques - adiabatic index, Herrera cracking concept and TOV equation, (v) total mass, effective mass and compactification factor and (vi) surface redshift. Specific numerical values of the compact star candidates LMC X-4 and SMC X-1 are calculated for central and surface densities as well as central pressure to compare the model value with actual observational data.Comment: 20 pages, 9 figures, 2 Table

Effects of different doses of x-rays on meiotic chromosomes of malePhysopelta schlanbuschi (Largidae: Heteroptera)

Male largid bugs,Physopelta schlanbuschi, having 2n=17 chromosomes (12 autosomes +2m+X1X2Y), were irradiated with x-ray doees of 300 r, 400 r and 500 r which yielded various types of chromosome aberrations in different stages of meiosis of which the common forms were breaks, fragment of unknown origin, constriction, gap etc. Among the 3 sex chromosomes, the two conspicuously large markers, X1 and Y, sometimes formed chiasmalike configuration in prophase I and metaphase I, while a number of anaphase I plates had a chromatid bridge, very likely formed by the X1 and the Y. The qualitative and quantitative assessments of chromosome aberrations in spermatogonial metaphase, prophase I, metaphase I, anaphase I and metaphase II were made at 13 intervals for the doses of 300 r and 400 r and 14 intervals for 500 r between 5 min and 1 week or more. The data showed over-all dose-dependent aberration effects and the sex chromosomes appeared relatively more vulnerable than the autosomes to different doses of x-rays. The testes of untreated males taken as controls had practically no aberration