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

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 %

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

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 $p$-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

Charge and spin order in one-dimensional electron systems with long-range Coulomb interactions

We study a system of electrons interacting through long--range Coulomb forces on a one--dimensional lattice, by means of a variational ansatz which is the strong--coupling counterpart of the Gutzwiller wave function. Our aim is to describe the quantum analogue of Hubbard's classical ``generalized Wigner crystal''. We first analyse charge ordering in a system of spinless fermions, with particular attention to the effects of lattice commensurability. We argue that for a general (rational) number of electrons per site $n$ there are three regimes, depending on the relative strength $V$ of the long--range Coulomb interaction (as compared to the hopping amplitude $t$). For very large $V$ the quantum ground state differs little from Hubbard's classical solution, for intermediate to large values of $V$ we recover essentially the Wigner crystal of the continuum model, and for small $V$ the charge modulation amounts to a small--amplitude charge--density wave. We then include the spin degrees of freedom and show that in the Wigner crystal regimes (i.e. for large $V$) they are coupled by an antiferromagnetic kinetic exchange $J$, which turns out to be smaller than the energy scale governing the charge degrees of freedom. Our results shed new light on the insulating phases of organic quasi--1D compounds where the long--range part of the interaction is unscreened, and magnetic and charge orderings coexist at low temperatures.Comment: 11 pages, 7 figures, accepted for publication on Phys. Rev.

Interaction induced collapse of a section of the Fermi sea in in the zig-zag Hubbard ladder

Using the next-nearest neighbor (zig-zag) Hubbard chain as an one dimemensional model, we investigate the influence of interactions on the position of the Fermi wavevectors with the density-matrix renormalization-group technique (DMRG). For suitable choices of the hopping parameters we observe that electron-electron correlations induce very different renormalizations for the two different Fermi wavevectors, which ultimately lead to a complete destruction of one section of the Fermi sea in a quantum critical point