Spaces of finite element differential forms

We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit commuting projections. We present two families of spaces in the case of simplicial meshes, and two other families in the case of cubical meshes. We make use of the exterior calculus and the Koszul complex to define and understand the spaces. These tools allow us to treat a wide variety of situations, which are often treated separately, in a unified fashion.Comment: To appear in: Analysis and Numerics of Partial Differential Equations, U. Gianazza, F. Brezzi, P. Colli Franzone, and G. Gilardi, eds., Springer 2013. v2: a few minor typos corrected. v3: a few more typo correction

An Example of Semiclassical Instanton-Like Scattering: (1+1) Dimensional Sigma Model

A solution to the classical field equations in the massless (1+1)-dimensional O(3) sigma model is found, which describes a multi-particle instanton-like transition at high energy. In the limit of small number of initial particles, the number of final particles is shown to be also small, and the probability of the transition is suppressed by $\exp(-2S_0)$, where $S_0$ is the instanton action. This solution, however, does not correspond to the maximum transition probability among all states with given number of incoming particles and energy. Unless the limit $g^2 n_{initial}\to0$ is exponentially sensitive to the structure of the initial state, our results imply that well above the sphaleron energy, the instanton-induced cross section becomes again suppressed by the instanton exponent, and the number of final paricles is again small.Comment: 28 pages, LaTeX preprint TPI-MINN-92/66-

Frequent induction of chromosomal aberrations in in vivo skin fibroblasts after allogeneic stem cell transplantation: hints to chromosomal instability after irradiation

BACKGROUND: Total body irradiation (TBI) has been part of standard conditioning regimens before allogeneic stem cell transplantation for many years. Its effect on normal tissue in these patients has not been studied extensively. METHOD: We studied the in vivo cytogenetic effects of TBI and high-dose chemotherapy on skin fibroblasts from 35 allogeneic stem cell transplantation (SCT) patients. Biopsies were obtained prospectively (n = 18 patients) before, 3 and 12 months after allogeneic SCT and retrospectively (n = 17 patients) 23-65 months after SCT for G-banded chromosome analysis. RESULTS: Chromosomal aberrations were detected in 2/18 patients (11 %) before allogeneic SCT, in 12/13 patients (92 %) after 3 months, in all patients after 12 months and in all patients in the retrospective group after allogeneic SCT. The percentage of aberrant cells was significantly higher at all times after allogeneic SCT compared to baseline analysis. Reciprocal translocations were the most common aberrations, but all other types of stable, structural chromosomal aberrations were also observed. Clonal aberrations were observed, but only in three cases they were detected in independently cultured flasks. A tendency to non-random clustering throughout the genome was observed. The percentage of aberrant cells was not different between patients with and without secondary malignancies in this study group. CONCLUSION: High-dose chemotherapy and TBI leads to severe chromosomal damage in skin fibroblasts of patients after SCT. Our long-term data suggest that this damage increases with time, possibly due to in vivo radiation-induced chromosomal instability

Semiclassical Study of Baryon and Lepton Number Violation in High-Energy Electroweak Collisions

We make use of a semiclassical method for calculating the suppression exponent for topology changing transitions in high-energy electroweak collisions. In the Standard Model these processes are accompanied by violation of baryon and lepton number. By using a suitable computational technique we obtain results for s-wave scattering in a large region of initial data. Our results show that baryon and lepton number violation remains exponentially suppressed up to very high energies of at least 30 sphaleron masses (250 TeV). We also conclude that the known analytic approaches inferred from low energy expansion provide reasonably good approximations up to the sphaleron energy (8 TeV) only.Comment: 23 pages, 18 figures. Phys.Rev.D journal version (two references added

Impact of early remission by induction therapy on allogeneic stem cell transplantation for acute myeloid leukemia with an intermediate risk karyotype in first complete remission

For patients with acute myeloid leukemia (AML) early achievement of remission during induction treatment is an important predictor for long-term outcome irrespective of the type of consolidation therapy employed. Here, we retrospectively examined the prognostic impact of early remission (ER) versus delayed remission (DR) in a cohort of 132 AML patients with an intermediate risk karyotype undergoing allogeneic stem cell transplantation (alloSCT) in first complete remission (CR1). In contrast to patients showing DR, patients achieving ER had a significantly higher 3-year overall survival (OS) and disease-free survival (DFS) of 76% versus 54% (p=0.03) and 76% versus 53% (p=0.03). Likewise, three years after alloSCT the cumulative incidence of relapse (CI-R) was significantly lower in the ER subgroup as compared to patients achieving DR, i.e. 10% versus 35% (p=0.004), whereas non-relapse mortality (NRM) did not differ significantly. Multivariate analysis identified DR as an independent prognosticator for an inferior DFS (HR 3.37, p=0.002) and a higher CI-R (HR 3.55, p=0.002). Taken together, these data may indicate that the rapid achievement of remission predicts a favorable outcome in patients with intermediate risk AML undergoing alloSCT in CR1. In turn, the adverse effect of DR may not be fully overcome by alloSCT

Angle dependence of Andreev scattering at semiconductor-superconductor interfaces

We study the angle dependence of the Andreev scattering at a semiconductor-superconductor interface, generalizing the one-dimensional theory of Blonder, Tinkham and Klapwijk. An increase of the momentum parallel to the interface leads to suppression of the probability of Andreev reflection and increase of the probability of normal reflection. We show that in the presence of a Fermi velocity mismatch between the semiconductor and the superconductor the angles of incidence and transmission are related according to the well-known Snell's law in optics. As a consequence there is a critical angle of incidence above which only normal reflection exists. For two and three-dimensional interfaces a lower excess current compared to ballistic transport with perpendicular incidence is found. Thus, the one-dimensional BTK model overestimates the barrier strength for two and three-dimensional interfaces.Comment: 8 pages including 3 figures (revised, 6 references added

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

Dynamics of Vortex Dipoles in Confined Bose-Einstein Condensates

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.Comment: 8 pages, 3 figures, to appear in Phys. Lett.

Nonlinear analysis of spacecraft thermal models

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.Comment: 29 pages, 4 figure

The clustering of ultra-high energy cosmic rays and their sources

The sky distribution of cosmic rays with energies above the 'GZK cutoff' holds important clues to their origin. The AGASA data, although consistent with isotropy, shows evidence for small-angle clustering, and it has been argued that such clusters are aligned with BL Lacertae objects, implicating these as sources. It has also been suggested that clusters can arise if the cosmic rays come from the decays of very massive relic particles in the Galactic halo, due to the expected clumping of cold dark matter. We examine these claims and show that both are in fact not justified.Comment: 13 pages, 8 figures, version in press at Phys. Rev.