Fracture and contact problems for an elastic wedge

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure

Regularized reconstruction in quantitative SPECT using CT side information from hybrid imaging

A penalized-likelihood (PL) SPECT reconstruction method using a modified regularizer that accounts for anatomical boundary side information was implemented to achieve accurate estimates of both the total target activity and the activity distribution within targets. In both simulations and experimental I-131 phantom studies, reconstructions from (1) penalized likelihood employing CT-side information-based regularization (PL-CT), (2) penalized likelihood with edge preserving regularization (no CT) and (3) penalized likelihood with conventional spatially invariant quadratic regularization (no CT) were compared with (4) ordered subset expectation maximization (OSEM), which is the iterative algorithm conventionally used in clinics for quantitative SPECT. Evaluations included phantom studies with perfect and imperfect side information and studies with uniform and non-uniform activity distributions in the target. For targets with uniform activity, the PL-CT images and profiles were closest to the 'truth', avoided the edge offshoots evident with OSEM and minimized the blurring across boundaries evident with regularization without CT information. Apart from visual comparison, reconstruction accuracy was evaluated using the bias and standard deviation (STD) of the total target activity estimate and the root mean square error (RMSE) of the activity distribution within the target. PL-CT reconstruction reduced both bias and RMSE compared with regularization without side information. When compared with unregularized OSEM, PL-CT reduced RMSE and STD while bias was comparable. For targets with non-uniform activity, these improvements with PL-CT were observed only when the change in activity was matched by a change in the anatomical image and the corresponding inner boundary was also used to control the regularization. In summary, the present work demonstrates the potential of using CT side information to obtain improved estimates of the activity distribution in targets without sacrificing the accuracy of total target activity estimation. The method is best suited for data acquired on hybrid systems where SPECT-CT misregistration is minimized. To demonstrate clinical application, the PL reconstruction with CT-based regularization was applied to data from a patient who underwent SPECT/CT imaging for tumor dosimetry following I-131 radioimmunotherapy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85409/1/pmb10_9_007.pd

Texturing of titanium (Ti6Al4V) medical implant surfaces with MHz-repetition-rate femtosecond and picosecond Yb-doped fiber lasers

Cataloged from PDF version of article.We propose and demonstrate the use of short pulsed fiber lasers in surface texturing using MHz-repetition-rate, microjoule- and sub-microjoule-energy pulses. Texturing of titanium-based (Ti6Al4V) dental implant surfaces is achieved using femtosecond, picosecond and (for comparison) nanosecond pulses with the aim of controlling attachment of human cells onto the surface. Femtosecond and picosecond pulses yield similar results in the creation of micron-scale textures with greatly reduced or no thermal heat effects, whereas nanosecond pulses result in strong thermal effects. Various surface textures are created with excellent uniformity and repeatability on a desired portion of the surface. The effects of the surface texturing on the attachment and proliferation of cells are characterized under cell culture conditions. Our data indicate that picosecond-pulsed laser modification can be utilized effectively in low-cost laser surface engineering of medical implants, where different areas on the surface can be made cell-attachment friendly or hostile through the use of different patterns. (C) 2011 Optical Society of Americ

The GREGOR Fabry-P\'erot Interferometer

The GREGOR Fabry-P\'erot Interferometer (GFPI) is one of three first-light instruments of the German 1.5-meter GREGOR solar telescope at the Observatorio del Teide, Tenerife, Spain. The GFPI uses two tunable etalons in collimated mounting. Thanks to its large-format, high-cadence CCD detectors with sophisticated computer hard- and software it is capable of scanning spectral lines with a cadence that is sufficient to capture the dynamic evolution of the solar atmosphere. The field-of-view (FOV) of 50" x 38" is well suited for quiet Sun and sunspot observations. However, in the vector spectropolarimetric mode the FOV reduces to 25" x 38". The spectral coverage in the spectroscopic mode extends from 530-860 nm with a theoretical spectral resolution R of about 250,000, whereas in the vector spectropolarimetric mode the wavelength range is at present limited to 580-660 nm. The combination of fast narrow-band imaging and post-factum image restoration has the potential for discovery science concerning the dynamic Sun and its magnetic field at spatial scales down to about 50 km on the solar surface.Comment: 14 pages, 17 figures, 4 tables; pre-print of AN 333, p.880-893, 2012 (AN special issue to GREGOR

Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams

We theoretically investigate the use of red-detuned Laguerre-Gaussian (LG) laser beams of varying azimuthal mode index for producing toroidal optical dipole traps in two-dimensional atomic Bose-Einstein condensates. Higher-order LG beams provide deeper potential wells and tighter confinement for a fixed toroid radius and laser power. Numerical simulations of the loading of the toroidal trap from a variety of initial conditions is also given.Comment: 12 pages, 5 figures, submitted to Phys. Rev.

A system of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify a system of ODEs similar to those from Comech and Pelinovsky (2003), which model the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, which is in accord with the conclusions of Pelinovsky, Afanasjev, and Kivshar (1996). For initial data which supports a soliton structure, a generic initial perturbation oscillates around the stable family of solitons. For initial data which is expected to disperse, the finite dimensional dynamics follow the unstable portion of the soliton curve.Comment: Minor edit

Spontaneous emission in a planar Fabry-Perot microcavity

Published versio

Localization of electromagnetic waves in a two dimensional random medium

Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many randomly distributed two dimensional dipoles. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for the total electromagnetic field. The results show that spatially localized electromagnetic waves are possible in such a simple but realistic disordered system. When localization occurs, a coherent behavior appears and is revealed as a unique property differentiating localization from either the residual absorption or the attenuation effects

A repertoire of biomedical applications of noble metal nanoparticles

Noble metals comprise any of several metallic chemical elements that are outstandingly resistant to corrosion and oxidation, even at elevated temperatures. This group is not strictly defined, but the tentative list includes ruthenium, rhodium, palladium, silver, osmium, iridium, platinum and gold, in order of atomic number. The emerging properties of noble metal nanoparticles are attracting huge interest from the translational scientific community and have led to an unprecedented expansion of research and exploration of applications in biotechnology and biomedicine. Noble metal nanomaterials can be synthesised both by top-down and bottom up approaches, as well as via organism-assisted routes, and subsequently modified appropriately for the field of use. Nanoscale analogues of gold, silver, platinum, and palladium in particular, have gained primary importance owing to their excellent intrinsic properties and diversity of applications; they offer unique functional attributes, which are quite unlike the bulk material. Modulation of noble metal nanoparticles in terms of size, shape and surface functionalisation has endowed them with unusual capabilities and manipulation at the chemical level, which can lead to changes in their electrical, chemical, optical, spectral and other intrinsic properties. Such flexibility in multi-functionalisation delivers ‘Ockham's razor’ to applied biomedical science. In this feature article, we highlight recent advances in the adaptation of noble metal nanomaterials and their biomedical applications in therapeutics, diagnostics and sensing

Growth of Sobolev norms and controllability of Schr\"odinger equation

In this paper we obtain a stabilization result for the Schr\"odinger equation under generic assumptions on the potential. Then we consider the Schr\"odinger equation with a potential which has a random time-dependent amplitude. We show that if the distribution of the amplitude is sufficiently non-degenerate, then any trajectory of system is almost surely non-bounded in Sobolev spaces