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Limit loads can be calculated with the finite element method (FEM) for any component, defect geometry, and loading. FEM suggests that published long crack limit formulae for axial defects under-estimate the burst pressure for internal surface defects in thick pipes while limit loads are not conservative for deep cracks and for pressure loaded crack-faces. Very deep cracks have a residual strength, which is modelled by a global collapse load. These observations are combined to derive new analytical local and global collapse loads. The global collapse loads are close to FEM limit analyses for all crack dimensions.
Improved collapse loads of thick-walled, crack containing pipes and vessels are suggested. Very deep cracks have a residual strength which is better modelled by a global limit load. In all burst tests, the ductility of pressure vessel steels was sufficiently high whereby the burst pressure could be predicted by limit analysis with no need to apply fracture mechanics. The relative prognosis error increases however, for long and deep defects due to uncertainties of geometry and strength data.
This paper presents the direct route to Design by Analysis (DBA) of the new European pressure vessel standard in the language of limit and shakedown analysis (LISA). This approach leads to an optimization problem. Its solution with Finite Element Analysis is demonstrated for some examples from the DBA-Manual. One observation from the examples is, that the optimisation approach gives reliable and close lower bound solutions leading to simple and optimised design decision.
Structural design analyses are conducted with the aim of verifying the exclusion of ratchetting. To this end it is important to make a clear distinction between the shakedown range and the ratchetting range. The performed experiment comprised a hollow tension specimen which was subjected to alternating axial forces, superimposed with constant moments. First, a series of uniaxial tests has been carried out in order to calibrate a bounded kinematic hardening rule. The load parameters have been selected on the basis of previous shakedown analyses with the PERMAS code using a kinematic hardening material model. It is shown that this shakedown analysis gives reasonable agreement between the experimental and the numerical results. A linear and a nonlinear kinematic hardening model of two-surface plasticity are compared in material shakedown analysis.
In the new European standard for unfired pressure vessels, EN 13445-3, there are two approaches for carrying out a Design-by-Analysis that cover both the stress categorization method (Annex C) and the direct route method (Annex B) for a check against global plastic deformation and against progressive plastic deformation. This paper presents the direct route in the language of limit and shakedown analysis. This approach leads to an optimization problem. Its solution with Finite Element Analysis is demonstrated for mechanical and thermal actions. One observation from the examples is that the so-called 3f (3Sm) criterion fails to be a reliable check against progressive plastic deformation. Precise conditions are given, which greatly restrict the applicability of the 3f criterion.
Reliability of the Primary Circuit Pressure Boundary of an HTR-Module under Accident Conditions
(1993)
In: Technical feasibility and reliability of passive safety systems for nuclear power plants. Proceedings of an Advisory Group Meeting held in Jülich, 21-24 November 1994. - Vienna , 1996. - Seite: 43 - 55 IAEA-TECDOC-920 Abstract: It is shown that the difficulty for probabilistic fracture mechanics (PFM) is the general problem of the high reliability of a small population. There is no way around the problem as yet. Therefore what PFM can contribute to the reliability of steel pressure boundaries is demonstrated with the example of a typical reactor pressure vessel and critically discussed. Although no method is distinguishable that could give exact failure probabilities, PFM has several additional chances. Upper limits for failure probability may be obtained together with trends for design and operating conditions. Further, PFM can identify the most sensitive parameters, improved control of which would increase reliability. Thus PFM should play a vital role in the analysis of steel pressure boundaries despite all shortcomings.
Fatigue analyses are conducted with the aim of verifying that thermal ratcheting is limited. To this end it is important to make a clear distintion between the shakedown range and the ratcheting range (continuing deformation). As part of an EU-supported research project, experiments were carried out using a 4-bar model. The experiment comprised a water-cooled internal tube, and three insulated heatable outer test bars. The system was subjected to alternating axial forces, superimposed with alternating temperatures at the outer bars. The test parameters were partly selected on the basis of previous shakedown analyses. During the test, temperatures and strains were measured as a function of time. The loads and the resulting stresses were confirmed on an ongoing basis during performance of the test, and after it. Different material models were applied for this incremental elasto-plastic analysis using the ANSYS program. The results of the simulation are used to verify the FEM-based shakedown analysis.
The structural reliability with respect to plastic collapse or to inadaptation is formulated on the basis of the lower bound limit and shakedown theorems. A direct definition of the limit state function is achieved which permits the use of the highly effective first order reliability methods (FORM) is achieved. The theorems are implemented into a general purpose FEM program in a way capable of large-scale analysis. The limit state function and its gradient are obtained from a mathematical optimization problem. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, the computing time, and the numerical error, leading to highly effective and precise reliability analyses.
Limit and shakedown analysis are effective methods for assessing the load carrying capacity of a given structure. The elasto–plastic behavior of the structure subjected to loads varying in a given load domain is characterized by the shakedown load factor, defined as the maximum factor which satisfies the sufficient conditions stated in the corresponding static shakedown theorem. The finite element dicretization of the problem may lead to very large convex optimization. For the effective solution a basis reduction method has been developed that makes use of the special problem structure for perfectly plastic material. The paper proposes a modified basis reduction method for direct application to the two-surface plasticity model of bounded kinematic hardening material. The considered numerical examples show an enlargement of the load carrying capacity due to bounded hardening.
The load-carrying capacity or the safety against plastic limit states are the central questions in the design of structures and passive components in the apparatus engineering. A precise answer is most simply given by limit and shakedown analysis. These methods can be based on static and kinematic theorems for lower and upper bound analysis. Both may be formulated as optimization problems for finite element discretizations of structures. The problems of large-scale analysis and the extension towards realistic material modelling will be solved in a European research project. Limit and shakedown analyses are briefly demonstrated with illustrative examples.
Sensitivity of and Influences on the Reliability of an HTR-Module Primary Circuit Pressure Boundary
(1993)
Shock waves, explosions, impacts or cavitation bubble collapses may generate stress waves in solids causing cracks or unexpected dammage due to focussing, physical nonlinearity or interaction with existing cracks. There is a growing interest in wave propagation, which poses many novel problems to experimentalists and theorists.
The nonlinear scalar constitutive equations of gases lead to a change in sound speed from point to point as would be found in linear inhomogeneous (and time dependent) media. The nonlinear tensor constitutive equations of solids introduce the additional local effect of solution dependent anisotropy. The speed of a wave passing through a point changes with propagation direction and its rays are inclined to the front. It is an open question whether the widely used operator splitting techniques achieve a dimensional splitting with physically reasonable results for these multi-dimensional problems. May be this is the main reason why the theoretical and numerical investigations of multi-dimensional wave propagation in nonlinear solids are so far behind gas dynamics. We hope to promote the subject a little by a discussion of some fundamental aspects of the solution of the equations of nonlinear elastodynamics. We use methods of characteristics because they only integrate mathematically exact equations which have a direct physical interpretation.
Soft Materials in Technology and Biology – Characteristics, Properties, and Parameter Identification
(2008)
Smoothed Finite Element Methods for Nonlinear Solid Mechanics Problems: 2D and 3D Case Studies
(2016)
The Smoothed Finite Element Method (SFEM) is presented as an edge-based and a facebased techniques for 2D and 3D boundary value problems, respectively. SFEMs avoid shortcomings of the standard Finite Element Method (FEM) with lower order elements such as overly stiff behavior, poor stress solution, and locking effects. Based on the idea of averaging spatially the standard strain field of the FEM over so-called smoothing domains SFEM calculates the stiffness matrix for the same number of degrees of freedom (DOFs) as those of the FEM. However, the SFEMs significantly improve accuracy and convergence even for distorted meshes and/or nearly incompressible materials.
Numerical results of the SFEMs for a cardiac tissue membrane (thin plate inflation) and an artery (tension of 3D tube) show clearly their advantageous properties in improving accuracy particularly for the distorted meshes and avoiding shear locking effects.
Limit Analysis of Defects
(2000)
Limit and shakedown theorems are exact theories of classical plasticity for the direct computation of safety factors or of the load carrying capacity under constant and varying loads. Simple versions of limit and shakedown analysis are the basis of all design codes for pressure vessels and pipings. Using Finite Element Methods more realistic modeling can be used for a more rational design. The methods can be extended to yield optimum plastic design. In this paper we present a first implementation in FE of limit and shakedown analyses for perfectly plastic material. Limit and shakedown analyses are done of a pipe–junction and a interaction diagram is calculated. The results are in good correspondence with the analytic solution we give in the appendix.
Safety and reliability of structures may be assessed indirectly by stress distributions. Limit and shakedown theorems are simplified but exact methods of plasticity that provide safety factors directly in the loading space. These theorems may be used for a direct definition of the limit state function for failure by plastic collapse or by inadaptation. In a FEM formulation the limit state function is obtained from a nonlinear optimization problem. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, the computing time, and the numerical error. Moreover, the direct way leads to highly effective and precise reliability analyses. The theorems are implemented into a general purpose FEM program in a way capable of large-scale analysis.
Structural design analyses are conducted with the aim of verifying the exclusion of ratcheting. To this end it is important to make a clear distinction between the shakedown range and the ratcheting range. In cyclic plasticity more sophisticated hardening models have been suggested in order to model the strain evolution observed in ratcheting experiments. The hardening models used in shakedown analysis are comparatively simple. It is shown that shakedown analysis can make quite stable predictions of admissible load ranges despite the simplicity of the underlying hardening models. A linear and a nonlinear kinematic hardening model of two-surface plasticity are compared in material shakedown analysis. Both give identical or similar shakedown ranges. Structural shakedown analyses show that the loading may have a more pronounced effect than the hardening model.
Numerical methods for limit and shakedown analysis. Deterministic and probabilistic problems.
(2003)
When confining pressure is low or absent, extensional fractures are typical, with fractures occurring on unloaded planes in rock. These “paradox” fractures can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. But this criterion makes unrealistic strength predictions in biaxial compression and tension. A new extension strain criterion overcomes this limitation by adding a weighted principal shear component. The weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting failure modes, which are unexpected in the understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak P. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
Load bearing capacity of thin shell structures made of elastoplastic material by direct methods
(2008)
7th International Conference on Reliability of Materials and Structures (RELMAS 2008). June 17 - 20, 2008 ; Saint Petersburg, Russia. pp 354-358. Reprint with corrections in red Introduction Analysis of advanced structures working under extreme heavy loading such as nuclear power plants and piping system should take into account the randomness of loading, geometrical and material parameters. The existing reliability are restricted mostly to the elastic working regime, e.g. allowable local stresses. Development of the limit and shakedown reliability-based analysis and design methods, exploiting potential of the shakedown working regime, is highly needed. In this paper the application of a new algorithm of probabilistic limit and shakedown analysis for shell structures is presented, in which the loading and strength of the material as well as the thickness of the shell are considered as random variables. The reliability analysis problems may be efficiently solved by using a system combining the available FE codes, a deterministic limit and shakedown analysis, and the First and Second Order Reliability Methods (FORM/SORM). Non-linear sensitivity analyses are obtained directly from the solution of the deterministic problem without extra computational costs.
Suburethral slings as well as different meshes are widely used treating stress urinary incontinence and prolaps in women. With the development of MiniSlings and special meshes using less alloplastic material anchorage systems become more important to keep devices in place and to put some tension especially on the MiniSlings. To date, there are many different systems of MiniSlings of different companies on the market which differ in the structure of the used meshes and anchors. A new objective measurement method to compare different properties of MiniSling systems (mesh and anchor) is presented in this article. Ballistic gelatine acts as soft tissue surrogate. Significant differences in parameters like pull-out strength of anchors or shrinkage of meshes under loading conditions have been determined. The form and size of the anchors as well as the structural stability of the meshes are decisive for a proper integration. The tested anchorings sytems showed markedly different mechanical function at their respective load bearing capacity. As the stable fixation of the device in tissue is a prerequisite for a permanet reinforcement, the proposed test system permits further optimisation of anchor and mesh devices to improve the success of the surgical treatment
Upper and lower bound theorems of limit analyses have been presented in part I of the paper. Part II starts with the finite element discretization of these theorems and demonstrates how both can be combined in a primal–dual optimization problem. This recently proposed numerical method is used to guide the development of a new class of closed-form limit loads for circumferential defects, which show that only large defects contribute to plastic collapse with a rapid loss of strength with increasing crack sizes. The formulae are compared with primal–dual FEM limit analyses and with burst tests. Even closer predictions are obtained with iterative limit load solutions for the von Mises yield function and for the Tresca yield function. Pressure loading of the faces of interior cracks in thick pipes reduces the collapse load of circumferential defects more than for axial flaws. Axial defects have been treated in part I of the paper.
Limit loads of circumferentially flawed pipes and cylindrical vessels under internal pressure
(2006)
Thermodynamic stability, configurational motions and internal forces of haemoglobin (Hb) of three endotherms (platypus, Ornithorhynchus anatinus; domestic chicken, Gallus gallus domesticus and human, Homo sapiens) and an ectotherm (salt water crocodile, Crocodylus porosus) were investigated using circular dichroism, incoherent elastic neutron scattering and coarse-grained Brownian dynamics simulations. The experimental results from Hb solutions revealed a direct correlation between protein resilience, melting temperature and average body temperature of the different species on the 0.1 ns time scale. Molecular forces appeared to be adapted to permit conformational fluctuations with a root mean square displacement close to 1.2 Å at the corresponding average body temperature of the endotherms. Strong forces within crocodile Hb maintain the amplitudes of motion within a narrow limit over the entire temperature range in which the animal lives. In fully hydrated powder samples of human and chicken, Hb mean square displacements and effective force constants on the 1 ns time scale showed no differences over the whole temperature range from 10 to 300 K, in contrast to the solution case. A complementary result of the study, therefore, is that one hydration layer is not sufficient to activate all conformational fluctuations of Hb in the pico- to nanosecond time scale which might be relevant for biological function. Coarse-grained Brownian dynamics simulations permitted to explore residue-specific effects. They indicated that temperature sensing of human and chicken Hb occurs mainly at residues lining internal cavities in the β-subunits.
Retinal endothelial function in cardiovascular risk patients: A randomized controlled exercise trial
(2020)
The aim of this study was to investigate, for the first time, the effects of high-intensity interval training (HIIT) on retinal microvascular endothelial function in cardiovascular (CV) risk patients. In the randomized controlled trial, middle-aged and previously sedentary patients with increased CV risk (aged 58 ± 6 years) with ≥ two CV risk factors were randomized into a 12-week HIIT (n = 33) or control group (CG, n = 36) with standard physical activity recommendations. A blinded examiner measured retinal endothelial function by flicker light-induced maximal arteriolar (ADmax) and venular (VDmax) dilatation as well as the area under the arteriolar (AFarea) and venular (VFarea) flicker curve using a retinal vessel analyzer. Standardized assessments of CV risk factors, cardiorespiratory fitness, and retinal endothelial function were performed before and after HIIT. HIIT reduced body mass index, fat mass, and low-density lipoprotein and increased muscle mass and peak oxygen uptake (VO2peak). Both ADmax (pre: 2.7 ± 2.1%, post: 3.0 ± 2.2%, P = .018) and AFarea (pre: 32.6 ± 28.4%*s, post: 37.7 ± 30.6%*s, P = .016) increased after HIIT compared with CG (ADmax, pre: 3.2 ± 1.8%, post: 2.9 ± 1.8%, P = .254; AFarea, pre: 41.6 ± 28.5%*s, post: 37.8 ± 27.0%*s, P = .186). Venular function remained unchanged after HIIT. There was a significant association between ∆-change VO2peak and ∆-changes ADmax and AFarea (P = .026, R² = 0.073; P = .019, R² = 0.081, respectively). 12-weeks of HIIT improved retinal endothelial function in middle-aged patients with increased CV risk independent of the reduction in classical CV risk factors. Exercise has the potential to reverse or at least postpone progression of small vessel disease in older adults with increased CV risk under standard medication. Dynamic retinal vessel analysis seems to be a sensitive tool to detect treatment effects of exercise interventions on retinal microvascular endothelial function in middle-aged individuals with increased CV risk.
The interest in PET detectors with monolithic block scintillators is growing. In order to obtain high spatial resolutions dedicated positioning algorithms are required. But even an ideal algorithm can only deliver information which is provided by the detector. In this simulation study we investigated the light distribution on one surface of cuboid LSO scintillators of different size. Scintillators with a large aspect ratio (small footprint and large height) showed significant position information only for a minimum interaction depth of the gamma particle. The results allow a quantitative estimate for a useful aspect ratio.
Plant growth and transport processes are highly dynamic. They are characterized by plant-internal control processes and by strong interactions with the spatially and temporally varying environment. Analysis of structure- function relations of growth and transport in plants will strongly benefit from the development of non-invasive techniques. PlanTIS (Plant Tomographic Imaging System) is designed for non-destructive 3D-imaging of positron emitting radiotracers. It will permit functional analysis of the dynamics of carbon distribution in plants including bulky organs. It will be applicable for screening transport properties of plants to evaluate e.g. temperature adaptation of genetically modified plants. PlanTIS is a PET scanner dedicated to monitor the dynamics of the 11C distribution within a plant while or after assimilation of 11CO2. Front end electronics and data acquisition architecture of the scanner are based on the ClearPETTM system [1]. Four detector modules form one of two opposing detector blocks. Optionally, a hardware coincidence detection between the blocks can be applied. In general the scan duration is rather long (~ 1 hour) compared to the decay time of 11C (20 min). As a result the count rates can vary over a wide range and accurate dead time correction is necessary.
Within the Crystal Clear Collaboration a modular system for a small animal PET scanner (ClearPET™) has been developed. The modularity allows the assembly of scanners of different sizes and characteristics in order to fit the specific needs of the individual member institutions. Now a first demonstrator is being completed in Julich. The system performs depth of interaction detection by using a phoswich arrangement combining LSO and LuYAP scintillators which are coupled to multi-channel photomultipliers (PMTs). A free-running ADC digitizes the signal from the PMT and the complete scintillation pulses are sampled by an FPGA and sent with 20 MB/S to a PC for preprocessing. The pulse provides information about the gamma energy and the scintillator material which identifies the interaction layer. Furthermore, the exact pulse starting time is obtained from the sampled data. This is important as no hardware coincidence detection is implemented. All single events are recorded and coincidences are identified by software. An advantage of that is that the coincidence window and the dimensions of the field of view can be adjusted easily. The ClearPET™ demonstrator is equipped with 10240 crystals on 80 PMTs. This paper presents an overview of the data acquisition system.
The small animal PET scanners developed by the Crystal Clear Collaboration (ClearPETtrade) detect coincidences by analyzing timemarks which are attached to each event. The scanners are able to save complete single list mode data which allows analysis and modification of the timemarks after data acquisition. The timemarks are obtained from the digitally sampled detector pulses by calculating the baseline crossing of the rising edge of the pulse which is approximated as a straight line. But the limited sampling frequency causes a systematic error in the determination of the timemark. This error depends on the phase of the sampling clock at the time of the event. A statistical method that corrects these errors will be presented
The Crystal Clear Collaboration has developed a modular system for a small animal PET scanner (ClearPET). The modularity allows the assembly of scanners of different sizes and characteristics in order to satisfy the specific needs of the individual member institutions. The system performs depth of interaction detection by using a phoswich arrangement combining LSO and LuYAP scintillators which are coupled to Multichannel Photomultipliers (PMTs). For each PMT a free running 40 MHz ADC digitizes the signal and the complete scintillation pulse is sampled by an FPGA and sent with 20 MB/s to a PC for preprocessing. The pulse provides information about the gamma energy and the scintillator material which identifies the interaction layer. Furthermore, the exact pulse starting time is obtained from the sampled data. This is important as no hardware coincidence detection is implemented. All single events are recorded and coincidences are identified by software. The system in Jülich (ClearPET Neuro) is equipped with 10240 crystals on 80 PMTs. The paper will present an overview of the data acquisition system.
Pulse shape discrimination of LSO and LuYAP scintillators for depth of interaction detection in PET
(2003)
A feasible way to gain the depth of interaction information in a PET scanner is the use of phoswich detectors. In general the layer of interaction is identified front the pulse shape of the corresponding scintillator material. In this work pulses from LSO and LuYAP crystals were investigated in order to find a practical method of distinguishing. It turned out that such a pulse processing could he kept simple due to an additional slow component in the light decay of the LuYAP pulse. At the same time the short decay time guarantees that the major amount of the light output is still collected within a short pulse recording time.
Pulse shape discrimination of LSO and LuYAP scintillators for depth of interaction detection in PET
(2003)
A feasible way to gain the depth of interaction information in a positron emission tomography scanner is the use of phoswich detectors. In general, the layer of interaction is identified from the pulse shape of the corresponding scintillator material. In this work, pulses from LSO and LuYAP crystals were investigated in order to find a practical method of distinguishing. It turned out that such a pulse processing could be kept simple because of an additional slow component in the light decay of the LuYAP pulse. At the same time, the short decay time guarantees that the major amount of the light output is still collected within a short pulse recording time.
Pulses from a position-sensitive photomultiplier (PS-PMT) are recorded by free-running ADCs at a sampling rate of 40 MHz. A four-channel acquisition board has been developed which is equipped with four 12-bit ADCs connected to one field programmable gate array (FPGA). The FPGA manages data acquisition and the transfer to the host computer. It can also work as a digital trigger, so a separate hardware trigger can be omitted. The method of free-running sampling provides a maximum of information, besides the pulse charge and amplitude also pulse shape and starting time are contained in the sampled data. This information is crucial for many tasks such as distinguishing between different scintillator materials, determination of radiation type, pile-up recovery, coincidence detection or time-of-flight applications. The absence of an analog integrator allows very high count rates to be dealt with. Since this method is to be employed in positron emission tomography (PET), the position of an event is also important. The simultaneous readout of four channels allows localization by means of center-of-gravity weighting. First results from a test setup with LSO scintillators coupled to the PS-PMT are presented here
A small PET system has been built up with two multichannel photomultipliers, which are attached to a matrix of 64 single LSO crystals each. The signal from each multiplier is being sampled continuously by a 12 bit ADC at a sampling frequency of 40 MHz. In case of a scintillation pulse a subsequent FPGA sends the corresponding set of samples together with the channel information and a time mark to the host computer. The data transfer is performed with a rate of 20 MB/s. On the host all necessary information is extracted from the data. The pulse energy is determined, coincident events are detected and multiple hits within one matrix can be identified. In order to achieve a narrow time window the pulse starting time is refined further than the resolution of the time mark (=25 ns) would allow. This is possible by interpolating between the pulse samples. First data obtained from this system will be presented. The system is part of developments for a much larger system and has been created to study the feasibility and performance of the technique and the hardware architecture.
Coincident events in two scintillator crystals coupled to photomultipliers (PMT) are detected by processing just the digital data of the recorded pulses. For this purpose the signals from both PMTs are continuously sampled by free-running ADCs at a sampling rate of 40 MHz. For each sampled pulse the starting time is determined by processing the pulse data. Even a fairly simple interpolating algorithm results in a FWHM of about 2 ns.
Within the developments for the Crystal Clear small animal PET project (CLEARPET) a dual head PET system has been established. The basic principle is the early digitization of the detector pulses by free running ADCs. The determination of the γ-energy and also the coincidence detection is performed by data processing of the sampled pulses on the host computer. Therefore a time mark is attached to each pulse identifying the current cycle of the 40 MHz sampling clock. In order to refine the time resolution the pulse starting time is interpolated from the samples of the pulse rise. The detector heads consist of multichannel PMTs with a single LSO scintillator crystal coupled to each channel. For each PMT only one ADC is required. The position of an event is obtained separately from trigger signals generated for each single channel. An FPGA is utilized for pulse buffering, generation of the time mark and for the data transfer to the host via a fast I/O-interface.
Pulses from a position-sensitive photomultiplier (PS-PMT) are recorded by free running ADCs at a sampling rate of 40 MHz. A four-channel acquisition-board has been developed which is equipped with four 12 bit-ADCs connected to one FPGA (field programmable gate array). The FPGA manages data acquisition and the transfer to the host computer. It can also work as a digital trigger, so a separate hardware-trigger can be omitted. The method of free running sampling provides a maximum of information, besides the pulse charge and amplitude also pulse shape and starting time are contained in the sampled data. These informations are crucial for many tasks such as distinguishing between different scintillator materials, determination of radiation type, pile-up recovery, coincidence detection or time-of-flight applications. The absence of an analog integrator allows coping with very high count rates. Since this method is going to be employed in positron emission tomography (PET), the position of an event is another important information. The simultaneous readout of four channels allows localization by means of center-of-gravity weighting. First results from a test setup with LSO-scintillators coupled to the PS-PMT are presented
The ClearPET® scanners developed by the Crystal Clear Collaboration use multichannel PMTs as photodetectors with scintillator pixels coupled individually to each channel. In order to localize an event each channel anode is connected to a comparator that triggers when the anode signal exceeds a common predefined threshold. Two major difficulties here are crosstalk of light and the gain nonuniformity of the PMT channels. Crosstalk can generate false triggering in channels adjacent to the actual event. On the one hand this can be suppressed by sufficiently increasing the threshold, but on the other hand a threshold too high can already prevent valid events on the lower gain channels from being detected. Finally, both effects restrict the dynamic range of pulse heights that can be processed. The requirements to the dynamic range are not low as the ClearPET® scanners detect the depth of interaction by phoswich pixels consisting of LSO and Lu0.7Y0.3AP, two scintillators with different light yields. We will present a model to estimate the achievable dynamic range and show solutions to increase it.
The readout of gamma detectors is considerably simplified when the event intensity is encoded as a pulse width (Pulse Width Modulation, PWM). Time-to-Digital-Converters (TDC) replace the conventional ADCs and multiple TDCs can be realized easily in one PLD chip (Programmable Logic Device). The output of a PWM stage is only one digital signal per channel which is well suited for transport so that further processing can be performed apart from the detector. This is particularly interesting for large systems with high channel density (e.g. high resolution scanners). In this work we present a circuit with a linear transfer function that requires a minimum of components by performing the PWM already in the preamp stage. This allows a very compact and also cost-efficient implementation of the front-end electronics.
Self-Adjoint Operator
(2009)
Unitary Operator
(2009)
Projection
(2009)
Operator
(2009)
Density Operator
(2009)
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.