Discrete Spectra of Semirelativistic Hamiltonians

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation. Every Hamiltonian in this class of operators consists of the relativistic kinetic energy \beta \sqrt{m^2 + p^2} (where \beta > 0 allows for the possibility of more than one particles of mass m) and a spherically symmetric attractive potential V(r), r = |x|. In general, accurate eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of a numerical approximation procedure. Our main emphasis, however, is on the derivation of rigorous semi-analytical expressions for both upper and lower bounds to the energy levels of such operators. We compare the bounds obtained within different approaches and present relationships existing between the bounds.Comment: 21 pages, 3 figure

A Variational Approach to the Spinless Relativistic Coulomb Problem

By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some Coulomb-type interaction.Comment: 7 pages, HEPHY-PUB 606/9

Relativistic Coulomb Problem: Analytic Upper Bounds on Energy Levels

The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic Schr\"odinger formalism towards incorporation of relativistic effects) with the Coulomb interaction potential (the static limit of the exchange of some massless bosons, as present in unbroken gauge theories). The nonlocal nature of the Hamiltonian encountered here, however, renders extremely difficult to obtain rigorous analytic statements on the corresponding solutions. In view of this rather unsatisfactory state of affairs, we derive (sets of) analytic upper bounds on the involved energy eigenvalues.Comment: 12 pages, LaTe

Pion Generalized Dipole Polarizabilities by Virtual Compton Scattering πe→πeγ\pi e \to \pi e\gamma

We present a calculation of the cross section and the event generator of the reaction $\pi e\to \pi e \gamma$. This reaction is sensitive to the pion generalized dipole polarizabilities, namely, the longitudinal electric $\alpha_L(q^2)$, the transverse electric $\alpha_T(q^2)$, and the magnetic $\beta(q^2)$ which, in the real-photon limit, reduce to the ordinary electric and magnetic polarizabilities $\bar{\alpha}$ and $\bar{\beta}$, respectively. The calculation of the cross section is done in the framework of chiral perturbation theory at ${\cal O}(p^4)$. A pion VCS event generator has been written which is ready for implementation in GEANT simulation codes or for independent use.Comment: 33 pages, Revtex, 15 figure

Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing

Magnetic Induction Tomography (MIT) is a non‐invasive imaging technique, which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters of an object from measurements made on its surface. With the exploitation of parallelism, it is possible to achieve high quality inexpensive MIT images for biomedical applications on clinically relevant time scales. In this paper we investigate the performance of different parallel implementations of the forward eddy current problem, which is the main computational component of the inverse problem through which measured voltages are converted into images. We show that a heterogeneous parallel method that exploits multiple CPUs and GPUs can provide a high level of parallel scaling, leading to considerably improved runtimes. We also show how multiple GPUs can be used in conjunction with deal.II, a widely‐used open source finite element library

Meson exchange and nucleon polarizabilities in the quark model

Modifications to the nucleon electric polarizability induced by pion and sigma exchange in the q-q potentials are studied by means of sum rule techniques within a non-relativistic quark model. Contributions from meson exchange interactions are found to be small and in general reduce the quark core polarizability for a number of hybrid and one-boson-exchange q-q models. These results can be explained by the constraints that the baryonic spectrum impose on the short range behavior of the mesonic interactions.Comment: 11 pages, 1 figure added, expanded discussio

Virtual reality surgery simulation: A survey on patient specific solution

For surgeons, the precise anatomy structure and its dynamics are important in the surgery interaction, which is critical for generating the immersive experience in VR based surgical training applications. Presently, a normal therapeutic scheme might not be able to be straightforwardly applied to a specific patient, because the diagnostic results are based on averages, which result in a rough solution. Patient Specific Modeling (PSM), using patient-specific medical image data (e.g. CT, MRI, or Ultrasound), could deliver a computational anatomical model. It provides the potential for surgeons to practice the operation procedures for a particular patient, which will improve the accuracy of diagnosis and treatment, thus enhance the prophetic ability of VR simulation framework and raise the patient care. This paper presents a general review based on existing literature of patient specific surgical simulation on data acquisition, medical image segmentation, computational mesh generation, and soft tissue real time simulation

The predictive value of early behavioural assessments in pet dogs: a longitudinal study from neonates to adults

Studies on behavioural development in domestic dogs are of relevance for matching puppies with the right families, identifying predispositions for behavioural problems at an early stage, and predicting suitability for service dog work, police or military service. The literature is, however, inconsistent regarding the predictive value of tests performed during the socialisation period. Additionally, some practitioners use tests with neonates to complement later assessments for selecting puppies as working dogs, but these have not been validated. We here present longitudinal data on a cohort of Border collies, followed up from neonate age until adulthood. A neonate test was conducted with 99 Border collie puppies aged 2–10 days to assess activity, vocalisations when isolated and sucking force. At the age of 40–50 days, 134 puppies (including 93 tested as neonates) were tested in a puppy test at their breeders' homes. All dogs were adopted as pet dogs and 50 of them participated in a behavioural test at the age of 1.5 to 2 years with their owners. Linear mixed models found little correspondence between individuals' behaviour in the neonate, puppy and adult test. Exploratory activity was the only behaviour that was significantly correlated between the puppy and the adult test. We conclude that the predictive validity of early tests for predicting specific behavioural traits in adult pet dogs is limited

Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes

In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied