A posteriori analysis of discontinuous galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator

Effect of nucleon exchange on projectile multifragmentation in the reactions of 28Si + 112Sn and 124Sn at 30 and 50 MeV/nucleon

Multifragmentation of quasiprojectiles was studied in reactions of 28Si beam with 112Sn and 124Sn targets at projectile energies 30 and 50 MeV/nucleon. The quasiprojectile observables were reconstructed using isotopically identified charged particles with Z_f <= 5 detected at forward angles. The nucleon exchange between projectile and target was investigated using isospin and excitation energy of reconstructed quasiprojectile. For events with total reconstructed charge equal to the charge of the beam (Z_tot = 14) the influence of beam energy and target isospin on neutron transfer was studied in detail. Simulations employing subsequently model of deep inelastic transfer, statistical model of multifragmentation and software replica of FAUST detector array were carried out. A concept of deep inelastic transfer provides good description of production of highly excited quasiprojectiles. The isospin and excitation energy of quasiprojectile were described with good overall agreement. The fragment multiplicity, charge and isospin were reproduced satisfactorily. The range of contributing impact parameters was determined using backtracing procedure.Comment: 11 pages, 8 Postscript figures, LaTeX, to appear in Phys. Rev. C ( Dec 2000

Absorbed radiation dosimetry of the D3-specific PET radioligand [18F]FluorTriopride estimated using rodent and nonhuman primate

[(18)F]FluorTriopride ([(18)F]FTP) is a dopamine D(3)-receptor preferring radioligand with potential for investigation of neuropsychiatric disorders including Parkinson disease, dystonia and schizophrenia. Here we estimate human radiation dosimetry for [(18)F]FTP based on the ex-vivo biodistribution in rodents and in vivo distribution in nonhuman primates. Biodistribution data were generated using male and female Sprague-Dawley rats injected with ~370 KBq of [(18)F]FTP and euthanized at 5, 30, 60, 120, and 240 min. Organs of interest were dissected, weighed and assayed for radioactivity content. PET imaging studies were performed in two male and one female macaque fascicularis administered 143-190 MBq of [(18)F]FTP and scanned whole-body in sequential sections. Organ residence times were calculated based on organ time activity curves (TAC) created from regions of Interest. OLINDA/EXM 1.1 was used to estimate human radiation dosimetry based on scaled organ residence times. In the rodent, the highest absorbed radiation dose was the upper large intestines (0.32-0.49 mGy/MBq), with an effective dose of 0.07 mSv/MBq in males and 0.1 mSv/MBq in females. For the nonhuman primate, however, the gallbladder wall was the critical organ (1.81 mGy/MBq), and the effective dose was 0.02 mSv/MBq. The species discrepancy in dosimetry estimates for [(18)F]FTP based on rat and primate data can be attributed to the slower transit of tracer through the hepatobiliary track of the primate compared to the rat, which lacks a gallbladder. Out findings demonstrate that the nonhuman primate model is more appropriate model for estimating human absorbed radiation dosimetry when hepatobiliary excretion plays a major role in radiotracer elimination

Symmetrised Characterisation of Noisy Quantum Processes

A major goal of developing high-precision control of many-body quantum systems is to realise their potential as quantum computers. Probably the most significant obstacle in this direction is the problem of "decoherence": the extreme fragility of quantum systems to environmental noise and other control limitations. The theory of fault-tolerant quantum error correction has shown that quantum computation is possible even in the presence of decoherence provided that the noise affecting the quantum system satisfies certain well-defined theoretical conditions. However, existing methods for noise characterisation have become intractable already for the systems that are controlled in today's labs. In this paper we introduce a technique based on symmetrisation that enables direct experimental characterisation of key properties of the decoherence affecting a multi-body quantum system. Our method reduces the number of experiments required by existing methods from exponential to polynomial in the number of subsystems. We demonstrate the application of this technique to the optimisation of control over nuclear spins in the solid state.Comment: About 12 pages, 5 figure

Using error correction to determine the noise model

Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is based on a three-bit quantum error correcting code carried out on a three-qubit nuclear magnetic resonance (NMR) quantum information processor. Utilizing both engineered and natural noise, the degree of correlations present in the noise affecting a two-qubit subsystem was determined. We measured a correlation factor of c=0.5+/-0.2 using the error correction protocol, and c=0.3+/-0.2 using a standard NMR technique based on coherence pathway selection. Although the error correction method demands precise control, the results demonstrate that the required precision is achievable in the liquid-state NMR setting.Comment: 10 pages, 3 figures. Added discussion section, improved figure

Inhomogeneous isospin distribution in the reactions of 28Si + 112Sn and 124Sn at 30 and 50 MeV/nucleon

We have created quasiprojectiles of varying isospin via peripheral reactions of 28Si + 112Sn and 124Sn at 30 and 50 MeV/nucleon. The quasiprojectiles have been reconstructed from completely isotopically identified fragments. The difference in N/Z of the reconstructed quasiprojectiles allows the investigation of the disassembly as a function of the isospin of the fragmenting system. The isobaric yield ratio 3H/3He depends strongly on N/Z ratio of quasiprojectiles. The dependences of mean fragment multiplicity and mean N/Z ratio of the fragments on N/Z ratio of the quasiprojectile are different for light charged particles and intermediate mass fragments. Observation of a different N/Z ratio of light charged particles and intermediate mass fragments is consistent with an inhomogeneous distribution of isospin in the fragmenting system.Comment: 5 pages, 4 Postscript figures, RevTe

The resource theory of quantum reference frames: manipulations and monotones

Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of superselection rule, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focussing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically nonincreasing under various classes of operations that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio

Thermal excitation of heavy nuclei with 5-15 GeV/c antiproton, proton and pion beams

Excitation-energy distributions have been derived from measurements of 5.0-14.6 GeV/c antiproton, proton and pion reactions with $^{197}$Au target nuclei, using the ISiS 4$\pi$ detector array. The maximum probability for producing high excitation-energy events is found for the antiproton beam relative to other hadrons, $^3$He and $\bar{p}$ beams from LEAR. For protons and pions, the excitation-energy distributions are nearly independent of hadron type and beam momentum above about 8 GeV/c. The excitation energy enhancement for $\bar{p}$ beams and the saturation effect are qualitatively consistent with intranuclear cascade code predictions. For all systems studied, maximum cluster sizes are observed for residues with E*/A $\sim$ 6 MeV.Comment: 14 pages including 5 figures and 1 table. Accepted in Physics Letter B. also available at http://nuchem.iucf.indiana.edu