Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Finite-volume form factors in semi-classical approximation

A semi-classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken phi(4) theories in 1 + 1 dimensions. (C) 2003 Elsevier B.V. All rights reserved.

A dynamical gluon mass solution in Mandelstam's approximation

We discuss the pure gauge Schwinger-Dyson equation for the gluon propagator in the Landau gauge within an approximation proposed by Mandelstam many years ago. We show that a dynamical gluon mass arises as a solution. This solution is obtained numerically in the full range of momenta that we have considered without the introduction of any ansatz or asymptotic expression in the infrared region. The vertex function that we use follows a prescription formulated by Cornwall to determine the existence of a dynamical gluon mass in the light cone gauge. The renormalization procedure differs from the one proposed by Mandelstam and allows for the possibility of a dynamical gluon mass. Some of the properties of this solution, such as its dependence on A(QCD) and its perturbative scaling behavior are also discussed.

Ps-He scattering using the three-state positronium close-coupling approximation

A three-state target elastic positronium close-coupling approximation (CCA) is employed to investigate Ps-He scattering in the energy range 0-200 eV with and without electron exchange. Low-lying phase shifts below the first excitation threshold and the total integrated cross sections using both the models are reported. Estimation of integrated excitation cross sections for Ps(1s --> 2s) and Ps(1s --> 2p) using CCA are presented for the first time. The present total cross sections are in good agreement with the measured data in the incident Ps energy range 20-30 eV.

Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Anomalous diffusion of pions at RHIC

After pointing out the difference between normal and anomalous diffusion, we consider a hadron resonance cascade (HRC) model simulation for particle emission at RHIC and point out that rescattering in an expanding hadron resonance gas leads to a heavy tail in the source distribution. The results are compared to recent PHENIX measurements of the tail of the particle emitting source in Au+Au collisions at RHIC. In this context, we show how can one distinguish experimentally the anomalous diffusion of hadrons from a second order QCD phase transition.

Blocking Radial Diffusion in a Double-Waved Hamiltonian Model

A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.

Diffusion and interface controlled reactions in alpha-(Cu-Al-Ag) alloys

The isothermal kinetics of Ag precipitation was studied in Cu-Al-Ag alloys with concentrations ranging from 2 to 8 wt.%Al and 2 to 12 wt.%Ag, using scanning electron microscopy (SEM), X-ray energy dispersive spectroscopy (EDX) and microhardness measurements. The results indicated a change in the precipitates growing mechanism from diffusion to interface controlled process, probably due to a change in the nature of the interface with the Ag and Al enrichment of the precipitates. (C) 2006 Elsevier B.V. All rights reserved.

NONLINEAR DIFFUSION PROCESS IN A BENARD SYSTEM AT THE CRITICAL-POINT FOR THE ONSET OF CONVECTION

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts.

ON NUCLEON-NUCLEUS SCATTERING AND THE RELATIVISTIC EIKONAL APPROXIMATION

We introduce a generalization of the relativistic eikonal amplitude originally developed to describe elastic scattering between structureless particles. The coherent and incoherent proton-nucleus scattering processes are analysed and closed-form expressions for elastic and inelastic amplitudes are derived. In particular, for the incoherent case, an energy-conserving version of Glauber's theory is obtained.

Positronium-alkali-ion scattering in the close-coupling approximation

We present results for low- and medium-energy elastic and capture cross sections for positronium-atom-alkali-ion scattering using the coupled static close-coupling approximation.

Diffusion coefficients during osmotic dehydration of tomatoes in ternary solutions

The apparent diffusion coefficients for sucrose, NaCl and water during osmotic dehydration of tomatoes in ternary solutions were determined. Long time experiments (up to 60 h) were carried out in order to determine equilibrium concentrations inside tomatoes, whereas short time experiments (up to 4 h) were performed to provide detailed information on kinetics of water loss and solids gain at the beginning of osmotic treatment. The mass transfer rates for water and solutes showed to be dependent of NaCl and sucrose concentrations in osmotic solution and simple regression models as functions of solutes concentration were determined for diffusion coefficients. Salt and sucrose diffusivities showed to be interdependent, with increasing NaCl concentration causing the enhancement of water loss, at the same time that higher sucrose contents hindered the excessive salt penetration. (C) 2003 Elsevier Ltd. All rights reserved.

UNITARY POLE APPROXIMATION FOR THE COULOMB-PLUS-YAMAGUCHI POTENTIAL AND APPLICATION TO A 3-BODY BOUND-STATE CALCULATION

The unitary pole approximation is used to construct a separable representation for a potential U which consists of a Coulomb repulsion plus an attractive potential of the Yamaguchi type. The exact bound-state wave function is employed. U is chosen as the potential which binds the proton in the 1d5/2 single-particle orbit in F-17. Using the separable representation derived for U, and assuming a separable Yamaguchi potential to describe the 1d5/2 neutron in O-17, the energies and wave functions of the ground state (1+) and the lowest 0+ state of F-18 are calculated in the Gore-plus-two-nucleons model solving the Faddeev equations.

Diffusion coefficient of K+ in ion exchanged glasses calculated from the refractive index and the Vickers hardness profiles

The top faces of float glass samples were exposed to vapors resulting from the decomposition of KNO3 at 565 degrees C for up to 32 h. X-ray dispersive spectra (EDS) show that K+ ions migrate into the glass. The K+ concentration profile was obtained and its diffusion coefficient was calculated by the Boltzmann-Matano technique. The mean diffusion coefficient was approximately 10 X 10(-11) cm(2) s(-1). It was observed that the refractive index and the Vickers hardness decrease with the depth (after the removal of successive layers), and their profiles were thus obtained. These profiles enabled the calculation of the diffusion coefficient of K+ through the Boltzmann-Matano technique, with mean results ranging between 6 x 10(-11) and 30 x 10(-11) cm(2) s(-1). (c) 2006 Elsevier B.V. All rights reserved.