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

Additive value of [18F]PI-2620 perfusion imaging in progressive supranuclear palsy and corticobasal syndrome

Purpose: Early after [18F]PI-2620 PET tracer administration, perfusion imaging has potential for regional assessment of neuronal injury in neurodegenerative diseases. This is while standard late-phase [18F]PI-2620 tau-PET is able to discriminate the 4-repeat tauopathies progressive supranuclear palsy and corticobasal syndrome (4RTs) from disease controls and healthy controls. Here, we investigated whether early-phase [18F]PI-2620 PET has an additive value for biomarker based evaluation of 4RTs. Methods: Seventy-eight patients with 4RTs (71 ± 7 years, 39 female), 79 patients with other neurodegenerative diseases (67 ± 12 years, 35 female) and twelve age-matched controls (69 ± 8 years, 8 female) underwent dynamic (0-60 min) [18F]PI-2620 PET imaging. Regional perfusion (0.5-2.5 min p.i.) and tau load (20-40 min p.i.) were measured in 246 predefined brain regions [standardized-uptake-value ratios (SUVr), cerebellar reference]. Regional SUVr were compared between 4RTs and controls by an ANOVA including false-discovery-rate (FDR, p < 0.01) correction. Hypoperfusion in resulting 4RT target regions was evaluated at the patient level in all patients (mean value - 2SD threshold). Additionally, perfusion and tau pattern expression levels were explored regarding their potential discriminatory value of 4RTs against other neurodegenerative disorders, including validation in an independent external dataset (n = 37), and correlated with clinical severity in 4RTs (PSP rating scale, MoCA, activities of daily living). Results: Patients with 4RTs had significant hypoperfusion in 21/246 brain regions, most dominant in thalamus, caudate nucleus, and anterior cingulate cortex, fitting to the topology of the 4RT disease spectrum. However, single region hypoperfusion was not specific regarding the discrimination of patients with 4RTs against patients with other neurodegenerative diseases. In contrast, perfusion pattern expression showed promise for discrimination of patients with 4RTs from other neurodegenerative diseases (AUC: 0.850). Discrimination by the combined perfusion-tau pattern expression (AUC: 0.903) exceeded that of the sole tau pattern expression (AUC: 0.864) and the discriminatory power of the combined perfusion-tau pattern expression was replicated in the external dataset (AUC: 0.917). Perfusion but not tau pattern expression was associated with PSP rating scale (R = 0.402; p = 0.0012) and activities of daily living (R = - 0.431; p = 0.0005). Conclusion: [18F]PI-2620 perfusion imaging mirrors known topology of regional hypoperfusion in 4RTs. Single region hypoperfusion is not specific for 4RTs, but perfusion pattern expression may provide an additive value for the discrimination of 4RTs from other neurodegenerative diseases and correlates closer with clinical severity than tau pattern expression

Efficient solvers for nonlinear time-periodic eddy current problems

This work deals with all aspects of the numerical simulation of nonlinear time-periodic eddy current problems, ranging from the description of the nonlinearity to an efficient solution procedure. Due to the periodicity of the solution, we suggest a truncated Fourier series expansion, i.e. a so-called multiharmonic ansatz, instead of a costly time-stepping scheme. Linearization is done by a Newton iteration, where the preconditioning of the linearized problems is a special issue: Since the matrices are non-symmetric, we need a special adaptation of a multigrid preconditioner to our problem. Eddy current problems comprise another difficulty that complicates the numerical simulation, namely the formation of extremely thin boundary layers. This challenge is handled by means of adaptive mesh refinement.

Numerical Analysis of Nonlinear Multiharmonic Eddy Current Problems

This work provides a complete analysis of eddy current problems, ranging from a proof of unique solvability to the analysis of a multiharmonic discretization technique. For proving existence and uniqueness, we use a Schur complement approach in order to combine the structurally di#erent results for conducting and non-conducting regions. For solving the time-dependent problem, we take advantage of the periodicity of the solution. Since the sources usually are alternating current, we propose a truncated Fourier series expansion, i.e. a so-called multiharmonic ansatz, instead of a costly time-stepping scheme. Moreover, we suggest to introduce a regularization parameter for the numerical solution, what ensures unique solvability not only in the factor space of divergence-free functions, but in the whole space H(curl). Finally, we provide estimates for the errors that are due to the truncated Fourier series, the spatial discretization and the regularization parameter.

A Survey in Mathematics for Industry - An efficient method for the numerical simulation of magneto-mechanical sensors and actuators

The dynamic behaviour of magneto-mechanical sensors and actuators can be completely described by Maxwell's and Navier-Lamé's partial differential equations (PDEs) with appropriate coupling terms reflecting the interactions of these fields and with the corresponding initial, boundary and interface conditions. Neglecting the displacement currents, which can be done for the classes of problems considered in this paper, and introducing the vector potential for the magnetic field, we arrive at a system of degenerate parabolic PDEs for the vector potential coupled with the hyperbolic PDEs for the displacements.Usually the computational domain, the finite element discretization, the time integration, and the solver are different for the magnetic and mechanical parts. For instance, the vector potential is approximated by edge elements whereas the finite element discretization of the displacements is based on nodal elements on different meshes. The most time consuming modules in the solution procedure are the solvers for both, the magnetical and the mechanical finite element equations arising at each step of the time integration procedure. We use geometrical multigrid solvers which are different for both parts. These multigrid solvers enable us to solve quite efficiently not only academic test problems, but also transient 3D technical magneto-mechanical systems of high complexity such as solenoid valves and electro-magnetic-acoustic transducers. The results of the computer simulation are in very good agreement with the experimental data