Nonexistence of solutions for singular quasilinear differential inequalities with a gradient nonlinearity

This paper is devoted to prove some new nonexistence theorems for the singular quasilinear differential inequalities with a gradient nonlinearity in bounded and unbounded domains. The proofs are based on the test function method developed by Mitidieri and Pohozaev.     

Stein’s method for invariant measures of diffusions via Malliavin calculus

Given a random variable F$F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and any probability measure with a density function which is continuous, bounded, strictly positive on an interval in the real line and admits finite variance. The bounds are given in terms of the Malliavin derivative of F$F$. Our approach is based on the theory of Itô diffusions and the stochastic calculus of variations. Several examples are considered in order to illustrate our general results.     

Decomposability for stable processes

We characterize all possible independent symmetric α-stable (SαS) components of an SαS process, 0<α<2. In particular, we focus on stationary SαS processes and their independent stationary SαS components. We also develop a parallel characterization theory for max-stable processes.     

Meixner polynomials in several variables satisfying bispectral difference equations

We construct a set _Md${\mathfrak{M}}_d$ whose points parametrize families of Meixner polynomials in d   variables. There is a natural bispectral involution b$\mathfrak{b}$ on _Md${\mathfrak{M}}_d$ which corresponds to a symmetry between the variables and the degree indices of the polynomials. We define two sets of d   commuting partial difference operators diagonalized by the polynomials. One of the sets consists of difference operators acting on the variables of the polynomials and the other one on their degree indices, thus proving their bispectrality. The two sets of partial difference operators are naturally connected via the involution b$\mathfrak{b}$.     

Magnetic properties of FeSiB thin films displaying stripe domains

FeSiB amorphous thin films with thicknesses from 25 to 600 nm have been produced by rf sputtering on Si₃N₄ substrates. A spin reorientation transition has been observed on the as-prepared samples, as a function of thickness and temperature. Spin reorientation transition is shown to depend on the thermal treatments to which the as-prepared samples have been submitted. Static hysteresis loops obtained as a function of temperature, and magnetic force microscopy images taken at room temperature at the remanence and as a function of an applied magnetic field, have been employed to study the magnetic domain configuration of all the samples, and to see how it is affected by sample thickness, measurement temperature and annealing conditions.     

Fe monolayers on InAs(0 0 1): An in situ study of surface, interface and volume magnetic anisotropy

The magnetic anisotropy of epitaxial Fe films with thicknesses in the range of 2-142 monolayers (ML) grown on {4×2} reconstructed InAs(0 0 1) was investigated by in situ ferromagnetic resonance. The easy magnetization direction was found to be parallel to the -direction for Fe films below 4 ML, while it rotates by 45^° toward the -direction. It is observed that both surface-interface and volume contribution to the perpendicular anisotropy favor an easy axis perpendicular to the film plane. The cubic surface-interface anisotropy is relatively large with easy axes along -directions in contrast to the volume contribution which favors easy axes along the -directions. The volume contribution is found to be larger than the Fe bulk cubic anisotropy. A thickness independent uniaxial anisotropy has been found in films with a thickness of 2 up to 142 ML.     

Memory and aging effects in interacting sub-10 nm nanomagnets with large uniaxial anisotropy

Using a nonequilibrium Monte Carlo method suitable to nanomagnetism, we investigate representative systems of interacting sub-10 nm grained nanomagnets with large uniaxial anisotropy. Various magnetization memory and aging effects are found in such systems. We explain these dynamical effects using the distributed relaxation times of the interacting nanomagnets due to their large anisotropy energies.     

Invasion percolation between two sites in two, three, and four dimensions

The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and an extraction site has been studied, in two, three, and four dimensions. This study is an extension of the recent study focused on two dimensions by Araújo et al. [A.D. Araújo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 041404] with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m)∝m^−α. It has been found that the index α for p_e<p_c, p_c being the percolation threshold of a regular percolation, appears to be independent of the value of p_e and is also independent of the lattice dimensionality. When p_e=p_c, α appears to depend marginally on the lattice dimensionality, and the relation α=τ−1, τ being the exponent associated with cluster size distribution of a regular percolation via n_s∝s^−τ, appears to be valid.