376 research outputs found
Alternative mechanisms of structuring biomembranes: Self-assembly vs. self-organization
We study two mechanisms for the formation of protein patterns near membranes
of living cells by mathematical modelling. Self-assembly of protein domains by
electrostatic lipid-protein interactions is contrasted with self-organization
due to a nonequilibrium biochemical reaction cycle of proteins near the
membrane. While both processes lead eventually to quite similar patterns, their
evolution occurs on very different length and time scales. Self-assembly
produces periodic protein patterns on a spatial scale below 0.1 micron in a few
seconds followed by extremely slow coarsening, whereas self-organization
results in a pattern wavelength comparable to the typical cell size of 100
micron within a few minutes suggesting different biological functions for the
two processes.Comment: 4 pages, 5 figure
A characterization of Dirac morphisms
Relating the Dirac operators on the total space and on the base manifold of a
horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps
which pull back (local) harmonic spinor fields onto (local) harmonic spinor
fields.Comment: 18 pages; restricted to the even-dimensional cas
Propagation Failure in Excitable Media
We study a mechanism of pulse propagation failure in excitable media where
stable traveling pulse solutions appear via a subcritical pitchfork
bifurcation. The bifurcation plays a key role in that mechanism. Small
perturbations, externally applied or from internal instabilities, may cause
pulse propagation failure (wave breakup) provided the system is close enough to
the bifurcation point. We derive relations showing how the pitchfork
bifurcation is unfolded by weak curvature or advective field perturbations and
use them to demonstrate wave breakup. We suggest that the recent observations
of wave breakup in the Belousov-Zhabotinsky reaction induced either by an
electric field or a transverse instability are manifestations of this
mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud
Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm
Some Curvature Problems in Semi-Riemannian Geometry
In this survey article we review several results on the curvature of
semi-Riemannian metrics which are motivated by the positive mass theorem. The
main themes are estimates of the Riemann tensor of an asymptotically flat
manifold and the construction of Lorentzian metrics which satisfy the dominant
energy condition.Comment: 25 pages, LaTeX, 4 figure
Frauenforschung in der Soziologie - quo vadis?
It is widely accepted that the devastating consequences of spinal cord injury are due to the failure of lesioned CNS axons to regenerate. The current study of the spontaneous tissue repair processes following dorsal hemisection of the adult rat spinal cord demonstrates a phase of rapid and substantial nerve fibre inâgrowth into the lesion that was derived largely from both rostral and caudal spinal tissues. The response was characterized by increasing numbers of axons traversing the clearly defined interface between the lesion and the adjacent intact spinal cord, beginning by 5âdays post operation (p.o.). Having penetrated the lesion, axons became associated with a framework of NGFrâpositive nonâneuronal cells (Schwann cells and leptomeningeal cells). Surprisingly few of these axons were derived from CGRPâ or SPâimmunoreactive dorsal root ganglion neurons. At the longest survival time (56âdays p.o.), there was a marked shift in the overall orientation of fibres from a largely rostroâcaudal to a dorsoâventral axis. Attempts to identify which recognition molecules may be important for these reâorganizational processes during attempted tissue repair demonstrated the widespread and intense expression of the cell adhesion molecules (CAM) L1 and NâCAM. Double immunofluorescence suggested that both Schwann cells and leptomeningeal cells contributed to the pattern of CAM expression associated with the cellular framework within the lesion
Size-Dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium
The spatiotemporal dynamics of an excitable medium with multiple spiral
defects is shown to vary smoothly with system size from short-lived transients
for small systems to extensive chaos for large systems. A comparison of the
Lyapunov dimension density with the average spiral defect density suggests an
average dimension per spiral defect varying between three and seven. We discuss
some implications of these results for experimental studies of excitable media.Comment: 5 pages, Latex, 4 figure
Tight Beltrami fields with symmetry
Let be a compact orientable Seifered fibered 3-manifold without a
boundary, and an -invariant contact form on . In a suitable
adapted Riemannian metric to , we provide a bound for the volume
and the curvature, which implies the universal tightness of the
contact structure .Comment: 26 page
Angular Correlations in Internal Pair Conversion of Aligned Heavy Nuclei
We calculate the spatial correlation of electrons and positrons emitted by
internal pair conversion of Coulomb excited nuclei in heavy ion collisions. The
alignment or polarization of the nucleus results in an anisotropic emission of
the electron-positron pairs which is closely related to the anisotropic
emission of -rays. However, the angular correlation in the case of
internal pair conversion exhibits diverse patterns. This might be relevant when
investigating atomic processes in heavy-ion collisions performed at the Coulomb
barrier.Comment: 27 pages + 6 eps figures, uses revtex.sty and epsf.sty,
tar-compressed and uuencoded with uufile
A spinorial energy functional: critical points and gradient flow
On the universal bundle of unit spinors we study a natural energy functional
whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi})
consisting of a Ricci-flat Riemannian metric g together with a parallel
g-spinor {\phi}. We investigate the basic properties of this functional and
study its negative gradient flow, the so-called spinor flow. In particular, we
prove short-time existence and uniqueness for this flow.Comment: Small changes, final versio
Individual Eigenvalue Distributions for the Wilson Dirac Operator
We derive the distributions of individual eigenvalues for the Hermitian
Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac
Operator DW. The framework we provide is valid in the epsilon regime of chiral
perturbation theory for any number of flavours Nf and for non-zero low energy
constants W6, W7, W8. It is given as a perturbative expansion in terms of the
k-point spectral density correlation functions and integrals thereof, which in
some cases reduces to a Fredholm Pfaffian. For the real eigenvalues of DW at
fixed chirality nu this expansion truncates after at most nu terms for small
lattice spacing "a". Explicit examples for the distribution of the first and
second eigenvalue are given in the microscopic domain as a truncated expansion
of the Fredholm Pfaffian for quenched D5, where all k-point densities are
explicitly known from random matrix theory. For the real eigenvalues of
quenched DW at small "a" we illustrate our method by the finite expansion of
the corresponding Fredholm determinant of size nu.Comment: 20 pages, 5 figures; v2: typos corrected, refs added and discussion
of W6 and W7 extende
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