Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Semiclassical scaling functions of sine-Gordon model

We present an analytic study of the finite size effects in sine-Gordon model, based on the semi-classical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi-periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the sine-Gordon model on the cylinder. (C) 2004 Elsevier B.V. All rights reserved.

Dynamical scaling properties of nanoporous undoped and Sb-doped SnO2 supported thin films during tri- and bidimensional structure coarsening

The coarsening of the nanoporous structure developed in undoped and 3% Sb-doped SnO2 sol-gel dip-coated films deposited on a mica substrate was studied by time-resolved small-angle x-ray scattering (SAXS) during in situ isothermal treatments at 450 and 650 degrees C. The time dependence of the structure function derived from the experimental SAXS data is in reasonable agreement with the predictions of the statistical theory of dynamical scaling, thus suggesting that the coarsening process in the studied nanoporous structures exhibits dynamical self-similar properties. The kinetic exponents of the power time dependence of the characteristic scaling length of undoped SnO2 and 3% Sb-doped SnO2 films are similar (alpha approximate to 0.09), this value being invariant with respect to the firing temperature. In the case of undoped SnO2 films, another kinetic exponent, alpha('), corresponding to the maximum of the structure function was determined to be approximately equal to three times the value of the exponent alpha, as expected for the random tridimensional coarsening process in the dynamical scaling regime. Instead, for 3% Sb-doped SnO2 films fired at 650 degrees C, we have determined that alpha(')approximate to 2 alpha, thus suggesting a bidimensional coarsening of the porous structure. The analyses of the dynamical scaling functions and their asymptotic behavior at high q (q being the modulus of the scattering vector) provided additional evidence for the two-dimensional features of the pore structure of 3% Sb-doped SnO2 films. The presented experimental results support the hypotheses of the validity of the dynamic scaling concept to describe the coarsening process in anisotropic nanoporous systems.

Scaling properties of the fermi-ulam accelerator model

The chaotic low energy region (chaotic sea) of the Fermi-Ulam accelerator model is discussed within a scaling framework near the integrable to non-integrable transition. Scaling results for the average quantities (velocity, roughness, energy etc.) of the simplified version of the model are reviewed and it is shown that, for small oscillation amplitude of the moving wall, they can be described by scaling functions with the same characteristic exponents. New numerical results for the complete model are presented. The chaotic sea is also characterized by its Lyapunov exponents.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

NLO QCD Corrections to the Polarized Photo- and Hadroproduction of Heavy Quarks

The complete details of our calculation of the NLO QCD corrections to heavy flavor photo- and hadroproduction with longitudinally polarized initial states are presented. The main motivation for investigating these processes is the determination of the polarized gluon density at the COMPASS and RHIC experiments, respectively, in the near future. All methods used in the computation are extensively documented, providing a self-contained introduction to this type of calculations. Some employed tools also may be of general interest, e.g., the series expansion of hypergeometric functions. The relevant parton level results are collected and plotted in the form of scaling functions. However, the simplification of the obtained gluon-gluon virtual contributions has not been completed yet. Thus NLO phenomenological predictions are only given in the case of photoproduction. The theoretical uncertainties of these predictions, in particular with respect to the heavy quark mass, are carefully considered. Also it is shown that transverse momentum cuts can considerably enhance the measured production asymmetries. Finally unpolarized heavy quark production is reviewed in order to derive conditions for a successful interpretation of future spin-dependent experimental data.

Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Structure of exotic three-body systems

The classification of large halos formed by two identical particles and a core is systematically addressed according to interparticle distances. The root-mean-square distances between the constituents are described by universal scaling functions obtained from a renormalized zero-range model. Applications for halo nuclei, Li-11 and Be-14, and for atomicn He-4(3) are briefly discussed. The generalization to four-body systems is proposed.

Borromean three-body heteroatomic resonances

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Range Corrections to Universal Tetramer Properties

The universal properties of weakly-bound tetramers close to the scaling limit are investigated by solving a subtracted set of Faddeev-Yakubovsky (FY) equations for identical bosons with a zero-range interaction. The solution demands a four-body scale independent of the trimer properties. Furthermore, the effect of a finite effective range is introduced in the FY equations, which we show produces results that are distinct from the scale variation. In particular range effects to two universal scaling functions for the tetramers are investigated. The correlation between successive tetramer energies corresponding to states within two Efimov trimer energies, proposed before and studied close to the unitary limit; and the correlation between the position of the four-atom recombination peaks. In this case, we found a shift in the scaling function due to the range, which can be associated to the shift of the data found for caesium atoms, with respect to zero-range calculations, due to a nonvanishing range in the actual experimental setups. © 2013 Springer-Verlag Wien.

Universalidade em sistemas de 3 e 4 bósons

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Expoentes de escala para mapeamentos discretos bidimensionais

Pós-graduação em Física - IGCE

Mesoscale dynamics and boundary-layer structure in topographically forced low-level jets

Two types of mesoscale wind-speed jet and their effects on boundary-layer structure were studied. The first is a coastal jet off the northern California coast, and the second is a katabatic jet over Vatnajökull, Iceland. Coastal regions are highly populated, and studies of coastal meteorology are of general interest for environmental protection, fishing industry, and for air and sea transportation. Not so many people live in direct contact with glaciers but properties of katabatic flows are important for understanding glacier response to climatic changes. Hence, the two jets can potentially influence a vast number of people. Flow response to terrain forcing, transient behavior in time and space, and adherence to simplified theoretical models were examined. The turbulence structure in these stably stratified boundary layers was also investigated. Numerical modeling is the main tool in this thesis; observations are used primarily to ensure a realistic model behavior. Simple shallow-water theory provides a useful framework for analyzing high-velocity flows along mountainous coastlines, but for an unexpected reason. Waves are trapped in the inversion by the curvature of the wind-speed profile, rather than by an infinite stability in the inversion separating two neutral layers, as assumed in the theory. In the absence of blocking terrain, observations of steady-state supercritical flows are not likely, due to the diurnal variation of flow criticality. In many simplified models, non-local processes are neglected. In the flows studied here, we showed that this is not always a valid approximation. Discrepancies between simulated katabatic flow and that predicted by an analytical model are hypothesized to be due to non-local effects, such as surface inhomogeneity and slope geometry, neglected in the theory. On a different scale, a reason for variations in the shape of local similarity scaling functions between studies is suggested to be differences in non-local contributions to the velocity variance budgets.