Analytic families of semigroups

The Cauchy Problem for linear partial differential equations with coefficients depending analytically on a parameter, motivates the study of analytic families of infinitesimal generators of semigroups. The relations between the three natural ways to understand “analyticity” of the family are clarified. This is then applied to obtain some general results on the stability of the analyticity of the family under perturbations of the generators.     

Transition from the ballistic to the diffusive regime in a turbid medium

By varying the absorption coefficient and width of an intralipid-India ink solution in a quasi-one-dimensional experiment, we investigate the transition between the ballistic and the diffusive regimes. The medium's attenuation coefficient changes abruptly between two different values within a single mean free path. This problem is analyzed both experimentally and theoretically, and it is demonstrated that the transition location depends on the scattering coefficient as well as on the measuring solid angle.     

Stabilizing stick-slip friction

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes. Such manipulation of collective modes may be generally relevant to extended nonlinear systems driven near to criticality.     

Long-Term Changes in a Heat Exchanger Steel

The steel ASTM A213 P22 is used for superheater outlet header in power plants. During duty cycles lasting over tens of years the temperature is of the order of 545°C and the pressure 125 atm. The microscopic changes in these steels are hard to analyze under working conditions, but they are believed to be responsible for the appearance of creeps in such devices. Investigation of the microscopic modifications will help to predict future failures due to creeps, increasing the reliability and saving a lot of money.We report the investigation of such changes in ASTM A213 P22 steel in use for 30 years as a Superheater header at Haifa power station. The analysis has been carried out using Mössbauer Spectroscopy, X-ray diffraction and optical microscopy. As a result it seems that the morphology and phase change of the carbide phases M₃C/M₇C₃ and M₂₃C₆ are the most prominent changes leading to the material failures.     

Stable quantum resonances in atom optics

A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold cesium atoms when driven in the presence of gravity, and leads to further predictions. The theory makes use of invariance properties of the system allowing for separation into independent kicked rotor problems. The analysis relies on a fictitious classical limit where the small parameter is not Planck's constant, but rather the detuning from the frequency that is resonant in the absence of gravity.     

Brain MRI lesion load quantification in multiple sclerosis: a comparison between automated multispectral and semi-automated thresholding computer-assisted techniques

Brain magnetic resonance imaging (MRI) lesion volume measurement is an advantageous tool for assessing disease burden in multiple sclerosis (MS). We have evaluated two computer-assisted techniques: MSA multispectral automatic technique that is based on bayesian classification of brain tissue and NIH image analysis technique that is based on local (lesion by lesion) thresholding, to establish reliability and repeatability values for each technique. Brain MRIs were obtained for 30 clinically definite relapsing-remitting MS patients using a 2.0 Tesla MR scanner with contiguous, 3 mm thick axial, T1, T2 and PD weighted modalities. Digital (Dicom 3) images were analyzed independently by three observers; each analyzed the images twice, using the two different techniques (Total 360 analyses). Accuracy of lesion load measurements using phantom images of known volumes showed significantly better results for the MSA multispectral technique (p < 0.001). The mean intra-and inter-observer variances were, respectively, 0.04 ± 0.4 (range 0.04–0.13), and 0.09 ± 0.6 (range 0.01–0.26) for the multispectral MSA analysis technique, 0.24 ± 2.27 (range 0.23–0.72) and 0.33 ± 3.8 (range 0.47–1.36) for the NIH threshold technique. These data show that the MSA multispectral technique is significantly more accurate in lesion volume measurements, with better results of within and between observers’ assessments, and the lesion load measurements are not influenced by increased disease burden. Measurements by the MSA multispectral technique were also faster and decreased analysis time by 43%. The MSA multispectral technique is a promising tool for evaluating MS patients. Non-biased recognition and delineation algorithms enable high accuracy, low intra-and inter-observer variances and fast assessment of MS related lesion load.     

Control of multiple filamentation in air

In this Letter we provide what is believed to be the first experimental evidence of suppression of the number of filaments for high-intensity laser pulses propagating in air by beam astigmatism. We also show that the number, pattern, and spatial stability of the filaments can be controlled by varying the angle that a focusing lens makes with the axial direction of propagation. This new methodology can be useful for applications involving atmospheric propagation, such as remote sensing.