Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls

We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.

5-ALA complete resections go beyond MR contrast enhancement: shift corrected volumetric analysis of the extent of resection in surgery for glioblastoma

BACKGROUND The technique of 5-aminolevulinic acid (5-ALA) tumor fluorescence is increasingly used to improve visualization of tumor tissue and thereby to increase the rate of patients with gross total resections. In this study, we measured the resection volumes in patients who underwent 5-ALA-guided surgery for non-eloquent glioblastoma and compared them with the preoperative tumor volume. METHODS We selected 13 patients who had received a complete resection according to intraoperative 5-ALA induced fluorescence and CRET according to post-operative T1 contrast-enhanced MRI. The volumes of pre-operative contrast enhancing tissue, post-operative resection cavity and resected tissue were determined through shift-corrected volumetric analysis. RESULTS The mean resection cavity (29 cm(3)) was marginally smaller than the pre-operative contrast-enhancing tumor (39 cm(3), p = 0.32). However, the mean overall resection volume (84 cm(3)) was significantly larger than the pre-operative contrast-enhancing tumor (39 cm(3), p = 0.0087). This yields a mean volume of resected 5-ALA positive, but radiological non-enhancing tissue of 45 cm(3). The mean calculated rim of resected tissue surpassed pre-operative tumor diameter by 6 mm (range 0-10 mm). CONCLUSIONS Results of the current study imply that (i) the resection cavity underestimates the volume of resected tissue and (ii) 5-ALA complete resections go significantly beyond the volume of pre-operative contrast-enhancing tumor bulk on MRI, indicating that 5-ALA also stains MRI non-enhancing tumor tissue. Use of 5-ALA may thus enable extension of coalescent tumor resection beyond radiologically evident tumor. The impact of this more extended resection method on time to progression and overall survival has not been determined, and potentially puts adjacent and functionally intact tissue at risk.

Critical point and scale setting in SU(3) plasma: An update

We explore a method developed in statistical physics which has been argued to have exponentially small finite-volume effects, in order to determine the critical temperature Tc of pure SU(3) gauge theory close to the continuum limit. The method allows us to estimate the critical coupling βc of the Wilson action for temporal extents up to Nτ∼20 with ≲0.1% uncertainties. Making use of the scale setting parameters r0 and t0−−√ in the same range of β-values, these results lead to the independent continuum extrapolations Tcr0=0.7457(45) and Tct0−−√=0.2489(14), with the latter originating from a more convincing fit. Inserting a conversion of r0 from literature (unfortunately with much larger errors) yields Tc/ΛMS¯¯¯¯¯=1.24(10).

Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

Hemodynamics analyses in treated and untreated carotid arteries of the same patient: A preliminary study based on three patient cases

Carotid atherosclerotic disease is highly related to cerebrovascular events. Carotid endarterectomy is the common operation method to treat this disease. In this study, hemodynamics analyses are performed on the carotid arteries in three patients, whose right carotid artery had been treated by carotid endarterectomy and the left carotid artery remained untreated. Flow and loading conditions are compared between these treated and untreated carotid arteries and evaluation of the operative results is discussed. Patient-specific models are reconstructed from MDCT data. Intraoperative ultrasound flow measurements are performed on the treated carotid arteries and the obtained data are used as the boundary conditions of the models and the validations of the computational results. Finite volume method is employed to solve the transport equations and the flow and loading conditions of the models are reported. The results indicate that: (i) in two of the three patients, the internal-to-external flow rate ratio in the untreated carotid artery is larger than that in the treated one, and the average overall flow split ratio by summing up the data of both the left and right carotid arteries is about 2.15; (ii) in the carotid bulb, high wall shear stress occurs at the bifurcation near the external carotid artery in all of the cases without hard plaques; (iii) the operated arteries present low time-averaged wall shear stress at the carotid bulb, especially for the treated arteries with patch technique, indicating the possibility of the recurrence of stenosis; (iv) high temporal gradient of wall shear stress (>35 Pa/s) is shown in the narrowing regions along the vessels; and (v) in the carotid arteries without serious stenosis, the maximum velocity magnitude during mid-diastole is 32~37% of that at systolic peak, however, in the carotid artery with 50% stenosis by hard plaques, this value is nearly doubled (64%). The computational work quantifies flow and loading distributions in the treated and untreated carotid arteries of the same patient, contributing to evaluation of the operative results and indicating the recurrent sites of potential atheromatous plaques.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

Progress in Simulations with Twisted Mass Fermions at the Physical Point

In this contribution, results from Nf = 2 lattice QCD simulations at one lattice spacing using twisted mass fermions with a clover term at the physical pion mass are presented. The mass splitting between charged and neutral pions (including the disconnected contribution) is shown to be around 20(20) MeV. Further, a first measurement using the clover twisted mass action of the average momentum fraction of the pion is given. Finally, an analysis of pseudoscalar meson masses and decay constants is presented involving linear interpolations in strange and charm quark masses. Matching to meson mass ratios allows the calculation of quark mass ratios: ms=ml = 27:63(13), mc=ml = 339:6(2:2) and mc=ms = 12:29(10). From this mass matching the quantities fK = 153:9(7:5) MeV, fD = 219(11) MeV, fDs = 255(12) MeV and MDs = 1894(93) MeV are determined without the application of finite volume or discretization artefact corrections and with errors dominated by a preliminary estimate of the lattice spacing.

Cement distribution, volume, and compliance in vertebroplasty: some answers from an anatomy-based nonlinear finite element study

STUDY DESIGN: The biomechanics of vertebral bodies augmented with real distributions of cement were investigated using nonlinear finite element (FE) analysis. OBJECTIVES: To compare stiffness, strength, and stress transfer of augmented versus nonaugmented osteoporotic vertebral bodies under compressive loading. Specifically, to examine how cement distribution, volume, and compliance affect these biomechanical variables. SUMMARY OF BACKGROUND DATA: Previous FE studies suggested that vertebroplasty might alter vertebral stress transfer, leading to adjacent vertebral failure. However, no FE study so far accounted for real cement distributions and bone damage accumulation. METHODS: Twelve vertebral bodies scanned with high-resolution pQCT and tested in compression were augmented with various volumes of cements and scanned again. Nonaugmented and augmented pQCT datasets were converted to FE models, with bone properties modeled with an elastic, plastic and damage constitutive law that was previously calibrated for the nonaugmented models. The cement-bone composite was modeled with a rule of mixture. The nonaugmented and augmented FE models were subjected to compression and their stiffness, strength, and stress map calculated for different cement compliances. RESULTS: Cement distribution dominated the stiffening and strengthening effects of augmentation. Models with cement connecting either the superior or inferior endplate (S/I fillings) were only up to 2 times stiffer than the nonaugmented models with minimal strengthening, whereas those with cement connecting both endplates (S + I fillings) were 1 to 8 times stiffer and 1 to 12 times stronger. Stress increases above and below the cement, which was higher for the S + I cases and was significantly reduced by increasing cement compliance. CONCLUSION: The developed FE approach, which accounts for real cement distributions and bone damage accumulation, provides a refined insight into the mechanics of augmented vertebral bodies. In particular, augmentation with compliant cement bridging both endplates would reduce stress transfer while providing sufficient strengthening.

Mesh-based vs. Image-based Statistical Appearance Model of the Human Femur: a Preliminary Comparison Study for the Creation of Finite Element Meshes

Statistical models have been recently introduced in computational orthopaedics to investigate the bone mechanical properties across several populations. A fundamental aspect for the construction of statistical models concerns the establishment of accurate anatomical correspondences among the objects of the training dataset. Various methods have been proposed to solve this problem such as mesh morphing or image registration algorithms. The objective of this study is to compare a mesh-based and an image-based statistical appearance model approaches for the creation of nite element(FE) meshes. A computer tomography (CT) dataset of 157 human left femurs was used for the comparison. For each approach, 30 finite element meshes were generated with the models. The quality of the obtained FE meshes was evaluated in terms of volume, size and shape of the elements. Results showed that the quality of the meshes obtained with the image-based approach was higher than the quality of the mesh-based approach. Future studies are required to evaluate the impact of this finding on the final mechanical simulations.

The COLOSS BEEBOOK Volume I, Standard methods for Apis mellifera research: Introduction

The COLOSS BEEBOOK is a practical manual compiling standard methods in all fields of research on the western honey bee, Apis mellifera. The COLOSS network was founded in 2008 as a consequence of the heavy and frequent losses of managed honey bee colonies experienced in many regions of the world (Neumann and Carreck, 2010). As many of the world’s honey bee research teams began to address the problem, it soon became obvious that a lack of standardized research methods was seriously hindering scientists’ ability to harmonize and compare the data on colony losses obtained internationally. In its second year of activity, during a COLOSS meeting held in Bern, Switzerland, the idea of a manual of standardized honey bee research methods emerged. The manual, to be called the COLOSS BEEBOOK, was inspired by publications with similar purposes for fruit fly research (Lindsley and Grell, 1968; Ashburner 1989; Roberts, 1998; Greenspan, 2004).

The COLOSS BEEBOOK Volume II, Standard methods for Apis mellifera pest and pathogen research: Introduction

The COLOSS BEEBOOK is a practical manual compiling standard methods in all fields of research on the western honey bee, Apis mellifera. The COLOSS network was founded in 2008 as a consequence of the heavy and frequent losses of managed honey bee colonies experienced in many regions of the world (Neumann and Carreck, 2010). As many of the world’s honey bee research teams began to address the problem, it soon became obvious that a lack of standardized research methods was seriously hindering scientists’ ability to harmonize and compare the data on colony losses obtained internationally. In its second year of activity, during a COLOSS meeting held in Bern, Switzerland, the idea of a manual of standardized honey bee research methods emerged. The manual, to be called the COLOSS BEEBOOK, was inspired by publications with similar purposes for fruit fly research (Lindsley and Grell, 1968; Ashburner, 1989; Roberts, 1998; Greenspan, 2004).

The COLOSS BEEBOOK Volume II: Standard methods for Apis mellifera pest and pathogen research

n recent years, declines of honey bee populations have received massive media attention worldwide, yet attempts to understand the causes have been hampered by a lack of standardisation of laboratory techniques. Published as a response to this, the COLOSS BEEBOOK is a unique collaborative venture involving 234 bee scientists from 34 countries, who have produced the definitive guide to how to carry out research on honey bees. It is hoped that these volumes will become the standards to be adopted by bee scientists worldwide. Volume II includes approximately 600 separate protocols dealing with the study of the pests and diseases of the honey bee, Apis mellifera. These cover epidemiology and surveying techniques, virus diseases, bacterial diseases such as European and American foulbrood, fungal and microsporidian diseases such as Nosema, mites such as Acarapis, Varroa and Tropilaelaps, and other pests such as the small hive beetle.

The COLOSS BEEBOOK Volume I: Standard Methods for Apis mellifera Research

In recent years, declines of honey bee populations have received massive media attention worldwide, yet attempts to understand the causes have been hampered by a lack of standardisation of laboratory techniques. Published as a response to this, the COLOSS BEEBOOK is a unique collaborative venture involving 234 bee scientists from 34 countries, who have produced the definitive guide to how to carry out research on honey bees. It is hoped that these volumes will become the standards to be adopted by bee scientists worldwide. Volume I includes approximately 1,100 separate protocols dealing with the study of the honey bee, Apis mellifera. These cover anatomy, behavioural studies, chemical ecology, breeding, genetics, instrumental insemination and queen rearing, pollination, molecular studies, statistics, toxicology and numerous other techniques

Image-based vs. mesh-based statistical appearance models of the human femur: Implications for finite element simulations.

Statistical appearance models have recently been introduced in bone mechanics to investigate bone geometry and mechanical properties in population studies. The establishment of accurate anatomical correspondences is a critical aspect for the construction of reliable models. Depending on the representation of a bone as an image or a mesh, correspondences are detected using image registration or mesh morphing. The objective of this study was to compare image-based and mesh-based statistical appearance models of the femur for finite element (FE) simulations. To this aim, (i) we compared correspondence detection methods on bone surface and in bone volume; (ii) we created an image-based and a mesh-based statistical appearance models from 130 images, which we validated using compactness, representation and generalization, and we analyzed the FE results on 50 recreated bones vs. original bones; (iii) we created 1000 new instances, and we compared the quality of the FE meshes. Results showed that the image-based approach was more accurate in volume correspondence detection and quality of FE meshes, whereas the mesh-based approach was more accurate for surface correspondence detection and model compactness. Based on our results, we recommend the use of image-based statistical appearance models for FE simulations of the femur.