81,783 research outputs found
Supersymmetric methods in the traveling variable: inside neurons and at the brain scale
We apply the mathematical technique of factorization of differential
operators to two different problems. First we review our results related to the
supersymmetry of the Montroll kinks moving onto the microtubule walls as well
as mentioning the sine-Gordon model for the microtubule nonlinear excitations.
Second, we find analytic expressions for a class of one-parameter solutions of
a sort of diffusion equation of Bessel type that is obtained by supersymmetry
from the homogeneous form of a simple damped wave equations derived in the
works of P.A. Robinson and collaborators for the corticothalamic system. We
also present a possible interpretation of the diffusion equation in the brain
contextComment: 14 pages, 1 figur
Stability of spherical stellar systems I : Analytical results
The so-called ``symplectic method'' is used for studying the linear stability
of a self-gravitating collisionless stellar system, in which the particles are
also submitted to an external potential. The system is steady and spherically
symmetric, and its distribution function thus depends only on the energy
and the squarred angular momentum of a particle. Assuming that
, it is first shown that stability holds with
respect to all the spherical perturbations -- a statement which turns out to be
also valid for a rotating spherical system. Thus it is proven that the energy
of an arbitrary aspherical perturbation associated to a ``preserving generator"
[i.e., one satisfying ] is always positive if and the
external mass density is a decreasing function of the distance to the
center. This implies in particular (under the latter condition) the stability
of an isotropic system with respect to all the perturbations. Some new remarks
on the relation between the symmetry of the system and the form of are
also reported. It is argued in particular that a system with a distribution
function of the form is necessarily spherically symmetric.Comment: uuencoded compressed postscript file containing 13 pages, accepted
for publication in MNRA
Magnetic Collapse of a Neutron Gas: No Magnetar Formation
A degenerate neutron gas in equilibrium with a background of electrons and
protons in a magnetic field exerts its pressure anisotropically, having a
smaller value perpendicular than along the magnetic field. For critical fields
the magnetic pressure may produce the vanishing of the equatorial pressure of
the neutron gas, and the outcome could be a transverse collapse of the star.
This fixes a limit to the fields to be observable in stable pulsars as a
function of their density. The final structure left over after the implosion
might be a mixed phase of nucleons and meson ()
condensate (a strange star also likely) or a black string, but no magnetar at
all.Comment: 5 pages, 1 latex file, 1 encapsulated figure. Submitted to Physical
Review Letters (24/11/2000
Magnetic collapse of a neutron gas: Can magnetars indeed be formed
A relativistic degenerate neutron gas in equilibrium with a background of
electrons and protons in a magnetic field exerts its pressure anisotropically,
having a smaller value perpendicular than along the magnetic field. For
critical fields the magnetic pressure may produce the vanishing of the
equatorial pressure of the neutron gas. Taking it as a model for neutron stars,
the outcome could be a transverse collapse of the star. This fixes a limit to
the fields to be observable in stable neutron star pulsars as a function of
their density. The final structure left over after the implosion might be a
mixed phase of nucleons and meson condensate, a strange star, or a highly
distorted black hole or black "cigar", but no any magnetar, if viewed as a
super strongly magnetized neutron star. However, we do not exclude the
possibility of a supersotrong magnetic fields arising in supernova explosions
which lead directly to strange stars. In other words, if any magnetars exist,
they cannot be neutron stars.Comment: 15 pages, 3 figures. European Physical Journal C in pres
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