4,797 research outputs found

### Neutrino Oscillations in Intermediate States.II -- Wave Packets

We analyze oscillations of intermediate neutrinos in terms of the scattering
of particles described by Gaussian wave packets. We study a scalar model as in
a previous paper (I) but in realistic situations, where the two particles of
the initial state and final state are wave packets and neutrinos are in the
intermediate state. The oscillation of the intermediate neutrino is found from
the time evolution of the total transition probability between the initial
state and final state. The effect of a finite lifetime and a finite relaxation
time are also studied. We find that the oscillation pattern depends on the
magnitude of wave packet sizes of particles in the initial state and final
state and the lifetime of the initial particle. For $\Delta m^2_{21}=3\times
10^{-2}$ eV$^2$, the oscillation probability deviates from that of the standard
formula if the wave packet sizes are around $10^{-13}$ m for 0.4 MeV neutrino.Comment: 29 pages, 11 figures. typos corrected, appendix adde

### On the Logarithmic Asymptotics of the Sixth Painleve' Equation (Summer 2007)

We study the solutions of the sixth Painlev\'e equation with a logarithmic
asymptotic behavior at a critical point. We compute the monodromy group
associated to the solutions by the method of monodromy preserving deformations
and we characterize the asymptotic behavior in terms of the monodromy itself.Comment: LaTeX with 8 figure

### Scattering for the Zakharov system in 3 dimensions

We prove global existence and scattering for small localized solutions of the
Cauchy problem for the Zakharov system in 3 space dimensions. The wave
component is shown to decay pointwise at the optimal rate of t^{-1}, whereas
the Schr\"odinger component decays almost at a rate of t^{-7/6}.Comment: Minor changes and referee's comments include

### Model building by coset space dimensional reduction in ten-dimensions with direct product gauge symmetry

We investigate ten-dimensional gauge theories whose extra six-dimensional
space is a compact coset space, $S/R$, and gauge group is a direct product of
two Lie groups. We list up candidates of the gauge group and embeddings of $R$
into them. After dimensional reduction of the coset space,we find fermion and
scalar representations of $G_{\mathrm{GUT}} \times U(1)$ with
$G_{\mathrm{GUT}}=SU(5), SO(10)$ and $E_6$ which accomodate all of the standard
model particles. We also discuss possibilities to generate distinct Yukawa
couplings among the generations using representations with a different
dimension for $G_{\mathrm{GUT}}=SO(10)$ and $E_6$ models.Comment: 14 pages; added local report number, added refferenc

### Movable algebraic singularities of second-order ordinary differential equations

Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n has a
(generally branched) solution with leading order behaviour proportional to
(z-z_0)^{-2/(N-1)} about a point z_0, where the coefficients a_n are analytic
at z_0 and a_N(z_0)\ne 0. We consider the subclass of equations for which each
possible leading order term of this form corresponds to a one-parameter family
of solutions represented near z_0 by a Laurent series in fractional powers of
z-z_0. For this class of equations we show that the only movable singularities
that can be reached by analytic continuation along finite-length curves are of
the algebraic type just described. This work generalizes previous results of S.
Shimomura. The only other possible kind of movable singularity that might occur
is an accumulation point of algebraic singularities that can be reached by
analytic continuation along infinitely long paths ending at a finite point in
the complex plane. This behaviour cannot occur for constant coefficient
equations in the class considered. However, an example of R. A. Smith shows
that such singularities do occur in solutions of a simple autonomous
second-order differential equation outside the class we consider here

### Shared Strategies for Behavioral Switching: Understanding How Locomotor Patterns are Turned on and Off

Animals frequently switch from one behavior to another, often to meet the demands of their changing environment or internal state. What factors control these behavioral switches and the selection of what to do or what not to do? To address these issues, we will focus on the locomotor behaviors of two distantly related “worms,” the medicinal leech Hirudo verbana (clade Lophotrochozoa) and the nematode Caenorhabditis elegans (clade Ecdysozoa). Although the neural architecture and body morphology of these organisms are quite distinct, they appear to switch between different forms of locomotion by using similar strategies of decision-making. For example, information that distinguishes between liquid and more solid environments dictates whether an animal swims or crawls. In the leech, dopamine biases locomotor neural networks so that crawling is turned on and swimming is turned off. In C. elegans, dopamine may also promote crawling, a form of locomotion that has gained new attention

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