A cell growth model revisited

In this paper a stochastic model for the simultaneous growth and division of a cell-population cohort structured by size is formulated. This probabilistic approach gives straightforward proof of the existence of the steady-size distribution and a simple derivation of the functional-differential equation for it. The latter one is the celebrated pantograph equation (of advanced type). This firmly establishes the existence of the steady-size distribution and gives a form for it in terms of a sequence of probability distribution functions. Also it shows that the pantograph equation is a key equation for other situations where there is a distinct stochastic framework

A conformal invariant growth model

We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption rates are local but the desorption rates are non-local, they depend not only on the cluster hit by the tile but also on the total number of peaks (local maxima) belonging to all the clusters of the configuration. The domain of the parameter is determined by the condition that the rates are non-negative. In the finite-size scaling limit, the model is conformal invariant in the whole open domain. The parameter appears in the sound velocity only. At the boundary of the domain, the stationary state is an adsorbing state and conformal invariance is lost. The model allows to check the universality of nonlocal observables in the raise and peel model. An example is given.Comment: 11 pages and 8 figure

Growth Model of Remmant Stands in Selectively Logged Forest, Papua

Sustainable forest management recently calls for growth information concerning integrated functions of ingrowth, upgrowth and mortality. This study was conducted in logging concessions of PT. Tunas Timber Lestari (TTL), PT. Wapoga Mutiara Timber (WMT) dan PT. Manokwari Mandiri Lestari (MML) in Papua. Then, this research was intended to build growth stands models in logged over forest. The data were obtained from permanent sample plots (PSPs) in three logging concession in Papua forest. Results revealed that characteristics of stand namely basal area, stem density and diameter had significant coefficients to model of ingrowth, upgrowth and mortality in each logging concession. Specifically, PT WMT showed the highest value of coefficient of determination (>80%, P<0.05). For PT MML only had significant model namely ingrowth and upgrowth model while PT TTL only shwed ingrowth model as significant equation

Partial regularity for a surface growth model

We prove two partial regularity results for the scalar equation $u_t+u_{xxxx}+\partial_{xx}u_x^2=0$, a model of surface growth arising from the physical process of molecular epitaxy. We show that the set of space-time singularities has (upper) box-counting dimension no larger than 7/6 and 1-dimensional (parabolic) Hausdorff measure zero. These parallel the results available for the three-dimensional Navier--Stokes equations. In fact the mathematical theory of the surface growth model is known to share a number of striking similarities with the Navier--Stokes equations, and the partial regularity results are the next step towards understanding this remarkable similarity. As far as we know the surface growth model is the only lower-dimensional “mini-model” of the Navier--Stokes equations for which such an analogue of the partial regularity theory has been proved. In the course of our proof, which is inspired by the rescaling analysis of Lin [Comm. Pure Appl. Math., 51(1998), pp. 241--257] and Ladyzhenskaya and Seregin [J. Math. Fluid Mech., 1(1999), pp. 356--387], we develop certain nonlinear parabolic Poincaré inequality, which is a concept of independent interest. We believe that similar inequalities could be applicable in other parabolic equations

The Structuralist Growth Model

This paper examines the underlying theory of structuralist growth models in an effort to compare that framework with the standard approach of Solow and others. Both the standard and structuralist models are solved in a common mathematical framework that emphasizes their similarities. It is seen that while the standard model requires the growth rate of the labor force to be taken as exogenously determined, the structuralist growth model must take investment growth to be determined exogenously in the long run. It is further seen that in order for the structuralist model to reliably converge to steady growth, considerable attention must be given to how agents make investment decisions. In many ways the standard model relies less on agency than does the structuralist. While the former requires a small number of plausible assumptions for steady growth to emerge, the structuralist model faces formidable challenges, especially if investment growth is thought to be determined by the rate of capacity utilization.

Growth model with restricted surface relaxation

We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson linear model, but only within a distance s. If the local minimum is out from this distance, the particle evaporates through a refuse mechanism similar to the Kim-Kosterlitz nonlinear model. In d=1, the growth exponent beta, measured from the temporal behavior of roughness, indicates that in the coarse-grained limit, the linear term of the Kardar-Parisi-Zhang equation dominates in short times (low-roughness) and, in asymptotic times, the nonlinear term prevails. The crossover between linear and nonlinear behaviors occurs in a characteristic time t_c which only depends on the magnitude of the parameter s, related to the nonlinear term. In d=2, we find indications of a similar crossover, that is, logarithmic temporal behavior of roughness in short times and power law behavior in asymptotic times

Foreign capital in a growth model

Within an endogenous growth framework, this paper empirically investigates the impact of financial capital on economic growth for a panel of 60 developing countries, through the channel of domestic capital formation. By estimating the model for different income groups, it is found that while private FDI flows exert beneficial complementarity effects on the domestic capital formation across all income-group countries, the official financial flows contribute to increasing investment in the middle income economies, but not in the low income countries. The latter appears to demonstrate that the aid-growth nexus is supported in the middle income countries, whereas the misallocation of official inflows is more likely to exist in the low income countries, suggesting that aid effectiveness remains conditional on the domestic policy environment

A Growth model for DNA evolution

A simple growth model for DNA evolution is introduced which is analytically solvable and reproduces the observed statistical behavior of real sequences.Comment: To be published in Europhysics Letter