Identification of Kelvin waves: numerical challenges

Kelvin waves are expected to play an essential role in the energy dissipation for quantized vortices. However, the identification of these helical distortions is not straightforward, especially in case of vortex tangle. Here we review several numerical methods that have been used to identify Kelvin waves within the vortex filament model. We test their validity using several examples and estimate whether these methods are accurate enough to verify the correct Kelvin spectrum. We also illustrate how the correlation dimension is related to different Kelvin spectra and remind that the 3D energy spectrum E(k) takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at http://www.springerlink.co

Diagrammatic Monte Carlo for Correlated Fermions

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t \sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.Comment: 4 pages, 5 figures, stylistic change

Compressive Sensing of Signals Generated in Plastic Scintillators in a Novel J-PET Instrument

The J-PET scanner, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The dis- cussed detector offers improvement of the Time of Flight (TOF) resolution due to the use of fast plastic scintillators and dedicated electronics allowing for sam- pling in the voltage domain of signals with durations of few nanoseconds. In this paper we show that recovery of the whole signal, based on only a few samples, is possible. In order to do that, we incorporate the training signals into the Tikhonov regularization framework and we perform the Principal Component Analysis decomposition, which is well known for its compaction properties. The method yields a simple closed form analytical solution that does not require iter- ative processing. Moreover, from the Bayes theory the properties of regularized solution, especially its covariance matrix, may be easily derived. This is the key to introduce and prove the formula for calculations of the signal recovery error. In this paper we show that an average recovery error is approximately inversely proportional to the number of acquired samples

System Response Kernel Calculation for List-mode Reconstruction in Strip PET Detector

Reconstruction of the image in Positron Emission Tomographs (PET) requires the knowledge of the system response kernel which describes the contribution of each pixel (voxel) to each tube of response (TOR). This is especially important in list-mode reconstruction systems, where an efficient analytical approximation of such function is required. In this contribution, we present a derivation of the system response kernel for a novel 2D strip PET.Comment: 10 pages, 2 figures; Presented at Symposium on applied nuclear physics and innovative technologies, Cracow, 03-06 June 201

Application of the Compress Sensing Theory for Improvement of the TOF Resolution in a Novel J-PET Instrument

Nowadays, in Positron Emission Tomography (PET) systems, a Time of Flight information is used to improve the image reconstruction process. In Time of Flight PET (TOF-PET), fast detectors are able to measure the difference in the arrival time of the two gamma rays, with the precision enabling to shorten significantly a range along the line-of-response (LOR) where the annihilation occurred. In the new concept, called J-PET scanner, gamma rays are detected in plastic scintillators. In a single strip of J-PET system, time values are obtained by probing signals in the amplitude domain. Owing to Compress Sensing theory, information about the shape and amplitude of the signals is recovered. In this paper we demonstrate that based on the acquired signals parameters, a better signal normalization may be provided in order to improve the TOF resolution. The procedure was tested using large sample of data registered by a dedicated detection setup enabling sampling of signals with 50 ps intervals. Experimental setup provided irradiation of a chosen position in the plastic scintillator strip with annihilation gamma quanta

A novel method for calibration and monitoring of time synchronization of TOF-PET scanners by means of cosmic rays

All of the present methods for calibration and monitoring of TOF-PET scanner detectors utilize radioactive isotopes such as e.g. $^{22}$Na or $^{68}$Ge, which are placed or rotate inside the scanner. In this article we describe a novel method based on the cosmic rays application to the PET calibration and monitoring methods. The concept allows to overcome many of the drawbacks of the present methods and it is well suited for newly developed TOF-PET scanners with a large longitudinal field of view. The method enables also monitoring of the quality of the scintillator materials and in general allows for the continuous quality assurance of the PET detector performance.Comment: 10 pages, 7 figure

Application of Compressive Sensing Theory for the Reconstruction of Signals in Plastic Scintillators

Compressive Sensing theory says that it is possible to reconstruct a measured signal if an enough sparse representation of this signal exists in comparison to the number of random measurements. This theory was applied to reconstruct signals from measurements of plastic scintillators. Sparse representation of obtained signals was found using SVD transform.Comment: 7 pages, 3 figures; Presented at Symposium on applied nuclear physics and innovative technologies, Cracow, 03-06 June 201