A conditional regularity result for p-harmonic flows

We prove an $\varepsilon$-regularity result for a wide class of parabolic systems $$u_t-\text{div}\big(|\nabla u|^{p-2}\nabla u) = B(u, \nabla u)$$ with the right hand side $B$ growing like $|\nabla u|^p$. It is assumed that the solution $u(t,\cdot)$ is uniformly small in the space of functions of bounded mean oscillation. The crucial tool is provided by a sharp nonlinear version of the Gagliardo-Nirenberg inequality which has been used earlier in an elliptic context by T. Rivi\`ere and the last named author.Comment: To appear in NoDEA. Referee suggestions implemente

Improved Unsteady RANS Models Applied to Jet Transverse to a Pipe Flow

An unsteady RANS model is developed in order to simulate the complex situations involving both free and bounded flows. This model tuned to catch coherent flow structures is developed both in the k-ε and k-l approaches. The full 3D geometry of a round jet exiting from a reservoir into a pipe has been computed. Periodic conditions are applied in order to compare with an experiments consisting of eight jets exiting in a cross pipe flow. Improvement has been obtained with this URANS turbulence model compared to RANS and good agreement compared with experiments has been obtained. Unsteady phenomena are reproduced by the model and provide more insight into the physical properties of the flow and of the transport of a passive scalar

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

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

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

Novel method for hit-position reconstruction using voltage signals in plastic scintillators and its application to Positron Emission Tomography

Currently inorganic scintillator detectors are used in all commercial Time of Flight Positron Emission Tomograph (TOF-PET) devices. The J-PET collaboration investigates a possibility of construction of a PET scanner from plastic scintillators which would allow for single bed imaging of the whole human body. This paper describes a novel method of hit-position reconstruction based on sampled signals and an example of an application of the method for a single module with a 30 cm long plastic strip, read out on both ends by Hamamatsu R4998 photomultipliers. The sampling scheme to generate a vector with samples of a PET event waveform with respect to four user-defined amplitudes is introduced. The experimental setup provides irradiation of a chosen position in the plastic scintillator strip with an annihilation gamma quanta of energy 511~keV. The statistical test for a multivariate normal (MVN) distribution of measured vectors at a given position is developed, and it is shown that signals sampled at four thresholds in a voltage domain are approximately normally distributed variables. With the presented method of a vector analysis made out of waveform samples acquired with four thresholds, we obtain a spatial resolution of about 1 cm and a timing resolution of about 80 p

Analysis framework for the J-PET scanner

J-PET analysis framework is a flexible, lightweight, ROOT-based software package which provides the tools to develop reconstruction and calibration procedures for PET tomography. In this article we present the implementation of the full data-processing chain in the J-PET framework which is used for the data analysis of the J-PET tomography scanner. The Framework incorporates automated handling of PET setup parameters' database as well as high level tools for building data reconstruction procedures. Each of these components is briefly discussed.Comment: 6 pages, 1 figur

Hit time and hit position reconstruction in the J-PET detector based on a library of averaged model signals

In this article we present a novel method of hit time and hit position reconstruction in long scintillator detectors. We take advantage of the fact that for this kind of detectors amplitude and shape of registered signals depends strongly on the position where particle hit the detector. The reconstruction is based on determination of the degree of similarity between measured and averaged signals stored in a library for a set of well-defined positions along the scintillator. Preliminary results of validation of the introduced method with experimental data obtained by means of the double strip prototype of the J-PET detector are presented

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