615 research outputs found
Improved Formulae for the Inductance of Straight Wires
The best analytical formulae for the self-inductance of rectangular coils of circular cross section available in the literature were derived from formulae for the partial inductance of straight wires, which, in turn, are based on the well-known formula for the mutual inductance of parallel current filaments, and on the exact value of the geometric mean distance (GMD) for integrating the mutual inductance formula over the cross section of the wire. But in this way, only one term of the mutual inductance formula is integrated, whereas it contains also other terms. In the formulae found in the literature, these other terms are either completely neglected, or their integral is only coarsely approximated. We prove that these other terms can be accurately integrated by using the arithmetic mean distance (AMD) and the arithmetic mean square distance (AMSD) of the wire cross section. We present general formulae for the partial and mutual inductance of straight wires of any cross section and for any frequency based on the use of the GMD, AMD, and AMSD. Since partial inductance of single wires cannot be measured, the errors of the analytical approximations are computed with the help of exact computations of the six-dimensional integral defining induction. These are obtained by means of a coordinate transformation that reduces the six-dimensional integral to a three-dimensional one, which is then solved numerically. We give examples of an application of our analytical formulae to the calculation of the inductance of short-circuited two-wire lines. The new formulae show a substantial improvement in accuracy for short wires
Transversal torus knots
We classify positive transversal torus knots in tight contact structures up
to transversal isotopy.Comment: 16 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol3/paper11.abs.htm
Improved Formulae for the Inductance of Straight Wires
The best analytical formulae for the self-inductance of rectangular coils of circular cross section available in the literature were derived from formulae for the partial inductance of straight wires, which, in turn, are based on the well-known formula for the mutual inductance of parallel current filaments, and on the exact value of the geometric mean distance (GMD) for integrating the mutual inductance formula over the cross section of the wire. But in this way, only one term of the mutual inductance formula is integrated, whereas it contains also other terms. In the formulae found in the literature, these other terms are either completely neglected, or their integral is only coarsely approximated. We prove that these other terms can be accurately integrated by using the arithmetic mean distance (AMD) and the arithmetic mean square distance (AMSD) of the wire cross section. We present general formulae for the partial and mutual inductance of straight wires of any cross section and for any frequency based on the use of the GMD, AMD, and AMSD. Since partial inductance of single wires cannot be measured, the errors of the analytical approximations are computed with the help of exact computations of the six-dimensional integral defining induction. These are obtained by means of a coordinate transformation that reduces the six-dimensional integral to a three-dimensional one, which is then solved numerically. We give examples of an application of our analytical formulae to the calculation of the inductance of short-circuited two-wire lines. The new formulae show a substantial improvement in accuracy for short wires
The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect
The GMD method (geometric mean distance) to calculate inductance offers undoubted advantages over other methods. But so far it seemed to be limited to the case where the current is uniformly distributed over the cross section of the conductor, i.e. to DC (direct current). In this paper, the definition of the GMD is extended to include cases of nonuniform distribution observed at higher frequencies as the result of skin effect. An exact relation between the GMD and the internal inductance per unit length for infinitely long conductors of circularly symmetric cross section is derived. It enables much simpler derivations of Maxwell’s analytical expressions for the GMD of circular and annular disks than were known before. Its salient application, however, is the derivation of exact expressions for the GMD of infinitely long round wires and tubular conductors with skin effect. These expressions are then used to verify the consistency of the extended definition of the GMD. Further, approximate formulae for the GMD of round wires with skin effect based on elementary functions are discussed. Total inductances calculated with the help of the derived formulae for the GMD with and without skin effect are compared to measurement results from the literature. For conductors of square cross section, an analytical approximation for the GMD with skin effect based on elementary functions is presented. It is shown that it allows to calculate the total inductance of such conductors for frequencies from DC up to 25 GHz to a precision of better than 1 %
The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect
The GMD method (geometric mean distance) to calculate inductance offers undoubted advantages over other methods. But so far it seemed to be limited to the case where the current is uniformly distributed over the cross section of the conductor, i.e. to DC (direct current). In this paper, the definition of the GMD is extended to include cases of nonuniform distribution observed at higher frequencies as the result of skin effect. An exact relation between the GMD and the internal inductance per unit length for infinitely long conductors of circularly symmetric cross section is derived. It enables much simpler derivations of Maxwell’s analytical expressions for the GMD of circular and annular disks than were known before. Its salient application, however, is the derivation of exact expressions for the GMD of infinitely long round wires and tubular conductors with skin effect. These expressions are then used to verify the consistency of the extended definition of the GMD. Further, approximate formulae for the GMD of round wires with skin effect based on elementary functions are discussed. Total inductances calculated with the help of the derived formulae for the GMD with and without skin effect are compared to measurement results from the literature. For conductors of square cross section, an analytical approximation for the GMD with skin effect based on elementary functions is presented. It is shown that it allows to calculate the total inductance of such conductors for frequencies from DC up to 25 GHz to a precision of better than 1 %
Insulin-like growth factor-I is necessary for neural stem cell proliferation and demonstrates distinct actions of epidermal growth factor and fibroblast growth factor-2
Neural stem cells (NSCs), when stimulated with epidermal growth factor (EGF) or fibroblast growth factor-2 (FGF-2), have the capacity to renew, expand, and produce precursors for neurons, astrocytes, and oligodendrocytes. We postulated that the early appearance of insulin-like growth factor (IGF-I) receptors during mouse striatum development implies a role in NSC regulation. Thus, we tested in vitro the action of IGF-I on the proliferation of striatal NSCs. In the absence of IGF-I, neither EGF nor FGF-2 was able to induce the proliferation of E14 mouse striatal cells. However, addition of IGF-I generated large proliferative clusters, termed spheres, in a dose-dependent manner. The newly generated spheres were multipotent, and clonal analysis revealed that EGF or FGF-2, in the presence of IGF-I, acted directly on NSCs. The actions of IGF-I suggest distinct modes of action of EGF or FGF-2 on NSCs. First, continuous versus delayed administration of these neurotrophic factors showed that neither IGF-I nor EGF had an effect on NSC survival, whereas FGF-2 promoted the survival or maintenance of the stem cell state of 50% of NSCs for 6 d. Second, short-term exposure to IGF-I induced the proliferation of NSCs in the presence of EGF, but not of FGF-2, through an autocrine secretion of IGF-I. These findings suggest that IGF-I is a key factor in the regulation of NSC activation and that EGF and FGF-2 control striatal NSC proliferation, in part, through distinct intracellular mechanisms
Nonequilibrium Approach to Bloch-Peierls-Berry Dynamics
We examine the Bloch-Peierls-Berry dynamics under a classical nonequilibrium
dynamical formulation. In this formulation all coordinates in phase space
formed by the position and crystal momentum space are treated on equal footing.
Explicitly demonstrations of the no (naive) Liouville theorem and of the
validity of Darboux theorem are given. The explicit equilibrium distribution
function is obtained. The similarities and differences to previous approaches
are discussed. Our results confirm the richness of the Bloch-Peierls-Berry
dynamics
Ab-Initio Calculation of the Metal-Insulator Transition in Sodium rings and chains and in mixed Sodium-Lithium systems
We study how the Mott metal-insulator transition (MIT) is influenced when we
deal with electrons with different angular momenta. For lithium we found an
essential effect when we include -orbitals in the description of the Hilbert
space. We apply quantum-chemical methods to sodium rings and chains in order to
investigate the analogue of a MIT, and how it is influenced by periodic and
open boundaries. By changing the interatomic distance we analyse the character
of the many-body wavefunction and the charge gap. In the second part we mimic a
behaviour found in the ionic Hubbard model, where a transition from a band to a
Mott insulator occurs. For that purpose we perform calculations for mixed
sodium-lithium rings. In addition, we examine the question of bond alternation
for the pure sodium system and the mixed sodium-lithium system, in order to
determine under which conditions a Peierls distortion occurs.Comment: 8 pages, 7 figures, accepted Eur. J. Phys.
Dielectric catastrophe at the magnetic field induced insulator to metal transition in Pr1-xCaxMnO3 (x=0.30, 0.37) crystals
The dielectric permittivity and resistivity have been measured simultaneously
as a function of magnetic field in Pr1-xCaxMnO3 crystals with different doping.
A huge increase of dielectric permittivity was detected near percolation
threshold. The dielectric and conductive properties are found to be mutually
correlated throughout insulator to metal transition evidencing the dielectric
catastrophe phenomenon. Data are analyzed in a framework of Maxwell-Garnett
theory and the Mott-Hubbard theory attributed to the role of strong Coulomb
interactions.Comment: 5 pages, 5 figure
Microencapsulated Bovine Chromaffin Cells In Vitro: Effect of Density and Coseeding with a NGF-Releasing Cell Line
Immobilization of discrete cell clusters
within a partially crosslinked matrix prevents
reaggregation of primary tissues and may
provide a means for long-term maintenance of
encapsulated cells. Dissociated bovine adrenal
chromaffin (BAC) cells were suspended
throughout crosslinked polyanionic microspheres
previously shown to be selectively
permeable. Microcapsules approximately 500
µm in diameter were seeded with: 1) three
different densities of BAC cells; and 2) BAC
cells suspended in Matrigel®
or coseeded with a
genetically modified nerve growth factor (NGF)-
releasing fibroblast cell line. Each group was
analyzed in vitro at 1, 4 and 8 weeks for
spontaneous and potassium-evoked release of
catecholamines, and maintained in vitro for up
to 12 weeks for morphological observations.
Over time, release of norepinephrine (NE) and
epinephrine (EPI) diminished, while dopamine
(DA) remained constant from the monoseeded
capsules. In the coseeded group, an increase in
potassium-evoked release of DA was observed
from 1 to 4 weeks, and remained at that level up
to 8 weeks. Encapsulated chromaffin cells
retained a rounded morphology typical of
undifferentiated cells. Intact chromaffin cells
with well preserved and abundant secretory granules were observed ultrastructurally after 4
weeks in vitro. Small neurites from the chromaffin
cells in the coseeded group were observed at 4
weeks with light microscopy, and up to 12 weeks
with electron microscopy. Under static incubation
conditions, 1 mM D-amphetamine resulted
in a significant increase in the output of NE and
DA from the coseeded capsules 8 weeks postimplantation,
as compared to microcapsules
loaded with chromaffin cells alone. Encapsulation
within an immobilization matrix allows
manipulation of the internal environment,
thereby providing the ability to pre-treat cells
with various factors in a non-invasive manner,
which may enhance long-term cellular viability
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