Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Growth in a Cross-Section of Cities: Location, Increasing Returns or Random Growth?

This article analyzes empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we implement a threshold nonlinearity test that extends standard linear growth regression models to a dataset on urban, climatological and macroeconomic variables on 1,175 U.S. cities. Our analysis reveals the existence of increasing returns when per-capita income levels are beyond $19; 264. Despite this, income growth is mostly explained by social and locational fundamentals. Population growth also exhibits two distinct equilibria determined by a threshold value of 116,300 inhabitants beyond which city population grows at a higher rate. Income and population growth do not go hand in hand, implying an optimal level of population beyond which income growth stagnates or deteriorates

Development of the femur - Implications for age and sex determination.

Growth of four variables of the femur (diapyseal length, diaphyseal length plus distal epiphysis, maximum length and vertical diameter of the head) was analyzed by polynomial regression for the purpose of evaluating its significance and capacity for age and sex determination throughout the entire life continuum. Materials included in analysis consisted of 346 specimens ranging from birth to 97 years of age from five documented osteological collections of Western European descent. Linear growth was displayed by each of the four variables. Significant sexual dimorphism was identified in two of the femoral measurements, including maximum length and vertical diameter of the head, from age 15 onward. These results indicate that the two variables may be of use in the determination of sex in sex determination from that age onward. Strong correlation coefficients were identified between femoral size and age for each of the four metric variables. These results indicate that any of the femoral measurements is likely to serve as a useful source to estimate sub-adult age in both archaeological and forensic samples.

Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

Horizontal innovation in the theory of growth and development

We analyze recent contributions to growth theory based on the model of expanding variety of Romer (1990). In the first part, we present different versions of the benchmark linear model with imperfect competition. These include the labequipment model, labor-for-intermediates and directed technical change . We review applications of the expanding variety framework to the analysis of international technology diffusion, trade, cross-country productivity differences, financial development and fluctuations. In many such applications, a key role is played by complementarities in the process of innovation.

Growth, convergence and public investment : a bayesian model averaging approach

The aim of this paper is twofold. First, we study the determinants of economic growth among a wide set of potential variables for the Spanish provinces (NUTS3). Among others, we include various types of private, public and human capital in the group of growth factors. Also,we analyse whether Spanish provinces have converged in economic terms in recent decades. Thesecond objective is to obtain cross-section and panel data parameter estimates that are robustto model speci¯cation. For this purpose, we use a Bayesian Model Averaging (BMA) approach.Bayesian methodology constructs parameter estimates as a weighted average of linear regression estimates for every possible combination of included variables. The weight of each regression estimate is given by the posterior probability of each model.

Growth, convergence and public investment : a bayesian model averaging approach

The aim of this paper is twofold. First, we study the determinants of economic growth among a wide set of potential variables for the Spanish provinces (NUTS3). Among others, we include various types of private, public and human capital in the group of growth factors. Also,we analyse whether Spanish provinces have converged in economic terms in recent decades. Thesecond objective is to obtain cross-section and panel data parameter estimates that are robustto model speci¯cation. For this purpose, we use a Bayesian Model Averaging (BMA) approach.Bayesian methodology constructs parameter estimates as a weighted average of linear regression estimates for every possible combination of included variables. The weight of each regression estimate is given by the posterior probability of each model.

Fluctuations in domain growth: Ginzburg-Landau equations with multiplicative noise

Ginzburg-Landau equations with multiplicative noise are considered, to study the effects of fluctuations in domain growth. The equations are derived from a coarse-grained methodology and expressions for the resulting concentration-dependent diffusion coefficients are proposed. The multiplicative noise gives contributions to the Cahn-Hilliard linear-stability analysis. In particular, it introduces a delay in the domain-growth dynamics.

Numerical algorithm for Ginzburg-Landau equations with multiplicative noise: Application to domain growth

We consider stochastic partial differential equations with multiplicative noise. We derive an algorithm for the computer simulation of these equations. The algorithm is applied to study domain growth of a model with a conserved order parameter. The numerical results corroborate previous analytical predictions obtained by linear analysis.

Interfacial growth in driven diffusive systems

We have studied the growth of interfaces in driven diffusive systems well below the critical temperature by means of Monte Carlo simulations. We consider the region beyond the linear regime and of large values of the external field which has not been explored before. The simulations support the existence of interfacial traveling waves when asymmetry is introduced in the model, a result previously predicted by a linear-stability analysis. Furthermore, the generalization of the Gibbs-Thomson relation is discussed. The results provide evidence that the external field is a stabilizing effect which can be considered as effectively increasing the surface tension.

Growth of unstable interfaces in disordered media

The effects of a disordered medium in the growth of unstable interfaces are studied by means of two local models with multiplicative and additive quenched disorder, respectively. For short times and large pushing the multiplicative quenched disorder is equivalent to a time-dependent noise. In this regime, the linear dispersion relation contains a destabilizing contribution introduced by the noise. For long times, the interface always gets pinned. We model the systematics of the pinned shapes by means of an effective nonlinear model. These results show good agreement with numerical simulations. For the additive noise we find numerically that a depinning transition occurs.

Quasi real-time Raman studies on the growth of Cu-In-S thin films

In this work annealing and growth of CuInS2 thin films is investigated with quasireal-time in situ Raman spectroscopy. During the annealing a shift of the Raman A1 mode towards lower wave numbers with increasing temperature is observed. A linear temperature dependence of the phonon branch of ¿2 cm¿1/100 K is evaluated. The investigation of the growth process (sulfurization of metallic precursors) with high surface sensitivity reveals the occurrence of phases which are not detected with bulk sensitive methods. This allows a detailed insight in the formation of the CuInS2 phases. Independent from stoichiometry and doping of the starting precursors the CuAu ordering of CuInS2 initially forms as the dominating ordering. The transformation of the CuAu ordering into the chalcopyrite one is, in contrast, strongly dependent on the precursor composition and requires high temperatures.

Langevin equations with multiplicative noise: Application to domain growth

Langevin Equations of Ginzburg-Landau form, with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hiliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical predictions of the linear analysis. We also present simulation results for spinodal decomposition at large times.

Differential growth responses to water balance of coexisting deciduous tree species are linked to wood density in a Bolivian tropical dry forest

A seasonal period of water deficit characterizes tropical dry forests (TDFs). There, sympatric tree species exhibit a diversity of growth rates, functional traits, and responses to drought, suggesting that each species may possess different strategies to grow under different conditions of water availability. The evaluation of the long-term growth responses to changes in the soil water balance should provide an understanding of how and when coexisting tree species respond to water deficit in TDFs. Furthermore, such differential growth responses may be linked to functional traits related to water storage and conductance. We used dendrochronology and climate data to retrospectively assess how the radial growth of seven coexisting deciduous tree species responded to the seasonal soil water balance in a Bolivian TDF. Linear mixed-effects models were used to quantify the relationships between basal area increment and seasonal water balance. We related these relationships with wood density and sapwood production to assess if they affect the growth responses to climate. The growth of all species responded positively to water balance during the wet season, but such responses differed among species as a function of their wood density. For instance, species with a strong growth response to water availability averaged a low wood density which may facilitate the storage of water in the stem. By contrast, species with very dense wood were those whose growth was less sensitive to water availability. Coexisting tree species thus show differential growth responses to changes in soil water balance during the wet season. Our findings also provide a link between wood density, a trait related to the ability of trees to store water in the stem, and wood formation in response to water availability.