Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations

We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric and magnetic field. Special emphasis is placed on an efficient implementation which is achieved by taking advantage of recurrence properties and the tensor-product structure of the chosen shape functions. These recurrences have been derived symbolically with computer algebra methods reminiscent of the holonomic systems approach.Comment: 16 pages, 1 figure, 1 table; Springer Wien, ISBN 978-3-7091-0793-

Fertilizing greenhouse vegetables

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Time evolution in linear response: Boltzmann equations and beyond

In this work a perturbative linear response analysis is performed for the time evolution of the quasi-conserved charge of a scalar field. One can find two regimes, one follows exponential damping, where the damping rate is shown to come from quantum Boltzmann equations. The other regime (coming from multiparticle cuts and products of them) decays as power law. The most important, non-oscillating contribution in our model comes from a 4-particle intermediate state and decays as 1/t^3. These results may have relevance for instance in the context of lepton number violation in the Early Universe.Comment: 19 page

Long-term outcomes of allogeneic haematopoietic stem cell transplantation for adult cerebral X-linked adrenoleukodystrophy

The adult cerebral inflammatory form of X-linked adrenoleukodystrophy is a rapidly progressive neurodegenerative disease, as devastating as childhood cerebral adrenoleukodystrophy. Allogeneic haematopoietic stem cell transplantation has been demonstrated to provide long-term neurological benefits for boys with the childhood cerebral form, but results in adults are sparse and inconclusive. We analysed data from 14 adult males with adult cerebral adrenoleukodystrophy treated with allogeneic haematopoietic stem cell transplantation on a compassionate basis in four European centres. All presented with cerebral demyelinating lesions and gadolinium enhancement. Median age at diagnosis of adult cerebral adrenoleukodystrophy was 33 years (range 21–48 years). In addition to cerebral inflammation, five patients had established severe motor disability from adrenomyeloneuropathy affecting only the spinal cord and peripheral nerves (Expanded Disability Status Scale score ≥ 6). Eight patients survived (estimated survival 57 ± 13%) with a median follow-up of 65 months (minimum 38 months). Death was directly transplant-/infection-related (n = 3), due to primary disease progression in advanced adult cerebral adrenoleukodystrophy (n = 1), or secondary disease progression (n = 2) after transient multi-organ failure or non-engraftment. Specific complications during stem cell transplantation included deterioration of motor and bladder functions (n = 12) as well as behavioural changes (n = 8). Arrest of progressive cerebral demyelination and prevention of severe loss of neurocognition was achieved in all eight survivors, but deterioration of motor function occurred in the majority (n = 5). Limited motor dysfunction (Expanded Disability Status Scale score < 6) prior to transplantation was associated with significantly improved survival [78 ± 14% (n = 9) versus 20 ± 18%(n = 5); P < 0.05] and maintenance of ambulation (Expanded Disability Status Scale score < 7) post-transplant (78% versus 0%; P = 0.021). In contrast, bilateral involvement of the internal capsule on brain MRI was associated with poorer survival [20 ± 18% (n = 5) versus 78 ± 14% (n = 9); P < 0.05]. This study is the first to support the feasibility, complications and potential long-term neurological benefit of allogeneic haematopoietic stem cell transplantation in adult cerebral adrenoleukodystrophy. Further studies are warranted to attempt to improve outcomes through patient selection and optimization of transplantation protocols

Analysis of a three-component model phase diagram by Catastrophe Theory: Potentials with two Order Parameters

In this work we classify the singularities obtained from the Gibbs potential of a lattice gas model with three components, two order parameters and five control parameters applying the general theorems provided by Catastrophe Theory. In particular, we clearly establish the existence of Landau potentials in two variables or, in other words, corank 2 canonical forms that are associated to the hyperbolic umbilic, D_{+4}, its dual the elliptic umbilic, D_{-4}, and the parabolic umbilic, D_5, catastrophes. The transversality of the potential with two order parameters is explicitely shown for each case. Thus we complete the Catastrophe Theory analysis of the three-component lattice model, initiated in a previous paper.Comment: 17 pages, 3 EPS figures, Latex file, continuation of Phys. Rev. B57, 13527 (1998) (cond-mat/9707015), submitted to Phys. Rev.

On the Global Existence of Bohmian Mechanics

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe

The effect of surgical change to hip geometry on hip biomechanics after primary total hip arthroplasty

First published: 06 October 2022. OnlinePublThe aim of this study was to determine the effect of surgical change to the acetabular offset and femoral offset on the abductor muscle and hip contact forces after primary THA using computational methods. Thirty-five patients undergoing primary THA were recruited. Patients underwent a computed tomography scan of their pelvis and hip, and underwent gait analysis pre- and 6-months post-operatively. Surgically induced changes in acetabular and femoral offset were used to inform a musculoskeletal model to estimated abductor muscle and hip joint contact forces. Two experiments were performed: (1) influence of changes in hip geometry on hip biomechanics with preoperative kinematics; and (2) influence of changes in hip geometry on hip biomechanics with postoperative kinematics. Superior and medial placement of the hip centre of rotation during THA was most influential in reducing hip contact forces, predicting 63% of the variance (p<0.001). When comparing the preoperative geometry and kinematics model, with postoperative geometry and kinematics, hip contact forces increased after surgery (0.68 BW, p=0.001). Increasing the abductor lever arm reduced abductor muscle force by 28% (p<0.001) and resultant hip contact force by 17% (0.6 BW, p=0.003), with both preoperative and postoperative kinematics. Failure to increase abductor lever arm increased resultant hip contact force 11% (0.33 BW, p<0.001). In conclusion, increasing the abductor lever arm provides a substantial biomechanical benefit to reduce hip abductor and resultant hip joint contact forces. The magnitude of this effect is equivalent to the average increase in hip contact force seen with improved gait from pre-to post-surgery. This article is protected by copyright. All rights reserved.Jasvir S. Bahl, John B. Arnold, David J. Saxby, Mark Taylor, Lucian B. Solomon, Dominic Thewli

Computation of the winding number diffusion rate due to the cosmological sphaleron

A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solution for a sphaleron model in $3+1$ spacetime dimensions.Comment: Some style corrections suggested by the referee are introduced (mainly in Sec.II), one reference added. To appear in Phys.Rev.D 29 pages, LaTeX, 3 Postscript figures, uses epsf.st

Electromagnetic form factors of light vector mesons

The electromagnetic form factors G_E(q^2), G_M(q^2), and G_Q(q^2), charge radii, magnetic and quadrupole moments, and decay widths of the light vector mesons rho^+, K^{*+} and K^{*0} are calculated in a Lorentz-covariant, Dyson-Schwinger equation based model using algebraic quark propagators that incorporate confinement, asymptotic freedom, and dynamical chiral symmetry breaking, and vector meson Bethe-Salpeter amplitudes closely related to the pseudoscalar amplitudes obtained from phenomenological studies of pi and K mesons. Calculated static properties of vector mesons include the charge radii and magnetic moments: r_{rho+} = 0.61 fm, r_{K*+} = 0.54 fm, and r^2_{K*0} = -0.048 fm^2; mu_{rho+} = 2.69, mu_{K*+} = 2.37, and mu_{K*0} = -0.40. The calculated static limits of the rho-meson form factors are similar to those obtained from light-front quantum mechanical calculations, but begin to differ above q^2 = 1 GeV^2 due to the dynamical evolution of the quark propagators in our approach.Comment: 8 pages of RevTeX, 5 eps figure