Scaling behavior in economics: II. Modeling of company growth

In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an ``optimal'' size. That model leads to an exponential distribution of the logarithm of the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent $\beta$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln z$, where $z$ defines the mean branching ratio of the hierarchical tree and $\Pi$ is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France (April 1997

Scaling behavior in economics: I. Empirical results for company growth

We address the question of the growth of firm size. To this end, we analyze the Compustat data base comprising all publicly-traded United States manufacturing firms within the years 1974-1993. We find that the distribution of firm sizes remains stable for the 20 years we study, i.e., the mean value and standard deviation remain approximately constant. We study the distribution of sizes of the ``new'' companies in each year and find it to be well approximated by a log-normal. We find (i) the distribution of the logarithm of the growth rates, for a fixed growth period of one year, and for companies with approximately the same size $S$ displays an exponential form, and (ii) the fluctuations in the growth rates -- measured by the width of this distribution $\sigma_1$ -- scale as a power law with $S$, $\sigma_1\sim S^{-\beta}$. We find that the exponent $\beta$ takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain: $\beta=0.20\pm0.03$ for sales, $\beta=0.18\pm0.03$ for number of employees, $\beta=0.18\pm0.03$ for assets, $\beta=0.18\pm0.03$ for cost of goods sold, and $\beta=0.20\pm0.03$ for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France (April 1997

Molecular dynamics simulations of oxide memristors: crystal field effects

We present molecular-dynamic simulations of memory resistors (memristors) including the crystal field effects on mobile ionic species such as oxygen vacancies appearing during operation of the device. Vacancy distributions show different patterns depending on the ratio of a spatial period of the crystal field to a characteristic radius of the vacancy-vacancy interaction. There are signatures of the orientational order and of spatial voids in the vacancy distributions for some crystal field potentials. The crystal field stabilizes the patterns after they are formed, resulting in a non-volatile switching of the simulated devices.Comment: 9 pages, 3 figure

The Effect of Burnout Towards OCB in the Companies on Workers of PT.X and PT.Y

Companies are growing and competing with each other to be the leading business in its own sector. The companies will utilize its resources and use it effectively and efficiently in order to be on top. One of the resources is the companies\u27 human resource which is the workers that run the company altogether by doing their job description based on their position. The human resources could produce better results if their state of mind is in the prime condition. The research aims to know the effect of burnout towards Organizational Citizenship Behavior of the workers in PT. X and PT. Y. This would let the researchers and companies to identify the effect of burnout to OCB which would let the companies formulate strategies to maintain the workers to reach high productivity yet retaining the welfare and loyalty of the workers. The research was done by gathering data from 100 samples using random sampling. Then the data was analyzed using multiple regression. The result of the research showed that burnout gives significant effect towards Organizational Citizenship Behavior. Furthermore the relationship that the independent and dependent variables shows are positive relationship which is contrary to the research conducted before by previous researchers

Scaling for the Percolation Backbone

We study the backbone connecting two given sites of a two-dimensional lattice separated by an arbitrary distance $r$ in a system of size $L$. We find a scaling form for the average backbone mass: $\sim L^{d_B}G(r/L)$, where $G$ can be well approximated by a power law for $0\le x\le 1$: $G(x)\sim x^{\psi}$ with $\psi=0.37\pm 0.02$. This result implies that $\sim L^{d_B-\psi}r^{\psi}$ for the entire range $0<r<L$. We also propose a scaling form for the probability distribution $P(M_B)$ of backbone mass for a given $r$. For $r\approx L, P(M_B)$ is peaked around $L^{d_B}$, whereas for $r\ll L, P(M_B)$ decreases as a power law, $M_B^{-\tau_B}$, with $\tau_B\simeq 1.20\pm 0.03$. The exponents $\psi$ and $\tau_B$ satisfy the relation $\psi=d_B(\tau_B-1)$, and $\psi$ is the codimension of the backbone, $\psi=d-d_B$.Comment: 3 pages, 5 postscript figures, Latex/Revtex/multicols/eps

Current-Controlled Negative Differential Resistance due to Joule Heating in TiO2

We show that Joule heating causes current-controlled negative differential resistance (CC-NDR) in TiO2 by constructing an analytical model of the voltage-current V(I) characteristic based on polaronic transport for Ohm's Law and Newton's Law of Cooling, and fitting this model to experimental data. This threshold switching is the 'soft breakdown' observed during electroforming of TiO2 and other transition-metal-oxide based memristors, as well as a precursor to 'ON' or 'SET' switching of unipolar memristors from their high to their low resistance states. The shape of the V(I) curve is a sensitive indicator of the nature of the polaronic conduction.Comment: 13 pages, 2 figure