Uncertainties in field-line tracing in the magnetosphere. <br>Part I: the axisymmetric part of the internal geomagnetic field

International audienceThe technique of tracing along magnetic field lines is widely used in magnetospheric physics to provide a "magnetic frame of reference'' that facilitates both the planning of experiments and the interpretation of observations. The precision of any such magnetic frame of reference depends critically on the accurate representation of the various sources of magnetic field in the magnetosphere. In order to consider this important problem systematically, a study is initiated to estimate first the uncertainties in magnetic-field-line tracing in the magnetosphere that arise solely from the published (standard) errors in the specification of the geomagnetic field of internal origin. Because of the complexity in computing these uncertainties for the complete geomagnetic field of internal origin, attention is focused in this preliminary paper on the uncertainties in magnetic-field-line tracing that result from the standard errors in just the axisymmetric part of the internal geomagnetic field. An exact analytic equation exists for the magnetic field lines of an arbitrary linear combination of axisymmetric multipoles. This equation is used to derive numerical estimates of the uncertainties in magnetic-field-line tracing that are due to the published standard errors in the axisymmetric spherical harmonic coefficients (i.e. gn0 ± ?gn0). Numerical results determined from the analytic equation are compared with computational results based on stepwise numerical integration along magnetic field lines. Excellent agreement is obtained between the analytical and computational methods in the axisymmetric case, which provides great confidence in the accuracy of the computer program used for stepwise numerical integration along magnetic field lines. This computer program is then used in the following paper to estimate the uncertainties in magnetic-field-line tracing in the magnetosphere that arise from the published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) geomagnetic field of internal origin. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, calculated here for the axisymmetric part of the internal geomagnetic field, should be regarded as "first approximations'' in the sense that such estimates are only as accurate as the published standard errors in the set of axisymmetric spherical harmonic coefficients. However, all procedures developed in this preliminary paper can be applied to the derivation of more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients

Uncertainties in field-line tracing in the magnetosphere. <br>Part II: the complete internal geomagnetic field

International audienceThe discussion in the preceding paper is restricted to the uncertainties in magnetic-field-line tracing in the magnetosphere resulting from published standard errors in the spherical harmonic coefficients that define the axisymmetric part of the internal geomagnetic field (i.e. gn0 ± ?gn0). Numerical estimates of these uncertainties based on an analytic equation for axisymmetric field lines are in excellent agreement with independent computational estimates based on stepwise numerical integration along magnetic field lines. This comparison confirms the accuracy of the computer program used in the present paper to estimate the uncertainties in magnetic-field-line tracing that arise from published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) internal geomagnetic field (i.e. gnm ± ?gnm and hnm ± ?hnm). An algorithm is formulated that greatly reduces the computing time required to estimate these uncertainties in magnetic-field-line tracing. The validity of this algorithm is checked numerically for both the axisymmetric part of the internal geomagnetic field in the general case (1 ? n ? 10) and the complete internal geomagnetic field in a restrictive case (0 ? m ? n, 1 ? n ? 3). On this basis it is assumed that the algorithm can be used with confidence in those cases for which the computing time would otherwise be prohibitively long. For the complete internal geomagnetic field, the maximum characteristic uncertainty in the geocentric distance of a field line that crosses the geomagnetic equator at a nominal dipolar distance of 2 RE is typically 100 km. The corresponding characteristic uncertainty for a field line that crosses the geomagnetic equator at a nominal dipolar distance of 6 RE is typically 500 km. Histograms and scatter plots showing the characteristic uncertainties associated with magnetic-field-line tracing in the magnetosphere are presented for a range of illustrative examples. Finally, estimates are given for the maximum uncertainties in the locations of the conjugate points of selected geophysical observatories. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, including the associated uncertainties in the locations of the conjugate points of geophysical observatories, should be regarded as "first approximations'' in the sense that these estimates are only as accurate as the published standard errors in the full set of spherical harmonic coefficients. As in the preceding paper, however, all computational techniques developed in this paper can be used to derive more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients

Multiple congenital oral granular cell tumours in a newborn black female: a case report

© 2008 Feller et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Vulnerable and exploitable:the need for organisational accountability and transparency in emerging and less developed economies

The aim of this paper is to provide an overview of the papers which appear in this special issue of Accounting Forum. The paper sets out the background and rationale for this special issue, introduces the papers contained within it and discusses their contributions to the literature on social and environmental accounting and accountability in emerging and less developed economies. This discussion is informed by the notions of vulnerability and exploitability. The final section of the paper provides conclusions and directions for future research in this under-researched area

Shar-pei Mediates Cell Proliferation Arrest During Imaginal Disc Growth in Drosophila

During animal development, organ size is determined primarily by the amount of cell proliferation, which must be tightly regulated to ensure the generation of properly proportioned organs. However, little is known about the molecular pathways that direct cells to stop proliferating when an organ has attained its proper size. We have identified mutations in a novel gene, shar-pei, that is required for proper termination of cell proliferation during Drosophila imaginal disc development. Clones of shar-pei mutant cells in imaginal discs produce enlarged tissues containing more cells of normal size. We show that this phenotype is the result of both increased cell proliferation and reduced apoptosis. Hence,shar-pei restricts cell proliferation and promotes apoptosis. By contrast, shar-pei is not required for cell differentiation and pattern formation of adult tissue. Shar-pei is also not required for cell cycle exit during terminal differentiation, indicating that the mechanisms directing cell proliferation arrest during organ growth are distinct from those directing cell cycle exit during terminal differentiation. shar-pei encodes a WW-domain-containing protein that has homologs in worms, mice and humans, suggesting that mechanisms of organ growth control are evolutionarily conserved

Topological Magnon Bands in a Kagome Lattice Ferromagnet

There is great interest in finding materials possessing quasiparticles with topological properties. Such materials may have novel excitations that exist on their boundaries which are protected against disorder. We report experimental evidence that magnons in an insulating kagome ferromagnet can have a topological band structure. Our neutron scattering measurements further reveal that one of the bands is flat due to the unique geometry of the kagome lattice. Spin wave calculations show that the measured band structure follows from a simple Heisenberg Hamiltonian with a Dzyaloshinkii-Moriya interaction. This serves as the first realization of an effectively two-dimensional topological magnon insulator—a new class of magnetic material that should display both a magnon Hall effect and protected chiral edge modes.United States. Dept. of Energy. Office of Basic Energy Sciences (Grant DE-FG02-07ER46134)National Science Foundation (U.S.) (Grant CHE 1041863