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Biomedical subjects

S Ciccariello

Publications and source records attributed to S Ciccariello.

6 recordsLinked to original sources
PubMed2005

The algebraic approach to the phase problem.

A rather detailed report is presented on the present status of the algebraic approach to the phase problem in the case of an ideal crystal in order to make clear that some points must still be proven for it to apply to neutron scattering. To make this extension, the most important results that were previously obtained in the case of X-ray scattering are derived again by a different procedure. By so doing, the three-dimensional case is treated explicitly, the polynomial equations in a single variable whose roots determine the positions of the scattering centres are explicitly reported and the procedure is shown to generalize to neutron scattering, overcoming the difficulty related to the non-positivity of the scattering density. In this way, it is fully proven that the atomicity assumption removes the phase ambiguity in the sense that the full diffraction pattern of an ideal crystal can uniquely be reconstructed from a suitable finite portion of it in both X-ray and neutron scattering. The procedures able to isolate these portions that contain the pattern's full information are also given.

Algorithms↗
PubMed2003

On the autocorrelation functions of right cylindrical particles.

The autocorrelation function of a finite particle with the shape of a right cylinder is determined by the autocorrelation function of the particle right section, whatever the latter's shape, and by the cylinder height. In fact, the first function is an integral transform of the second with a simple kernel depending on the cylinder height. This integral relation is solved to determine the autocorrelation function of the particle section in terms of the autocorrelation function of the full particle.

Journal Article↗
PubMed2002

The asymptotic leading term of anisotropic small-angle scattering intensities. II. Non-convex particles.

For anisotropic particulate samples with scattering contrast (delta n)(2), the leading asymptotic term of the scattering intensity, along a direction q (q/q) of reciprocal space, is [4 pi(2)(delta n)(2)/q(4)]sigmaj [1/kappaG.j(+/-q)]. Here, kappaG.j(+/-q)denotes the Gaussian curvature value at the points (labelled by j) of the interphase surface where the normal is either parallel or antiparallel to q. If the Gaussian curvature vanishes at, say, the jth of these points, the corresponding contribution takes the form Cj/qalpha with 2< or = alphaj<4, Cj and alphaj being determined by the local behaviour of the surface. However, the intensity detected by a counter pixel, with opening solid angle deltaomega(q0) along (mean) direction q0, asymptotically still behaves as 4pi(2) (delta n)(2)(deltaomega(q0))/q(4), where S(deltaomega(q0)) is the area of that part of the interface that has its normals inside deltaomega(q0).

Journal Article↗