Notes on drift theory

It is shown that there is a simpler way to derive the average guiding center drift of a distribution of particles than via the so-called single particle analysis. Based on this derivation it is shown that the entire drift formalism can be considerably simplified, and that results for low order anisotropies are more generally valid than is usually appreciated. This drift analysis leads to a natural alternative derivation of the drift velocity along a neutral sheet

Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition

This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, $L^1$ data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of $L^1$-based multi-scale methods with nonlinear spectral decompositions. We compare $L^1$ with $L^2$ scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of $L^1-TV$ promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.Comment: 13 pages, 7 figures, conference SSVM 201

PET attenuation coefficients from CT images: experimental evaluation of the transformation of CT into PET 511-keV attenuation coefficients

The CT data acquired in combined PET/CT studies provide a fast and essentially noiseless source for the correction of photon attenuation in PET emission data. To this end, the CT values relating to attenuation of photons in the range of 40-140keV must be transformed into linear attenuation coefficients at the PET energy of 511keV. As attenuation depends on photon energy and the absorbing material, an accurate theoretical relation cannot be devised. The transformation implemented in the Discovery LS PET/CT scanner (GE Medical Systems, Milwaukee, Wis.) uses a bilinear function based on the attenuation of water and cortical bone at the CT and PET energies. The purpose of this study was to compare this transformation with experimental CT values and corresponding PET attenuation coefficients. In 14 patients, quantitative PET attenuation maps were calculated from germanium-68 transmission scans, and resolution-matched CT images were generated. A total of 114 volumes of interest were defined and the average PET attenuation coefficients and CT values measured. From the CT values the predicted PET attenuation coefficients were calculated using the bilinear transformation. When the transformation was based on the narrow-beam attenuation coefficient of water at 511keV (0.096cm-1), the predicted attenuation coefficients were higher in soft tissue than the measured values. This bias was reduced by replacing 0.096cm-1 in the transformation by the linear attenuation coefficient of 0.093cm-1 obtained from germanium-68 transmission scans. An analysis of the corrected emission activities shows that the resulting transformation is essentially equivalent to the transmission-based attenuation correction for human tissue. For non-human material, however, it may assign inaccurate attenuation coefficients which will also affect the correction in neighbouring tissu

Generation of linear waves in the flow of Bose-Einstein condensate past an obstacle

The theory of linear wave structures generated in Bose-Einstein condensate flow past an obstacle is developed. The shape of wave crests and dependence of amplitude on coordinates far enough from the obstacle are calculated. The results are in good agreement with the results of numerical simulations obtained earlier. The theory gives a qualitative description of experiments with Bose-Einstein condensate flow past an obstacle after condensate's release from a trap.Comment: 11 pages, 3 figures, to be published in Zh. Eksp. Teor. Fi

Time-resolved Neutron-gamma-ray Data Acquisition for in Situ Subsurface Planetary Geochemistry

The current gamma-ray/neutron instrumentation development effort at NASA Goddard Space Flight Center aims to extend the use of active pulsed neutron interrogation techniques to probe the subsurface elemental composition of planetary bodies in situ. Previous NASA planetary science missions, that used neutron and/or gamma-ray spectroscopy instruments, have relied on neutrons produced from galactic cosmic rays. One of the distinguishing features of this effort is the inclusion of a high intensity 14.1 MeV pulsed neutron generator synchronized with a custom data acquisition system to time each event relative to the pulse. With usually only one opportunity to collect data, it is difficult to set a priori time-gating windows to obtain the best possible results. Acquiring time-tagged, event-by-event data from nuclear induced reactions provides raw data sets containing channel/energy, and event time for each gamma ray or neutron detected. The resulting data set can be plotted as a function of time or energy using optimized analysis windows after the data are acquired. Time windows can now be chosen to produce energy spectra that yield the most statistically significant and accurate elemental composition results that can be derived from the complete data set. The advantages of post-processing gamma-ray time-tagged event-by-event data in experimental tests using our prototype instrument will be demonstrated

Intermixed Time-Dependent Self-Focusing and Defocusing Nonlinearities in Polymer Solutions

[Image: see text] Low-power visible light can lead to spectacular nonlinear effects in soft-matter systems. The propagation of visible light through transparent solutions of certain polymers can experience either self-focusing or defocusing nonlinearity, depending on the solvent. We show how the self-focusing and defocusing responses can be captured by a nonlinear propagation model using local spatial and time-integrating responses. We realize a remarkable pattern formation in ternary solutions and model it assuming a linear combination of the self-focusing and defocusing nonlinearities in the constituent solvents. This versatile response of solutions to light irradiation may introduce a new approach for self-written waveguides and patterns

Pattern Forming Dynamical Instabilities of Bose-Einstein Condensates: A Short Review

In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities of Bose-Einstein condensates in one- and two-dimensional settings. In particular, we illustrate the trapping conditions that allow the reduction of the three-dimensional, mean field description of the condensates (through the Gross-Pitaevskii equation) to such lower dimensional settings, as well as to lattice settings. We then go on to study the modulational instability in one dimension and the snaking/transverse instability in two dimensions as typical examples of long-wavelength perturbations that can destabilize the condensates and lead to the formation of patterns of coherent structures in them. Trains of solitons in one-dimension and vortex arrays in two-dimensions are prototypical examples of the resulting nonlinear waveforms, upon which we briefly touch at the end of this review.Comment: 28 pages, 9 figures, publishe