68,397 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
Quantization of strings and branes coupled to BF theory
BF theory is a topological theory that can be seen as a natural
generalization of 3-dimensional gravity to arbitrary dimensions. Here we show
that the coupling to point particles that is natural in three dimensions
generalizes in a direct way to BF theory in d dimensions coupled to
(d-3)-branes. In the resulting model, the connection is flat except along the
membrane world-sheet, where it has a conical singularity whose strength is
proportional to the membrane tension. As a step towards canonically quantizing
these models, we show that a basis of kinematical states is given by `membrane
spin networks', which are spin networks equipped with extra data where their
edges end on a brane
Solutions of the Perturbed KDV Equation for Convecting Fluids by Factorizations
In this paper, we obtain some new explicit travelling wave solutions of the
perturbed KdV equation through recent factorization techniques that can be
performed when the coefficients of the equation fulfill a certain condition.
The solutions are obtained by using a two-step factorization procedure through
which the perturbed KdV equation is reduced to a nonlinear second order
differential equation, and to some Bernoulli and Abel type differential
equations whose solutions are expressed in terms of the exponential and
Weierstrass functionsComment: 4 pages, some changes in the text according to referees' suggestions,
added one reference, accepted at Central Europ. J. Phy
Majorana neutrino oscillations in vacuum
In the context of a type I seesaw scenario which leads to get light
left-handed and heavy right-handed Majorana neutrinos, we obtain expressions
for the transition probability densities between two flavor neutrinos in the
cases of left-handed and right-handed neutrinos. We obtain these expressions in
the context of an approach developed in the canonical formalism of Quantum
Field Theory for neutrinos which are considered as superpositions of
mass-eigenstate plane waves with specific momenta. The expressions obtained for
the left-handed neutrino case after the ultra-relativistic limit is taking lead
to the standard probability densities which describe light neutrino
oscillations. For the right-handed neutrino case, the expressions describing
heavy neutrino oscillations in the non-relativistic limit are different respect
to the ones of the standard neutrino oscillations. However, the right-handed
neutrino oscillations are phenomenologically restricted as is shown when the
propagation of heavy neutrinos is considered as superpositions of
mass-eigenstate wave packets.Comment: 25 pages, abstract changed, two sections added, some references adde
Nonlinear second order ODE's: Factorizations and particular solutions
We present particular solutions for the following important nonlinear second
order differential equations: modified Emden, generalized Lienard, convective
Fisher, and generalized Burgers-Huxley. For the latter two equations these
solutions are obtained in the travelling frame. All these particular solutions
are the result of extending a simple and efficient factorization method that we
developed in Phys. Rev. E 71 (2005) 046607Comment: 6 pages, v3=published versio
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