Application of vernier thinning techniques to segmented annular arrays

Due to the aperture periodicity, the inter-element spacing of two-dimensional squared arrays is maintained near lambda/2 in order to avoid grating lobes. This condition gives rise to severe problems derived from the huge number of array elements and from their little size that causes the signal to noise ratio to bring down. Vernier techniques have been proposed to lower the number of active elements, but the drastic reduction of the ultrasonic energy is still a great problem for the image contrast. In this work, vernier techniques for segmented annular (SA) arrays are theoretically studied. SA arrays produce lower grating lobes than squared arrays and, therefore, allow the element size to be increased beyond the lambda/2 constraint. Using larger elements, SA arrays have advantage to squared arrays because they have larger active area and smaller thinning order for the same complexity (number of channels) of the image system. Theoretical results of the vernier techniques applied to SA arrays in both radial and tangential directions are presented and compared with the equivalent squared array.     

Transient stationary waves and angular momentum

We report new transient stationary spherical waves generated by the time evolution of wave functions with angular momentum. In the study the 3D problem of the sudden release of a particle which initially was inside a spherical trap, the exact solution for the particle's time evolution is described by expected traveling incoming and outgoing spherical waves. However, unexpected transient stationary spherical waves are also present. The traveling waves have amplitudes describing diffraction in time, in a way similar to the optical diffraction by a single slit. In striking contrast with the similar 1D problem, the angular momentum generates unexpected transient stationary spherical waves which have their main contribution at points inside the sphere but only for very short times.     

Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

A modified Newton-Jarratt’s composition

A reduced composition technique has been used on Newton and Jarratt’s methods in order to obtain an optimal relation between convergence order, functional evaluations and number of operations. Following this aim, a family of methods is obtained whose efficiency indices are proved to be better for systems of nonlinear equations.     

Analytical perfect fluid perturbation for the matter dominated epoch

We present the analytical solution to the linear evolution equation of a one component Friedmann perturbation using an equation of state of the form p = (1/3)μσ²(t), where μ is the mass density and σ(t) is the root mean square (rms) velocity in the matter dominated epoch. It is assumed that this rms velocity depends only on the time coordinate and decreases as 1/a, a being the expansion factor of the Friedmann background. The evolution equations are written for scales below the horizon using the longitudinal gauge. The general solution, in the coordinate space, of the evolution equation for the scalar mode is obtained. In the case of spherical symmetry, this solution is expressed in terms of unidimensional integrals of the initial conditions: the initial values of the Newtonian potential and its first time derivative. This perfect fluid solution is a good approximation to the evolution of warm dark matter perturbations obtained by solving the Vlasov’s equation for collisionless particles.     

Some electronic correlation effects in the topological analysis of the Laplacian of the electronic charge density in C-n-butonium cations

In this work, we present a topological study of the Laplacian of the electronic density using a 6-311++G basis set, at Hartree-Fock (HF) and second-order M?ller-Plesset (MP2) (full-electron and frozen-core) levels of theory, for the carbocations 2-C-n-butonium generated upon the insertion of a proton into the secondary C-C bond during the protonation of n-butane. The charge concentration, CC, critical points of the Laplacian distribution at each valence shell, VS, of carbon atoms, and the charge concentration closer to hydrogen atoms are studied. Also, the bonding critical points of the electronic density are analyzed. We analyze some effects that Coulomb correlation has on topological features of the electronic distribution. It is shown that they are mainly reflected in a decreasing of the charge concentrations at the VS and in a contraction of the VS to the nuclei. They are more pronounced over C-C bonds than in C-H bonds. The sensitivity of some parameters derived from this topological analysis to the correlation effect of core electrons and subtle effects related to hyperconjugative interactions are shown. Some consequences of different schemes (double and triple split-valence basis set with diffuse and polarization functions) in the definition of subtle VS charge concentrations at 3c-2e bond paths are presented. It is also demonstrated here how the facts that allow us to understand the MP2 stability order found in the carbocationic species 2-C-n-butonium > 1-C-n-butonium > 2-H-n-butonium > 1-H-n-butonium are similarly depicted at correlated and uncorrelated levels of calculation.     

Imaging the Magnetic Reversal of Isolated and Organized Molecular‐Based Nanoparticles using Magnetic Force Microscopy

In the race towards miniaturization in nanoelectronics, magnetic nanoparticles (MNPs) have emerged as potential candidates for their integration in ultrahigh‐density recording media. Molecular‐based materials open the possibility to design new tailor‐made MNPs with variable composition and sizes, which benefit from the intrinsic properties of these materials. Before their implementation in real devices is reached, a precise organization on surfaces and a reliable characterization and manipulation of their individual magnetic behavior are required. In this paper, it is demonstrated how molecular‐based MNPs are accurately organized on surfaces and how the magnetic properties of the individual MNPs are detected and tuned by means of low‐temperature magnetic force microscopy (LT‐MFM) with variable magnetic field. The magnetization reversal on isolated and organized MNPs is investigated; in addition, the temperature dependence of their magnetic response is evaluated.     

Structure relations for monic orthogonal polynomials in two discrete variables

In this paper, extensions of several relations linking differences of bivariate discrete orthogonal polynomials and polynomials themselves are given, by using an appropriate vector–matrix notation. Three-term recurrence relations are presented for the partial differences of the monic polynomial solutions of admissible second order partial difference equation of hypergeometric type. Structure relations, difference representations as well as lowering and raising operators are obtained. Finally, expressions for all matrix coefficients appearing in these finite-type relations are explicitly presented for a finite set of Hahn and Kravchuk orthogonal polynomials.